Forming of the diameter tolerances of the insulated core to provide the guaranteed achievement of the required quality indicators of the symmetrical communication cable (lan-cable)

Abstract

A LAN-cable was considered as an object of research. A mathematical description of the mutual influence on the far and near ends in symmetrical communication cables is presented. It’s assumed that the tightening of the tolerance for the diameter of the insulated core will ensure the guaranteed achievement of the required quality indicators of the symmetrical communication cable. An algorithm for calculating the mutual influence between two and four circuit is given. A mathematical description was obtained and a simulation model of the mutual influence on the near and far ends was constructed for two twisted pairs, taking into account the length of the chain and the frequency of the transmitted signal. Computer studies were performed when the diameters of isolated LAN-cable cores were varied, taking into account its length, the mutual influence on the near end of the coefficients of the capacitive coupling, and transient attenuation on the near end. The obtained results confirmed the hypothesis and are the basis for the synthesis of automatic control systems for the LAN-cable manufacturing process.

 

Full Text

Введение

В [1] рассматривалась задача расчета взаимного влияния в симметричной цепи между витыми парами, проводами витых пар и четырьмя витыми парами по расположению жил пучка в поперечном сечении. В частности, расчета рабочих и взаимных емкостей и емкостных связей. Но не рассматривался расчет влияний на дальний и ближний конец.

Известно из [2, 3, 4], что если положение проводов является функцией длины, как это, например, имеет место у кабелей звездной скрутки и у линий с двумя скрученными цепями, то возможно получить распределение связей по всей длине. Нужно вычислить по распределению связей напряжения в начале и в конце линии, подверженной влиянию, расчетом переходных затуханий на ближнем и дальнем концах.

Данные величины можно определить из рис. 1, на котором показаны влияющая цепь 1 и подверженная влиянию цепь 2; остальные, как их принято называть, третьи цепи не показаны на рисунке. Цепи 1 и 2 замкнуты на свои волновые сопротивления Z1 и Z2. Напряжение U 20 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyvamaaBa aaleaacaaIYaGaaGimaaqabaaaaa@3870@ на ближнем к передатчику конце линии, подверженной влиянию, называется напряжением влияния на ближний конец, а напряжение U 2l MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyvamaaBa aaleaacaaIYaGaamiBaaqabaaaaa@38A7@ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzagaeaaaaaaaaa8qacaWFtacaaa@39C3@ на дальний конец [2, 3].

В зависимости от того, в какой точке цепи определяется переходный разговор, различают переходное затухание при влиянии на ближний и дальний концы. Если рассматривается влияние между концами взаимовлияющих цепей, находящихся в одном пункте, то говорят о переходном затухании при влиянии на ближний конец b N MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOyamaaBa aaleaacaWGobaabeaaaaa@37DA@ . Когда же рассматривают влияние между концами влияющей цепи и цепи, подверженной влиянию, находящимися в разных пунктах, то говорят о переходном затухании при влиянии на дальний конец b F MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOyamaaBa aaleaacaWGgbaabeaaaaa@37D2@ [5].

 

Рис. 1. Схема для определения влияния на дальний и ближний концы

 

Определить взаимные влияния на ближнем конце можно по формуле

N 12 = U 20 U 10 Z 1 Z 2 , MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamOtamaaBa aaleaacaaIXaGaaGOmaaqabaGccqGH9aqpdaWcaaqaaiaadwfadaWg aaWcbaGaaGOmaiaaicdaaeqaaaGcbaGaamyvamaaBaaaleaacaaIXa GaaGimaaqabaaaaOWaaOaaaeaadaWcaaqaaiaadQfadaWgaaWcbaGa aGymaaqabaaakeaacaWGAbWaaSbaaSqaaiaaikdaaeqaaaaaaeqaaO Gaaiilaaaa@4303@ (1)

где U 20 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyvamaaBa aaleaacaaIYaGaaGimaaqabaaaaa@3870@ и U 10 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyvamaaBa aaleaacaaIXaGaaGimaaqabaaaaa@386F@ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzagaeaaaaaaaaa8qacaWFtacaaa@39C3@ напряжение влияния на ближний конец;

Z 1 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOwamaaBa aaleaacaaIXaaabeaaaaa@37BA@ и Z 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOwamaaBa aaleaacaaIYaaabeaaaaa@37BB@ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzagaeaaaaaaaaa8qacaWFtacaaa@39C3@ волновые сопротивления.

На дальнем конце:

F 12 = U 2l U 1l Z 1 Z 2 , MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamOramaaBa aaleaacaaIXaGaaGOmaaqabaGccqGH9aqpdaWcaaqaaiaadwfadaWg aaWcbaGaaGOmaiaadYgaaeqaaaGcbaGaamyvamaaBaaaleaacaaIXa GaamiBaaqabaaaaOWaaOaaaeaadaWcaaqaaiaadQfadaWgaaWcbaGa aGymaaqabaaakeaacaWGAbWaaSbaaSqaaiaaikdaaeqaaaaaaeqaaO Gaaiilaaaa@4369@ (2)

где U 2l MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyvamaaBa aaleaacaaIYaGaamiBaaqabaaaaa@38A7@ и U 1l MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyvamaaBa aaleaacaaIXaGaamiBaaqabaaaaa@38A6@ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzagaeaaaaaaaaa8qacaWFtacaaa@39C3@ напряжение влияния на дальний конец.

Или, выражая через соответствующие переходные затухания:

b N ln N 12 =ln U 20 U 10 Z 1 Z 2 ; MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamOyamaaBa aaleaacaWGobaabeaakiabggMi6kabgkHiTiGacYgacaGGUbWaaqWa aeaacaWGobWaaSbaaSqaaiaaigdacaaIYaaabeaaaOGaay5bSlaawI a7aiabg2da9iGacYgacaGGUbWaaqWaaeaadaWcaaqaaiaadwfadaWg aaWcbaGaaGOmaiaaicdaaeqaaaGcbaGaamyvamaaBaaaleaacaaIXa GaaGimaaqabaaaaOWaaOaaaeaadaWcaaqaaiaadQfadaWgaaWcbaGa aGymaaqabaaakeaacaWGAbWaaSbaaSqaaiaaikdaaeqaaaaaaeqaaa GccaGLhWUaayjcSdGaai4oaaaa@51C4@ (3)

b F ln F 12 =ln U 2l U 1l Z 1 Z 2 . MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamOyamaaBa aaleaacaWGgbaabeaakiabggMi6kabgkHiTiGacYgacaGGUbWaaqWa aeaacaWGgbWaaSbaaSqaaiaaigdacaaIYaaabeaaaOGaay5bSlaawI a7aiabg2da9iGacYgacaGGUbWaaqWaaeaadaWcaaqaaiaadwfadaWg aaWcbaGaaGOmaiaadYgaaeqaaaGcbaGaamyvamaaBaaaleaacaaIXa GaamiBaaqabaaaaOWaaOaaaeaadaWcaaqaaiaadQfadaWgaaWcbaGa aGymaaqabaaakeaacaWGAbWaaSbaaSqaaiaaikdaaeqaaaaaaeqaaa GccaGLhWUaayjcSdGaaiOlaaaa@5215@ (4)

У высокочастотных цепей влияние на ближний конец, как правило, значительно больше, чем на дальний. Поэтому на практике при любых обстоятельствах стараются избегать влияния на ближний конец. Но вследствие отражений (неудовлетворительное согласование нагрузочного сопротивления с волновым сопротивлением или скачки волнового сопротивления) направление волн может измениться на обратное, в результате чего энергия пойдет к дальнему концу цепи, подверженной влиянию. Следовательно, в результате отражений и влияний на ближний конец возникает дополнительное влияние на дальний конец. Но эту часть влияния мы учитывать не будем, так как при эксплуатации и настройке можно обеспечить хорошее согласование и эта составляющая не будет играть ощутимой роли [2]. Также будем пренебрегать неоднородностями волновых сопротивлений и неоднородностью диэлектрика.

Взаимное влияние в пучке z вызывается электрическими и магнитными полями, а описывается это влияние обобщенными телеграфными уравнениями для связанных цепей (3, 4):

U k = 1 jω K 1k d I 1 dx + K 2k d I 2 dx ++ K k d I k dx ++ K zk d I z dx ; MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaeyOeI0Iaam yvamaaBaaaleaacaWGRbaabeaakiabg2da9maalaaabaGaaGymaaqa aiaadQgacqaHjpWDaaWaaeWaaeaacaWGlbWaaSbaaSqaaiaaigdaca WGRbaabeaakmaalaaabaGaamizaiaadMeadaWgaaWcbaGaaGymaaqa baaakeaacaWGKbGaamiEaaaacqGHRaWkcaWGlbWaaSbaaSqaaiaaik dacaWGRbaabeaakmaalaaabaGaamizaiaadMeadaWgaaWcbaGaaGOm aaqabaaakeaacaWGKbGaamiEaaaacqGHRaWkcqWIVlctcqGHRaWkca WGlbWaaSbaaSqaaiaadUgaaeqaaOWaaSaaaeaacaWGKbGaamysamaa BaaaleaacaWGRbaabeaaaOqaaiaadsgacaWG4baaaiabgUcaRiabl+ UimjabgUcaRiaadUeadaWgaaWcbaGaamOEaiaadUgaaeqaaOWaaSaa aeaacaWGKbGaamysamaaBaaaleaacaWG6baabeaaaOqaaiaadsgaca WG4baaaaGaayjkaiaawMcaaiaacUdaaaa@6539@ (5)

d U k dx =jω L 1k I 1 + L 2k I 2 ++ L k I k ++ L zk I z , MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq GHsislcaWGKbGaamyvamaaBaaaleaacaWGRbaabeaaaOqaaiaadsga caWG4baaaiabg2da9iaadQgacqaHjpWDdaqadaqaaiaadYeadaWgaa WcbaGaaGymaiaadUgaaeqaaOGaamysamaaBaaaleaacaaIXaaabeaa kiabgUcaRiaadYeadaWgaaWcbaGaaGOmaiaadUgaaeqaaOGaamysam aaBaaaleaacaaIYaaabeaakiabgUcaRiabl+UimjabgUcaRiaadYea daWgaaWcbaGaam4AaaqabaGccaWGjbWaaSbaaSqaaiaadUgaaeqaaO Gaey4kaSIaeS47IWKaey4kaSIaamitamaaBaaaleaacaWG6bGaam4A aaqabaGccaWGjbWaaSbaaSqaaiaadQhaaeqaaaGccaGLOaGaayzkaa Gaaiilaaaa@5BC6@ (6)

где U k MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyvamaaBa aaleaacaWGRbaabeaaaaa@37EA@ напряжение k-й цепи;

I k MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysamaaBa aaleaacaWGRbaabeaaaaa@37DE@ ток k-й цепи;

L k , L zk MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamitamaaBa aaleaacaWGRbaabeaakiaacYcacaaMc8UaamitamaaBaaaleaacaWG 6bGaam4Aaaqabaaaaa@3D12@ индуктивность k-й; z и k-й цепи;

K k , K zk MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4samaaBa aaleaacaWGRbaabeaakiaacYcacaaMc8Uaam4samaaBaaaleaacaWG 6bGaam4Aaaqabaaaaa@3D10@ потенциальный коэффициент k-й; z и k-й цепи.

Эти уравнения называют еще основными уравнениями теории влияния.

Постановка задачи

Для гарантированного обеспечения требуемых параметров качества изготавливаемого кабеля необходимо изготавливать изолированную жилу с диаметром

D= D и +X MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiraiabg2 da9iaadseadaWgaaWcbaGaamioeaqabaGccqGHRaWkcaWGybaaaa@3B42@ ,

где X=+ X В MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiwaiabg2 da9iabgUcaRiaadIfadaWgaaWcbaGaamOeeaqabaaaaa@3A5D@ или X= X Н MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiwaiabg2 da9iabgkHiTiaadIfadaWgaaWcbaGaamyheaqabaaaaa@3A73@ ;

+ X В MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaey4kaSIaam iwamaaBaaaleaacaWGsqaabeaaaaa@387A@ верхний предел допуска;

X Н MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0Iaam iwamaaBaaaleaacaWGDqaabeaaaaa@3890@ нижний предел допуска.

Выдвинем предположение, что ужесточение допуска на диаметр изолированной жилы гарантированно обеспечит требуемые показатели качества LAN-кабеля. Одним из таких показателей является переходное затухание.

Зададимся следующими начальными условиями.

В качестве объекта исследования рассмотрим LAN MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzagaeaaaaaaaaa8qacaWFtacaaa@39C3@ кабель категории 5е, на рис. 2 представлены его характеристики. Данный кабель, CCA-UU004-5E-PVC-GY, содержит 4 витые пары сплошных алюминиевых проводников, лакированных чистой медью (ССА). Кабель выполнен в неэкранированном исполнении и является экономичным решением, при этом полностью соответствует заявленной категории 5e и скорости передачи в 1Гбит/с и использующейся для внутренней прокладки [6].

Введем ограничения:

- цепи будут нескрещенные параллельные;

- цепи имеют пренебрежимо малую внутреннюю индуктивность.

Рассмотрим частные случаи получения взаимного влияния на дальний и ближний конец для двух и четырех цепей. Найдем доказательство выдвинутого предположения.

 

Рис.2. Характеристики кабеля CCA-UU004-5E-PVC-GY

 

Математическое описание взаимного влияния на ближний и дальний конец в симметричных кабелях связи

Для доказательства выдвинутого предположения обратимся к теории расчета взаимного влияния по связям. Решение систем уравнений (5 и 6) достаточно сложное, поэтому сделаны ограничения:

MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbcKqzagaeaaaaaaaaa8qacaWFtacaaa@39C5@ для цепей с пренебрежимо малой внутренней индуктивностью справедливо уравнение

L ik = 1 υ 2 K ik , MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamitamaaBa aaleaacaWGPbGaam4AaaqabaGccqGH9aqpdaWcaaqaaiaaigdaaeaa cqaHfpqDdaahaaWcbeqaaiaaikdaaaaaaOGaam4samaaBaaaleaaca WGPbGaam4AaaqabaGccaGGSaaaaa@41FB@ (7)

где L ik MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamitamaaBa aaleaacaWGPbGaam4Aaaqabaaaaa@38CF@ индуктивность i-й и k-й цепи;

MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzagaeaaaaaaaaa8qacaWFtacaaa@39C3@ нескрещенные параллельные цепи, у которых L и K не зависят от x.

В итоге для k-й цепи получаем следующее дифференциальное уравнение 2-го порядка с постоянными коэффициентами:

d 2 U k d x 2 + ω 2 υ 2 U k =0. MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca WGKbWaaWbaaSqabeaacaaIYaaaaOGaamyvamaaBaaaleaacaWGRbaa beaaaOqaaiaadsgacaWG4bWaaWbaaSqabeaacaaIYaaaaaaakiabgU caRmaalaaabaGaeqyYdC3aaWbaaSqabeaacaaIYaaaaaGcbaGaeqyX du3aaWbaaSqabeaacaaIYaaaaaaakiaadwfadaWgaaWcbaGaam4Aaa qabaGccqGH9aqpcaaIWaGaaiOlaaaa@489A@ (8)

Общее решение примет вид

U k = A k e γx + B k e +γx , MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamyvamaaBa aaleaacaWGRbaabeaakiabg2da9iaadgeadaWgaaWcbaGaam4Aaaqa baGccaWGLbWaaWbaaSqabeaacqGHsislcqaHZoWzcaWG4baaaOGaey 4kaSIaamOqamaaBaaaleaacaWGRbaabeaakiaadwgadaahaaWcbeqa aiabgUcaRiabeo7aNjaadIhaaaGccaGGSaaaaa@48C1@ (9)

где A k MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqamaaBa aaleaacaWGRbaabeaaaaa@37D6@ и B k MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOqamaaBa aaleaacaWGRbaabeaaaaa@37D7@ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzagaeaaaaaaaaa8qacaWFtacaaa@39C3@ постоянные интегрирования.

Чтобы определить постоянную распространения всех волн, нужно подставить (9) в (8), в итоге получим

γ=j ω υ , MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaeq4SdCMaey ypa0JaamOAamaalaaabaGaeqyYdChabaGaeqyXduhaaiaacYcaaaa@3EE7@ (10)

где γ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4SdCgaaa@379B@ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzagaeaaaaaaaaa8qacaWFtacaaa@39C3@ постоянная распространения волн;

ω MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyYdChaaa@37C1@ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzagaeaaaaaaaaa8qacaWFtacaaa@39C3@ круговая частота;

υ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyXduhaaa@37BB@ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzagaeaaaaaaaaa8qacaWFtacaaa@39C3@ скорость распространения сигнала во всех цепях.

Подставляя уравнение (9) в уравнение (6), получим токи во всех z цепях на основании системы z уравнений. Для наглядности приведем k-е уравнение [2]:

L 1k I 1 + L 2k I 2 ++ L kk I k ++ L zk I z = 1 υ A k e γx B k e +γx . MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamitamaaBa aaleaacaaIXaGaam4AaaqabaGccaWGjbWaaSbaaSqaaiaaigdaaeqa aOGaey4kaSIaamitamaaBaaaleaacaaIYaGaam4AaaqabaGccaWGjb WaaSbaaSqaaiaaikdaaeqaaOGaey4kaSIaeS47IWKaey4kaSIaamit amaaBaaaleaacaWGRbGaam4AaaqabaGccaWGjbWaaSbaaSqaaiaadU gaaeqaaOGaey4kaSIaeS47IWKaey4kaSIaamitamaaBaaaleaacaWG 6bGaam4AaaqabaGccaWGjbWaaSbaaSqaaiaadQhaaeqaaOGaeyypa0 ZaaSaaaeaacaaIXaaabaGaeqyXduhaamaabmaabaGaamyqamaaBaaa leaacaWGRbaabeaakiaadwgadaahaaWcbeqaaiabgkHiTiabeo7aNj aadIhaaaGccqGHsislcaWGcbWaaSbaaSqaaiaadUgaaeqaaOGaamyz amaaCaaaleqabaGaey4kaSIaeq4SdCMaamiEaaaaaOGaayjkaiaawM caaiaac6caaaa@65E7@ (11)

Постоянные A k MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqamaaBa aaleaacaWGRbaabeaaaaa@37D6@ и B k MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOqamaaBa aaleaacaWGRbaabeaaaaa@37D7@ определяются из граничных условий в начале и в конце каждой цепи, все цепи должны быть замкнуты обоими концами на свои волновые сопротивления [2]:

Z k = L k K k . MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamOwamaaBa aaleaacaWGRbaabeaakiabg2da9maakaaabaGaamitamaaBaaaleaa caWGRbaabeaakiaadUeadaWgaaWcbaGaam4Aaaqabaaabeaakiaac6 caaaa@3EB1@ (12)

 

Рис. 3. Схема для определения знака тока I k0 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysamaaBa aaleaacaWGRbGaaGimaaqabaaaaa@3898@ в начале и конце цепи I kl MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysamaaBa aaleaacaWGRbGaamiBaaqabaaaaa@38CF@

 

Согласно обозначениям, приведенным на рис. 3, и направлениям токов, указанным стрелками, согласно закону Ома получим:

U kl = I kl Z k (k=1,2,3z); MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamyvamaaBa aaleaacaWGRbGaamiBaaqabaGccqGH9aqpcaWGjbWaaSbaaSqaaiaa dUgacaWGSbaabeaakiaadQfadaWgaaWcbaGaam4AaaqabaGccaaMc8 UaaiikaiaadUgacqGH9aqpcaaIXaGaaiilaiaaykW7caaIYaGaaiil aiaaykW7caaIZaGaaGPaVlablAciljaadQhacaGGPaGaai4oaaaa@4FC7@ (13)

U k0 = I k0 Z k (k=2,3,4z). MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamyvamaaBa aaleaacaWGRbGaaGimaaqabaGccqGH9aqpcqGHsislcaWGjbWaaSba aSqaaiaadUgacaaIWaaabeaakiaadQfadaWgaaWcbaGaam4Aaaqaba GccaaMc8UaaiikaiaadUgacqGH9aqpcaaIYaGaaiilaiaaykW7caaI ZaGaaiilaiaaykW7caaI0aGaaGPaVlablAciljaadQhacaGGPaGaai Olaaaa@503C@ (14)

Взаимное влияние между двумя цепями

Влияющую цепь обозначим 1, подверженную влиянию MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzagaeaaaaaaaaa8qacaWFtacaaa@39C3@ 3. Для цепи 1 получим только одну волну (15) с учетом сделанных допущений: согласование на конце цепи и пренебрежение обратным влиянием цепи, подверженной влиянию.

U 1 = U 10 e γx ; MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamyvamaaBa aaleaacaaIXaaabeaakiabg2da9iaadwfadaWgaaWcbaGaaGymaiaa icdaaeqaaOGaamyzamaaCaaaleqabaGaeyOeI0Iaeq4SdCMaamiEaa aakiaacUdaaaa@41BE@ (15)

I 1 = U 10 Z 1 e γx . MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamysamaaBa aaleaacaaIXaaabeaakiabg2da9maalaaabaGaamyvamaaBaaaleaa caaIXaGaaGimaaqabaaakeaacaWGAbWaaSbaaSqaaiaaigdaaeqaaa aakiaadwgadaahaaWcbeqaaiabgkHiTiabeo7aNjaadIhaaaGccaGG Uaaaaa@4385@ (16)

Уравнения (9) и (11) при k = 3 примут следующий вид:

U 3 = A 3 e γx + B 3 e +γx ; MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamyvamaaBa aaleaacaaIZaaabeaakiabg2da9iaadgeadaWgaaWcbaGaaG4maaqa baGccaWGLbWaaWbaaSqabeaacqGHsislcqaHZoWzcaWG4baaaOGaey 4kaSIaamOqamaaBaaaleaacaaIZaaabeaakiaadwgadaahaaWcbeqa aiabgUcaRiabeo7aNjaadIhaaaGccaGG7aaaaa@4837@ (17)

L 13 I 1 + L 33 I 3 = 1 υ A 3 e γx B 3 e +γx . MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamitamaaBa aaleaacaaIXaGaaG4maaqabaGccaWGjbWaaSbaaSqaaiaaigdaaeqa aOGaey4kaSIaamitamaaBaaaleaacaaIZaGaaG4maaqabaGccaWGjb WaaSbaaSqaaiaaiodaaeqaaOGaeyypa0ZaaSaaaeaacaaIXaaabaGa eqyXduhaamaabmaabaGaamyqamaaBaaaleaacaaIZaaabeaakiaadw gadaahaaWcbeqaaiabgkHiTiabeo7aNjaadIhaaaGccqGHsislcaWG cbWaaSbaaSqaaiaaiodaaeqaaOGaamyzamaaCaaaleqabaGaey4kaS Iaeq4SdCMaamiEaaaaaOGaayjkaiaawMcaaiaac6caaaa@53E5@ (18)

Для нахождения постоянных A 3 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqamaaBa aaleaacaaIZaaabeaaaaa@37A3@ и B 3 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOqamaaBa aaleaacaaIZaaabeaaaaa@37A4@ нужно воспользоваться граничными условиями в начале и в конце цепи.

В начале определим постоянную A 3 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqamaaBa aaleaacaaIZaaabeaaaaa@37A3@ . Для этого из уравнения (17) выразим B 3 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOqamaaBa aaleaacaaIZaaabeaaaaa@37A4@ и подставим в уравнение (16), получим:

L 13 I 1 + L 33 I 3 = 1 υ A 3 e γx U 3 + A 3 e γx . MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamitamaaBa aaleaacaaIXaGaaG4maaqabaGccaWGjbWaaSbaaSqaaiaaigdaaeqa aOGaey4kaSIaamitamaaBaaaleaacaaIZaGaaG4maaqabaGccaWGjb WaaSbaaSqaaiaaiodaaeqaaOGaeyypa0ZaaSaaaeaacaaIXaaabaGa eqyXduhaamaabmaabaGaamyqamaaBaaaleaacaaIZaaabeaakiaadw gadaahaaWcbeqaaiabgkHiTiabeo7aNjaadIhaaaGccqGHsislcaWG vbWaaSbaaSqaaiaaiodaaeqaaOGaey4kaSIaamyqamaaBaaaleaaca aIZaaabeaakiaadwgadaahaaWcbeqaaiabgkHiTiabeo7aNjaadIha aaaakiaawIcacaGLPaaacaGGUaaaaa@569E@ (19)

С учетом того, что x=0, (14) примет вид: U 30 = I 30 Z 3 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyvamaaBa aaleaacaaIZaGaaGimaaqabaGccqGH9aqpcqGHsislcaWGjbWaaSba aSqaaiaaiodacaaIWaaabeaakiaadQfadaWgaaWcbaGaaG4maaqaba aaaa@3EB1@ ; также учитывая Z 1 = L 11 υ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOwamaaBa aaleaacaaIXaaabeaakiabg2da9iaadYeadaWgaaWcbaGaaGymaiaa igdaaeqaaOGaeqyXduhaaa@3D0E@ и уравнения (15, 16), получим:

L 13 U 10 υ L 11 + L 33 I 3 + U 3 = 1 υ 2 A 3 . MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca WGmbWaaSbaaSqaaiaaigdacaaIZaaabeaakiaadwfadaWgaaWcbaGa aGymaiaaicdaaeqaaaGcbaGaeqyXduNaamitamaaBaaaleaacaaIXa GaaGymaaqabaaaaOGaey4kaSIaamitamaaBaaaleaacaaIZaGaaG4m aaqabaGccaWGjbWaaSbaaSqaaiaaiodaaeqaaOGaey4kaSIaamyvam aaBaaaleaacaaIZaaabeaakiabg2da9maalaaabaGaaGymaaqaaiab ew8a1baacaaIYaGaamyqamaaBaaaleaacaaIZaaabeaakiaac6caaa a@4EE1@ (20)

Учитывая, что L 33 = z 3 υ MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGI8VfYJbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabiGaaiaacaqabeaadaqaaqaaaOqaaiaadYeadaWgaa WcbaGaaG4maiaaiodaaeqaaOGaeyypa0ZaaSaaaeaacaWG6bWaaSba aSqaaiaaiodaaeqaaaGcbaGaeqyXduhaaaaa@3E0A@ и I 3 = U 3 z 3 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGI8VfYJbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabiGaaiaacaqabeaadaqaaqaaaOqaaiaadMeadaWgaa WcbaGaaG4maaqabaGccqGH9aqpdaWcaaqaaiaadwfadaWgaaWcbaGa aG4maaqabaaakeaacaWG6bWaaSbaaSqaaiaaiodaaeqaaaaaaaa@3D46@ , уравнение (20) примет вид:

A 3 = L 13 U 10 2 L 11 + U 3 . MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamyqamaaBa aaleaacaaIZaaabeaakiabg2da9maalaaabaGaamitamaaBaaaleaa caaIXaGaaG4maaqabaGccaWGvbWaaSbaaSqaaiaaigdacaaIWaaabe aaaOqaaiaaikdacaWGmbWaaSbaaSqaaiaaigdacaaIXaaabeaaaaGc cqGHRaWkcaWGvbWaaSbaaSqaaiaaiodaaeqaaOGaaiOlaaaa@4564@ (21)

Теперь найдем постоянную B 3 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOqamaaBa aaleaacaaIZaaabeaaaaa@37A4@ , для этого приравняем x = l, формула (13) примет вид U 3l = I 3l Z 3 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyvamaaBa aaleaacaaIZaGaamiBaaqabaGccqGH9aqpcaWGjbWaaSbaaSqaaiaa iodacaWGSbaabeaakiaadQfadaWgaaWcbaGaaG4maaqabaaaaa@3E32@ . Теперь выразим из (17) постоянную A 3 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqamaaBa aaleaacaaIZaaabeaaaaa@37A3@ и подставим в уравнение (18), получим:

L 13 I 1 + L 33 I 3 = 1 υ U 3 B 3 e +γl B 3 e +γl , MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamitamaaBa aaleaacaaIXaGaaG4maaqabaGccaWGjbWaaSbaaSqaaiaaigdaaeqa aOGaey4kaSIaamitamaaBaaaleaacaaIZaGaaG4maaqabaGccaWGjb WaaSbaaSqaaiaaiodaaeqaaOGaeyypa0ZaaSaaaeaacaaIXaaabaGa eqyXduhaamaabmaabaGaamyvamaaBaaaleaacaaIZaaabeaakiabgk HiTiaadkeadaWgaaWcbaGaaG4maaqabaGccaWGLbWaaWbaaSqabeaa cqGHRaWkcqaHZoWzcaWGSbaaaOGaeyOeI0IaamOqamaaBaaaleaaca aIZaaabeaakiaadwgadaahaaWcbeqaaiabgUcaRiabeo7aNjaadYga aaaakiaawIcacaGLPaaacaGGSaaaaa@567B@ (22)

где l MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiBaaaa@36E5@ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzagaeaaaaaaaaa8qacaWFtacaaa@39C3@ длина цепи.

Учитывая вышеописанные выражения для L 33 , L 11 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamitamaaBa aaleaacaaIZaGaaG4maaqabaGccaGGSaGaaGPaVlaadYeadaWgaaWc baGaaGymaiaaigdaaeqaaaaa@3D23@ и I 3 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysamaaBa aaleaacaaIZaaabeaaaaa@37AB@ , подставим их в (22) и выразим B 3 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOqamaaBa aaleaacaaIZaaabeaaaaa@37A4@ :

B 3 = L 13 U 10 2 L 11 e 2γl . MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamOqamaaBa aaleaacaaIZaaabeaakiabg2da9iabgkHiTmaalaaabaGaamitamaa BaaaleaacaaIXaGaaG4maaqabaGccaWGvbWaaSbaaSqaaiaaigdaca aIWaaabeaaaOqaaiaaikdacaWGmbWaaSbaaSqaaiaaigdacaaIXaaa beaaaaGccaWGLbWaaWbaaSqabeaacqGHsislcaaIYaGaeq4SdCMaam iBaaaakiaac6caaaa@4905@ (23)

Подставим полученные выражения для постоянных (21) и (23) в (17), тем самым получим уравнение для U 3 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyvamaaBa aaleaacaaIZaaabeaaaaa@37B7@ :

U 3 = L 13 U 10 2 L 11 e γx 1 e 2γ(lx) = I 3 Z 3 . MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamyvamaaBa aaleaacaaIZaaabeaakiabg2da9maalaaabaGaamitamaaBaaaleaa caaIXaGaaG4maaqabaGccaWGvbWaaSbaaSqaaiaaigdacaaIWaaabe aaaOqaaiaaikdacaWGmbWaaSbaaSqaaiaaigdacaaIXaaabeaaaaGc caWGLbWaaWbaaSqabeaacqGHsislcqaHZoWzcaWG4baaaOWaaeWaae aacaaIXaGaeyOeI0IaamyzamaaCaaaleqabaGaeyOeI0IaaGOmaiab eo7aNjaacIcacaWGSbGaeyOeI0IaamiEaiaacMcaaaaakiaawIcaca GLPaaacqGH9aqpcqGHsislcaWGjbWaaSbaaSqaaiaaiodaaeqaaOGa amOwamaaBaaaleaacaaIZaaabeaakiaac6caaaa@58D7@ (24)

Введем нормированные величины для напряжения U MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyvaaaa@36CE@ и тока I MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaaaa@36C2@ :

u 3 = U 3 Z 3 ; MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamyDamaaBa aaleaacaaIZaaabeaakiabg2da9maalaaabaGaamyvamaaBaaaleaa caaIZaaabeaaaOqaamaakaaabaGaamOwamaaBaaaleaacaaIZaaabe aaaeqaaaaakiaacUdaaaa@3E68@ (25)

i 3 = I 3 Z 3 . MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamyAamaaBa aaleaacaaIZaaabeaakiabg2da9maalaaabaGaamysamaaBaaaleaa caaIZaaabeaaaOqaamaakaaabaGaamOwamaaBaaaleaacaaIZaaabe aaaeqaaaaakiaac6caaaa@3E43@ (26)

Используя нормированные величины и вводя коэффициент связи, получим:

χ 13 = L 13 L 11 L 33 = K 13 K 11 K 33 . MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaeq4Xdm2aaS baaSqaaiaaigdacaaIZaaabeaakiabg2da9maalaaabaGaamitamaa BaaaleaacaaIXaGaaG4maaqabaaakeaadaGcaaqaaiaadYeadaWgaa WcbaGaaGymaiaaigdaaeqaaOGaamitamaaBaaaleaacaaIZaGaaG4m aaqabaaabeaaaaGccqGH9aqpdaWcaaqaaiaadUeadaWgaaWcbaGaaG ymaiaaiodaaeqaaaGcbaWaaOaaaeaacaWGlbWaaSbaaSqaaiaaigda caaIXaaabeaakiaadUeadaWgaaWcbaGaaG4maiaaiodaaeqaaaqaba aaaOGaaiOlaaaa@4C51@ (27)

С учетом (27) выражение (24) примет следующий вид:

u 3 = i 3 = 1 2 u 10 χ 13 e 2γx 1 e 2γ(lx) . MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamyDamaaBa aaleaacaaIZaaabeaakiabg2da9iabgkHiTiaadMgadaWgaaWcbaGa aG4maaqabaGccqGH9aqpdaWcaaqaaiaaigdaaeaacaaIYaaaaiaadw hadaWgaaWcbaGaaGymaiaaicdaaeqaaOGaeq4Xdm2aaSbaaSqaaiaa igdacaaIZaaabeaakiaadwgadaahaaWcbeqaaiabgkHiTiaaikdacq aHZoWzcaWG4baaaOWaaeWaaeaacaaIXaGaeyOeI0IaamyzamaaCaaa leqabaGaeyOeI0IaaGOmaiabeo7aNjaacIcacaWGSbGaeyOeI0Iaam iEaiaacMcaaaaakiaawIcacaGLPaaacaGGUaaaaa@5745@ (28)

Это уравнение напряжения в любой точки цепи 3. Рассмотрев алгоритм получения постоянных A 3 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqamaaBa aaleaacaaIZaaabeaaaaa@37A3@ , B 3 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOqamaaBa aaleaacaaIZaaabeaaaaa@37A4@ и нахождения уравнения напряжения для любой точки определенной цепи, рассмотрим более сложный пример MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzagaeaaaaaaaaa8qacaWFtacaaa@39C3@ взаимное влияние между четырьмя цепями.

Взаимное влияние между четырьмя цепями

Вывод уравнений взаимного влияния между четырьмя цепями сводится к нахождению напряжений и токов «третьих» цепях MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzagaeaaaaaaaaa8qacaWFtacaaa@39C3@ в данном случае это цепи 3 и 4. Влияние на цепь 2 будет суммой всех влияний цепей 1, 3 и 4 соответственно.

При условии пренебрежения обратным влиянием уравнения (9) и (11) при k = 2 для случая взаимного влияния четырех цепей будут выглядеть следующим образом:

U 2 = A 2 e γx + B 2 e +γx ; MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamyvamaaBa aaleaacaaIYaaabeaakiabg2da9iaadgeadaWgaaWcbaGaaGOmaaqa baGccaWGLbWaaWbaaSqabeaacqGHsislcqaHZoWzcaWG4baaaOGaey 4kaSIaamOqamaaBaaaleaacaaIYaaabeaakiaadwgadaahaaWcbeqa aiabgUcaRiabeo7aNjaadIhaaaGccaGG7aaaaa@4834@ (29)

L 12 I 1 + L 22 I 2 + L 32 I 3 + L 42 I 4 = 1 υ A 2 e γx B 2 e +γx . MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamitamaaBa aaleaacaaIXaGaaGOmaaqabaGccaWGjbWaaSbaaSqaaiaaigdaaeqa aOGaey4kaSIaamitamaaBaaaleaacaaIYaGaaGOmaaqabaGccaWGjb WaaSbaaSqaaiaaikdaaeqaaOGaey4kaSIaamitamaaBaaaleaacaaI ZaGaaGOmaaqabaGccaWGjbWaaSbaaSqaaiaaiodaaeqaaOGaey4kaS IaamitamaaBaaaleaacaaI0aGaaGOmaaqabaGccaWGjbWaaSbaaSqa aiaaisdaaeqaaOGaeyypa0ZaaSaaaeaacaaIXaaabaGaeqyXduhaam aabmaabaGaamyqamaaBaaaleaacaaIYaaabeaakiaadwgadaahaaWc beqaaiabgkHiTiabeo7aNjaadIhaaaGccqGHsislcaWGcbWaaSbaaS qaaiaaikdaaeqaaOGaamyzamaaCaaaleqabaGaey4kaSIaeq4SdCMa amiEaaaaaOGaayjkaiaawMcaaiaac6caaaa@5E27@ (30)

Величины I 3 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysamaaBa aaleaacaaIZaaabeaaaaa@37AB@ и I 4 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysamaaBa aaleaacaaI0aaabeaaaaa@37AC@ можно найти из уравнения (24); учитывая, что L 33 = Z 3 υ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamitamaaBa aaleaacaaIZaGaaG4maaqabaGccqGH9aqpdaWcaaqaaiaadQfadaWg aaWcbaGaaG4maaqabaaakeaacqaHfpqDaaaaaa@3D24@ и L 44 = Z 4 υ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamitamaaBa aaleaacaaI0aGaaGinaaqabaGccqGH9aqpdaWcaaqaaiaadQfadaWg aaWcbaGaaGinaaqabaaakeaacqaHfpqDaaaaaa@3D27@ , получим:

I 3 = U 3 Z 3 = L 13 U 10 2 L 11 L 33 υ e γx (1 e 2γ(lx) ); MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamysamaaBa aaleaacaaIZaaabeaakiabg2da9iabgkHiTmaalaaabaGaamyvamaa BaaaleaacaaIZaaabeaaaOqaaiaadQfadaWgaaWcbaGaaG4maaqaba aaaOGaeyypa0JaeyOeI0YaaSaaaeaacaWGmbWaaSbaaSqaaiaaigda caaIZaaabeaakiaadwfadaWgaaWcbaGaaGymaiaaicdaaeqaaaGcba GaaGOmaiaadYeadaWgaaWcbaGaaGymaiaaigdaaeqaaOGaamitamaa BaaaleaacaaIZaGaaG4maaqabaGccqaHfpqDaaGaamyzamaaCaaale qabaGaeyOeI0Iaeq4SdCMaamiEaaaakiaacIcacaaIXaGaeyOeI0Ia amyzamaaCaaaleqabaGaeyOeI0IaaGOmaiabeo7aNjaacIcacaWGSb GaeyOeI0IaamiEaiaacMcaaaGccaGGPaGaai4oaaaa@5DF9@ (31)

I 4 = U 4 Z 4 = L 14 U 10 2 L 11 L 44 υ e γx (1 e 2γ(lx) ). MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamysamaaBa aaleaacaaI0aaabeaakiabg2da9iabgkHiTmaalaaabaGaamyvamaa BaaaleaacaaI0aaabeaaaOqaaiaadQfadaWgaaWcbaGaaGinaaqaba aaaOGaeyypa0JaeyOeI0YaaSaaaeaacaWGmbWaaSbaaSqaaiaaigda caaI0aaabeaakiaadwfadaWgaaWcbaGaaGymaiaaicdaaeqaaaGcba GaaGOmaiaadYeadaWgaaWcbaGaaGymaiaaigdaaeqaaOGaamitamaa BaaaleaacaaI0aGaaGinaaqabaGccqaHfpqDaaGaamyzamaaCaaale qabaGaeyOeI0Iaeq4SdCMaamiEaaaakiaacIcacaaIXaGaeyOeI0Ia amyzamaaCaaaleqabaGaeyOeI0IaaGOmaiabeo7aNjaacIcacaWGSb GaeyOeI0IaamiEaiaacMcaaaGccaGGPaGaaiOlaaaa@5DF2@ (32)

Подставив в уравнение (30) уравнения (16, 31 и 32) и выразив из уравнения (29) постоянную B 2 e +γx MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOqamaaBa aaleaacaaIYaaabeaakiaadwgadaahaaWcbeqaaiabgUcaRiabeo7a NjaadIhaaaaaaa@3C4A@ , а также учитывая, что x = 0, получим постоянную A 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqamaaBa aaleaacaaIYaaabeaaaaa@37A2@ :

A 2 = L 12 U 10 2 L 11 L 32 L 13 U 10 4 L 11 L 33 1 e 2γl L 42 L 14 U 10 4 L 11 L 44 1 e 2γl . MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamyqamaaBa aaleaacaaIYaaabeaakiabg2da9maalaaabaGaamitamaaBaaaleaa caaIXaGaaGOmaaqabaGccaWGvbWaaSbaaSqaaiaaigdacaaIWaaabe aaaOqaaiaaikdacaWGmbWaaSbaaSqaaiaaigdacaaIXaaabeaaaaGc cqGHsisldaWcaaqaaiaadYeadaWgaaWcbaGaaG4maiaaikdaaeqaaO GaamitamaaBaaaleaacaaIXaGaaG4maaqabaGccaWGvbWaaSbaaSqa aiaaigdacaaIWaaabeaaaOqaaiaaisdacaWGmbWaaSbaaSqaaiaaig dacaaIXaaabeaakiaadYeadaWgaaWcbaGaaG4maiaaiodaaeqaaaaa kmaabmaabaGaaGymaiabgkHiTiaadwgadaahaaWcbeqaaiabgkHiTi aaikdacqaHZoWzcaWGSbaaaaGccaGLOaGaayzkaaGaeyOeI0YaaSaa aeaacaWGmbWaaSbaaSqaaiaaisdacaaIYaaabeaakiaadYeadaWgaa WcbaGaaGymaiaaisdaaeqaaOGaamyvamaaBaaaleaacaaIXaGaaGim aaqabaaakeaacaaI0aGaamitamaaBaaaleaacaaIXaGaaGymaaqaba GccaWGmbWaaSbaaSqaaiaaisdacaaI0aaabeaaaaGcdaqadaqaaiaa igdacqGHsislcaWGLbWaaWbaaSqabeaacqGHsislcaaIYaGaeq4SdC MaamiBaaaaaOGaayjkaiaawMcaaiaac6caaaa@7057@ (33)

Выразив из уравнения (29) постоянную A 2 e γx MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqamaaBa aaleaacaaIYaaabeaakiaadwgadaahaaWcbeqaaiabgkHiTiabeo7a NjaadIhaaaaaaa@3C54@ и учитывая, что x = l, и подставив в уравнение (30) уравнения (16, 31 и 32), получим постоянную B 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOqamaaBa aaleaacaaIYaaabeaaaaa@37A3@ :

B 2 = e γl L 12 U 10 2 L 11 + L 32 L 13 U 10 4 L 11 L 33 + L 42 L 14 U 10 4 L 11 L 44 . MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamOqamaaBa aaleaacaaIYaaabeaakiabg2da9iaadwgadaahaaWcbeqaaiabgkHi Tiabeo7aNjaadYgaaaGcdaqadaqaaiabgkHiTmaalaaabaGaamitam aaBaaaleaacaaIXaGaaGOmaaqabaGccaWGvbWaaSbaaSqaaiaaigda caaIWaaabeaaaOqaaiaaikdacaWGmbWaaSbaaSqaaiaaigdacaaIXa aabeaaaaGccqGHRaWkdaWcaaqaaiaadYeadaWgaaWcbaGaaG4maiaa ikdaaeqaaOGaamitamaaBaaaleaacaaIXaGaaG4maaqabaGccaWGvb WaaSbaaSqaaiaaigdacaaIWaaabeaaaOqaaiaaisdacaWGmbWaaSba aSqaaiaaigdacaaIXaaabeaakiaadYeadaWgaaWcbaGaaG4maiaaio daaeqaaaaakiabgUcaRmaalaaabaGaamitamaaBaaaleaacaaI0aGa aGOmaaqabaGccaWGmbWaaSbaaSqaaiaaigdacaaI0aaabeaakiaadw fadaWgaaWcbaGaaGymaiaaicdaaeqaaaGcbaGaaGinaiaadYeadaWg aaWcbaGaaGymaiaaigdaaeqaaOGaamitamaaBaaaleaacaaI0aGaaG inaaqabaaaaaGccaGLOaGaayzkaaGaaiOlaaaa@6638@ (34)

После подстановки в уравнение (29) уравнения полученных постоянных (33) и (34) получим окончательное решение для U 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyvamaaBa aaleaacaaIYaaabeaaaaa@37B6@ в виде

U 2 = U 10 e γx L 12 2 L 11 1 e 2γ(lx) L 32 L 13 4 L 11 L 33 1 e 2γ L 42 L 14 4 L 11 L 44 1 e 2γ . MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamyvamaaBa aaleaacaaIYaaabeaakiabg2da9iaadwfadaWgaaWcbaGaaGymaiaa icdaaeqaaOGaamyzamaaCaaaleqabaGaeyOeI0Iaeq4SdCMaamiEaa aakmaabmaabaWaaSaaaeaacaWGmbWaaSbaaSqaaiaaigdacaaIYaaa beaaaOqaaiaaikdacaWGmbWaaSbaaSqaaiaaigdacaaIXaaabeaaaa GcdaqadaqaaiaaigdacqGHsislcaWGLbWaaWbaaSqabeaacqGHsisl caaIYaGaeq4SdCMaaiikaiaadYgacqGHsislcaWG4bGaaiykaaaaaO GaayjkaiaawMcaaiabgkHiTmaalaaabaGaamitamaaBaaaleaacaaI ZaGaaGOmaaqabaGccaWGmbWaaSbaaSqaaiaaigdacaaIZaaabeaaaO qaaiaaisdacaWGmbWaaSbaaSqaaiaaigdacaaIXaaabeaakiaadYea daWgaaWcbaGaaG4maiaaiodaaeqaaaaakmaabmaabaGaaGymaiabgk HiTiaadwgadaahaaWcbeqaaiabgkHiTiaaikdacqaHZoWzaaaakiaa wIcacaGLPaaacqGHsisldaWcaaqaaiaadYeadaWgaaWcbaGaaGinai aaikdaaeqaaOGaamitamaaBaaaleaacaaIXaGaaGinaaqabaaakeaa caaI0aGaamitamaaBaaaleaacaaIXaGaaGymaaqabaGccaWGmbWaaS baaSqaaiaaisdacaaI0aaabeaaaaGcdaqadaqaaiaaigdacqGHsisl caWGLbWaaWbaaSqabeaacqGHsislcaaIYaGaeq4SdCgaaaGccaGLOa GaayzkaaaacaGLOaGaayzkaaGaaiOlaaaa@7B90@ (35)

Вводим нормированные величины для напряжения U:

u 2 = U 2 Z 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyDamaaBa aaleaacaaIYaaabeaakiabg2da9maalaaabaGaamyvamaaBaaaleaa caaIYaaabeaaaOqaamaakaaabaGaamOwamaaBaaaleaacaaIYaaabe aaaeqaaaaaaaa@3C99@ . (36)

Коэффициенты связи согласно [2] будут равны:

χ 12 = L 12 L 11 L 22 = K 12 K 11 K 22 ; χ 32 = L 32 L 33 L 22 = K 32 K 33 K 22 ; χ 42 = L 42 L 44 L 22 = K 42 K 44 K 22 ; χ 14 = L 14 L 11 L 44 = K 14 K 11 K 44 . MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqbaeqabqqaaa aabaGaeq4Xdm2aaSbaaSqaaiaaigdacaaIYaaabeaakiabg2da9maa laaabaGaamitamaaBaaaleaacaaIXaGaaGOmaaqabaaakeaadaGcaa qaaiaadYeadaWgaaWcbaGaaGymaiaaigdaaeqaaOGaamitamaaBaaa leaacaaIYaGaaGOmaaqabaaabeaaaaGccqGH9aqpdaWcaaqaaiaadU eadaWgaaWcbaGaaGymaiaaikdaaeqaaaGcbaWaaOaaaeaacaWGlbWa aSbaaSqaaiaaigdacaaIXaaabeaakiaadUeadaWgaaWcbaGaaGOmai aaikdaaeqaaaqabaaaaOGaai4oaaqaaiabeE8aJnaaBaaaleaacaaI ZaGaaGOmaaqabaGccqGH9aqpdaWcaaqaaiaadYeadaWgaaWcbaGaaG 4maiaaikdaaeqaaaGcbaWaaOaaaeaacaWGmbWaaSbaaSqaaiaaioda caaIZaaabeaakiaadYeadaWgaaWcbaGaaGOmaiaaikdaaeqaaaqaba aaaOGaeyypa0ZaaSaaaeaacaWGlbWaaSbaaSqaaiaaiodacaaIYaaa beaaaOqaamaakaaabaGaam4samaaBaaaleaacaaIZaGaaG4maaqaba GccaWGlbWaaSbaaSqaaiaaikdacaaIYaaabeaaaeqaaaaakiaacUda aeaacqaHhpWydaWgaaWcbaGaaGinaiaaikdaaeqaaOGaeyypa0ZaaS aaaeaacaWGmbWaaSbaaSqaaiaaisdacaaIYaaabeaaaOqaamaakaaa baGaamitamaaBaaaleaacaaI0aGaaGinaaqabaGccaWGmbWaaSbaaS qaaiaaikdacaaIYaaabeaaaeqaaaaakiabg2da9maalaaabaGaam4s amaaBaaaleaacaaI0aGaaGOmaaqabaaakeaadaGcaaqaaiaadUeada WgaaWcbaGaaGinaiaaisdaaeqaaOGaam4samaaBaaaleaacaaIYaGa aGOmaaqabaaabeaaaaGccaGG7aaabaGaeq4Xdm2aaSbaaSqaaiaaig dacaaI0aaabeaakiabg2da9maalaaabaGaamitamaaBaaaleaacaaI XaGaaGinaaqabaaakeaadaGcaaqaaiaadYeadaWgaaWcbaGaaGymai aaigdaaeqaaOGaamitamaaBaaaleaacaaI0aGaaGinaaqabaaabeaa aaGccqGH9aqpdaWcaaqaaiaadUeadaWgaaWcbaGaaGymaiaaisdaae qaaaGcbaWaaOaaaeaacaWGlbWaaSbaaSqaaiaaigdacaaIXaaabeaa kiaadUeadaWgaaWcbaGaaGinaiaaisdaaeqaaaqabaaaaOGaaiOlaa aaaaa@8BA9@ (37)

Учитывая выражение (27) для коэффициента связи χ 13 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Xdm2aaS baaSqaaiaaigdacaaIZaaabeaaaaa@394F@ , получим уравнение для u 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyDamaaBa aaleaacaaIYaaabeaaaaa@37D6@ :

u 2 = u 10 e γx χ 12 2 1 e 2γ(lx) χ 32 χ 13 4 1 e 2γl χ 42 χ 14 4 1 e 2γl . MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamyDamaaBa aaleaacaaIYaaabeaakiabg2da9iaadwhadaWgaaWcbaGaaGymaiaa icdaaeqaaOGaamyzamaaCaaaleqabaGaeyOeI0Iaeq4SdCMaamiEaa aakmaabmaabaWaaSaaaeaacqaHhpWydaWgaaWcbaGaaGymaiaaikda aeqaaaGcbaGaaGOmaaaadaqadaqaaiaaigdacqGHsislcaWGLbWaaW baaSqabeaacqGHsislcaaIYaGaeq4SdCMaaiikaiaadYgacqGHsisl caWG4bGaaiykaaaaaOGaayjkaiaawMcaaiabgkHiTmaalaaabaGaeq 4Xdm2aaSbaaSqaaiaaiodacaaIYaaabeaakiabeE8aJnaaBaaaleaa caaIXaGaaG4maaqabaaakeaacaaI0aaaamaabmaabaGaaGymaiabgk HiTiaadwgadaahaaWcbeqaaiabgkHiTiaaikdacqaHZoWzcaWGSbaa aaGccaGLOaGaayzkaaGaeyOeI0YaaSaaaeaacqaHhpWydaWgaaWcba GaaGinaiaaikdaaeqaaOGaeq4Xdm2aaSbaaSqaaiaaigdacaaI0aaa beaaaOqaaiaaisdaaaWaaeWaaeaacaaIXaGaeyOeI0IaamyzamaaCa aaleqabaGaeyOeI0IaaGOmaiabeo7aNjaadYgaaaaakiaawIcacaGL PaaaaiaawIcacaGLPaaacaGGUaaaaa@75B5@ (38)

Из уравнения (38) получим уравнения для влияния на ближний конец:

N 12 = u 20 u 10 = χ 12 2 χ 32 χ 13 4 χ 42 χ 14 4 1 e 2γl MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOtamaaBa aaleaacaaIXaGaaGOmaaqabaGccqGH9aqpdaWcaaqaaiaadwhadaWg aaWcbaGaaGOmaiaaicdaaeqaaaGcbaGaamyDamaaBaaaleaacaaIXa GaaGimaaqabaaaaOGaeyypa0ZaaeWaaeaadaWcaaqaaiabeE8aJnaa BaaaleaacaaIXaGaaGOmaaqabaaakeaacaaIYaaaaiabgkHiTmaala aabaGaeq4Xdm2aaSbaaSqaaiaaiodacaaIYaaabeaakiabeE8aJnaa BaaaleaacaaIXaGaaG4maaqabaaakeaacaaI0aaaaiabgkHiTmaala aabaGaeq4Xdm2aaSbaaSqaaiaaisdacaaIYaaabeaakiabeE8aJnaa BaaaleaacaaIXaGaaGinaaqabaaakeaacaaI0aaaaaGaayjkaiaawM caamaabmaabaGaaGymaiabgkHiTiaadwgadaahaaWcbeqaaiabgkHi TiaaikdacqaHZoWzcaWGSbaaaaGccaGLOaGaayzkaaaaaa@5F35@ (39)

и на дальний конец:

F 12 = u 2l u 1l = χ 32 χ 13 4 χ 42 χ 14 4 1 e 2γl . MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamOramaaBa aaleaacaaIXaGaaGOmaaqabaGccqGH9aqpdaWcaaqaaiaadwhadaWg aaWcbaGaaGOmaiaadYgaaeqaaaGcbaGaamyDamaaBaaaleaacaaIXa GaamiBaaqabaaaaOGaeyypa0ZaaeWaaeaacqGHsisldaWcaaqaaiab eE8aJnaaBaaaleaacaaIZaGaaGOmaaqabaGccqaHhpWydaWgaaWcba GaaGymaiaaiodaaeqaaaGcbaGaaGinaaaacqGHsisldaWcaaqaaiab eE8aJnaaBaaaleaacaaI0aGaaGOmaaqabaGccqaHhpWydaWgaaWcba GaaGymaiaaisdaaeqaaaGcbaGaaGinaaaaaiaawIcacaGLPaaadaqa daqaaiaaigdacqGHsislcaWGLbWaaWbaaSqabeaacqGHsislcaaIYa Gaeq4SdCMaamiBaaaaaOGaayjkaiaawMcaaiaac6caaaa@5D20@ (40)

Соответственно переходное затухание на ближнем конце согласно [5] будет равно

A 0 =20lg 2 N 12 ; MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamyqamaaBa aaleaacaaIWaaabeaakiabg2da9iaaikdacaaIWaGaciiBaiaacEga daqadaqaamaalaaabaGaaGOmaaqaaiaad6eadaWgaaWcbaGaaGymai aaikdaaeqaaaaaaOGaayjkaiaawMcaaiaacUdaaaa@429A@ (41)

на дальнем конце:

A l =20lg 2 F 12 . MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamyqamaaBa aaleaacaWGSbaabeaakiabg2da9iaaikdacaaIWaGaciiBaiaacEga daqadaqaamaalaaabaGaaGOmaaqaaiaadAeadaWgaaWcbaGaaGymai aaikdaaeqaaaaaaOGaayjkaiaawMcaaiaac6caaaa@42BC@ (42)

Определение взаимного влияния на дальний и ближний конец для двух витых пар

Уравнения (39) и (40) являются конечным результатом для влияния в пучке из идеальных цепей с учетом того, что все они замкнуты на свои волновые сопротивления.

Для нахождения коэффициентов K 12 , K 32 , K 42 , K 14 , K 13 , K 11 , K 22 , K 33 , K 44 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4samaaBa aaleaacaaIXaGaaGOmaaqabaGccaGGSaGaaGPaVlaadUeadaWgaaWc baGaaG4maiaaikdaaeqaaOGaaiilaiaaykW7caWGlbWaaSbaaSqaai aaisdacaaIYaaabeaakiaacYcacaaMc8Uaam4samaaBaaaleaacaaI XaGaaGinaaqabaGccaGGSaGaaGPaVlaadUeadaWgaaWcbaGaaGymai aaiodaaeqaaOGaaiilaiaaykW7caWGlbWaaSbaaSqaaiaaigdacaaI XaaabeaakiaacYcacaaMc8Uaam4samaaBaaaleaacaaIYaGaaGOmaa qabaGccaGGSaGaaGPaVlaadUeadaWgaaWcbaGaaG4maiaaiodaaeqa aOGaaiilaiaaykW7caWGlbWaaSbaaSqaaiaaisdacaaI0aaabeaaaa a@5E37@ из выражений (25, 37), нужно найти значения матрицы

K L = C L 1 . MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaam4samaaBa aaleaacaWGmbaabeaakiabg2da9iaadoeadaqhaaWcbaGaamitaaqa aiabgkHiTiaaigdaaaGccaGGUaaaaa@3E1E@ (43)

Матрица C L MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaBa aaleaacaWGmbaabeaaaaa@37B9@ из четырех цепей будет выглядеть следующим образом [2]:

C L = C II C III C IIII C IIV C III C IIII C IIIII C IIIV C IIII C IIIII C IIIIII C IIIIV C IVI C IVII C IVIII C IVIV , MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaam4qamaaBa aaleaacaWGmbaabeaakiabg2da9maabmaabaqbaeqabqabaaaaaeaa caWGdbWaaSbaaSqaaiaadMeacaaMc8UaamysaaqabaaakeaacaWGdb WaaSbaaSqaaiaadMeacaaMc8UaamysaiaadMeaaeqaaaGcbaGaam4q amaaBaaaleaacaWGjbGaaGPaVlaadMeacaWGjbGaamysaaqabaaake aacaWGdbWaaSbaaSqaaiaadMeacaaMc8UaamysaiaadAfaaeqaaaGc baGaam4qamaaBaaaleaacaWGjbGaamysaiaaykW7caWGjbaabeaaaO qaaiaadoeadaWgaaWcbaGaamysaiaadMeacaaMc8UaamysaiaadMea aeqaaaGcbaGaam4qamaaBaaaleaacaWGjbGaamysaiaaykW7caWGjb GaamysaiaadMeaaeqaaaGcbaGaam4qamaaBaaaleaacaWGjbGaamys aiaaykW7caWGjbGaamOvaaqabaaakeaacaWGdbWaaSbaaSqaaiaadM eacaWGjbGaamysaiaaykW7caWGjbaabeaaaOqaaiaadoeadaWgaaWc baGaamysaiaadMeacaWGjbGaaGPaVlaadMeacaWGjbaabeaaaOqaai aadoeadaWgaaWcbaGaamysaiaadMeacaWGjbGaaGPaVlaadMeacaWG jbGaamysaaqabaaakeaacaWGdbWaaSbaaSqaaiaadMeacaWGjbGaam ysaiaaykW7caWGjbGaamOvaaqabaaakeaacaWGdbWaaSbaaSqaaiaa dMeacaWGwbGaaGPaVlaadMeaaeqaaaGcbaGaam4qamaaBaaaleaaca WGjbGaamOvaiaaykW7caWGjbGaamysaaqabaaakeaacaWGdbWaaSba aSqaaiaadMeacaWGwbGaaGPaVlaadMeacaWGjbGaamysaaqabaaake aacaWGdbWaaSbaaSqaaiaadMeacaWGwbGaaGPaVlaadMeacaWGwbaa beaaaaaakiaawIcacaGLPaaacaGGSaaaaa@989D@ (44)

где с учетом того, что C ik = C ki MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaBa aaleaacaWGPbGaam4AaaqabaGccqGH9aqpcaWGdbWaaSbaaSqaaiaa dUgacaWGPbaabeaaaaa@3CA8@ ,

C II , C IIII , C IIIIII , C IVIV MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaBa aaleaacaWGjbGaaGPaVlaadMeaaeqaaOGaaiilaiaaykW7caWGdbWa aSbaaSqaaiaadMeacaWGjbGaaGPaVlaadMeacaWGjbaabeaakiaacY cacaaMc8Uaam4qamaaBaaaleaacaWGjbGaamysaiaadMeacaaMc8Ua amysaiaadMeacaWGjbaabeaakiaacYcacaWGdbWaaSbaaSqaaiaadM eacaWGwbGaaGPaVlaadMeacaWGwbaabeaaaaa@522E@ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzagaeaaaaaaaaa8qacaWFtacaaa@39C3@ рабочие емкости;

C III , C IIII , C IIV , C IIIII , C IIIV , C IIIIV MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaBa aaleaacaWGjbGaaGPaVlaadMeacaWGjbaabeaakiaacYcacaaMc8Ua am4qamaaBaaaleaacaWGjbGaaGPaVlaadMeacaWGjbGaamysaaqaba GccaGGSaGaaGPaVlaadoeadaWgaaWcbaGaamysaiaaykW7caWGjbGa amOvaaqabaGccaGGSaGaam4qamaaBaaaleaacaWGjbGaamysaiaayk W7caWGjbGaamysaiaadMeaaeqaaOGaaiilaiaaykW7caWGdbWaaSba aSqaaiaadMeacaWGjbGaaGPaVlaadMeacaWGwbaabeaakiaacYcaca WGdbWaaSbaaSqaaiaadMeacaWGjbGaamysaiaaykW7caWGjbGaamOv aaqabaaaaa@60A8@ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzagaeaaaaaaaaa8qacaWFtacaaa@39C3@ взаимные емкости.

Так как вычисление обратной матрицы C L MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaBa aaleaacaWGmbaabeaaaaa@37B9@ вручную представляет собой громадные расчеты, используем ПО MathCad [7]. Согласно выражениям (25, 37) нас интересуют коэффициенты K 12 , K 32 , K 42 , K 14 , K 13 , K 11 , K 22 , K 33 , K 44 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4samaaBa aaleaacaaIXaGaaGOmaaqabaGccaGGSaGaaGPaVlaadUeadaWgaaWc baGaaG4maiaaikdaaeqaaOGaaiilaiaaykW7caWGlbWaaSbaaSqaai aaisdacaaIYaaabeaakiaacYcacaaMc8Uaam4samaaBaaaleaacaaI XaGaaGinaaqabaGccaGGSaGaaGPaVlaadUeadaWgaaWcbaGaaGymai aaiodaaeqaaOGaaiilaiaaykW7caWGlbWaaSbaaSqaaiaaigdacaaI XaaabeaakiaacYcacaaMc8Uaam4samaaBaaaleaacaaIYaGaaGOmaa qabaGccaGGSaGaaGPaVlaadUeadaWgaaWcbaGaaG4maiaaiodaaeqa aOGaaiilaiaaykW7caWGlbWaaSbaaSqaaiaaisdacaaI0aaabeaaaa a@5E37@ , которые соотносятся с элементами матрицы K L MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4samaaBa aaleaacaWGmbaabeaaaaa@37C1@ ; учитывая, что K ik = K ki MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4samaaBa aaleaacaWGPbGaam4AaaqabaGccqGH9aqpcaWGlbWaaSbaaSqaaiaa dUgacaWGPbaabeaaaaa@3CB8@ , получим:

K 12 = K III ; K 32 = K IIIII ; K 42 = K IVII ; K 14 = K IIV ; K 13 = K IIII ; K 11 = K II ; K 22 = K IIII ; K 33 = K IIIIII ; K 44 = K IVIV . MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaWGlb WaaSbaaSqaaiaaigdacaaIYaaabeaakiabg2da9iaadUeadaWgaaWc baGaamysaiaaykW7caWGjbGaamysaaqabaGccaGG7aGaaGPaVlaayk W7caaMc8Uaam4samaaBaaaleaacaaIZaGaaGOmaaqabaGccqGH9aqp caWGlbWaaSbaaSqaaiaadMeacaWGjbGaamysaiaaykW7caWGjbGaam ysaaqabaGccaaMc8Uaai4oaiaaykW7caaMc8UaaGPaVlaadUeadaWg aaWcbaGaaGinaiaaikdaaeqaaOGaeyypa0Jaam4samaaBaaaleaaca WGjbGaamOvaiaaykW7caWGjbGaamysaaqabaGccaGG7aGaaGPaVlaa ykW7caWGlbWaaSbaaSqaaiaaigdacaaI0aaabeaakiabg2da9iaadU eadaWgaaWcbaGaamysaiaaykW7caWGjbGaamOvaaqabaGccaGG7aGa aGPaVlaaykW7caaMc8Uaam4samaaBaaaleaacaaIXaGaaG4maaqaba GccqGH9aqpcaWGlbWaaSbaaSqaaiaadMeacaaMc8UaamysaiaadMea caWGjbaabeaakiaaykW7caGG7aGaaGPaVdqaaiaadUeadaWgaaWcba GaaGymaiaaigdaaeqaaOGaeyypa0Jaam4samaaBaaaleaacaWGjbGa aGPaVlaaykW7caWGjbaabeaakiaacUdacaaMc8UaaGPaVlaaykW7ca WGlbWaaSbaaSqaaiaaikdacaaIYaaabeaakiabg2da9iaadUeadaWg aaWcbaGaamysaiaadMeacaaMc8UaaGPaVlaaykW7caWGjbGaamysaa qabaGccaGG7aGaaGPaVlaaykW7caWGlbWaaSbaaSqaaiaaiodacaaI Zaaabeaakiabg2da9iaadUeadaWgaaWcbaGaamysaiaadMeacaWGjb GaaGPaVlaaykW7caWGjbGaamysaiaadMeaaeqaaOGaai4oaiaaykW7 caaMc8UaaGPaVlaadUeadaWgaaWcbaGaaGinaiaaisdaaeqaaOGaey ypa0Jaam4samaaBaaaleaacaWGjbGaamOvaiaaykW7caaMc8Uaamys aiaadAfaaeqaaOGaaiOlaaaaaa@B970@ (45)

Значения элементов матрицы (45) легко получить с помощью ПО MathCad и соответственно получить значения коэффициентов связи (25, 37), но этот алгоритм можно использовать, если известны рабочие и взаимные емкости в матрице (44). Так как данные значения можно получить только экспериментальным путем, то в выражении (39) множитель, учитывающий длину цепи, примем равным единице, а N 12 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOtamaaBa aaleaacaaIXaGaaGOmaaqabaaaaa@386A@ выразим из формулы (41). Согласно [8] минимальное переходное затухание для LAN-кабеля категории 5e на ближнем конце A 0 =35,3 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqamaaBa aaleaacaaIWaaabeaakiabg2da9iaaiodacaaI1aGaaiilaiaaioda caaMc8oaaa@3D24@ дБ/100 м. Примем A 0 =45 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqamaaBa aaleaacaaIWaaabeaakiabg2da9iaaisdacaaI1aGaaGPaVdaa@3BB8@ дБ/100 м из расчета того, что при максимальном значении множителя 1 e 2γl MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaaca aIXaGaeyOeI0IaamyzamaaCaaaleqabaGaeyOeI0IaaGOmaiabeo7a NjaadYgaaaaakiaawIcacaGLPaaaaaa@3E87@ переходное затухание будет не менее 35,3 дБ/100м. Получим следующее соотношение:

A 0 =20lg(2)20lg( N 12 ); 20lg( N 12 )=20lg(2)45; N 12 = 10 1,948 =0.01127. MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGceaqabeaacaWGbb WaaSbaaSqaaiaaicdaaeqaaOGaeyypa0JaaGOmaiaaicdaciGGSbGa ai4zaiaacIcacaaIYaGaaiykaiabgkHiTiaaikdacaaIWaGaciiBai aacEgacaGGOaGaamOtamaaBaaaleaacaaIXaGaaGOmaaqabaGccaGG PaGaai4oaaqaaiaaikdacaaIWaGaciiBaiaacEgacaGGOaGaamOtam aaBaaaleaacaaIXaGaaGOmaaqabaGccaGGPaGaeyypa0JaaGOmaiaa icdaciGGSbGaai4zaiaacIcacaaIYaGaaiykaiabgkHiTiaaisdaca aI1aGaai4oaaqaaiaad6eadaWgaaWcbaGaaGymaiaaikdaaeqaaOGa eyypa0JaaGymaiaaicdadaahaaWcbeqaaiabgkHiTiaaigdacaGGSa GaaGyoaiaaisdacaaI4aaaaOGaeyypa0JaaGimaiaac6cacaaIWaGa aGymaiaaigdacaaIYaGaaG4naiaac6caaaaa@695C@ (46)

Чтобы рассчитать влияние и переходное затухание на ближнем конце, учитывая длину цепи и частоту передаваемого сигнала, нужно знать значение множителя 1 e 2γl MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaaca aIXaGaeyOeI0IaamyzamaaCaaaleqabaGaeyOeI0IaaGOmaiabeo7a NjaadYgaaaaakiaawIcacaGLPaaaaaa@3E87@ в выражении (39). Данный множитель согласно [2] для длин меньше 1 км имеет вид

1 e 2γl 1cos2 ω υ l 2 + sin2 ω υ l 2 = 22cos π l λ/4 . MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaWaaqWaaeaaca aIXaGaeyOeI0IaamyzamaaCaaaleqabaGaeyOeI0IaaGOmaiabeo7a NjaadYgaaaaakiaawEa7caGLiWoacqGHijYUdaGcaaqaamaabmaaba GaaGymaiabgkHiTiGacogacaGGVbGaai4CaiaaikdadaWcaaqaaiab eM8a3bqaaiabew8a1baacaWGSbaacaGLOaGaayzkaaWaaWbaaSqabe aacaaIYaaaaOGaey4kaSYaaeWaaeaaciGGZbGaaiyAaiaac6gacaaI YaWaaSaaaeaacqaHjpWDaeaacqaHfpqDaaGaamiBaaGaayjkaiaawM caamaaCaaaleqabaGaaGOmaaaaaeqaaOGaeyypa0ZaaOaaaeaacaaI YaGaeyOeI0IaaGOmaiGacogacaGGVbGaai4CamaabmaabaGaeqiWda 3aaSaaaeaacaWGSbaabaGaeq4UdWMaai4laiaaisdaaaaacaGLOaGa ayzkaaaaleqaaOGaaiOlaaaa@6934@ (47)

С учетом того, что λ= 2πυ ω MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4UdWMaey ypa0ZaaSaaaeaacaaIYaGaeqiWdaNaeqyXduhabaGaeqyYdChaaaaa @3ECB@ , формула (47) примет вид

1 e 2γl = 22cos 2ωl υ , MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaWaaqWaaeaaca aIXaGaeyOeI0IaamyzamaaCaaaleqabaGaeyOeI0IaaGOmaiabeo7a NjaadYgaaaaakiaawEa7caGLiWoacqGH9aqpdaGcaaqaaiaaikdacq GHsislcaaIYaGaci4yaiaac+gacaGGZbWaaeWaaeaadaWcaaqaaiaa ikdacqaHjpWDcaWGSbaabaGaeqyXduhaaaGaayjkaiaawMcaaaWcbe aakiaacYcaaaa@4F10@ (48)

где υ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyXduhaaa@37BB@ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzagaeaaaaaaaaa8qacaWFtacaaa@39C3@ скорость распространения сигнала;

λ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4UdWgaaa@37A8@ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzagaeaaaaaaaaa8qacaWFtacaaa@39C3@ длина волны;

γ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4SdCgaaa@379B@ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzagaeaaaaaaaaa8qacaWFtacaaa@39C3@ постоянная распространения волн;

π MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiWdahaaa@37B1@ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbcKqzagaeaaaaaaaaa8qacaWFtacaaa@39C5@ число ПИ.

Скорость распространения сигнала для кабелей в диапазоне высоких частот находится по следующей формуле [9]:

υ= 1 LC , MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaeqyXduNaey ypa0ZaaSaaaeaacaaIXaaabaWaaOaaaeaacaWGmbGaam4qaaWcbeaa aaGccaGGSaaaaa@3CFD@ (49)

где L MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamitaaaa@36C5@ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzagaeaaaaaaaaa8qacaWFtacaaa@39C3@ индуктивность кабеля;

C MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qaaaa@36BC@ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzagaeaaaaaaaaa8qacaWFtacaaa@39C3@ емкость цепи.

Индуктивность находится по формуле [9]

L= 4ln ar r +μQ(kr) 10 4 , MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamitaiabg2 da9maadmaabaGaaGinaiabgwSixlGacYgacaGGUbWaaSaaaeaacaWG HbGaeyOeI0IaamOCaaqaaiaadkhaaaGaey4kaSIaeqiVd0Maamyuai aacIcacaWGRbGaamOCaiaacMcaaiaawUfacaGLDbaacqGHflY1caaI XaGaaGimamaaCaaaleqabaGaeyOeI0IaaGinaaaakiaacYcaaaa@507C@ (50)

где a MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyyaaaa@36DA@ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzagaeaaaaaaaaa8qacaWFtacaaa@39C3@ расстояние между жилами;

r MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCaaaa@36EB@ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzagaeaaaaaaaaa8qacaWFtacaaa@39C3@ радиус жилы;

μ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiVd0gaaa@37AA@ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzagaeaaaaaaaaa8qacaWFtacaaa@39C3@ относительная магнитная проницаемость металла, из которого изготовлена жила;

Q(kr) MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyuaiaacI cacaWGRbGaamOCaiaacMcaaaa@3A0A@ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzagaeaaaaaaaaa8qacaWFtacaaa@39C3@ табулированное значение бесселевой функции.

Значение бесселевой функции определяется по формуле [9]

Q(kr)= μ a ωσ r, MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamyuaiaacI cacaWGRbGaamOCaiaacMcacqGH9aqpdaGcaaqaaiabeY7aTnaaBaaa leaacaWGHbaabeaakiabeM8a3jabeo8aZbWcbeaakiabgwSixlaadk hacaGGSaaaaa@468B@ (51)

где σ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdmhaaa@37B7@ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzagaeaaaaaaaaa8qacaWFtacaaa@39C3@ проводимость материала;

μ a MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiVd02aaS baaSqaaiaadggaaeqaaaaa@38BC@ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzagaeaaaaaaaaa8qacaWFtacaaa@39C3@ абсолютная магнитная проницаемость материала.

В свою очередь, круговая частота находится по формуле [9]

ω=2πf, MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaeqyYdCNaey ypa0JaaGOmaiabec8aWjaadAgacaGGSaaaaa@3DDE@ (52)

где MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzagaeaaaaaaaaa8qacaWFtacaaa@39C3@ частота передаваемого сигнала.

Абсолютная магнитная проницаемость материала рассчитывается по формуле [9]

μ a = μ 0 μ, MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaeqiVd02aaS baaSqaaiaadggaaeqaaOGaeyypa0JaeqiVd02aaSbaaSqaaiaaicda aeqaaOGaeqiVd0Maaiilaaaa@3FDB@ (53)

где μ 0 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiVd02aaS baaSqaaiaaicdaaeqaaaaa@3890@ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzagaeaaaaaaaaa8qacaWFtacaaa@39C3@ постоянная магнитная проницаемость материала.

Емкость цепи определяется по формуле [10]

C= χ ук ε 10 6 36ln a r ψ , MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaam4qaiabg2 da9maalaaabaGaeq4Xdm2aaSbaaSqaaiaadoebcaWG6qaabeaakiab ew7aLjabgwSixlaaigdacaaIWaWaaWbaaSqabeaacqGHsislcaaI2a aaaaGcbaGaaG4maiaaiAdaciGGSbGaaiOBamaabmaabaWaaSaaaeaa caWGHbaabaGaamOCaaaacqaHipqEaiaawIcacaGLPaaaaaGaaiilaa aa@4CF0@ (54)

где χ ук MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Xdm2aaS baaSqaaiaadoebcaWG6qaabeaaaaa@3966@ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzagaeaaaaaaaaa8qacaWFtacaaa@39C3@ коэффициент укрутки;

ε MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdugaaa@379B@ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzagaeaaaaaaaaa8qacaWFtacaaa@39C3@ эффективная диэлектрическая проницаемость изоляции;

ψ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiYdKhaaa@37C2@ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzagaeaaaaaaaaa8qacaWFtacaaa@39C3@ поправочный коэффициент, учитывающий близость жил.

Поправочный коэффициент, учитывающий близость жил, в нашем случае для двойной парной скрутки, находится по формуле [9]

ψ= 0.65 d ДП + d 1 d 2 a 2 0.65 d ДП + d 1 d 2 + a 2 , MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaeqiYdKNaey ypa0ZaaSaaaeaadaWadaqaamaabmaabaGaaGimaiaac6cacaaI2aGa aGynaiaadsgadaWgaaWcbaGaamifeiaad+bbaeqaaOGaey4kaSIaam izamaaBaaaleaacaaIXaaabeaakiabgkHiTiaadsgaaiaawIcacaGL PaaadaahaaWcbeqaaiaaikdaaaGccqGHsislcaWGHbWaaWbaaSqabe aacaaIYaaaaaGccaGLBbGaayzxaaaabaWaamWaaeaadaqadaqaaiaa icdacaGGUaGaaGOnaiaaiwdacaWGKbWaaSbaaSqaaiaadsbbcaWGFq aabeaakiabgUcaRiaadsgadaWgaaWcbaGaaGymaaqabaGccqGHsisl caWGKbaacaGLOaGaayzkaaWaaWbaaSqabeaacaaIYaaaaOGaey4kaS IaamyyamaaCaaaleqabaGaaGOmaaaaaOGaay5waiaaw2faaaaacaGG Saaaaa@5CCA@ (55)

где d ДП MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizamaaBa aaleaacaWGuqGaam4heaqabaaaaa@384E@ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzagaeaaaaaaaaa8qacaWFtacaaa@39C3@ диаметр двойной парной скрутки;

d MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizaaaa@36DD@ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzagaeaaaaaaaaa8qacaWFtacaaa@39C3@ диаметр жилы;

d 1 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizamaaBa aaleaacaaIXaaabeaaaaa@37C4@ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzagaeaaaaaaaaa8qacaWFtacaaa@39C3@ диаметр изолированной жилы.

Диаметр двойной парной скрутки определяется по формуле

d ДП = D и1 + D и2 , MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamizamaaBa aaleaacaWGuqGaam4heaqabaGccqGH9aqpcaWGebWaaSbaaSqaaiaa dIdbcaaIXaaabeaakiabgUcaRiaadseadaWgaaWcbaGaamioeiaaik daaeqaaOGaaiilaaaa@40EA@ (56)

где D и1 , D и2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiramaaBa aaleaacaWG4qGaaGymaaqabaGccaGGSaGaaGPaVlaadseadaWgaaWc baGaamioeiaaikdaaeqaaaaa@3D1C@ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzagaeaaaaaaaaa8qacaWFtacaaa@39C3@ диаметры изолированных жил в паре.

Расстояние между жилами находится по следующей формуле:

a= D и1 + D и2 2 . MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamyyaiabg2 da9maalaaabaGaamiramaaBaaaleaacaWG4qGaaGymaaqabaGccqGH RaWkcaWGebWaaSbaaSqaaiaadIdbcaaIYaaabeaaaOqaaiaaikdaaa GaaiOlaaaa@403A@ (57)

Для связи коэффициентов К1, К2, К3 с диаметром изоляции нужно выразить данные коэффициенты через межосевые расстояния жил в четверке d ij MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizamaaBa aaleaacaWGPbGaamOAaaqabaaaaa@38E6@ . Согласно [1, 10, 11, 12, 13] коэффициенты емкостной связи будут равны

K 1 = K c ( d 13 d 23 d 14 + d 24 ); K 2 = K c ( d 13 d 23 + d 14 d 24 ); K 3 = K c ( d 13 + d 23 d 14 d 24 ). MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqbaeqabmqaaa qaaiaadUeadaWgaaWcbaGaaGymaaqabaGccqGH9aqpcaWGlbWaaSba aSqaaiaadogaaeqaaOGaaiikaiaadsgadaWgaaWcbaGaaGymaiaaio daaeqaaOGaeyOeI0IaamizamaaBaaaleaacaaIYaGaaG4maaqabaGc cqGHsislcaWGKbWaaSbaaSqaaiaaigdacaaI0aaabeaakiabgUcaRi aadsgadaWgaaWcbaGaaGOmaiaaisdaaeqaaOGaaiykaiaacUdaaeaa caWGlbWaaSbaaSqaaiaaikdaaeqaaOGaeyypa0Jaam4samaaBaaale aacaWGJbaabeaakiaacIcacaWGKbWaaSbaaSqaaiaaigdacaaIZaaa beaakiabgkHiTiaadsgadaWgaaWcbaGaaGOmaiaaiodaaeqaaOGaey 4kaSIaamizamaaBaaaleaacaaIXaGaaGinaaqabaGccqGHsislcaWG KbWaaSbaaSqaaiaaikdacaaI0aaabeaakiaacMcacaGG7aaabaGaam 4samaaBaaaleaacaaIZaaabeaakiabg2da9iaadUeadaWgaaWcbaGa am4yaaqabaGccaGGOaGaamizamaaBaaaleaacaaIXaGaaG4maaqaba GccqGHRaWkcaWGKbWaaSbaaSqaaiaaikdacaaIZaaabeaakiabgkHi TiaadsgadaWgaaWcbaGaaGymaiaaisdaaeqaaOGaeyOeI0Iaamizam aaBaaaleaacaaIYaGaaGinaaqabaGccaGGPaGaaiOlaaaaaaa@71B4@ (58)

Константа K c MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4samaaBa aaleaacaWGJbaabeaaaaa@37D8@ согласно [10] равна 15 10 12 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGymaiaaiw dacqGHflY1caaIXaGaaGimamaaCaaaleqabaGaeyOeI0IaaGymaiaa ikdaaaaaaa@3DBE@ Ф.

Для связи межосевых расстояний и соответствующих диаметров изоляции воспользуемся следующей функциональной схемой (рис. 4). Из нее не составит труда вывести выражения зависимости диаметра изоляции от межосевого расстояния:

d 12 = D и1 + D и2 2 ; d 13 = D и1 + D и3 2 ; d 34 = D и3 + D и4 2 ; d 24 = D и2 + D и4 2 , MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGc9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabeqaamaabaabaaGceaqabeaacaWGKb WaaSbaaSqaaiaaigdacaaIYaaabeaakiabg2da9maalaaabaGaamir amaaBaaaleaacaWG4qGaaGymaaqabaGccqGHRaWkcaWGebWaaSbaaS qaaiaadIdbcaaIYaaabeaaaOqaaiaaikdaaaGaai4oaiaaykW7caaM c8UaaGPaVlaadsgadaWgaaWcbaGaaGymaiaaiodaaeqaaOGaeyypa0 ZaaSaaaeaacaWGebWaaSbaaSqaaiaadIdbcaaIXaaabeaakiabgUca RiaadseadaWgaaWcbaGaamioeiaaiodaaeqaaaGcbaGaaGOmaaaaca GG7aaabaGaamizamaaBaaaleaacaaIZaGaaGinaaqabaGccqGH9aqp daWcaaqaaiaadseadaWgaaWcbaGaamioeiaaiodaaeqaaOGaey4kaS IaamiramaaBaaaleaacaWG4qGaaGinaaqabaaakeaacaaIYaaaaiaa cUdacaaMc8UaaGPaVlaaykW7caWGKbWaaSbaaSqaaiaaikdacaaI0a aabeaakiabg2da9maalaaabaGaamiramaaBaaaleaacaWG4qGaaGOm aaqabaGccqGHRaWkcaWGebWaaSbaaSqaaiaadIdbcaaI0aaabeaaaO qaaiaaikdaaaGaaiilaaaaaa@6C41@ (59)

где D иn MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiramaaBa aaleaacaWG4qGaamOBaaqabaaaaa@389D@ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzagaeaaaaaaaaa8qacaWFtacaaa@39C3@ диаметр изолированный жилы (n = 1…4).

 

Рис. 4. Схема разреза двух витых пар с обозначенными межосевыми расстояниями:

  d 13 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizamaaBa aaleaacaaIXaGaaG4maaqabaaaaa@3881@ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzafaeaaaaaaaaa8qacaWFtacaaa@3983@ межосевое расстояние между жилами 1 и 3; d 14 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizamaaBa aaleaacaaIXaGaaGinaaqabaaaaa@3882@ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzafaeaaaaaaaaa8qacaWFtacaaa@3983@ межосевое расстояние между жилами 1 и 4; d 12 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizamaaBa aaleaacaaIXaGaaGOmaaqabaaaaa@3880@ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzafaeaaaaaaaaa8qacaWFtacaaa@3983@ межосевое расстояние между жилами 1 и 2; d 24 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizamaaBa aaleaacaaIYaGaaGinaaqabaaaaa@3883@ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzafaeaaaaaaaaa8qacaWFtacaaa@3983@ межосевое расстояние между жилами 2 и 4; d 34 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizamaaBa aaleaacaaIZaGaaGinaaqabaaaaa@3884@ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzafaeaaaaaaaaa8qacaWFtacaaa@3983@ межосевое расстояние между жилами 3 и 4; d 23 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizamaaBa aaleaacaaIYaGaaG4maaqabaaaaa@3882@ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzafaeaaaaaaaaa8qacaWFtacaaa@3983@ межосевое расстояние между жилами 2 и 3

 

Для определения межосевых расстояний d 23 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizamaaBa aaleaacaaIYaGaaG4maaqabaaaaa@3882@ и d 14 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizamaaBa aaleaacaaIXaGaaGinaaqabaaaaa@3882@ построим следующую схему (рис. 5).

Согласно рис. 4 для нахождения межосевых расстояний d 23 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizamaaBa aaleaacaaIYaGaaG4maaqabaaaaa@3882@ и d 14 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizamaaBa aaleaacaaIXaGaaGinaaqabaaaaa@3882@ нужно воспользоваться следующими формулами [14]:

d 23 = d 34 2 + d 24 2 2 d 34 d c 24 os D 4 ; d 14 = d 13 2 + d 34 2 2 d 13 d c 34 os D 3 . MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaWGKb WaaSbaaSqaaiaaikdacaaIZaaabeaakiabg2da9maakaaabaGaamiz amaaDaaaleaacaaIZaGaaGinaaqaaiaaikdaaaGccqGHRaWkcaWGKb Waa0baaSqaaiaaikdacaaI0aaabaGaaGOmaaaakiabgkHiTiaaikda caWGKbWaaSbaaSqaaiaaiodacaaI0aaabeaakiaadsgadaWgbaWcba GaaGOmaiaaisdaaeqaaOGaci4yaiaac+gacaGGZbGaamiramaaBaaa leaacaaI0aaabeaaaeqaaOGaai4oaaqaaiaadsgadaWgaaWcbaGaaG ymaiaaisdaaeqaaOGaeyypa0ZaaOaaaeaacaWGKbWaa0baaSqaaiaa igdacaaIZaaabaGaaGOmaaaakiabgUcaRiaadsgadaqhaaWcbaGaaG 4maiaaisdaaeaacaaIYaaaaOGaeyOeI0IaaGOmaiaadsgadaWgaaWc baGaaGymaiaaiodaaeqaaOGaamizamaaBeaaleaacaaIZaGaaGinaa qabaGcciGGJbGaai4BaiaacohacaWGebWaaSbaaSqaaiaaiodaaeqa aaqabaGccaGGUaaaaaa@64BB@ (60)

 

 

Рис. 5. Схема разреза двух витых пар с обозначенными межосевыми расстояниями:

  d 23 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizamaaBa aaleaacaaIYaGaaG4maaqabaaaaa@3882@ и d 14 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizamaaBa aaleaacaaIXaGaaGinaaqabaaaaa@3882@ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzafaeaaaaaaaaa8qacaWFtacaaa@3983@ межосевое расстояние между жилами; 1, 2, 3, 4 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzafaeaaaaaaaaa8qacaWFtacaaa@3983@ жилы; D 3 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiramaaBa aaleaacaaIZaaabeaaaaa@37A6@ и D 4 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiramaaBa aaleaacaaI0aaabeaaaaa@37A7@ MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzafaeaaaaaaaaa8qacaWFtacaaa@3983@ углы между межосевыми расстояниями d 13 , d 34 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizamaaBa aaleaacaaIXaGaaG4maaqabaGccaGGSaGaaGPaVlaadsgadaWgaaWc baGaaG4maiaaisdaaeqaaaaa@3D56@ и d 24 , d 34 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizamaaBa aaleaacaaIYaGaaGinaaqabaGccaGGSaGaaGPaVlaadsgadaWgaaWc baGaaG4maiaaisdaaeqaaaaa@3D58@ соответственно.

 

Как видно из выражений (59, 60), в идеальном случае, если все диаметры всех двух витых пар будут одинаковыми, то коэффициенты К2, К3 будут равны нулю, а К1 будет минимален. Но следует учитывать, что при наложении изоляции экструзионной линией на жилы полученные диаметры изоляции неидеальны и будут колебаться в некоторых пределах.

Исследование влияния диаметра изолированной жилы на переходное затухание

Проведем исследования по имитационной модели, построенной в ПО MathCad [6], согласно формулам (39, 41, 47 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzagaeaaaaaaaaa8qacaWFtacaaa@39C3@ 60). Для случая, когда диаметры изолированных жил одинаковы, зададимся следующими параметрами [15]:

l=100м;f=100 10 6 Гц;r=0,25мм;κ=1,02;ε=1,4;d=0,5мм; μ 0 =4π 10 7 Гн/м; μ 1 =1Гн/м;σ=57 10 2 См/м. MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaWGSb Gaeyypa0JaaGymaiaaicdacaaIWaGaamipeiaacUdacaaMc8UaamOz aiabg2da9iaaigdacaaIWaGaaGimaiabgwSixlaaigdacaaIWaWaaW baaSqabeaacaaI2aaaaOGaaGPaVlaadobbcaWGgrGaai4oaiaaykW7 caWGYbGaeyypa0JaaGimaiaacYcacaaIYaGaaGynaiaaykW7caWG8q GaamipeiaacUdacaaMc8UaeqOUdSMaeyypa0JaaGymaiaacYcacaaI WaGaaGOmaiaacUdacaaMc8UaeqyTduMaeyypa0JaaGymaiaacYcaca aI0aGaai4oaiaaykW7caWGKbGaeyypa0JaaGimaiaacYcacaaI1aGa aGPaVlaadYdbcaWG8qGaai4oaiaaykW7caaMc8oabaGaeqiVd02aaS baaSqaaiaaicdaaeqaaOGaeyypa0JaaGinaiabec8aWjabgwSixlaa igdacaaIWaWaaWbaaSqabeaacqGHsislcaaI3aaaaOGaaGPaVlaado bbcaWG9qGaai4laiaadYdbcaGG7aGaaGPaVlabeY7aTnaaBaaaleaa caaIXaaabeaakiabg2da9iaaigdacaaMc8Uaam4eeiaad2dbcaGGVa GaamipeiaacUdacaaMc8Uaeq4WdmNaeyypa0JaaGynaiaaiEdacqGH flY1caaIXaGaaGimamaaCaaaleqabaGaaGOmaaaakiaaykW7caWGHq Gaamipeiaac+cacaWG8qGaaiOlaaaaaa@9B3C@

Полученные расчеты по имитационной модели для случая, когда диаметры изолированных жил одинаковы, представлены в табл. 1.

 

Таблица 1 Влияние диаметров изолированных жил на переходное затухание на ближнем конце

Диаметры изоляций, мм

D и1 , D и4 / D и2 , D и3 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaWGeb WaaSbaaSqaaiaadIdbcaaIXaaabeaakiaacYcacaaMc8UaaGPaVlaa dseadaWgaaWcbaGaamioeiaaisdaaeqaaOGaai4laaqaaiaadseada WgaaWcbaGaamioeiaaikdaaeqaaOGaaiilaiaaykW7caWGebWaaSba aSqaaiaadIdbcaaIZaaabeaaaaaa@4697@

1 e 2γl MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaqWaaeaaca aIXaGaeyOeI0IaamyzamaaCaaaleqabaGaeyOeI0IaaGOmaiabeo7a NjaadYgaaaaakiaawEa7caGLiWoaaaa@4020@

Влияние на ближнем конце N 12 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOtamaaBa aaleaacaaIXaGaaGOmaaqabaaaaa@386A@ , 1/сд

Переходное затухание на ближнем конце A 0 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqamaaBa aaleaacaaIWaaabeaaaaa@37A0@ ,

дБ/100 м

Коэффициенты емкостной связи K 1 , K 2 , K 3 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4samaaBa aaleaacaaIXaaabeaakiaacYcacaaMc8Uaam4samaaBaaaleaacaaI YaaabeaakiaacYcacaaMc8Uaam4samaaBaaaleaacaaIZaaabeaaaa a@3FA6@ , 10 11 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGymaiaaic dadaahaaWcbeqaaiabgkHiTiaaigdacaaIXaaaaaaa@39F9@

0,92/0,92

1,9299

0,0217

35,4415

K1=1,14322943

K2=0

K3=0

0,91/0,91

1,9532

0.0220

35,6796

K1=1,13080303

K2=0

K3=0

0,9/0,9

0,7346

0,0082

44,5302

K1=1,11837662

K2=0

K3=0

0,89/0,89

1,9186

0,02162

36,5630

K1=1,10595021

K2=0

K3=0

0,88/0,88

1,9227

0,02166

36,9320

K1=1,10595021

K2=0

K3=0

0,904/0,904

1,9144

0,02157

36,0662

K1=1,12334718

K2=0

K3=0

0,903/0,903

1,8375

0,0207

36,4579

K1=1,12210454

K2=0

K3=0

0,902/0,902

0,3703

0,0041

50,4310

K1=1,12086191

K2=0

K3=0

0,901/0,901

0,6891

0,0077

45,0493

K1=1,11961926

K2=0

K3=0

0,899/0,899

1,3749

0,0154

39,1217

K1=1,11713398

K2=0

K3=0

0,898/0,898

1,1270

0,0127

40,8852

K1=1,11589134

K2=0

K3=0

0,897/0,897

1,5265

0,0172

38,3120

K1=1,11464872

K2=0

K3=0

0,896/0,896

0.9862

0.0111

42.0929

K1=1.11340606

K2=0

K3=0

0,9004/

0,9004

1,9396

0,0218

36,0578

K1=1,11887367

K2=0

K3=0

0,9003/0,9003

1,21408

0,0136

40,1800

K1=1,11874941

K2=0

K3=0

0,9002/0,9002

0,9583

0,0108

42,2135

K1=1,11862515

K2=0

K3=0

0,9001/0,9001

1,9953

0,02248

35,8472

K1=1,11850088

K2=0

K3=0

0,8999/0,8999

1,3450

0,0151

39,3049

K1=1,11825235

K2=0

K3=0

0,8998/0,8998

1,9287

0,02173

39,2592

K1=1,11812809

K2=0

K3=0

0,8997/0,8997

0,42676

0,0048

49,2585

K1=1,11800383

K2=0

K3=0

0,8996/0,8996

1,5159

0,0170

38,2275

K1=1,11787956

K2=0

K3=0

 

Согласно [8] переходное затухание на ближнем конце для LAN-кабеля категории 5е должно быть не менее 35,3 дБ/100м. Проанализировав значения полученных переходных затуханий, можно сделать вывод, что ужесточение допуска на диаметр изолированной жилы обеспечивает гарантированное достижение требуемых показателей качества, а именно переходного затухания на ближнем конце, тем самым подтверждая ранее выдвинутое предположение.

Как видно из таблицы, наилучшие результаты достигаются при допуске, когда X В =0 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiwamaaBa aaleaacaWGsqaabeaakiabg2da9iaaicdaaaa@3962@ и X Н =0 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiwamaaBa aaleaacaWGDqaabeaakiabg2da9iaaicdaaaa@396D@ ; при допуске, когда X В =+0,001 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiwamaaBa aaleaacaWGsqaabeaakiabg2da9iabgUcaRiaaicdacaGGSaGaaGim aiaaicdacaaIXaaaaa@3D23@ и X В =+0,002 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiwamaaBa aaleaacaWGsqaabeaakiabg2da9iabgUcaRiaaicdacaGGSaGaaGim aiaaicdacaaIYaaaaa@3D24@ ; при допуске, когда X В =+0,0002 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiwamaaBa aaleaacaWGsqaabeaakiabg2da9iabgUcaRiaaicdacaGGSaGaaGim aiaaicdacaaIWaGaaGOmaaaa@3DDE@ и X Н =0,0003 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiwamaaBa aaleaacaWGDqaabeaakiabg2da9iabgkHiTiaaicdacaGGSaGaaGim aiaaicdacaaIWaGaaG4maaaa@3DF5@ . Следовательно, придерживаясь этих значений допусков на диаметр изоляции при изготовлении изолированных жил LAN-кабеля, можно достичь наибольшего значения переходного затухания. Также из результатов видно, что ужесточение допуска на диаметр приводит к незначительному, но все-таки уменьшению коэффициента емкостной связи К1.

Для полноты эксперимента рассмотрим случай, когда диаметры изолированных жил в паре разные. Значения параметров возьмем из предыдущего эксперимента с учетом лишь того, что диаметр изолированной жилы будем находить по следующей формуле: d 1 = D и1 + D и2 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizamaaBa aaleaacaaIXaaabeaakiabg2da9maalaaabaGaamiramaaBaaaleaa caWG4qGaaGymaaqabaGccqGHRaWkcaWGebWaaSbaaSqaaiaadIdbca aIYaaabeaaaOqaaiaaikdaaaaaaa@3F79@ .

Полученные расчеты по имитационной модели для случая, когда диаметры изолированных жил в паре разные, представлены в табл. 2.

 

Таблица 2 Влияние диаметров изолированных жил на переходное затухание на ближнем конце

Диаметры изоляций, мм

D и1 , D и4 / D и2 , D и3 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaWGeb WaaSbaaSqaaiaadIdbcaaIXaaabeaakiaacYcacaaMc8UaaGPaVlaa dseadaWgaaWcbaGaamioeiaaisdaaeqaaOGaai4laaqaaiaadseada WgaaWcbaGaamioeiaaikdaaeqaaOGaaiilaiaaykW7caWGebWaaSba aSqaaiaadIdbcaaIZaaabeaaaaaa@4697@

1 e 2γl MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaqWaaeaaca aIXaGaeyOeI0IaamyzamaaCaaaleqabaGaeyOeI0IaaGOmaiabeo7a NjaadYgaaaaakiaawEa7caGLiWoaaaa@4020@

Влияние на ближнем конце N 12 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOtamaaBa aaleaacaaIXaGaaGOmaaqabaaaaa@386A@ , 1/сд

Переходное затухание на ближнем конце A 0 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqamaaBa aaleaacaaIWaaabeaaaaa@37A0@ , дБ/100 м

Коэффициенты емкостной связи

K 1 , K 2 , K 3 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4samaaBa aaleaacaaIXaaabeaakiaacYcacaaMc8Uaam4samaaBaaaleaacaaI YaaabeaakiaacYcacaaMc8Uaam4samaaBaaaleaacaaIZaaabeaaaa a@3FA6@ , 10 11 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGymaiaaic dadaahaaWcbeqaaiabgkHiTiaaigdacaaIXaaaaaaa@39F9@

0,91/0,92

0,4617

0,0118

44,5672

K1=1,13700174

K2=− 0,010606482

K3=0,010606482

0,9/0,91

0,3256

0,0085

47,3342

K1=1,12457517

K2=−0,010606480

K3=0,010606480

0,89/0,9

1,9949

0,0542

31,3326

K1=1,1121486

K2=−0,010606477

K3=0,010606477

0,88/0,89

0,4647

0,0130

43,7371

K1=1,09972203

K2=−0,010606474

K3=0,010606474

0,903/0,904

0,3888

0,0104

45,6789

K1=1,12272571

K2=−0,0010606600

K3=0,0010606600

0,902/0,903

1,5981

0,0428

33,3759

K1=1,12148307

K2=−0,0010606600

K3=0,0010606600

0,901/0,902

0,4756

0,0128

43,8762

K1=1,12024043

K2=−0,0010606600

K3=0,0010606600

0,9/0,901

0,2927

0,0079

48,0659

K1=1,11899779

K2=−0,0010606600

K3=0,0010606600

0,899/0,9

1,8775

0,0508

31,8995

K1=1,11775515

K2=−0,0010606600

K3=0,0010606600

0,898/0,899

1,3335

0,0362

34,8454

K1=1,11651251

K2=−0,0010606600

K3=0,0010606600

0,897/0,898

1,9991

0,0544

31,3034

K1=1,11402723

K2=−0,0010606600

K3=0,0010606600

0,896/0,897

1,0039

0,0274

37,2609

K1=1,11402723

K2=−0,0010606600

K3=0,0010606600

0,9003/0,9004

1,8870

0,0509

31,8695

K1=1,11881154

K2=−0,00010606601

K3=0,00010606601

0,9002/0,9003

0,1492

0,0040

53,9021

K1=1,11868728

K2=−0,00010606601

K3=0,00010606601

0,9001/0,9002

1,7553

0,0474

32,4931

K1=1,11856301

K2=−0,00010606601

K3=0,00010606601

0,9/0,9001

1,6124

0,0436

33,2279

K1=1,11843875

K2=−0,00010606601

K3=0,00010606601

0,8999/0,9

0,3626

0,0098

46,1846

K1=1,11831448

K2=−0,00010606601

K3=0,00010606601

0,8998/0,8999

1,9214

0,0520

31,6999

K1=1,11819022

K2=−0,00010606601

K3=0,00010606601

0,8997/0,8998

1,3741

0,0372

34,9501

K1=1,11806596

K2=−0,00010606601

K3=0,00010606601

0,8996/0,8997

0,6370

0,0172

41,2835

K1=1,11794169

K2=−0,00010606601

K3=0,00010606601

 

Проанализировав значения полученных переходных затуханий для разных диаметров изоляций, можно сделать вывод, что ужесточение допуска на диаметр изолированной жилы обеспечивает гарантированное достижение требуемых показателей качества, а именно переходного затухания на ближнем конце, тем самым подтверждая ранее выдвинутое предположение.

Как видно из таблицы, наилучшие результаты достигаются при допуске, когда X B =+0,01 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGI8VfYJbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabiGaaiaacaqabeaadaqaaqaaaOqaaiaadIfadaWgaa WcbaGaamOqaaqabaGccqGH9aqpcqGHRaWkcaaIWaGaaiilaiaaicda caaIXaaaaa@3D5B@ , и диаметрах изоляции 0,9/0,91 и 0,91/0,92 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqefeKCPfgBaG qbaKqzagaeaaaaaaaaa8qacaWFtacaaa@39C3@ это означает, что в паре одна изолированная жила имеет диаметр 0,91 мм, а другая 0,92 мм; при допуске, когда X B =+0,001 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGI8VfYJbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabiGaaiaacaqabeaadaqaaqaaaOqaaiaadIfadaWgaa WcbaGaamOqaaqabaGccqGH9aqpcqGHRaWkcaaIWaGaaiilaiaaicda caaIWaGaaGymaaaa@3E15@ , и диаметрах изоляции 0,9/0,901 и 0,903/0,904; при допуске, когда X B =+0,0001 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGI8VfYJbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabiGaaiaacaqabeaadaqaaqaaaOqaaiaadIfadaWgaa WcbaGaamOqaaqabaGccqGH9aqpcqGHRaWkcaaIWaGaaiilaiaaicda caaIWaGaaGimaiaaigdaaaa@3ECF@ , и диаметрах изоляции 0,9002/0,9003; X H =0,0001 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGI8VfYJbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabiGaaiaacaqabeaadaqaaqaaaOqaaiaadIfadaWgaa WcbaGaamisaaqabaGccqGH9aqpcqGHsislcaaIWaGaaiilaiaaicda caaIWaGaaGimaiaaigdaaaa@3EE0@ и диаметрах изоляции 0,8999/0,9. Следовательно, придерживаясь этих значений допусков на диаметр изоляции при изготовлении изолированных жил LAN-кабеля, можно достичь наибольшего значения переходного затухания. Также из результатов видно, что ужесточение допуска на диаметр приводит к незначительному уменьшению коэффициента емкостной связи К1 и к значительному уменьшению коэффициентов емкостной связи К2 и К3.

Заключение

Получены соотношения, связывающие диаметр изоляции и межосевые расстояния жил кабеля с коэффициентами емкостной связи К1, К2, К3.

Исходя из математического описания взаимного влияния на дальний и ближний конец в симметричных цепях получены соотношения для взаимного влияния между двумя витыми парами, а также соотношения, связывающие диаметр изоляции с коэффициентами связи, из которых непосредственно складывается влияние на дальний и ближний конец и, как следствие, переходные затухания. При условии, что не учитываются неоднородности волновых сопротивлений, неоднородности диэлектрика, рассматриваемые цепи имеют малую внутреннюю индуктивность, цепи нескрещенные параллельные.

Проведены экспериментальные исследования согласно имитационной модели. Получены результаты для случая, когда диаметры изолированных жил имеют одинаковое значение и когда диаметры изолированных жил имеют разные значения. Проведен анализ полученных результатов. Наилучшие показатели переходного затухания на ближнем конце достигаются при X B =0 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGI8VfYJbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabiGaaiaacaqabeaadaqaaqaaaOqaaiaadIfadaWgaa WcbaGaamOqaaqabaGccqGH9aqpcaaIWaaaaa@3A54@ и X H =0 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGI8VfYJbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabiGaaiaacaqabeaadaqaaqaaaOqaaiaadIfadaWgaa WcbaGaamisaaqabaGccqGH9aqpcaaIWaaaaa@3A5A@ ; XB=+0,001 и X B =+0,002 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGI8VfYJbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabiGaaiaacaqabeaadaqaaqaaaOqaaiaadIfadaWgaa WcbaGaamOqaaqabaGccqGH9aqpcqGHRaWkcaaIWaGaaiilaiaaicda caaIWaGaaGOmaaaa@3E16@ ; X B =+0,0002 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGI8VfYJbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabiGaaiaacaqabeaadaqaaqaaaOqaaiaadIfadaWgaa WcbaGaamOqaaqabaGccqGH9aqpcqGHRaWkcaaIWaGaaiilaiaaicda caaIWaGaaGimaiaaikdaaaa@3ED0@  и X H =0,0003 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGI8VfYJbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabiGaaiaacaqabeaadaqaaqaaaOqaaiaadIfadaWgaa WcbaGaamisaaqabaGccqGH9aqpcqGHsislcaaIWaGaaiilaiaaicda caaIWaGaaGimaiaaiodaaaa@3EE2@ в случае, когда диаметры изолированных жил одинаковые. В случае, когда диаметры изолированных жил разные, наилучшие результаты достигаются при X B =+0,001 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGI8VfYJbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabiGaaiaacaqabeaadaqaaqaaaOqaaiaadIfadaWgaa WcbaGaamOqaaqabaGccqGH9aqpcqGHRaWkcaaIWaGaaiilaiaaicda caaIWaGaaGymaaaa@3E15@ , X B =+0,0001, MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGI8VfYJbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabiGaaiaacaqabeaadaqaaqaaaOqaaiaadIfadaWgaa WcbaGaamOqaaqabaGccqGH9aqpcqGHRaWkcaaIWaGaaiilaiaaicda caaIWaGaaGimaiaaigdacaGGSaaaaa@3F7F@ X H =0,0001 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiFGI8VfYJbba91rFfpec8Eeeu0xXdbba9frFj0=OqFf ea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr 0=vqpWqaaeaabiGaaiaacaqabeaadaqaaqaaaOqaaiaadIfadaWgaa WcbaGaamisaaqabaGccqGH9aqpcqGHsislcaaIWaGaaiilaiaaicda caaIWaGaaGimaiaaigdaaaa@3EE0@ .

Доказано, что гарантированное достижение требуемых показателей качества изготавливаемого LAN-кабеля обеспечивается ужесточением допусков на диаметр изолированных кабельных жил. Сформулированы величины допусков порядка 4 мкм на диаметр кабельных жил, изготавливаемых на экструзионных линиях, при выдерживании которых эксплуатационные характеристики симметричного кабеля вне зависимости от последующих производственных операций будут соответствовать требуемым значениям.

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About the authors

Vladimir Yu. Denisov

Samara Space Centre

Author for correspondence.
Email: journal@eco-vector.com

Engineer

Russian Federation, 18, Zemetsa str., Samara, 443009

References

  1. Denisov V.Yu., Mitroshin V.N., Chostkovskiy B.K. Mathematical description of mutual influence in a symmetric circuit (LAN cable) based on the basis of the equation of partial capacities Maxwell // Vestn. Samar. Gos. Tekhn. Un-ta. Ser. Tekhnicheskie nauki. 2019. No. 1(61). Pp. 110–127.
  2. Kleyn V. Theory of mutual influence in communication lines. Moscow. Leningrad. GEI, 1957. 326 p.
  3. Semenov A.B., Strizhakov S.K., Suncheley I.R. Structured Cabling Systems. Moscow. IT Co., DMK Press, 2014. 640 p.
  4. Samarskiy P.A. Basics of structured cabling systems. Moscow. DMK Pres, 2016. 216 p.
  5. Grodnev I.I., Shvartsman O.V. Theory of guiding communication systems. Moscow. Svyaz’, 1978. 296 p.
  6. Cable CCA-UU004-5E-PVC-GY // Netlan. http://www.netlancables.ru/CCA-UU004-5E-PVC-GY.cdr.pdf
  7. Plis A.I., Slivina N.A. Mathcad: mathematical workshop for economists and engineers. 1999. 656 p.
  8. GOST R 54429-2011. Kabeli svyazi simmetrichnyye dlya stifrovyh sistem peredachi. http://docs.cntd.ru/document/1200088857
  9. Calculation and design of communication cables and radio frequency cables. Edited by E.T. Larina. Moscow. MEI, 1982. 104 p.
  10. Chostkovskiy B.K. Strukturno-parametricheskiy sintez sistem optimal’nogo upravleniya sovmeshchennymi tekhnologicheskimi protsessami proizvodstva kabeley svyazi po ekspluatatsionnym kriteriyam kachestva. Diss. … dokt. tekhn. nauk. Samara, Samar. Gos. Tekhn. Un-t, 2007. 265 p.
  11. Chostkovskiy B.K., Smorodinov D.A. Mathematical model of twisted pairs radio-frequency cable of control object // Vestn. Samar. Gos. Tekhn. Un-ta. Ser. Fiziko-matematicheskie nauki. 2008. No. 1 (16). Pp. 113–118.
  12. Milovanov A.M., Chostkovskiy B.K. Regulation of capacitance coupling coefficients // Tekhnicheskaya kibernetika: Sbornik nauchn. tr. Kuibyshev. 1974. Pp. 120–123.
  13. Elagin Yu.V. Information and measurement system for measuring and registering capacitance connections of cable fours during the twisting process // Vsesoyuznaya nuchn.-tekhn konf. «Avtomatizaciya i mekhanizaciya kabel'nogo proizvodstva»: Tez. dokladov. Moscow. Informelektro, 1977. Pp. 51–52.
  14. Bronshteyn I.N., Semendyaev K.A. Math reference. Moscow, GITTL, 1957. 608 p.
  15. Handbook of electrical materials. Edited by Yu.V. Korickiy, V.V. Pasynkov, B.M. Tareev. V. 3. 3rd ed. revised. Leningrad. Energoatomizdat. Leningr. otd-nie, 1988. 728 p.

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