T Parameters: Me Suna Su? (Misalai Masu Lafiya Da Tarihin Yadda A Yi Koyarwa Daga T Parameters Wajen Bincike Wadannan Parameters)

فیلڈ: Karkashin Kuliya da Dukkana

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misali t parametere

Misali T Parametere?

T parametere suna nufin parametere na kungiyar hanyar ko da ABCD parametere. A cikin kungiyar biyu, port-1 yana da muhimmanci a matsayin gaba-gaban da shi ya zama, port-2 yana da muhimmanci a matsayin gaba-gaban da shi ya samu. A diagrammin kungiya, terminalai na port-1 suka nufin port na input (gaba-gaban da shi ya zama). Duk da haka, terminalai na port-2 suka nufin port na output (gaba-gaban da shi ya samu).

kungiyar biyu t parametere

T-parametere a Kungiyar Biyu

Don kungiyar biyu na musamman, zaɓuɓɓukan T-parametere su ne;

(1) $\begin{equation*} V_S=AV_R + BI_R \end{equation*}$

(2) $\begin{equation*} I_S=CV_R + DI_R \end{equation*}$

Amsa;

VS = Tsari na mafi yawa gadi
IS = Tsari na mafi yawa karami
VR = Gadi na tsari na mafi girma
IR = Karami na tsari na mafi girma

Wadannan halayansu a yi amfani da su don bincike modello mai karamin lissafi na tsarin gadi. Halayansa A da D ba da alama. Alama na halayansa B da C shi ne ohm da mho, yawanci.

$\begin{bmatrix} V_S \\ I_S \end{bmatrix} = \begin{bmatrix} A & B \\ C & D \end{bmatrix} \begin{bmatrix} V_R \\ I_R \end{bmatrix}$

Don samun ukuwar T-parameters, ya kamata a futa da a gane tsari na mafi girma. Idan tsari na mafi girma ta fitarwa, karami na tsari na mafi girma IR tana zama zero. Ya kamata a saka wannan ukuwar a cikin turukan da kuma a samu ukuwar A da C.

$I_R=0$

open circuit condition

Daga kungiyar-1;

$V_S=AV_R + B(0)$

$V_S=AV_R$

$A = \left \frac{V_S}{V_R} \right|_ {I_R=0}$

Daga tushen-2;

$I_S = CV_R + D(0)$

$I_S = CV_R$

$C = \left \frac{I_S}{V_R} \right|_ {I_R=0}$

Idan lokacin da na kuma ta hanyar shi, tsari a tushen yadda aka bayar VR ya zama zero. Tana iya samun wannan darajar a cikin tambayar, za a iya samun damar B da D.

$V_R = 0$

short circuit condition

Daga tambayar-1;

$V_S=A(0) + BI_R$

$V_S = BI_R$

$B = \left \frac{V_S}{I_R} \right|_ {V_R=0}$

Daga tambayar-2;

$I_S=C (0) + DI_R$

$I_S = DI_R$

$D = \left \frac{I_S}{I_R} \right|_ {V_R=0}$

Misalai na T Parameters da Solved Example Problem

Sabbin da zama da suka da wuya ita ce a tara da kungiyar da ta faruwa masu hanyar yadda aka bayyana a wannan rubutun. Tabbatar da manyan paramaito na T na wannan kungiyar.

t parameter example

Misalai na Paramaito na T

A nan, amfani na gaba ce amfani na kusa.

$I_S = I_R$

(3) $\begin{equation*} I_S = (0)V_R + (1) I_R \end{equation*}$

Na bi, muna amfani da KVL zuwa wannan kungiyar,

$V_S = V_R + I_S Z_1$

$V_S = V_R + I_R Z_1$

(4) $\begin{equation*} V_S = (1)V_R + (Z_1) I_R \end{equation*}$

Ko kula da takarda ɗaya da ƙarfin ɗaya;

$A = 1, \, B = Z_1$

Samun hanyar likitoci-2 da 3;

$C = 0, \, D = 1$

T Parameters of a Transmission Line

A cikin tsari na lura, likitoci suna dacewa ne;

Likitoci mai tsari
Likitoci mai yamma
Likitoci mai gaba

Yanzu, zan iya samun T-parameters don duk tsofinta likitoci.

Likitoci Mai Tsari

Zaɓuwar hanyar karkashin kula da ɗalilai kimanin ɗaya ɗaya na 80km kuma sautin shi na ɗaya ɗaya na 20kV yana cikin zaɓuwar karkashin kula mai tsawo. Saboda tsawon ɗaya ɗaya da sautin mafi tsawo, kapasitasar zaɓuwar kula tana ci gaba.

Saboda haka, a nan ba ni nufin ɗaya ɗaya haddadin da indaktansan wajen rarrabta zaɓuwar karkashin kula mai tsawo. Tushen bayanin zaɓuwar karkashin kula mai tsawo yana cikin hotuna ta haka:

t parameter of short transmission line

T-parameter of Short Transmission Line

Amsa,
IR = Iya karkashin kula na ƙarin
VR = Sautin karkashin kula na ƙarin
Z = Haddidin takwas
IS = Iya karkashin kula na baya
VS = Sautin karkashin kula na baya
R = Haddidar zaɓuwar kula
L = Indaktansar zaɓuwar kula

Idan iya ya karkasha a kan zaɓuwar kula, yana faruwa a haddidar zaɓuwar kula da yake faruwa a indaktansar reaktansi.

Daga wannan netwarki, iya karkashin kula na baya ce ɗaya ɗaya da iya karkashin kula na ƙarin.

$I_S = I_R$

$V_S = V_R + I_R Z$

Yanzu wa samunan da suka cikin wannan samunani da samunan T-parameters (samuna 1 da 2). Sai dai shigar da abubuwan da aka ambata na A, B, C, da D don fito mai tsayawa.

$A = 1, B = Z, C = 0, D = 1$

Fito Mai Tsayawa

Fito da ke yanki girma daga 80km zuwa 240km kuma kwana ke iya 20kV zuwa 100kV ana kira shi da fito mai tsayawa.

A halin fito mai tsayawa, bai kamata mu nema capacitance ba. Muna bukatar haduwa da capacitance yayin amfani da mudel na fito mai tsayawa.

Kamar yadda ya kasancewa a cikin capacitance, an kara fitowa mai tsayawa zuwa uku:

Hanyar End Condenser
Hanyar Nominal T
Hanyar Nominal π

Yadda na End Condenser

A cikin yadda na, yadda na capacitance ta karamin shi ita ce da aka fada a tafin karamin shi. Bayanin grafika na Yadda na End Condenser ya danganta a tunani.

t parameter of end condenser method

T-parameters na Yadda na End Condenser

Daga baya;
IC = Karamin capacitor = YVR

Daga bayanan tunani,

$I_S = I_C + I_R$

(5) $\begin{equation*} I_S = Y V_R + I_R \end{equation*}$

A nan KVL, zan iya rubuta;

$V_S = V_R + Z I_S$

$V_S = V_R + Z (I_C + I_R)$

$V_S = V_R + Z (Y V_R + I_R)$

$V_S = V_R + Z Y V_R + Z I_R$

(6) $\begin{equation*} V_S = V_R (1 + ZY) + Z I_R \end{equation*}$

Tana da tsari-5 da 6 tare da tsari na T parameters;

$A = 1 + ZY, \; B = Z , \; C = Y , \; D = 1$

Haruffar T na Sunan

A cikin harkar, tafasa da aka shiga ita ce ke kusa da wata zuwa mazaunin gasar. Koyar kan taswirin haruffar T na sunan ya danganta da haka:

t parameter of nominal t method

T-Parametar na Haruffar T na Sunan

Daga baya,
IC = Kirkiyar fitaccen tafas = YVC
VC = Kirkiyar fitaccen tafas

$V_S = V_C + I_S \frac{Z}{2}$

$V_C = V_R + I_R \frac{Z}{2}$

Daga KCL;

$I_S = I_R + I_C$

$I_S = I_R + Y V_C$

$I_S = I_R + Y (V_R + I_R \frac{Z}{2})$

$I_S = I_R + Y V_R + Y I_R \frac{Z}{2})$

(7) $\begin{equation*} I_S = Y V_R + I_R (1 + \frac{YZ}{2}) \end{equation*}$

A nan,

$V_S = V_R + I_R \frac{Z}{2} + I_S \frac{Z}{2}$

$V_S = V_R + I_R \frac{Z}{2} + \frac{Z}{2} \left[ YV_R + I_R (1 + \frac{YZ}{2}) \right]$

$V_S = V_R + I_R \frac{Z}{2} + \frac{Z}{2} YV_R + \frac{Z}{2} I_R (1 + \frac{YZ}{2})$

(8) $\begin{equation*} V_S = V_R \left( 1 + \frac{YZ}{2} \right) + I_R \left( Z + \frac{YZ^2}{4} \right) \end{equation*}$

A nan, koyi kungiyar-7 da kungiyar-8 da T parameter kuma muka samu

$A = 1 + \frac{YZ}{2}$

$B = Z(1+\frac{YZ}{4})$

$C = Y$

$D = 1 + \frac{YZ}{2}$

Rutukan π na Mafi Yawan Noma

A tattarun wannan metoda, kafin kashi da shirya da shi yana zama daidai. Daidai na biyu yana aiki a gaba da maimakon bayyana da tsarin bayyana. Taswira mai sauƙi da ya nuna hanyar da ake amfani da ita a tattarun rutukan π.

t parameter of nominal pi method

T-parametar na Rutukan π

$I_S = I_1 + I_{C2}$

$I_1 = I_R + I_{C1}$

$I_{C1} = \frac{Y}{2} V_R \; and \; I_{C2} = \frac{Y}{2} V_S$

Daga haka, zan iya rubuta;

$V_S = V_R + I_1 Z$

$V_S = V_R + (I_R + I_{C1}) Z$

$V_S = V_R + Z (I_R + \frac{Y}{2} V_R)$

$V_S = V_R + Z I_R + Z \frac{Y}{2} V_R$

(9) $\begin{equation*} V_S = V_R \left(1 + \frac{YZ}{2} \right) + Z I_R \end{equation*}$

A nan,

$I_S = I_1 + I_{C2}$

$I_S = (I_R + I_{C1}) + I_{C2}$

$I_S = I_R + \frac{Y}{2} V_R + \frac{Y}{2} V_S$

Zaɓe yadda VS a cikin wannan kungiyar,

$I_S = I_R + \frac{Y}{2} V_R + \frac{Y}{2} \left[ V_R \left(1 + \frac{YZ}{2} \right) + Z I_R \right]$

$I_S = I_R + \frac{Y}{2} V_R + \frac{Y}{2} (1 + \frac{YZ}{2}) V_R + \frac{Y}{2} I_R Z$

(10) $\begin{equation*} I_S = I_R \left[ 1 + \frac{YZ}{2} \right] + Y V_R \left[ 1 + \frac{YZ}{4} \right] \end{equation*}$

A cikin tsarin tushen 9 da 10 da tushen T parametata, muna samun;

$A = 1 + \frac{YZ}{2}$

$B = Z$

$C = Y \left( 1 + \frac{YZ}{4} \right)$

$D = 1 + \frac{YZ}{2}$

Yanayin Hanyar Karami

A yanayin hanyar karami ita ce da ake fada ta hanyar jerin tashin. Ba za a iya cewa shi ne mafi tsawon tashin ba. Yanayin hanyar karami na yanayi a cikin jerin tashin ya zama kamar yadda ake bayyana a cikin wannan takarda.

t parameter of long transmission line

T-parameter na Long Transmission Line

Zaɓi na layin da ya kai X km. Don tafiya layin da ya kai, zan yi nemo babban batun (dx) na layi. Kuma ana bayyana haka a cikin wannan shahararren.

long transmission line t parameter

Zdx = series impedance
Ydx = shunt impedance

Voltage yana ƙara zuwa masu layi. Saboda haka, ƙaramin voltage shine;

$dV = IZdx$

$\frac{dV}{dx} = IZ$

Duk da haka, karamin amfani a zama;

$dI = VYdx$

$\frac{dI}{dx} = VY$

Idan an yi tashin wannan mafi yawan;

$\frac{d^2V}{dx^2} = Z \frac{dI}{dx} = ZVY$

Bayanin jihar wannan mafi yawa shi ne;

$V = K_1 cosh(x\sqrt{YZ}) + K_2 sinh(x \sqrt{YZ})$

A nan, koyi wannan tambayar da X,

$\frac{dv}{dx} = K_1 \sqrt{YZ} sinh(x\sqrt{YZ}) + K_2 \sqrt{YZ} cosh(x\sqrt{YZ})$

$IZ = K_1 \sqrt{YZ} sinh(x\sqrt{YZ}) + K_2 \sqrt{YZ} cosh(x\sqrt{YZ})$

$I = \sqrt{\frac{Y}{Z}} \left[ K_1 sinh(x\sqrt{YZ}) + K_2 cosh(x\sqrt{YZ})$

A nan, zan iya samun hanyar da ke K1 da K2;

Don haka, za a fara;

$x=0, \; V=V_R, \; I=I_R$

Wadannan bayanan zuwa turuntukan yadda ake yi a karshe;

$V_R = K_1 cosh 0 + K_2 sinh 0$

$V_R = K_1 + 0$

$K_1 = V_R$

$I_R = \sqrt{\frac{Y}{Z}} \left[ K_1 sinh 0 + K_2 cosh 0 \right]$

$I_R = \sqrt{\frac{Y}{Z}} [0+K_2]$

$K_2 = \sqrt{\frac{Z}{Y}}$

Saboda haka,

$V_S = V_R cosh (x\sqrt{YZ}) + \sqrt{\frac{Z}{Y}} I_R sinh (x\sqrt{YZ})$

$I_S = \sqrt{\frac{Y}{Z}} V_R sinh (x\sqrt{YZ}) + I_R cosh (x\sqrt{YZ})$

$Z_C = \sqrt{\frac{Z}{Y}} \, and \, \gamma = \sqrt{YZ}$

Daga,

ZC = Amfani da Zan iya kawo
ɣ = Sabbin Tsarin Kadan

$V_S = V_R cosh \gamma x + I_R Z_C sinh \gamma x$

$I_S = \frac{V_R}{Z_C} sinh \gamma x + I_R cosh \gamma x$

Samun hanyar wannan tushen da za su iya haɗa da tushen T-parameters;

$A=cosh \gamma x$

$B=Z_C sinh \gamma x$

$C=\frac{sinh \gamma x}{Z_C}$

$D=\cos \gamma x$

Dono da T paramatar zuwa wasu Paramatar Daban-daban

A muke so ku fada wasu paramatar daga tasirin T paramatar. Don haka, zan iya samun kwamfuta na wasu paramatar a cikin T paramatar.

Amsa wata tafar ta biyu mai shiga kamar yadda aka nuna a cikin wannan rasa.

conversion of t parameters to other parameters

A cikin wannan hoton, an yi lalacewar tsari na yaduwar gwamnati. Saboda haka, za a duba wasu canza a cikin tasirin T paramatar.

$V_S = V_1, \; V_R = V_2, \; I_S = I_1, \; I_R = -I_2,$

Zabe da T parameters shine;

(11) $\begin{equation*} V_1 = AV_2 - BI_2 \end{equation*}$

(12) $\begin{equation*} I_1 = CV_2 - DI_2 \end{equation*}$

T parameter zuwa Z parameters

Wadannan set of equations ya nuna Z parameters.

(13) $\begin{equation*} V_1 = Z_{11}I_1 + Z_{12}I_2 \end{equation*}$

(14) $\begin{equation*} V_2 = Z_{21}I_1 + Z_{22}I_2 \end{equation*}$

A nan, za zama tushen tushen parametoci Z daidai daga parametoci T.

$CV_2 = I_1 + DI_2$

(15) $\begin{equation*} V_2 = \frac{1}{C}I_1 + \frac{D}{C} I_2 \end{equation*}$

A nan haka tafi shawarwari kwaikwaya-14 da kwaikwaya-15

$Z_{21} = \frac{1}{C}, \quad Z_{22} = \frac{D}{C}$

Daga baya,

$V_1 = A \left[ \frac{1}{C} I_1 + \frac{D}{C}I_2 \right] - BI_2$

$V_1 = \frac{A}{C} I_1 + \frac{AD}{C}I_2 - BI_2$

(16) $\begin{equation*} V_1 = \frac{A}{C}I_1 + \left( \frac{AD-BC}{C} \right) I_2 \end{equation*}$

Bayyana tushen (13) da tushen (16);

$Z_{11} = \frac{A}{C}, \quad Z_{12} = \frac{AD-BC}{C}$

T parameter to Y parameters

Kungiyar tushon Y parameters shine;

(17) $\begin{equation*} I_1 = Y_{11}V_1 + Y_{12}V_2 \end{equation*}$

(18) $\begin{equation*} I_2 = Y_{21}V_1 + Y_{22}V_2 \end{equation*}$

Daga fasahar-12;

$DI_2 = CV_2 - I_1$

$I_2 = \frac{C}{D}V_2 - \frac{1}{D}I_1$

Saka wannan ma'aiki a zuwa equation-11;

$V_1 = AV_2 - B \left[ \frac{C}{D}V_2 - \frac{1}{D}I_1 \right]$

$V_1 = AV_2 -\frac{BC}{D}V_2 + \frac{B}{D}I_1$

$V_1 = V_2 \left[ \frac{AD-BC}{D} \right] +\frac{B}{D}I_1$

$\frac{B}{D}I_1 = V_1 - V_2 \left[ \frac{AD-BC}{D} \right]$

(19) $\begin{equation*} I_1 = \frac{D}{B}V_1 - \frac{BC-AD}{B}V_2 \end{equation*}$

Karin bayanin daɗi na tarihin daɗi (19) da tarihin daɗi (17);

$Y_{11} = \frac{D}{B}, \quad Y_{12} = \frac{BC-AD}{B}$

Daga tashin-11;

$BI_2 = AV_2 - V_1$

(20) $\begin{equation*} I_2 = \frac{A}{B} V_2 - \frac{1}{B}V_1 \end{equation*}$

Samun hanyar tashin-18;

$Y_{21} = \frac{-1}{B}, \quad Y_{22} = \frac{A}{B}$

T parameter to H parameters

Jamiyar kalmomi na H parameters shine;

(21) $\begin{equation*} V_1 = H_{11}I_1 + H_{12}V_2 \end{equation*}$

(22) $\begin{equation*} I_2 = H_{21}I_1 + H_{22}V_2 \end{equation*}$

Daga tushen-12;

$DI_2 = CV_2 - I_1$

(23) $\begin{equation*} I_2 = \frac{C}{D} V_2 - \frac{1}{D}I_1 \end{equation*}$

Samun hukuma da wannan tushen sama da tushen-22;

$H_{21} = \frac{-1}{D}, \quad H_{22} = \frac{C}{D}$

$V_1 = AV_2 - B \left[ \frac{C}{D} V_2 - \frac{1}{D}I_1 \right]$

$V_1 = AV_2 - \frac{BC}{D}V_2 + \frac{B}{D}I_1$

(24) $\begin{equation*} V_1 = V_2 \left[ \frac{AD-BC}{D} \right] + \frac{B}{D}I_1 \end{equation*}$

$H_{11} = \frac{B}{D}, \quad H_{12} = \frac{AD-BC}{D}$

Bayanin: Jin hadada, labarai mai gaskiya na biyan kan, idani babu hakkin ayawalci, zaka iya tabbatar wajen rayuwa.

Ba da kyau kuma kara mai rubutu!

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