﻿ Module 6.4 Generator and Load Mismatches
Module 6.4 Generator and Load Mismatches
 Resistance      Reactance
 Tool Bar
 Reflection coefficient of the generator, $\Gamma_{G}$ = Reflection coefficient of the load, $\Gamma_{L}$ = Voltage standing wave ratio on the line, $SWR$ = Input reflection coefficient at the generator, $\Gamma_{IN}$ = Output reflection coefficient at the load, $\Gamma_{OUT}$ = The power delivered to the load ${\rm P}=\frac{1}{2} \left|V_{G} \right|^{2} \frac{R_{IN} }{(R_{IN} +R_{G} )^{2} +(X_{IN} +X_{G} )^{2}}=$ (mW) The power delivered to the input terminal ${\rm P}_{{\rm IN}} =\frac{1}{2} \left|\frac{V_{G} \sqrt{Z_{0} } }{Z_{G} +Z_{0} } \right|^{2} \frac{1-\left|\Gamma _{IN} \right|^{2} }{\left|1-\Gamma _{G} \Gamma _{IN} \right|^{2}}=$ (mW) The power available from the generator ${\rm P}_{{\rm AVS}} =\frac{1}{2} \left|\frac{V_{G} \sqrt{Z_{0} } }{Z_{G} +Z_{0} } \right|^{2} \frac{1}{1-\left|\Gamma _{G} \right|^{2}}=$ (mW) The power available from the network ${\rm P}_{{\rm AVN}} =\frac{1}{2} \left|\frac{V_{G} \sqrt{Z_{0} } }{Z_{G} +Z_{0} } \right|^{2} \frac{\left|1-\Gamma _{OUT} \Gamma _{L} \right|^{2} }{\left|1-\Gamma _{G} \Gamma _{L} \right|^{2} (1-\left|\Gamma _{OUT} \right|^{2} )}=$ (mW)

### Introduction:

本模組我們將探討信號源與負載端不匹配於無損傳輸線造成之駐波效應與功率分配，並藉由調整 toolbar 以觀察駐波效應之動態行為與負載功率之分配變化。
Ex.1：信號源與負載端皆為匹配 ( $Z_G = Z_L = Z_0$ )，
此時負載端之功率分配為最大！
Ex.2：信號源端為匹配時 ( $Z_G = Z_0$ )，則可從信號源
分配到的功率 ( $P_{AVS}$ ) 為最大！

### Parameters:

1. $V_{G}$ : Generator voltage, (V)
2. $Z_{G}$ : Generator impedance, (Ω)
3. $Z_{L}$ : Load impedance, (Ω)
4. $Z_{0}$ : Characteristic impedance of the transmission line, (Ω)
5. $\beta$ : Phase constant, (rad/m)
6. $f$ : Operating frequency, (GHz)
7. $d$ : Length of the transmission line, (cm)