| Module 5.4 Generator and Load Mismatches |
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| | | | | | | | 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)
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Introduction: In this module, we discuss the generator and load mismatch effects on the standing wave pattern and power distribution of a lossless transmission line. By adjusting the range sliders, you can observe the dynamic behavior of the standing wave and the variation of the average power delivered to the load.
Ex.1：When the generator and the load impedances are both matched to the line ( \(Z_G = Z_L = Z_0\) ), the maximum power delivered to the load is obtained. Ex.2：When the generator impedance is matched to the line ( \(Z_G = Z_0\) )，, the average power available from the source (PAVS) reaches its maximum. | 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)
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