COMPARISON OF POWER GAIN DEFINITIONS A silicon bipolar junction transistor has the following scattering parameters at 1.0 GHz, with a 50Ω reference impedance: S11 = 0.38∠−158°, S12 = 0.11∠54°, S21 = 3.50∠80°, S22 = 0.40∠ −43° ,The source impedance is ZS = 25 Ω and the load impedance is ZL = 40 Ω.

Question

COMPARISON OF POWER GAIN DEFINITIONS

A silicon bipolar junction transistor has the following scattering parameters at 1.0 GHz, with a 50Ω reference impedance:

[latex]S_{11} = 0.38∠−158°[/latex]

[latex]S_{12} = 0.11∠54°[/latex]

[latex]S_{21} = 3.50∠80°[/latex]

[latex]S_{22} = 0.40∠ −43°[/latex]

The source impedance is [latex]Z_{S} = 25 Ω[/latex] and the load impedance is [latex]Z_{L} = 40 Ω[/latex] .Compute the power gain, the available power gain, and the transducer power gain

Accepted Answer

From (12.1a) and (12.1b) the reflection coefficients at the source and load are

[latex]\Gamma _{S}=\frac{Z_{S}-Z_{0}}{Z_{S}+Z_{0}}=\frac{25-50}{25+50} = -0.333[/latex]

[latex]\Gamma _{L}=\frac{Z_{L}-Z_{0}}{Z_{L}+Z_{0}}=\frac{40-50}{40+50} = -0.111[/latex]

From (12.3a) and (12.3b) the reflection coefficients seen looking at the input and output of the terminated network are

[latex]\Gamma_{in}=S_{11}+\frac{S_{12}S_{21}\Gamma _{L}}{1-S_{22}\Gamma _{L}} = 0.365\angle-152^{\circ },[/latex]

[latex]\Gamma _{out}=S_{22}+\frac{S_{12}S_{21}\Gamma _{S}}{1-S_{11}\Gamma _{S}} = 0.545\angle -43^{\circ },[/latex]

Then from (12.8) the power gain is

[latex]G= \frac{\left|S_{21}\right| ^{2}(1-\left|\Gamma _{L}\right|^{2} ) }{(1-\left|\Gamma _{in}\right|^{2} )\left|1-S_{22}\Gamma _{L}\right|^{2} }=13.1[/latex]

From (12.12) the available power gain is

[latex]G_{A}=\frac{\left|S_{21}\right| ^{2}(1-\left|\Gamma _{S}\right|^{2} ) }{\left|1-S_{11}\Gamma _{S}\right|^{2} (1-\left|\Gamma _{out}\right|^{2} ) }=19.8[/latex]

From (12.13) the transducer power gain is

[latex]G_{T}=\frac{\left|S_{21}\right|^{2}(1-\left|\Gamma_{S} \right|^{2} )(1-\left|\Gamma _{L}\right|^{2} ) }{\left|1-\Gamma _{S} \Gamma _{in}\right|^{2}\left|1-S_{22} \Gamma _{L}\right|^{2}}=12.6 [/latex]

Question 12.1: COMPARISON OF POWER GAIN DEFINITIONS A silicon bipolar junct...

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