Microwave Engineering

Excercise 0: Revision Problems

Problem 1

A $50\Omega$ Source has $2W$ maximum available power. Determine its Thevenin and Norton equivalent circuits.

Solution

$$R_{source}=R_{thevenin}=50\Omega$$ as if we turned off source and see from output terminal we will find only it $$P_{max}={{V_{thevenin}}^2 \over 4R_{thevening}}=2W$$ $$V_{th}=20V$$ $$I_{norton}={V_{thevenin} \over R_{thevenin}}=0.4A$$

Problem 2

If the source of Problem (1) is to be connected to a load of impedance $75-j25 \Omega$, design the required matching network. Hence, determine its Z, Y and ABCD parameters.

Solution

$$Z=\begin{bmatrix}Z_{11} & Z_{12}\\Z_{21} & Z_{22}\end{bmatrix}, Y=\begin{bmatrix}Y_{11} & Y_{12}\\Y_{21} & Y_{22}\end{bmatrix}, T=\begin{bmatrix}A & B\\C & D\end{bmatrix}$$ $$\begin{bmatrix}V_{1} \\ V_{2}\end{bmatrix}=\begin{bmatrix}Z_{11} & Z_{12}\\Z_{21} & Z_{22}\end{bmatrix}\begin{bmatrix}I_{1} \\ I_{2}\end{bmatrix}$$ $$Z_{11}=\left.\frac{V_1}{I_1}\right\vert_{I_2=0}=75-j25$$ $$Z_{12}=\left.\frac{V_2}{I_1}\right\vert_{I_2=0}=75-j25$$ $$Z_{21}=\left.\frac{V_1}{I_2}\right\vert_{I_1=0}=75-j25$$ $$Z_{22}=\left.\frac{V_2}{I_2}\right\vert_{I_1=0}=75-j25$$