Synthesis of electrical networks

H. Baher

Chapter 3 Synthesis of Lossless One-ports - all with Video Answers

Educators

Chapter Questions

Problem 1

Show that each of the following functions is a reactance function, and find the Foster and Cauer forms.
$$
\begin{aligned}
& Z(p)=\frac{4 p^4+13 p^2+3}{p^5+5 p^3+4 p} \\
& Z(p)=\frac{\left(p^2+1\right)\left(p^2+3\right)}{p\left(p^2+2\right)\left(p^2+4\right)}
\end{aligned}
$$

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Numerade Educator

Problem 2

Two impedances $Z_1(p)$ and $Z_2(p)$ are said to be 'reciprocals' if they satisfy
$$
Z_1(p) Z_2(p)=1
$$

If $Z_1$ is a Foster function given by
$$
Z_1(p)=\frac{p\left(p^2+3\right)\left(p^2+5\right)}{\left(p^2+2\right)\left(p^2+4\right)} .
$$
realize $Z_1(p)$ and from the resulting network, construct a lossless one-port which realizes $Z_2(p)$.

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Problem 3

Consider the Foster impedance
$$
Z(p)=\frac{\left(p^2+1\right)\left(p^2+3\right)\left(p^2+6\right)}{p\left(2 p^2+3\right)\left(p^2+5\right)}
$$

Extract two successive poles at $p=\infty$ from $Z$ and the inverted remainder. Evaluate the remaining impedance and realize it in Foster's first form.

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