Chapter 5, Problem 19P

The circuit shown in Fig. P5.19 consist of a resistor R, an inductor L, and a capacitor C. The impedance of the resistor is $Z_1=R\Omega$, the impedance of the inductor is $Z_2=j\omega L\Omega$ and the impedance of the capacitor is $Z_3=\frac{1}{j\omega C}\Omega$ where $j=\sqrt{-1}$. For a particular design $R=100\Omega ,L=15mH,C=25\mu F$ and $\omega =120\pi rad/s$.

1. Compute the quantity $Z_2+Z_3$, and express the result in both rectangular and polar forms.
2. Compute the quantity $Z_1+Z_2+Z_3$, and express the result in both rectangular and polar forms.
3. Compute the transfer function $H=\frac{Z_2+Z_3}{Z_1+Z_2+Z_3}$ and express the result in both rectangular and polar forms.
4. Determine the complex conjugate of $H$ and compute the product $H{H}^{*}$.

Figure P5.19 Transfer function of series-parallel circuit for problem P5-19.