Exercise 9.7 Something else like a Wien bridge oscillator

a)

An answer:

$$\begin{array}{rcll}& H_{\mathit{loop}}(\mathit{j\omega })& =A\cdot H_1(\mathit{j\omega })\cdot H_2(\mathit{j\omega })& \\ & & H_1(\mathit{j\omega })=\frac{R_1}{R_1+\mathit{j\omega L}}=\frac{1}{1+\mathit{j\omega }\frac{L}{R_1}}& \\ & & H_2(\mathit{j\omega })=\frac{R_2}{R_2+1∕\mathit{j\omega C}}=\frac{\mathit{j\omega }{R}_{2}C}{1+\mathit{j\omega C}{R}_2}& \\ & H_{\mathit{loop}}(\mathit{j\omega })& =A\cdot \frac{1}{1+\mathit{j\omega }\frac{L}{R_1}}\cdot \frac{\mathit{j\omega }{R}_{2}C}{1+\mathit{j\omega C}{R}_2}& \\ & & =A\cdot \frac{\mathit{j\omega }{R}_{2}C}{1+\mathit{j\omega }(\frac{L}{R_1}+R_{2}C)-{\omega }^2\frac{R_2}{R_1}\mathit{LC}}& \end{array}$$

$$\begin{array}{rcll}& {\omega }_{\mathit{osc}}& =\frac{1}{\sqrt{\frac{R_2}{R_1}\mathit{LC}}}& \end{array}$$

b)

An answer:

$$\begin{array}{llll}\hfill & A=1+\frac{L}{R_1{R}_{2}C}& \hfill & \end{array}$$