Chapter 6

An opamp has an open-loop transfer function given by $$ A(s)=\frac{A_{0}\left(1+\frac{s}{\omega_{z}}\right)}{\left(1+\frac{s}{\omega_{1}}\right)\left(1+\frac{s}{\omega_{2}}\right)} $$ Assume \(\mathrm{A}_{0}=10^{4}\) and \(\omega_{2}=10^{8} \mathrm{rad} / \mathrm{s}\). The feedback network has a gain \(\beta=0.5\). The frequency of the zero is \(70 \%\) higher than the resulting open-loop unity-gain frequency, \(\omega_{2}=1.7 \omega_{\mathrm{t}}\). Find \(\omega_{1}\) and \(\omega_{\mathrm{t}}\) so that the phase margin is \(80^{\circ}\).

An opamp has an open-loop transfer function given by $$ \mathrm{A}(\mathrm{s}) \cong \frac{\mathrm{A}_{0}\left(1+\mathrm{s} \tau_{\mathrm{z}}\right)}{\mathrm{s} \tau_{1}\left(1+\mathrm{s} \tau_{2}\right)} $$ Find the transfer function of the closed-loop amplifier, assuming a feedback factor \(\beta\) exists. Find approximate equations for the resonant frequency and the Q factor of the denominator of the transfer function of the closed- loop amplifier.