Question 3 of 5: Zener-Feedback Op-Amp Waveform

Question 3: Zener-Feedback Op-Amp Waveform (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. Inverting configuration in which the Zener \(D_1\) is the only feedback element (anode at the \(v_-\) node, cathode at \(v_o\)); \(R_1=10\ \text{k}\Omega\), \(V_Z=5\ \text{V}\), \(V_F=0.7\ \text{V}\), slew rate \(SR=0.5\ \text{V/}\mu\text{s}\); the input triangle reaches \(+10\ \text{V}\) at 50 µs and \(-10\ \text{V}\) at 100 µs.

Find. The output waveform \(v_o(t)\) with its clamp levels and slew-limited edges.

Approach. Because a diode always conducts in one direction, negative feedback is always present, so \(v_-\) stays a virtual ground; determine which way \(D_1\) conducts for each input polarity, read off the clamp level, then apply the slew-rate limit to the transitions.

1. Positive input half. For \(v_s\gt0\) the current \(i=v_s/R_1\) flows from the virtual ground toward \(v_o\), i.e. anode→cathode — \(D_1\) is forward. Then \(v_o=v_- - V_F=-0.7\ \text{V}\): $$\boxed{v_o=-0.7\ \text{V}\quad(v_s\gt0).}$$
2. Negative input half. For \(v_s\lt0\) the current reverses and \(D_1\) conducts in Zener breakdown, holding \(v_o-v_-=V_Z\): $$\boxed{v_o=+5\ \text{V}\quad(v_s\lt0).}$$ The output is therefore a hard clamp toggling between \(-0.7\ \text{V}\) and \(+5\ \text{V}\); \(R_1\) only sets the (irrelevant) diode current, not the levels.
3. Slew-limited transitions. Each edge spans \(\Delta v_o=5-(-0.7)=5.7\ \text{V}\); at \(0.5\ \text{V/}\mu\text{s}\) the op amp needs $$t_{edge}=\frac{5.7\ \text{V}}{0.5\ \text{V/}\mu\text{s}}=11.4\ \mu\text{s}.$$
4. Locate the edges. \(v_s\) crosses zero at \(t=0\) (going +), \(t=75\ \mu\text{s}\) (going −) and \(t=125\ \mu\text{s}\) (going +). So \(v_o\) ramps from \(+5\) down to \(-0.7\) over \(0\!-\!11.4\ \mu\text{s}\), holds \(-0.7\) to \(75\ \mu\text{s}\), ramps up to \(+5\) over \(75\!-\!86.4\ \mu\text{s}\), holds to \(125\ \mu\text{s}\), then ramps down again — a slew-rounded rectangular wave.