DC Restorer (Clamper) Driving a Voltage Follower — Steady State at $v_{in}=0$: 17-Comp-A1, Undated paper, Q5

Question 5: DC Restorer (Clamper) Driving a Voltage Follower — Steady State at $v_{in}=0$ (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. Series capacitor $C$ from $v_{in}$ to node $A$; diode $D_1$ (anode at $A$, cathode at ground) shunts $A$; node $A$ drives the op-amp's non-inverting input; the op-amp is wired as a unity-gain follower (output tied to the inverting input), output node $B=V_{out}$, with $R_L=1\text{k}\Omega$ from $B$ to ground. $V_{ref}=0\text{V}$; supplies $\pm12\text{V}$; $V_F=0.7\text{V}$.

Find. The steady-state $V_{out}$ for $v_{in}=0$ with a physical explanation; sketches of $V_{out}(t)$, $V_A(t)$, $V_B(t)$.

Check — engineering assumption

The source states $v_{in}=0$ for BOTH sub-parts, which is unusual for a DC-restorer question. Solved literally as given below; the concept aside separately summarizes how the SAME circuit clamps a genuine periodic input, since that is very likely the intended full picture.

Approach. A clamper's output level is set entirely by the charge parked on its series capacitor, and that charge only changes when the input has enough $dV/dt$ to forward-bias the clamp diode. A literally constant input provides no such event.

Explain (part a). Because $v_{in}(t)\equiv0$ for all $t$, $dv_{in}/dt=0$ everywhere, so no displacement current ever flows through $C$ and $D_1$ never experiences a forward-bias event. With no charging path ever activated, the capacitor holds whatever charge it started with — zero, for a circuit beginning from rest — and the "restorer" simply never restores anything, because there is no waveform edge for it to act on.
Calculate (part a). With zero charge on $C$, node $A$ sits at the same potential as $v_{in}$ straight through the (uncharged) capacitor: $V_A=v_{in}=\boxed{0\text{ V}}$ for all $t$. The op-amp follower forces $V_{out}=V_B=V_A=\boxed{0\text{ V}}$ for all $t$ as well. Consistency check: $D_1$ (anode at $A=0\text{V}$, cathode at ground $=0\text{V}$) sits at exactly zero net forward bias, consistent with carrying zero current at every instant — a self-consistent equilibrium.
Sketch (part b). $V_A(t)$, $V_B(t)$, and $V_{out}(t)$ are all flat lines at $0\text{V}$ for all $t$ (Fig. Q5) — there are no peak, period, or transition values to mark, since nothing in the circuit ever moves away from its zero-charge, zero-current starting point.

Fig. Q5 — $V_A$, $V_B$, $V_{out}$ all coincide at a flat $0\text{V}$ line: with $v_{in}\equiv0$, the clamper never has an event to charge its capacitor.

Final Results — Question 5
Quantity	Value
$V_A(t)$	$0\text{V}$ for all $t$
$V_B(t)=V_{out}(t)$	$0\text{V}$ for all $t$
$D_1$ conduction	Never (zero net forward bias at all times)

Topic: Series-capacitor diode clamper (DC restorer) driving a unity-gain buffer.

Key relations: Clamped peak $=V_{ref}+V_F$ for a genuinely time-varying input; steady state requires the capacitor's charge to balance the diode's forward drop against the waveform's peak.

Why this works: A clamper only shifts a DC level when its input has enough $dV/dt$ at some point in the cycle to forward-bias the clamp diode and pump charge onto the capacitor; a constant input never creates that event, so the output never departs from its (zero) initial condition. For contrast: if $v_{in}(t)$ were instead a genuine periodic waveform, $C$ would charge through $D_1$ until the waveform's positive peak sat at exactly $+V_F=0.7\text{V}$, shifting the whole waveform down by (peak amplitude $-0.7\text{V}$) — that shifted, clamped waveform is what a non-degenerate version of this question would ask for.

Common pitfall: Reflexively applying "the peak clamps to $+V_F$" to any input without first checking whether the input actually varies; for a strictly constant input, the clamping mechanism never engages at all.

Source: Sedra & Smith, Microelectronic Circuits, Diode Clamping / DC Restorer Circuits.

Question 5 of 7: DC Restorer (Clamper) Driving a Voltage Follower — Steady State at $v_{in}=0$

Question 5: DC Restorer (Clamper) Driving a Voltage Follower — Steady State at $v_{in}=0$ (20 marks)