22-Elec-A5 Electronics · May 2017

Question 2 of 5: Op-Amp Peak / Envelope Detector

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Question 2: Op-Amp Peak / Envelope Detector (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. Buffer $A_1$ (voltage follower) drives diode $D_1$ (anode at $A_1$’s output) into a parallel $R\Vert C$ to ground; that node feeds a second follower $A_2$ whose output is $v_{OUT}$ across $R_L$. The input $v_{IN}$ is a sinusoid whose amplitude grows linearly from 0 to about 2 V over 10 ms (a rising “burst”, roughly 8–9 cycles).

Find. (a) the shape of $v_{OUT}(t)$; (b) the function of the circuit.

Approach. Follower $A_1$ reproduces $v_{IN}$ at low impedance; $D_1$ lets $C$ charge only on the rising part of each positive peak and blocks the discharge, so $C$ holds the most recent peak while $R$ slowly bleeds it. Because $A_1$’s feedback is taken before the diode, the diode’s 0.7 V is not cancelled — the held value is (peak $-\,0.7$ V). $A_2$ buffers the held voltage so the load $R_L$ cannot discharge $C$.

1. Charging law. On a rising positive half-cycle $D_1$ conducts and $C$ charges toward $v_{C}=v_{IN,\text{pk}}-0.7$ V (the follower sources current; the 0.7 V drop is uncompensated).
2. Hold / bleed time constant. When $v_{IN}$ falls, $D_1$ blocks and $C$ discharges only through $R$: $\ \tau=RC=(1\ \text{k}\Omega)(2\ \mu\text{F})=2\ \text{ms}.$ Since $\tau$ is comparable to the signal period, the output droops slightly between peaks (a small sawtooth ripple on the envelope).
3. Dead zone. The peak reaches 0.7 V only when $0.2\,t\;[\text{V/ms}]=0.7$, i.e. $t=3.5$ ms; before that $D_1$ never conducts and $\boxed{v_{OUT}=0\ \text{for }0\le t\lesssim3.5\ \text{ms}}.$
4. Rising envelope. For $3.5\ \text{ms}\lesssim t\le10\ \text{ms}$ the output tracks the growing positive peaks, $v_{OUT}\approx(0.2\,t-0.7)$ V, reaching $2-0.7=1.3$ V at $t=10$ ms.
5. Decay after the burst. Once the input stops, $C$ discharges through $R$: $v_{OUT}(t)=1.3\,e^{-(t-10\ \text{ms})/2\ \text{ms}}$ V, falling to near zero within $\sim3\tau\approx6$ ms.

(b) Function. The circuit is a peak (envelope) detector: it rectifies and holds the positive peaks of the input, so its output follows the amplitude envelope of the signal — the classic AM-demodulator / envelope-follower front end. $A_1$ provides a low-impedance drive to charge $C$ quickly and $A_2$ isolates the hold capacitor from the load $R_L$ (a buffered peak detector).