Question 5 of 6: Bridge Rectifier with a Failed Diode
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Notes on this paper
Paper format. National Exams, May 2013 — 07-Elec-A5 Electronics. Three hours, closed book; one approved Casio or Sharp calculator permitted. Six questions are printed, each worth 20 marks, and five constitute a complete paper — all six are solved below as a study resource. Op-amps are ideal with ±15 V supplies unless stated otherwise.
Reference texts. A. S. Sedra & K. C. Smith, Microelectronic Circuits, 8th ed. (Oxford): Ch. 5–7 (MOSFET and BJT amplifiers, common-emitter and common-gate stages), Ch. 4 (diode limiters, clamps and rectifiers), Ch. 13–14 (CMOS/NMOS inverter VTC and noise margins), and Ch. 2 (op-amp precision rectifiers and slew rate).
Question 5: Bridge Rectifier with a Failed Diode (20 marks)
Find. The output waveform, $V_p$, $V_r$, the average output, and the diode conduction time $t_{on}$.
[Figure not reproduced: Q5 circuit (redrawn): full-wave bridge with the left node grounded and the output taken from the right node into the C||R filter. D1 (red X) is open. The surviving pair D2, D3 conducts only on the POSITIVE half of v_s, so the stage is now a half-wave rectifier. See the official exam paper.]
Approach. Establish that losing $D_1$ turns the bridge into a half-wave rectifier, then apply the standard peak / ripple / average / conduction-angle relations for a capacitor-filtered rectifier, using the triangular slope for the conduction interval.
Effect of the open diode. In the bridge, $D_1$ conducts (with $D_4$) on the negative half of $v_s$. With $D_1$ open that half can no longer conduct, while the surviving pair $D_2,D_3$ still conducts on the positive half. The stage is now a half-wave rectifier: $C$ recharges only once per input period, so the ripple frequency drops from 2 kHz to $$f=1\ \text{kHz},\qquad T=1\ \text{ms}.$$
(b) Peak voltage. The diodes are ideal (zero drop), so $C$ charges to the input peak: $$\boxed{V_p=10\ \text{V}}.$$
(b) Ripple. Between charging pulses $C$ discharges through $R$ for one full period. The standard estimate $$V_r\approx\frac{V_p\,T}{RC}=\frac{10\times1\ \text{ms}}{5\ \text{ms}}=\boxed{2\ \text{V}}$$ (the exact exponential $V_p(1-e^{-T/RC})=1.81$ V is close, confirming the linear approximation).
(c) Average output. The output rides between $V_p$ and $V_p-V_r$, so $$V_{o,avg}\approx V_p-\frac{V_r}{2}=10-1=\boxed{9\ \text{V}}.$$
(d) Conduction interval. On the rising edge the triangle climbs at $|dv/dt|=20\ \text{V}/0.5\ \text{ms}=40\ \text{V}/\text{ms}$. The diodes conduct only while the input rises from $V_p-V_r$ back up to $V_p$, a climb of $V_r$: $$t_{on}\approx\frac{V_r}{|dv/dt|}=\frac{2\ \text{V}}{40\ \text{V}/\text{ms}}=0.05\ \text{ms}=\boxed{50\ \mu\text{s}}.$$
Output v_o with D1 open (blue): the bridge acts as a HALF-wave rectifier, so C recharges only once per 1 ms period (positive peaks). Peak V_p=10 V, peak-to-peak ripple ~2 V, average ~9 V. Dashed grey = triangular input.
