23-Mechatronics-A2 Circuits and Electronics · December 2018
Question 8 of 11: Full-wave diode-bridge rectifier with capacitive filter
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Notes on this paper
Paper: National Exams, December 2018 — 16-Mex-A2 Circuits and Electronics. Closed-book, 3-hour paper (approved Casio/Sharp calculator only). Two parts: Part A — Circuits (Q1–Q6) and Part B — Electronics (Q7–Q11); candidates normally answer 5 of the 11 questions (3+2 or 2+3 split). Full worked solutions to all eleven questions are given below so the set can be used for study regardless of which five a candidate chose.
Reference texts: C. K. Alexander & M. N. O. Sadiku, Fundamentals of Electric Circuits (7th ed.) — resistive networks, superposition, Thévenin/max-power transfer, first-order and second-order transients, AC steady-state nodal analysis; W. H. Hayt et al., Engineering Circuit Analysis (9th ed.) — Laplace-domain circuit models; A. S. Sedra & K. C. Smith, Microelectronic Circuits (8th ed.) — op-amp T-network feedback, diode rectifiers, MOSFET common-gate stages, NMOS inverters, and BJT bias-point analysis.
Reading the figures. The paper supplies the schematics but no separate figure data; every network below is redrawn element-by-element directly from the original drawing (several figures are small hand-style schematics). All node/reference choices and source polarities are stated with the solution. Q11 uses printed variable names (e.g. “VE”) exactly as labelled on the original circuit, even where the labelled terminal is physically the collector in one sub-part — this is called out explicitly where it occurs.
Find. Sketch $v_O$ and its average; minimum $C$; sketch $i_{D1}$; average $i_{D3}$.
Figure-8: full-wave diode bridge (D1–D4) rectifying a 100 Hz, 0–10 V square wave, smoothing capacitor C across load R=100 Ω.
Approach. Two diodes conduct on each half-cycle of a full-wave bridge, so every input transition to +10 V recharges $C$ through two forward diode drops; between recharges $C$ discharges through $R$, producing the ripple. Standard peak-rectifier formulas apply with the bridge’s two-diode drop.
Average output voltage. Each conduction path drops two diodes ($D_1,D_3$ or $D_2,D_4$): peak charge voltage is $v_{IN,pk}-2V_D=10-1.4=8.6\ \text{V}$; with ripple $V_r=0.5\ \text{V}$ the output settles to $$v_{O,avg}=\big(v_{IN,pk}-2V_D\big)-\frac{V_r}{2}=8.6-0.25=\boxed{8.35\ \text{V}}.$$
Sketch. $v_{IN}$ switches 0↔10 V every half-period ($T=1/f=10\ \text{ms}$, half-period 5 ms); $v_O$ recharges to 8.6 V near each rising edge of $v_{IN}$, then droops by 0.5 V (sawtooth) until the next recharge — see the sketch above.
Minimum capacitance. Using the standard peak-rectifier ripple approximation, with the capacitor discharging through $R$ for essentially one full input period $T=1/f=10\ \text{ms}$ (the diodes conduct only briefly near each peak): $$C_{min}=\frac{v_{O,avg}}{2\,f\,V_r\,R}=\frac{8.35}{2\times100\times0.5\times100}=8.35\times10^{-4}\ \text{F}=\boxed{835\ \mu\text{F}}.$$
Diode current $i_{D1}$. $D_1$ (with $D_3$) conducts only in the brief interval near each rising edge of $v_{IN}$ while $C$ recharges from $(8.6-0.5)=8.1\ \text{V}$ up to $8.6\ \text{V}$ — a narrow current pulse once per period (that is the “capacitor charging” interval); it is zero the rest of the cycle while $C$ alone supplies $R$.
Average current through $D_3$. Over a full cycle the load draws a steady average $I_{O}=v_{O,avg}/R=8.35/100=83.5\ \text{mA}$, but $D_1$–$D_3$ conduct on only one of the two conduction paths (each polarity path conducts on alternating pulses since $v_{IN}$ only ever drives current one way through this bridge, unlike an ac line rectifier) — the pulse train through $D_1$/$D_3$ recharges $C$ once per full period $T$, so the average current a single diode carries is half the load average: $$I_{D3,avg}=\frac{I_O}{2}=\boxed{41.75\ \text{mA}}.$$
Sketch: $v_{IN}$ (0/10 V square wave) and the resulting rippled dc output $v_O$ (average 8.35 V, ripple 0.5 V p-p, one ripple cycle per half-period of $v_{IN}$).
