The 12 V Bench Supply That Drops Out Under Load
A vocational lab group is building a 12 V regulated bench supply for a soldering-practice station. The transformer is rated 15–0–15 V, 1 A; a bridge rectifier feeds a 1000 µF filter capacitor, and the output goes to a 7812 regulator bolted to a small aluminium bracket. At no load the unregulated rail measures 19.8 V DC. With a 15 Ω, 10 W dummy load connected (about 800 mA), the unregulated rail falls to an average of 15.6 V but shows 7.8 V peak-to-peak ripple on the oscilloscope. The 7812 output then measures only 9.8 V with noticeable 100 Hz ripple, and the regulator tab becomes too hot to touch within two minutes. Mains at the time is 215 V. The group has spare 4700 µF/35 V capacitors, 1N5408 diodes, a small TO-220 heatsink, and an 18–0–18 V transformer. They want a reliable 12 V, 0.8 A output before the practical exam.
1. Using the measured values, calculate the ripple with the 1000 µF capacitor and explain why the 7812 output is 9.8 V rather than 12 V. Identify which operating limit is being exceeded.
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For a full-wave rectifier at 50 Hz, ripple is approximately Vr = I/(2fC) = 0.8/(2 × 50 × 1000 × 10^-6) = 8.0 V peak-to-peak, which agrees with the 7.8 V measured. For a sawtooth, Vavg = Vpeak − Vr/2, so Vpeak ≈ 15.6 + 3.9 = 19.5 V and the trough is Vpeak − Vr ≈ 11.5 V. A 7812 needs its input to stay above 12 V plus roughly 2 V dropout, i.e. about 14 V at the trough. The 11.5 V trough is below that, so the regulator drops out; the output follows the trough minus dropout, giving about 9.5–9.8 V with 100 Hz ripple superimposed. The limit being exceeded is minimum input voltage, not current rating. The hot tab is a separate problem: dissipation is roughly (15.6 − 9.8) × 0.8 ≈ 4.6 W, and a bare TO-220 cannot safely dissipate that without a heatsink.
2. Select a fix from the available parts and justify it with calculations. State the resulting worst-case regulator dissipation and one remaining transformer limitation.
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Fit the 4700 µF capacitor: Vr = 0.8/(2 × 50 × 4700 × 10^-6) = 1.70 V peak-to-peak. With a peak near 19.5 V, the trough becomes about 17.8 V, comfortably above the 14 V dropout limit even if mains falls slightly. Average input is about 18.6 V, so regulator dissipation is (18.6 − 12) × 0.8 ≈ 5.3 W. A small TO-220 heatsink plus the junction-to-case resistance must keep the junction below 125 °C; with roughly 5 °C/W heatsink and 3 °C/W junction-to-case, the rise is about 42 °C, acceptable in a 40 °C lab. Do not choose the 18–0–18 V transformer: its higher peak raises dissipation to roughly (22 − 12) × 0.8 ≈ 8 W. The remaining limitation is that a capacitor-input rectifier draws RMS current about 1.6–1.8 times the DC load, so 0.8 A DC means about 1.3 A RMS; the 1 A transformer is marginal and should be replaced with a 2 A type or the load reduced. The 1N5408 diodes are adequate for the surge current.