Rectifiers, Smoothing and Regulation

Every semiconductor in a radio needs a steady voltage of one polarity: a transistor biased by a voltage that reverses fifty times a second is not an amplifier, it is a buzzer. The mains, on the other hand, delivers 230 V that reverses fifty times a second and nothing else. A power supply is the machine that bridges those two facts, and it is worth understanding properly for two reasons — the examiner asks about it in every paper, and it is the one part of a station that can kill you.

The chain

Almost every linear supply is the same five blocks in the same order.

The transformer's job is covered in the transformers lesson, and its second job — putting an insulating barrier between the mains and everything you can touch — matters at least as much as the turns ratio.

Half-wave rectification

A single diode in series with the load conducts on the half cycles that forward bias it and blocks the rest. The output is a train of humps with a gap the size of a hump between them.

• One diode.
• Ripple at 50 Hz on Indian mains — one output pulse per input cycle.
• Poor: half the input is thrown away, the transformer is used on only half of each cycle, and the long gaps make the ripple hard to smooth.

It survives in low-current corners — a bias supply, a small mains adaptor — and nowhere else.

Full-wave with a centre-tapped transformer

Give the secondary a centre tap, call that the zero, and the two ends swing positive alternately. One diode from each end feeds the load, so on every half cycle one of them conducts and the load current never stops.

• Two diodes, plus a centre-tapped transformer.
• Ripple at 100 Hz — two pulses per input cycle.
• Only half the winding is working at any instant, so for a given transformer the output voltage is half what a bridge would give from the same secondary.

The bridge rectifier

Four diodes arranged in a diamond, conducting in diagonal pairs. On one half cycle one pair conducts and on the other half cycle the other pair does — and, crucially, the current through the load runs the same way both times.

• Four diodes, no centre tap.
• Ripple at 100 Hz.
• The whole secondary works on both halves of every cycle, so transformer utilisation is the best of the three. This is what almost every modern supply uses, and the four diodes usually arrive in one moulded block with four legs.

India runs on 50 Hz

The higher ripple frequency of the full-wave circuits is a second advantage beyond efficiency: pulses arriving twice as often leave the reservoir capacitor half as long to droop, so the same smoothing is achieved with roughly half the capacitance.

Peak inverse voltage

While a diode is blocking, the reverse peak of the waveform stands across it. The peak inverse voltage (PIV) rating is the largest reverse voltage a diode can withstand without breaking down, and choosing a diode means comparing that rating with the worst reverse voltage the circuit can produce.

Two things catch people out. First, the relevant figure is the peak, so a 12 V RMS secondary produces 1.414 × 12 = 17 V peak, not 12. Second, once a reservoir capacitor is fitted it holds the cathode at the peak while the anode swings to the opposite peak, so the diode in a half-wave circuit sees twice the peak. Fit a diode rated comfortably above the calculation — a factor of two is normal practice, and the extra costs a few rupees.

The reservoir capacitor

A large capacitor connected straight across the rectifier output does something very simple: it charges up to the peak of each pulse, and then, while the rectifier is not conducting, it supplies the load from its own stored charge. The output no longer falls to zero between pulses; it sags a little and is topped up again. What remains of the sag is the ripple.

Two things set how much ripple is left:

• Capacitance. More farads, more charge stored, less droop.
• Load current. The capacitor discharges faster into a heavier load, so ripple grows as you draw more current. A supply that looks beautifully clean on a voltmeter with nothing connected can hum badly on transmit.

Set the lab below to Half-wave, no capacitor and read the ripple figure. Then slide the capacitor up and watch it collapse. Then switch to Bridge with the same capacitance and compare. Finally, drop the load resistance from 1000 Ω to a few hundred and watch the ripple climb again — that is the load-current effect in one slider.

Filters beyond a single capacitor

Capacitor-input

The capacitor comes first, straight after the diodes. Off load the output rises almost to the peak of the secondary, which is high and useful; under load it sags, because the capacitor only gets brief charging pulses. High output, poor regulation, and a fierce current spike through the diodes at each peak.

Choke-input

An inductor comes first, with the capacitor after it. The choke opposes any change of current and so keeps the current flowing steadily through the whole cycle. The output settles near the average of the rectified wave rather than the peak, so it is lower — but it barely moves as the load changes. Lower output voltage, much better regulation. Chokes are big, heavy and expensive, which is why they have all but vanished from modern equipment.

The pi filter

Named for the shape of the Greek letter π: a capacitor, then a series element (choke or resistor), then a second capacitor. The first capacitor does the bulk of the smoothing, the series element drops what ripple is left, and the second capacitor cleans up the remainder. It gives excellent smoothing with capacitor-input's high output voltage — and inherits capacitor-input's mediocre regulation.

Measuring how good a supply is

Smaller is better. Unsmoothed, a half-wave rectifier has a ripple factor of about 1.21 — that is, 121 per cent — and a full-wave one about 0.482. Every stage of filtering cuts it, and a well-made regulated supply reaches a small fraction of one per cent.

Worked example — percentage regulation

A supply measures 12 V with nothing connected and 10 V at its rated current.

(12 − 10) ÷ 10 × 100 = 2 ÷ 10 × 100 = 20 per cent.

Note the divisor: it is the full-load voltage, not the no-load one. Dividing by 12 gives 17 per cent, which is the wrong answer offered in the paper. A 20 per cent figure is poor — that supply would drop two volts every time you keyed the transmitter. A regulated supply is comfortably under one per cent.

Regulators

The zener shunt regulator

A zener diode is run reverse biased, in its breakdown region, where its voltage barely changes over a wide range of current. It is connected across the load — in shunt — with a series resistor between it and the raw DC. The resistor drops the surplus voltage; the zener passes whatever current the load does not want, so the total through the resistor stays roughly constant and so does the voltage across the load. It is cheap, it is two components, and it is only good for small currents, because everything the load does not use is wasted as heat in the zener and the resistor.

The series-pass regulator

Put a transistor in series with the load and hold its base at a fixed potential, usually with a zener. The transistor then drops exactly enough voltage to keep the output where it should be, adjusting continuously as the load changes. Add an amplifier that compares the output with the reference and drives the base, and the regulation becomes very good indeed. The surplus voltage still becomes heat, all of it in the pass transistor — which is why a linear bench supply has a substantial heatsink and why a 13.8 V supply run from a 20 V rail runs hot.

The three-terminal IC regulator

The whole series-pass arrangement — reference, error amplifier, pass transistor, current limit and thermal shutdown — shrunk onto one chip with three legs: input, common and output. The 78xx family gives fixed positive voltages (7805 for 5 V, 7812 for 12 V), the 79xx family the negative equivalents, and the LM317 is adjustable by two resistors. A capacitor at the input and another at the output, a heatsink, and the job is done. This is what you will actually build.

The bleeder resistor

A resistor permanently connected across the output. It has two jobs, and both matter:

1. Safety. When the supply is switched off, the reservoir capacitors are still charged, and a large capacitor in a high-voltage supply can hold a lethal charge for a long time. The bleeder discharges them.
2. Regulation. It keeps a small minimum current always flowing, which stops a capacitor-input supply's output climbing to the full peak when nothing else is connected, and steadies the regulation generally.