Chapter 16: The Power Supply

It converts the AC mains into a DC voltage

Despite its name, a power supply makes no power of its own: it converts the mains AC into the DC voltage that electronic equipment needs. It stores almost nothing, and turning DC into AC is what an inverter does.

To break the circuit if too much current flows

A fuse melts and opens the circuit when an overload on the output, or a fault, draws too much current. It responds to current, not voltage, and while intact it does not limit the current at all.

A lowpass filter

The series inductor opposes the AC ripple but passes DC, and the capacitor shunts the ripple away from the load, so DC passes and the ripple is attenuated: a lowpass filter. A highpass filter would block the DC.

They reduce the ripple on the DC output

Together they form a lowpass filter, which passes the DC but cuts the ripple down to a tolerable level; passing the ripple and blocking DC would be a highpass filter. Their stored energy lasts only milliseconds.

It is pulsating DC that still rises and falls

A rectifier turns AC into DC that flows one way but pulses, falling towards zero between peaks; the filter smooths these pulses into a nearly steady voltage. Its output is no longer AC.

Its smoothing capacitor starts fully discharged

An empty capacitor at first acts almost like a short circuit, so it draws a large charging current. An inductor opposes exactly that kind of sudden change in current, which is why it is used to limit this inrush.

It slows the rise, so the current builds up gradually

An inductor opposes any change in the current through it, so the charging current into the empty capacitor rises gradually instead of in one damaging surge. Storing charge is what a capacitor does, not an inductor.

The secondary winding’s inductance and resistance

The secondary winding has inductance of its own, which the manual credits with slowing the surge into the empty capacitor, and its resistance helps too. A capacitor’s leads have far too little inductance to matter.

The capacitor charges to the peak, not the RMS value

AC voltages are given as RMS, and a sine wave peaks about 41% higher, near 17 V for 12 V RMS, so the capacitor charges to that peak less the diode drops. A bridge rectifier does not double the voltage.

About 41% higher

Peak = √2 × RMS = 1,414 × RMS, about 41% higher; turned round, the RMS value is about 71% of the peak. Taking 71% as the increase mixes up the two figures.

20 V

The secondary gives 230 ÷ 16 = 14,375 V RMS, and the capacitor charges to its peak: 1,414 × 14,375 = 20,3 V, nearest 20 V. Taking the RMS figure as the DC output gives 14 V.

10,1 V

The peak is 1,414 × 8 = 11,3 V, and two bridge diodes conduct in series on each half cycle: 11,3 − 2 × 0,6 = 10,1 V. Taking off only one drop gives 10,7 V.

100 Hz

A bridge is a full-wave rectifier, giving an output pulse on each half cycle, so the ripple frequency is twice the mains frequency: 2 × 50 = 100 Hz. Ripple at 50 Hz means half-wave rectification.

Any full-wave rectifier, however many diodes it has

Any full-wave rectifier, four-diode bridge or two-diode centre-tap, delivers a pulse on each half cycle, so its ripple is at twice the input frequency. The number of diodes does not set the ripple frequency.

50 Hz

A half-wave rectifier passes one half of each cycle, so the capacitor gets one charging pulse per cycle and the ripple is at the mains frequency, 50 Hz. Ripple at 100 Hz comes from full-wave rectification.

Some ripple remains, and its voltage varies with the load

Even after the filter some ripple remains, and the output sags from its unloaded peak as the load grows, from about 17 V to 11 V in the manual’s example. An unregulated supply wastes little power as heat.

It falls, as the capacitor drains faster

With more load the capacitor discharges further between peaks, and the transformer and diodes drop more voltage, so the output sags below its unloaded peak. Diodes conducting harder drop more voltage, not less.

It stores energy to feed the load between peaks

Storing energy between ripple peaks is the smoothing capacitor’s job; a regulator stores none. It does hold the output steady against changes in input or load, removes most remaining ripple, and IC types limit short-circuit current.

Limit their current and power to safe levels

Most IC regulators limit their own current and power dissipation automatically, so the supply survives a short circuit at its output. The mains fuse is there for faults inside the supply itself.

It adjusts its resistance fast enough to cancel it

The regulator adjusts its internal resistance continually, and fast enough to cancel the rise and fall of its input, so its output stays clean. Storing charge between peaks is how the smoothing capacitor works.

The regulator itself removes most of the remaining ripple

The regulator follows and cancels the ripple on its input, so a smoothing capacitor alone gives adequate ripple rejection. A regulator stores no charge; it acts like a continually adjusted resistor.

A short circuit could occur inside the device itself

Even a supply whose regulator protects its output can develop a short circuit inside, ahead of the regulator, drawing a dangerous current that only the mains fuse will break. A fuse is far too slow to stop spikes.

Providing a steady reference voltage for the regulator

A Zener alone suits only low currents, so it typically stabilises a reference voltage that controls the regulator’s output. The load current itself flows through the regulator, not through the Zener.

A Zener alone can handle only small currents

A Zener regulator wastes power in its series resistor and in the Zener itself, so it suits only low currents; for amperes, a Zener just sets a reference. A Zener holds its voltage from only a few milliamperes.

Many devices made and joined on one piece of silicon

An integrated circuit is a whole circuit, with many transistors, diodes and other parts, made and wired together on a single chip of silicon. A three-terminal regulator looks like a transistor but holds a complete circuit.

A centre tap on its secondary winding

A centre tap on the secondary lets each diode use one half of the winding on alternate half cycles, giving full-wave rectification with two diodes. A tap on the primary would not split the secondary’s output.

One half, between an end and the centre tap

On each half cycle one diode conducts, and the current returns through the centre tap, so only half the secondary is in use at a time. The two diodes never conduct together.

One, at one end of the winding

Only the diode at the end that is positive conducts; the other is reverse-biased until the next half cycle. So the current passes through one diode, losing about 0,6 V, not the 1,2 V of a bridge.

11,5 V

The whole secondary gives 230 ÷ 10 = 23 V, and the centre tap splits it into two halves of 11,5 V each, one used on each half cycle. 23 V is the voltage across the whole winding.

16,4 V

Each diode uses only half the secondary, which peaks at 34 ÷ 2 = 17 V, and one diode conducts at a time: 17 − 0,6 = 16,4 V. Using the whole winding gives 33,4 V.

The voltage between VOut and Gnd

The regulator keeps VOut a fixed voltage above Gnd, say 12 V, by adjusting itself all the time; the voltage between VIn and VOut is what changes, taking up the ripple and the input’s variations.

In series with it, between it and the supply

The regulator acts like a variable resistor in series with the load, between VIn and VOut, adjusted all the time to keep VOut steady. A control across the load would make a shunt regulator, such as a Zener.

A linear power supply

A mains transformer followed by rectification and regulation is the linear design. A switching supply rectifies the mains first and controls its output by fast switching.

It rectifies it into a high DC voltage

A switching supply has no mains transformer: its bridge and capacitor turn the mains straight into high-voltage DC, about 324 V from 230 V (the manual’s 338 V is for 240 V), which is then switched at high frequency.

To keep the DC output isolated from the mains

A 1:1 transformer gives no change in voltage; it is there so that the DC output has no direct connection to the mains, for safety. C2 does the filtering, and in practice the turns ratio usually lowers the voltage too.

By adjusting the duty cycle of its switch

Control electronics watch the output and change the duty cycle, the share of each cycle that the switch is on: more on-time passes more power. A varying series resistance is how a linear regulator works.

It rises, as more power is passed on

The longer the switch is on in each cycle, the more power reaches the transformer and the higher the output voltage; a short on-time gives a low output. That is how the duty cycle sets the voltage.

30%

Duty cycle = on-time ÷ whole period × 100% = 3 ÷ 10 × 100% = 30%. Dividing the on-time by the off-time, 3 ÷ 7, gives 43%, which is not the duty cycle.

40%

The period is 1 ÷ 125 kHz = 8 µs, so the duty cycle is 3 ÷ 8 = 37,5%, nearest 40%. Dividing the on-time by the 5 µs off-time gives 60%.

Feedback

Control electronics in a switching supply watch the output voltage and adjust the switching to hold it steady: that monitoring loop is feedback. Feedforward would act on the input without looking at the output.

On, it drops almost no voltage; off, it passes no current

Power = voltage × current. Switched fully on, the switch carries current with little voltage across it; switched off, it has voltage across it but no current; either way the product is small.

12,5 W

The regulator drops 17 − 12 = 5 V while the full 2,5 A flows through it: 5 × 2,5 = 12,5 W of heat. 30 W is the power delivered to the load.

65%

The same current flows in and out, so efficiency = 12 ÷ 19 = 0,632, about 63%, nearest 65%. The other 37% is lost as heat in the regulator, hence the 35% option.

It works at a much higher frequency

The core a transformer needs shrinks as the frequency rises, so at around 100 kHz instead of 50 Hz it can be very small. For the same power the current is much the same; DC would not work at all.

Each discharge between pulses lasts only a very short time

Pulses arrive many thousands of times a second, so the capacitor discharges only briefly before it is topped up again, and much less capacitance holds the ripple down. A capacitor’s charge, Q = CV, does not depend on frequency.

They run from any mains voltage without a selector switch

Many switching supplies run from any mains voltage without a selector switch to change, which suits travellers. They do not convert the mains frequency; the mains is rectified to DC first.

RF interference, often across the HF bands

Their fast square-wave switching can spread strong RF interference over the HF bands and beyond, a real problem for amateurs, although well designed and shielded supplies need not interfere. Mains hum comes from ripple.

Its square waves are rich in harmonics

A square wave contains many harmonics, whole-number multiples of its frequency, so a supply switching at 100 kHz puts signals on 200 kHz, 300 kHz and so on, far into HF. The switching frequency itself stays put.

At 50 kHz and every multiple of 50 kHz

Its square-wave switching has harmonics at every multiple of 50 kHz, so signals appear every 50 kHz across the spectrum, through the HF bands and possibly beyond. 50 Hz is the mains frequency, not the switching frequency.

Gate motors and LED lights

Cheap, unshielded switching supplies sit in gate motors and even LED lights, and can spread interference across HF and possibly into VHF and UHF. Kettles and filament lamps have no switching supply.

Personal computers

High power needs and tight space make switching supplies the choice for nearly all personal computers, and a computer supply can sometimes be converted for use in the shack. Older hi-fi amplifiers used heavy mains transformers.

They are hard to design and can be dangerous to build

Switching supplies are hard to get right, and inside them the mains is rectified straight to a high DC voltage, which makes them dangerous to work on. The linear supplies earlier in the chapter suit home building.

The chemical reaction inside it

A cell’s voltage is set by the chemistry of the reaction inside it, about 2 V for lead-acid and 1,2 V for NiCd. A bigger cell of the same type gives more capacity, not more voltage.

About 2 V

A lead-acid cell gives about 2 V, so six of them in series make a 12 V car battery. About 1,5 V is the figure for an ordinary non-rechargeable torch cell.

1,2 V

A NiCd cell gives 1,2 V, so ten of them in series make a 12 V battery. 1,5 V is the voltage of an ordinary non-rechargeable cell, which NiCd cells replace in many gadgets.

6 cells

Each lead-acid cell gives about 2 V, so 12 ÷ 2 = 6 cells in series. Eight cells would suit 1,5 V torch cells, which a car battery does not use.

10 cells

Each NiCd cell gives 1,2 V, so 12 ÷ 1,2 = 10 cells in series. Eight cells would be right only for 1,5 V cells, and six for 2 V lead-acid cells.

In series, so their voltages add

Cells in series add their voltages, as six 2 V lead-acid cells make 12 V; cells in parallel keep one cell’s voltage and add their capacity instead. Transformers do not work on DC.

The electric charge it can deliver

Current × time is charge, so A.h measures charge, as the coulomb does: 1 A.h = 3 600 C. Energy would need the voltage too, in watt-hours.

20 A.h

Capacity = current × time = 2,5 × 8 = 20 A.h; dividing 8 by 2,5 gives 3,2 A.h. The manual’s example of 10 A for two hours is in fact 20 A.h, not 10 A.h.

5 hours

Time = capacity ÷ current = 2 000 mA.h ÷ 400 mA = 5 hours. Dividing the other way, 400 ÷ 2 000, gives 0,2 hours, about 12 minutes.

8 hours

Time = 7 A.h ÷ 0,9 A = 7,8 hours, nearest 8 hours, if the battery delivers its full rated capacity. Multiplying instead, 7 × 0,9 = 6,3, gives the 6 hours option.

12 V and 14 A.h

In parallel the voltage stays that of one battery, 12 V, while the capacities add, 7 + 7 = 14 A.h, and the internal resistance halves. 24 V and 7 A.h is what a series connection gives.

6 V and 2 500 mA.h

In series the voltages add, 4 × 1,5 = 6 V, but the same current flows through every cell, so the capacity stays 2 500 mA.h. Capacities add only for cells in parallel.

The higher cell would flatten itself charging the other

Cells in parallel are forced to one voltage, so current flows from the higher cell into the lower one, flattening the higher cell as it tries to charge the other. Voltages add only in series.

About 14 V

To push charge in, the charger must sit a little above the battery’s nominal voltage, so a 12 V lead-acid battery is usually charged at about 14 V. At 12 V almost no charge would flow.

13,8 V DC

A 12 V car’s electrical system runs at a nominal 13,8 V while the engine charges the battery, so mobile radios are designed for 13,8 V. 12 V is the battery’s nominal label, not the design voltage.

3 A

The guideline caps the charging current at capacity ÷ 4 h: 12 A.h ÷ 4 h = 3 A. 12 A, the one-hour rate, is far too fast.

700 mA

Four-hour rate: 2 700 mA.h ÷ 4 h = 675 mA, nearest 700 mA. 2,7 A is the one-hour rate, four times too high.

It overheats inside and may be damaged

Too high a charging rate heats the battery’s internal structure and can deform and damage it. Too low a rate is the one that takes too long and may never reach full capacity.

More than 10 hours

At 1 A it would take 10 hours to put back 10 A.h, but charging is not 100% efficient, so more than 10 A.h is needed and the charge takes longer. Exactly 10 hours ignores those losses.

They adjust voltage and current to the battery’s response

An intelligent charger monitors how the battery responds and adjusts the voltage and current to suit, preventing damage and giving the best lifetime and efficiency. A fixed current for a set time is a simple charger’s method.

A trickle charge

The small current that keeps a fully charged battery topped up is a trickle charge. A boost charge is the opposite, a short burst at a high rate.

It may leak, burst or even explode

Non-rechargeable cells are not built to take a charging current, so they may heat up, leak, burst or even explode: never try to recharge them. Any charge they take is small and not worth the risk.

Lithium-ion and lithium-polymer types

Lithium, lithium-ion and lithium-polymer batteries perform well but can catch fire or explode when charged wrongly or damaged, so never leave them charging unattended. NiCd cells are far more forgiving.

Never leave them unattended while they charge

Lithium batteries can catch fire or explode if charged wrongly, so they must never be left unattended on charge. Running them completely flat first harms lithium cells; that habit dates from NiCd days.