Practical_Electronics-May_2019

Practical Electronics | May | 2019 45

full-wave rectifier rather than a half-wave
rectifier). With a 24V RMS secondary, this
circuit will deliver approximately 65V
at load currents of up to 50mA.
Fig.6.2(a) shows a simple voltage tripler.
The upper part of this circuit (C1/C2
and D1/D2) forms a voltage doubler
with double the peak secondary voltage
appearing across C2. To this is added the
negative peak voltage produced by the
rectifying action of D3 which charges C3
on negative-going half cycles. Thus, the
voltage appearing across the load (RL)
will be approximately three times the
peak secondary voltage delivered by T1.
With a sinusoidal AC input, three
1N4001 diodes, and an RMS secondary
voltage (VS) the peak DC voltage
appearing across the load (RL) is
approximately given by:

Vout = (3 × 1.4 × VS) – (3 × 0.7V)
= 4.2VS – 2.1V

Thus, with a transformer delivering 24V
RMS from its secondary, the no-load
output voltage will be approximately 98V
and also with load currents of up to 50mA.
Fig.6.2(b) shows a simple voltage
quadrupler. The upper part of this circuit
(C1/C2 and D1/D2) forms a voltage
doubler with double the peak secondary
voltage appearing across C2.

The lower part of the circuit (C3/C4

and D3/D4) forms a further negative

output voltage doubler, with its output

appearing across C4. The resulting

output voltage delivered to the load

(RL) is the sum of the voltages appearing

across C2 and C4. With a sinusoidal

AC input, four 1N4001 diodes, and an

RMS secondary voltage (VS) the peak DC

voltage appearing across the load (RL)

will be approximately:

Vout = (2 × (2 × 1.4 × VS)) – (4 × 0.7V)

= 4VS – 2.8V

With a transformer delivering 24V RMS

from its secondary, the no-load output

voltage will be approximately 130V,

which can be maintained at load currents

of up to 50mA.

Higher voltages

It is possible to generate much higher

voltage using multiplier arrangements,

but at the cost of poor regulation and

limited output current. The general

arrangement of an n-tupler ladder voltage

multiplier is shown in Fig.6.3. Originally

devised by John Cockcroft and Ernest

Walton more than 90 years ago, this

circuit was employed in a high-voltage

DC power supply for use with a nuclear

particle accelerator.

The Cockcroft-Walton

arrangement cascades

ladder networks of

rectifiers and reservoir

capacitors, and offers

the advantage of not

requiring a bulky and

expensive high-voltage

transformer. Note that in

Fig.6.3 we have added a

shunt resistor in parallel

with each reservoir

capacitor. These

not only assist with

equalising the voltages

developed across the

reservoir capacitors, but

also provide a discharge

path for the capacitors,

making the circuit safe to

handle when the power

is no longer applied.

Typical values for the

shunt resistors are in

the range 47kΩ to 1MΩ.

It should perhaps be

emphasised that a high-

order Cockcroft-Walton power supply

is only capable of delivering relatively

small currents. For example, a nine-times

multiplier (n = 9) will only be capable of

delivering a few tens of milliamps. This

may be sufficient for a few applications

but wholly insufficient for many others.

Reservoir capacitors

In both switched-mode and conventional

linear supplies, the reservoir capacitors

have the important role of ‘holding-

up’ the output voltage from the bridge

rectifier. The capacitors will charge on

each peak of the applied voltage (during

which the respective rectifier diodes will

be conducting) and it will retain this

charge when the secondary voltage falls

(see Fig.6.4). The general rule of thumb is

to use a capacitor, suitably rated in terms

of working voltage and ripple current,

with a value that is as large as possible

within the physical constraints of the

board on which it is mounted.

It is possible to obtain a rough ‘ball

park’ value of the capacitance required

by assuming that the capacitor has a

maximum discharge time equivalent

to the time for one half-cycle of the AC

supply (recall that the bridge rectifier is

providing full-wave rectification, and

so the ‘ripple’ frequency will be 100Hz,

twice the 50Hz frequency for a standard

UK mains supply). The recommended

value of capacitor can then be estimated

from the relationship:

Where Imax is the maximum load current,

tdmax is the maximum discharge time,

Vpk and Vtr are the peak and trough

voltages respectively (see Fig.6.5) and

the DC output voltage (VDC) is simply

the average of these two.

Let’s take a simple example based on a

reservoir capacitor that what we might

need for a basic audio amplifier operating

Fig.6.3. Voltage multiplier Cockcroft-Walton ‘n-tupler’ ladder.

Fig.6.4. A bridge rectifier with, and without, reservoir capacitor. Note how the current flows
alternately into and out of the capacitor in order to maintain current through the load.

max d max

pk tr

It

C

VV

×

=

−

××−

−

−

×× × −

−

π

π

⎛⎞

⎜⎟

⎝⎠

π ××× ×−

1 1

×

×

× × ×

×⎛⎞

⎜⎟

⎝⎠

× ×⎛⎞

⎜⎟

⎝⎠

⎛⎞

× ×⎜⎟

⎝⎠

Fig.6.5. Effect of a reservoir capacitor on the output waveform of a full-wave
bridge rectified DC power supply.