The capacitor acts a bit like a battery when used in the power supply.  This is basically how it works:

The transformer / bridge rectifier provides power in pulses.  A pulse will charge up the capacitors in the supply.  During the time between pulses the capacitors are providing all the current to the load.  This diminishes the charge in the capacitor, so the power supply output voltage falls (sag).  This continues until such time as the next transformer pulse comes along and recharges the capacitor.

This effect is called voltage ripple.  If you want to read more about how this works, please see my article on power supply basics as well as this article on power supply Q&A.

If the capacitor provides the power to the load between transformer pulses, it makes sense that the larger the capacitor we use, the more power it can store.  The more storage we have the less quickly a load can discharge that stored energy.  The less we discharge a capacitor, the less its output voltage will sag.  So then it makes sense that the more capacitance we have, the less power supply voltage ripple we will have for a given load.

So why not just have infinite capacitance then?
1  Capacitors can be expensive – especially for large values.
2.  Capacitors take up space.

Fortunately there are ways to calculate the amount of capacitance we need so you don’t need to guess at how much to use:  Seeing as the amount of capacitance determines the power supply output voltage ripple, we simply need to decide how much voltage ripple is acceptable.

Standard practice is to have 1V P-P or less voltage ripple on the supply lines.  This is a very generalized rule of thumb and does not apply equally to all circuits.  For example, a filament light bulb can work well without any capacitors.  On the other side of the scale you will often find audio circuits which have absolutely massive amounts of capacitance.

The formula to calculate capacitance is as follows:

C (Farad) = I (Amp) x t (seconds) / ΔV (Volt)

Where:
C = Total amount of capacitance in Farad.
I = Current draw in Ampere.
t = Time in seconds.
ΔV = Change in voltage.

Right, so let’s assume you live in a country that has an AC mains frequency of 50Hz.  After the transformer / bridge rectifier combination this will be turned in to pulses at 100Hz, thus 100 times per second.  We therefore know that we have a pulse every 0.01 second.

Next, let’s assume we have a maximum load of 5 Amp, and we want the voltage ripple (change in voltage or ΔV) to be a maximum of 1 V.

Our formula therefore looks like this:

C (Farad) = I (Amp) x t (seconds) / ΔV (Volt)
C = 5 Amp x 0.01 second /  1 V
C = 50’000 uF

So from this we know that in order to maintain a power supply ripple voltage of 1V or less for loads up to 5 Amp continuously, we need a capacitor with a minimum size of 50’000 uF.  Easy right 🙂

What if we have less?

Well, the simple answer is that less than 50’000uF of capacitance will mean that we have more than 1V worth of ripple on the power supply output when loaded with 5 Amp.  While this may not be a problem for powering light bulb, it can be a problem in other types of circuit – especially audio power amplifiers:

Let’s look at a simple power amplifier circuit:

This amplifier is based on the design by Rod Elliott with some component changes.  It is a class AB amplifier with a compound pair output stage.  In this example it runs on 22V rails and is driving a 4 ohm resistive dummy load (RLoad).

We drive the input such that we get an average of 25 Watt into the 4 ohm dummy load which equates to an RMS output current of around 2.5A.

The power supply for the amplifier is a very simple capacitive filter type.  In this example we are using a small 50VA transformer with 4’700uF of capacitance per rail.

We will look how the amplifier performs with different amounts of capacitance.  In all cases we will look at 3 things:  Amplifier output, rail voltage ripple and THD.

Test 1

4’700 uF capacitance per power supply rail, 1kHz sine wave, 25 Watt average output into 4Ω dummy load.

The red line represents the output voltage of the +22V rail, the green line represents the output voltage of the -22V rail, and the blue line represents the outut from the amplifier.

Amplifier output:  Nice and clean with no obvious issues.
Voltage ripple:  1.57V P-P ripple on the +22V rail and 1.66V P-P ripple on the -22V rail.
THD:  0.073% @ 1kHz.

Some output ripple is visible on the power supply rails, though it has no significant impact on the amplifier yet.

Test 2

2’200 uF capacitance per power supply rail, 1kHz sine wave, 25 Watt average output into 4Ω dummy load.

The red line represents the output voltage of the +22V rail, the green line represents the output voltage of the -22V rail, and the blue line represents the outut from the amplifier.

Amplifier output:  Nice and clean with no obvious issues.
Voltage ripple:  3.24V P-P ripple on the +22V rail and 3.4V P-P ripple on the -22V rail.
THD:  0.08% @ 1kHz.

As can be seen, the power supply ripple voltage has increased (as expected), but the amplifier output waveform still looks reasonable.  THD has increased a little, but not enough to cause undue concern yet.

Test 3

1’000 uF capacitance per power supply rail, 1kHz sine wave, 25 Watt average output into 4Ω dummy load.

The red line represents the output voltage of the +22V rail, the green line represents the output voltage of the -22V rail, and the blue line represents the outut from the amplifier.

Amplifier output:  Where the power supply rails sag to their lowest points we can start seeing some issues on the amplifier output waveform.
Voltage ripple:  7.2V P-P ripple on the +22V rail and 6.7V P-P ripple on the -22V rail.
THD:  0.14% @ 1kHz.

The power supply ripple voltage has increased to the point where it is directly affecting the the amplifier output waveform, and THD has suffered accordingly.

Test 4

470 uF capacitance per power supply rail, 1kHz sine wave, 25 Watt average output into 4Ω dummy load.

The red line represents the output voltage of the +22V rail, the green line represents the output voltage of the -22V rail, and the blue line represents the outut from the amplifier.

Amplifier output:  Power supply sag and ripple is affecting the amplifier output waveform drastically.
Voltage ripple:  12.9V P-P ripple on the +22V rail and 12.9V P-P ripple on the -22V rail.
THD:  6.45% @ 1kHz.

The power supply ripple voltage has increased to the point where it is heavily affecting the the amplifier output waveform, and THD has suffered accordingly.

First conclusion

Based on what we see above, there is a direct correlation between the output voltage ripple and the amplifier’s ability to faithfully produce the output required at a given power level.

So, let’s try something different:  We know that a filtered power supply reduces ripple quite well, so why not just do that to get rid of the problem?  The answer will be obvious to more experienced designers, but let’s go through the same set of tests with a capacitance multiplier power supply.  Everything else is kept the same – we simply add a capacitance multiplier filter to the existing power supply which then looks like this:

Test 5

4’700 uF capacitance per power supply rail, capacitance multiplier filter, 1kHz sine wave, 25 Watt average output into 4Ω dummy load.

The red line represents the output voltage of the +22V rail, the green line represents the output voltage of the -22V rail, and the blue line represents the outut from the amplifier.

The very first thing that becomes obvious is that the average voltage level of our power supply has dropped down a bit with the capacitance multiplier.  This is because of the additional losses incurred by passing the power supply through the transistor as well as the low-pass filter effect of the capacitance multiplier.

Amplifier output:  Nice and clean with no obvious issues.
Voltage ripple:  0.7V P-P ripple on the +22V rail and 0.85V P-P ripple on the -22V rail.
THD:  0.27% @ 1kHz.

The output voltage ripple has been reduced dramatically, but somehow the THD is quite a bit higher than with the  power supply using only the 4’700uF caps.  Why is this?  It is because of the reduced headroom caused by the lower average power supply rail voltage.  This normally affects the VAS (Voltage Amplification Stage) of an amplifier the most but also has some impact on the input stage when current sources and mirrors are not used to ensure a good PSRR.

Test 6

2’200 uF capacitance per power supply rail, capacitance multiplier filter, 1kHz sine wave, 25 Watt average output into 4Ω dummy load.

The red line represents the output voltage of the +22V rail, the green line represents the output voltage of the -22V rail, and the blue line represents the outut from the amplifier.

Amplifier output:  Nice and clean with no obvious issues.
Voltage ripple:  0.87V P-P ripple on the +22V rail and 0.95V P-P ripple on the -22V rail.
THD:  0.34% @ 1kHz.

The average voltage of the power supply rails have dropped a little more, thus the headroom has decreased further thereby increasing the THD slightly.

Test 7

1’000 uF capacitance per power supply rail, capacitance multiplier filter, 1kHz sine wave, 25 Watt average output into 4Ω dummy load.

The red line represents the output voltage of the +22V rail, the green line represents the output voltage of the -22V rail, and the blue line represents the outut from the amplifier.

Amplifier output:  Seems nice and clean with no obvious issues.
Voltage ripple:  1.94V P-P ripple on the +22V rail and 1.78V P-P ripple on the -22V rail.
THD:  2.27% @ 1kHz.

Why has the THD gone up so much when everything else looks reasonable?  The average voltage of the power supply rails have now dropped to the point where the amplifier output is being clipped as can be seen from the close-up of the waveform below, thus the THD has increased dramatically.

Second conclusion

Any further tests using less filter capacitance is moot beyond this point.  The average rail voltage of the power supplies will continue to sag to lower values, thus causing more clipping on the amplifier output.

As can be seen, there is no substitute or easy workaround for using the correct amount of bulk storage / filter capacitance in a power supply.

What about using higher rail voltages?  Sure, you could implement higher rail voltages to the point where the rail voltage ripple is so far above the output waveform peaks that it doesn’t matter, but as output power levels increase you will encounter the exact same thing, so this won’t work.

What about using a higher powered (larger) transformer?  As long as the transformer is specified to produce the current demanded by the circuit, using a larger transformer will have very little to no impact on the power supply output voltage ripple.  This is because the AC Mains frequency remains at 50Hz no matter what size your transformer is, therefore we can only recharge our bulk storage capacitors a maximum of 100 times per second.  In-between these pulses the capacitors are doing all the work, so we are right back to having enough capacitance.

Myths

There are a number of myths about capacitance in the power supply.  I won’t go into too much detail here, but do want to touch on a couple of points:

1.  Capacitance makes things slow / sluggish

The role of the bulk storage / filter capacitors in the power supply is to help provide a clean and stable output voltage.  How a cleaner and more stable power supply voltage can make something slow or sluggish is completely beyond comprehension – it simply doesn’t make sense.

2.  Less capacitance sounds better / More capacitance sounds worse.

Well, what can I say about this one?  How something “sounds” is difficult at best to describe.  What I will say is that *if* adding more capacitance makes an amplifier sound worse then there is something else wrong with the amplifier.  The correct amount, type, and location of bulk supply and local bypass capacitors will allow an amplifier to faithfully produce the output required of it – nothing more and nothing less.

Perhaps some people like the sound of power supply voltage ripple introduced into their amplifier output, or maybe the sound of the onset of clipping on the amplifier output somehow makes things exciting to listen to?  I know that it isn’t my cup of tea however.