# What's the hype behind energy storage in capacitors?

When a company advertises their amplifier has over 100,000 micro-farads of capacitance, what exactly does it mean? The simple answer is not that much. The amount of capacitance has the least effect upon how much energy can be stored. The most important [ multiplying ] effect is caused by the VOLTAGE that these capacitors have applied to them! Energy storage is measured in Joules. The formula for energy storage is as follows:

J = ½CE² = 1 watt/second

where J = joules, C = farads and E = voltage of the charge.

[as can be seen here, the voltage [E] squared is the most important factor]

What we have here that determines the quantity more than anything else is at what voltage this charge is sitting at. For example:

Where C = 100,000 µF and E = 10 V
energy = 0.5 x 0.1 x 10² = 5 Joules

Where C = 100,000 µF and E = 100 V
energy = 0.5 x 0.1 x 100² = 500 Joules

Where C = 100,000 µF and E = 500 V
energy = ½ x 0.1 x 500² = 12,500 Joules

Taking into account that an average solid state amplifier rated at 250 watts RMS per channel runs at about = +\- 75 Volts. If they are advertising 100,000 µF then what they are saying is they have 50,000 µF operating at + 75 Volts and 50,000 µF operating at -75 Volts. If we calculate the energy storage we end up with the following:

J = [½ x 0.05 x 75²] x 2 = 281.25 joules [ for both channels]

## Let's compare this against a Wyetech Topaz 211A amplifier that produces 18 watts.

First thing is that the Topaz amp has two separate power supplies....one for the output 211 tube and one for the front end circuit that includes the amplification and driver stage. The Voltage that drives the output tube is conservatively held at 1150 Volts, which includes enough voltage to also bias the tube. The total effective capacitance of the Π filter that contains 3 capacitors [and two chokes] is equal to a total of only 50 µF of capacitance. Hard to believe?   Let's see how much energy storage that amounts to:

C = 50 µF   E = 1150 Volts   J = ½ x 0.000050 x 1150² = 33. 06 Joules

OK, we still have to add the other power supply, which is....

C = 88 µF   E = 430 Volts   J = ½ x 0.000088 x 430² = 8. 14 Joules

for a total of 41. 2 joules

## Now lets calculate the total energy for every watt rms of audio output power

Solid state amp = 281.25 joules ÷ 250 watts = 1.12 [both channels] = 0.56 joules/Watt/channel

Topaz 211A amp = 41.2 joules ÷18 watts = 2.29 [both channels] = 1.14 joules/watt/channel

Hmmm, the Topaz has almost seven times less total energy storage that the solid state amp, but has double the energy storage per watt of output power! Wait, there is more that matters than just this rating. Energy storage is only one part of the equation. Two other very pertinent facts come into play that determine the quality of the sound in respect to power supply design.

1. The Topaz uses only pure polypropylene fast capacitors in the power supplies. These pure capacitors can charge-and-discharge a lot faster than any electrolytic capacitor can. Because of this along with fact number...
2. The Topaz power supplies use a total of four very large chokes [20/20/30/30 Henries] in conjunction with the capacitors in two double Π filter networks.   The use of chokes in a Πfilter has a multiplying effect in reducing the ripple on the DC power. Ex... 50 µF x 20 Henries = 1000. It would take about 1000 µF or more to have the same filtering effect as what is occurring when combining these values of capacitance/inductance in the circuit.

Of course we haven't even mentioned the fact that inductors [chokes] also store and release energy. The whole object of producing DC power is to reduce the ripple and to provide the instantaneous current demands that the power supply must produce. The Topaz DC power supplies not only provide the necessary ripple reduction but can supply the instantaneous demands much faster from it's energy storage capacitors than those which use electrolytic capacitors in the power supply.

The reason why most tube amplifier companies almost exclusive make use of electrolytic capacitors is because it cost less and takes up a lot less space. [real estate that also cost money] The space density reduction can vary from 10 to 100 times less using electrolytic capacitors over pure capacitors that use an insulator film and foil without chemical doping.

## Does Wyetech Labs just like to be different or do they have a valid reason for doing this?

The Topaz represents the best that can be done when cost is no object. We wanted to not only produce the best sound, but also establish our place in the market. Can we design amplifiers that cost less, but are still way ahead in terms of dollar value and sound performance. The answer is definitely YES. We have done it with our new Onyx mono-block amplifiers, that make extensive use of electrolytics, in conjunction with wire wound resistors that are less costly than the chokes and polypropylene capacitors that they take the place of.   This method, which we call brute-force, because almost all of the filtering effect is from the capacitors, just like that used in solid-state amplifiers. Of course, it required more than 50 times more capacitance than what was used in the 18 watt Topaz. The result is excellence almost on a par with the Topaz, but not quite as refined in resolution of detail, air and nuance of minute sound structures.

It must also be remembered that all our amplifiers operate in class "A1" which draws a steady average current from the power supplies that contributes to better sound as well.

## How does the new ONYX amplifier rate in the energy storage debate?

Let's take a look. There are two high voltage supplies. One for the input and driver stage and one for the output stage. The average voltage applied to the 3 caps in the input supply is 430 Volts DC and a combined capacitance of 1,410 µF. The average voltage applied to the output supply is 275 Volts using 4 - 1000 µF caps.

Output Power Supply Energy = J = ½ x .004 x 275² = 151. 25

Input Power Supply Energy = J = ½ x .0014 x 430² = 130. 35

Total energy storage = = 281.6 joules/channel

The total energy per watt of output power of the ONYX is therefore

281.6 ÷ 13 = 21.6 joules

The Onyx single channel monoblocks are rated at 13 watts RMS but have the same amount of energy storage as that found in your typical solid-state 250 watt RMS stereo amplifier. It is also a whopping 38 times more energy storage per watt of actual output power!

All design methods have a direct effect on sound quality and to point out in an advertisement bragging that this amplifier contains 100,000 micro-farads of capacitance is pure unadulterated meaningless information. When it comes to tube amplifiers, which operate at much higher voltages, it is like comparing apples vis-à-vis oranges. What you really need to know is energy storage obtained from the capacitor bank as well as the myriad of other pertinent data, that only a real good designer could hope to have the knowledge to comprehend all the attributes and how they inter-relate to sound quality and the cost of the final product.