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CAPACITORS
or
How to get a charge out of life


    In order for a project to perform at its peak, when it involves capacitors the values play an inescapable and enormous role. Second to this is the type of capacitor used. In an amplifier the capacitor is a device which has both become quite an integral part of the sonic purity chain and a rare one. Most solid state amplifiers now (and since the sixties), and some tube amplifier circuits, being designed direct coupled allows for the need of only a handful of capacitors, where before then they were everywhere. Like the coil, or choke, or transformer, they have been done away with more for cost than for any real sonic advantage (many high end tube amplifiers costing up to $20,000 U.S. use interstage transformers and are said to sound extraordinarily good).

    One of the supposed sonic disadvantages is phase shift distortion. While I understand the concern, I read in Wireless and Electronics World (c. 1989) that to worry about the phase shift caused by capacitors in the audio chain is futile since there are tons of phase shifts introduced in the recording at the studio to begin with. That coupled with the study done according to "The Psychology of Music" we cannot discern phase shifts anyway except under a specific laboratory test. The only real concern for phase shift is when designing a circuit that uses inverted feedback. A shift of a certain amount could cause unwanted oscillation, or insufficient reduction in amplitude, hence poor linearity. More on this later.

    So it should not come as a surprise that some of my solid state projects have capacitors coupling some stages. But what kind of distortions or sonic disadvantages do capacitors introduce in the signal? And how do I choose a value? Type? And what about power supply filtering?

CHOOSING THE RIGHT CAP FOR THE JOB

    Whether we design an amp with direct coupled components or tubes or op-amps, there will come a time where a capacitor is needed, at least at the input. So what value do we make it?

    First we need to know how a cap is made and what makes it work. I will not get too deep into the makeup of the materials or converting stored energy into joules and the like. We'll leave that bit of stuff to those who want to impress someone, and to text references. But we need to understand at least the capacitive reactance, the time constant and the makeup of some of the different types of capacitors and how each performs and which is better than the other for a specific purpose.

    This is but four of the many schematic representations of fixed value capacitors. The ones with the plus sign are polarized capacitors.

    A capacitor is made up of two pieces of metal separated by a non conductor, or insulator. The distance between the plates and the size of the plates make for its capacitance, or amount of charge storage. The plate size allows for the amount of electric charge due to its size, whereas the space between the plates allows for potential capability due to the distance. In other words, the larger plates hold more electrons and the gap or insulation allows for a higher voltage before the electricity just has to jump the gap. So the type of dielectric, or the filler in between makes for the level of voltage. Once the capacitor fills up, it can no longer accept current on its plates. Nothing happens. But if a certain voltage level is passed, it can cause current to jump across the space between the plates and discharge to a certain degree. In capacitors that use an insulating dielectric other than air this is called punch through. Simple, isn't it? It is because an electric current punches through the material.

THE TIME CONSTANT

    When a voltage source is connected to the capacitor, each polarity per plate, the attraction each polarity has for the other causes current to flow into the plates. When an equilibrium of charge potential (voltage) occurs, no more current flows. The rate at which the plates fill up is known as its time constant. What the calculation is for determining the capacitance and time constant from the dimensions of the plates and insulation I leave in my textbooks and do not pretend to know off hand (I do not make capacitors so why should I bother memorizing them?), but I do know that most capacitors are marked with their capacitance and voltage rating, so I don't need to memorize them, and time constant can be determined easily with the equation t=RC. Yup, it is that simple. The time it takes for a capacitor to charge to 63.5% is determined by its capacitance times the resistance in series or in parallel with it.

    For example, If I have a capacitor of 1 microfarad and a resistance of 100 ohms then the time it takes to charge up (to the 63.5%) will be 0.0001 second. If I had a cap of 1000 microfarads and a resistor of 1K ohms it will take that capacitor 1 second to charge. This is very useful in determining several things. One is the value needed for a circuit that needs a certain amount of time for functioning. A delayed turn on circuit for amplifiers is one.

    From the time constant, one can determine also the value of the frequency where the capacitor will have a reactance equal to about 10 - 15 % of resistance. This can be determined by this simple equation f=1/t. So the cap whose time constant above was 0.0001 has a frequency determined reactance of about 15 ohms at 10 kilohertz. We can check this by using the formula for capacitive reactance.

    Oh, by the way, capacitive reactance is the reactive resistance a capacitor has to an alternating currrent. As I mentioned earlier, the capacitor stores energy and stops with a power source connected to it, but this is for DC. AC constantly changes polarity so the capacitor will charge and discharge at a certain rate. But because of its size it can charge and discharge up to a certain point before it resists changing. This is because it will not be able to react slowly enough. It tends to retain more charge during the changing directions because the frequency allows the capacitor do do so due to its time constant. In other words, the lower frequencies will be met with a resistance to change in polarity.

    To explain this more simply, let's say we have a water tank that holds a gallon of water. Now this tank can be filled with 2/3 gallon per second. I then turn on the water source and have it go in one direction. The tank fills up in a bit over one second. It has a valve control to slow the water flow down as it gets filled (Oh, yeah, we might as well call it a toilet tank). But then I decide that I want the water to go back and forth, or alternate. I have it do so at about ten times per second. No sooner does the water flow one way than it needs to go the opposite direction. The tank did not have a chance to fill up during that time because it needs 1 second to be 2/3 full. So the water continues through without stopping to fill the tank, because the tanks not being filled causes the valve to remain open. So there is a relatively free (that is, without resistance) alternating flow. But then I start to slow the reversing down. I slow it to 1 time per second. Now what happens is that the tank fills up but because of the reversal, it drains out and reopens the valve and allows more water to flow back in to fill it up again. The fact that the tanks valve now can regulate the flow is its reactance to the flow of water. If I slow down the process even further, the reactance causes flow to virtually stop during each direction because the water has filled up the tank before its one direction cycle has completed. Water will no longer flow until the direction changes, and the same thing happens to the flow but in the other direction at this slower rate. The flow is therefore reduced in intensity.

    This is the same with a capacitor. Alternating current flows easily as long as the reactance is smaller than the time constant. But as the signal becomes equal to or less than the time constant, then the capacitor resists or reacts to the change in current flow more and more. In other words, the lower the frequency the higher the capacitive reactance.

    This formula shows the relationship:

Xc=1/2PiFC

Where:

Xc = capacitive reactance in Ohms
Pi = 3.14159265359
F = frequency
C = capacitance in farads

    Let's test this using the above example of the  0.0001 time constant. We were given the value of the capacitor as 1 microfarad. The frequency determined by its time constant is 10 kilohertz. So:

Xc= 1/2(3.14159)(10000)(0.000001)

Xc is 15 ohms.

    If we decrease the frequency to 1 kilohertz, then the reactance will be 150 ohms.

    To illustrate this, one can plug in several frequencies for the same capacitor and draw an X-Y chart with frequency along one axis and resistance on the other axis, It will look like this (with both values increasing going away from the X-Y crossing point):

    On the left of the chart, the line starts at infinity very close to a zero frequency. DC does not flow through a capacitor and is considered a frequency of 0.0 Hertz. At the other end is a point where the reactance does not get that much lower as frequency increases. Fact is, it does decrease but at such a low rate that it doesn't matter. Actually, if I were to extend this chart to the highest frequencies we will note increases in reatance and at least one point where it will act as an open circuit. These are where inherent inductance comes into play. These cause the capacitor to act as an inductor where reactance increases in direct proportion to frequency. In other words as frequency gets higher the reactance of an inductor increases, opposite the capacitor. At one point the inherent inductance and capacitance can act as a tuned circuit and produce a near infinite impedance. But those frequencies don't appear in audio, except for the larger value capacitors found in electrolytics.

    Just imagine that as AC flows through a capacitor, the flow causes a corresponding magnetic field to grow and collapse. As this occurs, it induces a current into the other parts of the capacitor. Hence the inductance. The more area there isto induce current the more incutance a capacitor has. Large value electrolytics have lots of "inductable" area.

DIELECTRIC INSULATORS

    There are many materials that are used as the dielectric. Mica, plastic, paper, and ceramic are what come to mind. They are the most popular. Air capacitors are, or were, what were used in radio tuning capacitors. Now tuning capacitors are very small and use plastic insulation. Since they do not see high voltages, one does not worry about punch through.

    Mica was used since the before the twenties. I have a couple of radios from the twenties that have mica capacitors. They are usually in very small value caps for RF stages and for trimmer capacitors. Nikola Tesla recommended it as the insulator of choice for the high voltage Tesla Coil construction in the late 1800's.

    The advantages of using the insulating materials is that 1) higher voltages can be used, 2) smaller values can be made 3) physically smaller capacitors can be made with the same values as larger ones. The example of #3 is that I recently rebuilt a mid 30's radio and needed to replace the filter capacitors for the power supply. The schematic called for two 8 microfarad 450 volt capacitors. I was able to obtain one 10 microfarad and one 20 microfarad capacitor at 650 volts each. Both caps were about 1/2 inch in diameter and about 1 inch long. The original cap was about 3 inches by 2 inches by one and a half inch (it was a two in one block). Certainly a big size difference considering the values.

    Due to the dielectric constant of the materials one can have a larger charge on the plates before sufficient potential will overcome the insulating properties. So #1 is satisfied here. Also, being able to make smaller plates much closer together allows for the making of smaller large value capacitors.

OK, SO WHAT OF IT?

    In audio, we want to pick components that make the listening experience the best it can be. Before I make my comments on the differences in sonic character of capacitors, I would like to make this comment:

    Once we get used to the sound of a certain amplifier and its components, any change of components will sound like an improvement or a degradation. This is an oddity of human psychoacoustics that is inescapable. When we make a change and deem it an improvement, after a month or so we tend to get used to or bored with the sound and believe that making another change has actually made an improvement. However, all we have done is change the condition of the sonic character. In other words, we made a change in the frequency response, even if ever so slightly. This will help us fully understand the following.

    How do I go about picking the best capacitors for my amplifier? Personally, I have heard very little difference among polypropylene or electrolytic aluminum cans or ceramic capacitors. Crazy as this sounds the biggest differences that I have heard came when using two capacitors in parallel to make a larger cap. When I replaced the two with a single one of equivalent value, the sound seemed better. I have read that there is a sonic difference between ceramics and polyester or polypropylene caps, and one brand over the other. But I have also read that some have gotten better results from Sprague orange drops over 'Super Audio ultra mega caps', which cost ten times more than the Spragues. I have no affiliation with them but I prefer Spragues myself, just from good personal experience.

    For interstage connection, I do not recommend electrolytics. They tend to have very non-linear responses (See this test comparison by Steve Bench). I discovered this fro myself by experiment as a lad when I wanted to make a tone control for a radio I had. At first I used the typical values for tone controls, namely 0.1 microfarads. They attenuated the high end but I wanted more of a coutour because I did not like too much midrange. I then played with a much larger value electrolytic. I think it was about 47 microfarad. Perhaps 100 microfarad. In any event the result was interesting. Instead of the typical roll off one would expect, what I got was a response more like a loudness curve. I got attenuation of the mid-range but not the highs, until I fully rotated the control pot. It wasn't until about ten years later that I read an article that said that electrolytics begin to behave like coils above a certian frequency. A couple of years ago a friend directed me to another article which discussed a phenomenon called "soakage". Electrolytics have a tendency to have their plates recharged by charge stored up in the dielectric. So, the cap can actually act as a choke to higher frequencies, having a higher reactance, and not a lower one as should be expected with capacitors.

    This is why one hears a difference in response between electrolytics and other types. It is also another reason that many claim to get a "faster" sound from bypassing electrolytics with a smaller value cap. What is happening is now the higher frequencies are passing what is essentially a block. So bypassing a bypass cap in a stage of amplification that has an electrolytic with a polypropeline of a smaller value, let's say 0.1 microfarad bypassing a 47 microfarad electrolytic, will result in a better frequency response than not doing so.

    Also, since the filters in a power supply are not only there to filter out ripple, but to isolate the stages of amplification from each other, bypassing a filter cap with a smaller value will ensure that all frequencies of audio from one channel of an amp will not bleed over to the other via the power supply. The smaller capacitor also has a much lower time constant, so it can recover from fast attack transients quicker than the larger electrolytic, hence increasing its apparent "speed".

ALRIGHT, SO WHAT VALUE DO I USE?

    For whatever purpose in an amplifer you use, I recommend this rule of thumb: whatever the frequency is, calculate the capacitor to have a reactance of one tenth the load. This has been taught in my school, although some claim that it is not very accurate. However, this alows for an assured "flat" response down (or up) to that frequency.

    For interstage and bypass capacitors, use the lowest frequency you desire to amplify. Let us say you have a cap going to the input of your amplifier. Your amplifier has an input impedance of 100K. You want to amplify down to 10 hertz. With this info we use the above formula for capacitive reactance and say we want a reactance of 1/10th the input impedance, or 10K.

Xc=1/(2(pi)(f)(c))

We rearrange the formula so we can solve for the capacitance value c.

c=1/(2(pi)(f)Xc))

c=1/(2(3.1415)(10)(10 000))

c=1/628300

c= 1.59 uF

    So we need a capacitor with a value at least 1.59 microfarads. I have only seen 1 microfarads and 2.2 microfarads available, so we can go with the 2.2 microfarads.

    For a power supply, however, we have one frequency only to work with, the AC ripple. For most power supplies, this is 120 hertz. This is because the power supply will likely be a full wave one and the frequency of the AC line is 60 hertz. The rectifier in a full wave uses both halves of the 60 hertz. In doing so it doubles the frequency to 120 hertz.

    So now using the above rule of thumb how do we determine the size for the first capacitor after the recitfier (this is the critical one)? First determine the total idle current of the amplifier. Suppose we have a power supply in a tube amplifier of 450 volts. At idle this amp draws a relatively constant 200 milliamps. Using good ole Ohms law we have a constant idle load of R=V/I or 450/0.2 or about 2250 ohms. So we now have a frequency and a load impedance. Let's calculate:

remember, 1/10th of 2250 is 225.

c=1/(2(3.1415)(120)(225))

c=1/169641

c=5.89 microfarads.

    This value is not at all unreasonable. But I would use a 10 microfarad cap. This is the cap before the choke. After the choke use as much as your budget can stand. I actually do not use much more than about 250 microfarads. Not for tubes anyway. I have had much success in doing it this way. Hum is reduced to nothing.

    Now, on a more interesting note, what voltage do we want to use? I personally use enough to cover peak voltage. More is better but not necessaarily practical, if budget will not permit. In the voltage department there is no such thing as overkill, so it wouldn't hurt to go with higher if you can afford it. So, with a power supply voltage of 450, what cap value should I really have as far as voltage is concerned?

    The value assumes that the final voltage is taken at idle, with all tubes warmed up. This implies that the starting voltage could be higher. One way to verify this is to remove all but the rectifier tube and measure the voltage. It should go up to peak. If the power transformer says its secondary voltage is 450-0-450, this means that its RMS value is 450 volts. However, RMS value is actualy 0.707 that of peak voltage. The peak voltage is gotten from taking the full wave and dividing it in half. The top of the wave is the peak. So, multiplying 450 volts by 1.414 to determine peak voltage one gets 636 volts. However, if memory serves, the capacitor will actually see about 90 percent of peak, or about 570 volts. So using a capacitor rated for 650 volts will be sufficient.

    However, some engineers like to go about 50% above peak voltage. This would mean using a capacitor rated for 1000 volts or more. I don't know about you, but 1000 volt caps cost quite a bit more than 650 volters. So my recommendation is use a 650 volter for the first cap, and 450 volters for the subsequent caps, since there is a voltage drop across the choke and the rectifier tube (assumingyou are using a tube rectifier. In lieu of the choke, some amps use a 1 to 5 K ten watt resistor).

    One reason for the recommendation is that since tube rectifiers (indirectly heated cathode ones, that is. Directly heated cathode rectifiers can have full voltage much sooner) warm up as they go, the voltage at the first capacitor rises in concert with the tube, so it may never really see a full peak voltage. By the time the first cap sees full peak voltage the rest of the tubes have begun to conduct, bringing down the voltage to its idle rating anyway. So using a much larger cap is really not all that necessary.

    Solid state rectifiers, however, do turn on instantly. So the recommendation is that you might be better off using a higher voltage rating for the first cap. But the rule still applies for the capacitance rating as for tubes. (I have done this with solid state amplifiers and the results were the same. Ripple reduction to nothing with my scope set at the most sensitive  level.)

    Remeber too that voltage ratings on capacitors are usually for constant voltage. But in order to be on the safe side, use the above recommendation.
 
     Well, this is about as far as I think we need to go with understanding the differences in capacitors and how to choose them. One needs to be moderate when choosing the right values. Do not overdo the values. Some have done this to "extend" the low frequency response only to cause other problems like compression and motorboating. Even if the capacitor's value starts a roll off at a frequency of 40 hertz, it is likely that the negative feedback circuit brings back the low frequency response anyway, since that is one of the functions of NFB. Follow the above guidelines and things will work out well for you.

Have Fun!!

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