Nature of capacitors in circuits

[candidate]

Keeping things simple:

A stompbox circuit has two parts?  The power signal section and the sound signal section?

Still keeping things simple: 

Capacitors do two things?  Process power and process frequencies?

In different sections of a stompbox circuit I'm guessing capacitors are capable of both their duties, perhaps even at the same time, and if so how do their functions interact.  How well can a capacitor store charge while filtering a frequency?

[Ripthorn]

A capacitor does both jobs at the same time, it doesn't care what part of the circuit it is in.  The impedance of the capacitor depends not only on its capacitance, but also on the frequency.  When it is filtering power, the capacitor is simply wired so that it only passes DC to the components down the line and it shunts AC (or the ripple on the DC).  When the capacitor is set up like an input/output cap, it is wired to block DC and only let AC pass through.  How much AC is passed in either case depends on the frequency of the AC signal (which is all the "sound" portion of a circuit refers to).  That is why bigger caps keep more bass when set up as a DC blocking cap and why bigger caps reduce how much ripple is on the DC when set up as an AC shunt.

So to recap, a capacitor only does ONE thing, but depending on how you connect it to the rest of the circuit, it can accomplish several different results.  It's not just that a capacitor stores charge (though that is what it does), it's also about how that capacitor behaves after it is charged and depending on what kind of voltage is fed to it.

[bigchasbroon]

 ;Dn

This is great stuff can anyone show some examples?

[R.G.]

A capacitor is a thing which stores electrical energy in an electrostatic field. It consists of two conductors separated by an insulator - that's all that's needed.

For a short intro to caps, read "How it works" at geofex.com. In fact, read all of geofex.com and then ask questions.

The voltage on a capacitor is proportional to the charge you put into it, and follow the relationship Q (charge) = C* V (voltage). In fact, capacitance itself is defined as the ratio of the voltage divided by the charge, just like resistance is defined as the ratio of the voltage you get when you force a current through it, or R = V/I.

More interestingly, capacitors delay voltage build up. If you investigate what happens when you take a battery or some source of electrical current and connect it to a capacitor, you find that the voltage cannot change instantly like it can on a resistor. You have to shovel electrical charge in to make the voltage change, according to V = Q/C from above. So the voltage on a capacitor will ramp up, not step up instantly. There's an equation for this, of course: I = C dv/dt, which looks suspiciously like calculus, but means:

=> the current into or out of a capacitor is equal to the capacitor's value times the rate of change of voltage across the cap in volts per second <=

[/b]

This one property is responsible for both the frequency filtering, storage, and DC blocking properties of a capacitor. You push charge into a capacitor, and its voltage builds up at a speed dependent on how much current you push in and the value of capacitance. When you quit pushing, the voltage remains there, and it will come back out if it can. If it can't come back out (that is, there is no conductive path to let it out) then it will stay there. That's why capacitors do all of the three major applications for them at the same time. It's all the same to the capacitor.

Capacitors used for blocking DC and letting AC through between stages use the property that once the capacitor is charged up to the difference in DC voltage between stages, the output from the first stage will pull one side of the capacitor up and down; since this voltage can't change instantly, the other side of the cap, connected to the second stage input also is pullled up and down, transferring the signal. The capacitor DOES start charging up as the signal is transferred, but it charges up on way the same amount that it discharges the other way as the signal goes first one way, then the other. And the value of the capacitor chosen is big enough that the capacitor never gets the chance to "eat" much of the signal by charging up either way.

In fact, if you look at it right, that is how a blocking capacitor causes bass rolloff. At low frequencies, it has a significant charging/discharging effect, sufficient to cause some signal loss when it interacts with the resistances it's connected to. Hence the need to make coupling capacitors big enough to not lose signal at the frequencies you want, and the need to calculate them compared to the resistances in the circuit.

And that's the same property which makes them useful for filtering: a cap in series with a signal but loaded by a resistor lets through high frequencies better than low frequencies because the voltage across it can only change at a speed determined by the current pushed into/pulled out of it; the resistance to ground after a series capacitor reacts equally well at all frequencies, so the capacitor lets through high frequencies to this resistor much better than lows. If you reverse the two positions, putting signal into a series resistor followed by a capacitor to ground, the capacitor lets high frequencies through to ground better than lows because its voltage to ground can't change any faster than the resistor will let through signal current. So the lows come through, the highs get shunted to ground. And DC comes through perfectly, because the cap is an insulator to DC.

And that's how power supply filters work. Big capacitor, low resistance. Lots of charge stored in the cap to ground by very low resistance from the voltage source (usually transformer and diodes) in widely spaced pulses charge up the cap to a DC voltage. Between pulses, the capacitor lets the circuit have the stored charge. The voltage across the cap rises quickly during charging, but only a small fraction of the DC voltage. The voltage drops slowly while the circuit uses some of the stored charge between pulses.

So all of the uses for a capacitor come from the one fundamental property of storing energy in an electrical field by forcing charge to be separated across an insulator.

[candidate]

So the capacitor is charging and discharging at a frequency of hertz?

[R.G.]

Capacitors charge and discharge at a frequency of whatever current is pressed into them. The bigger the capacitor, the more current ( that is, electrical charges in motion) is needed to raise the voltage. A one microfarad cap's voltage rises by one volt if you force one micro-coulomb into it. Since one ampere per second equals movement of one coulomb, then you could raise the voltage on a 1uF capacitor by one volt by supplying it with one micro ampere for one second.

If you had a 0.01uF capacitor (100 times smaller than the 1uF) then the same 1uA for 1 second would raise its voltage by 100V.

Notice that the capacitor doesn't much care how fast its voltage rises if you have the current available to pay for that rise. The same 1uF cap that rose 1V in one second with 1uA of current will rise 1V in one microsecond with one ampere of current. So you CAN drive a 1uF capacitor to charge and discharge one million times per second if you want to build a circuit to force one ampere into and out of it a million times a second. In fact, the gates of many big power mosfets are best described as 1nF to 2nF capacitors, and the gate drivers needed to turn these things on and off in sub-microsecond times have to supply as much as several amperes for short times.

In a power supply, the filter caps are charged up to, say 10V. The load may be 100ma, and it will drain a 2000uF capacitor down by V = i/C per second. If I is 100ma, and C is 2000uF, then the voltage declines by 0.1/0.002 = 50V per second. Luckily, the capacitor is recharged by the power supply rectifier diodes twice each power line cycle or every 8.6mS, so the voltage only drops by 50V/sec times 0.0086 seconds, or 0.43V before another charge pulse comes along. It's charging and discharging 120 times per second.

If you took the same 2000uF cap and hooked it up to a source of 1000hz, then the voltage across the capacitor could only change by 0.12V if it transferred the same current - now it's passing the 1000Hz through it with very little change in the capacitor voltage. At 1Hz, the same capacitor would charge and discharge by 120 V every cycle, and so it would hardly pass any of the "signal" - it's all taken up in the capacitor charging and discharging.

Does that help or is it confusing?

[Eb7+9]

in practical terms a capacitor is basically a (quasi-instantaneous) charge counter - the voltage across a capacitor "measures" the amount of charge differential found across its plates ... this takes place through the relationship V = q/C (where q = total charge)

recall that charge equals sum of electrons, know the voltage across a capacitor C and you know how many extra electrons lie on the negative plate

---

the more complex concept of Current now involves a definition based on Differential Calculus, namely dq/dt = I
along with V = q /C this leads to the following: dV/dt = (1/C)*dq/dt = I/C ... which defines slewing (volts/sec)

by the use of a basic theorem in analysis we can also write equivalently q = Int(I) over time ...
hence the voltage across a capacitor at any point in time is the result of a running Current "integration" - or a continuous sum of charge going in and out of the capacitor ... that's what theory really tells us

For example, a large capacitor that has relatively little current drawn from it will have a steady voltage (dV/dt low) by the equation dV/dt = I/C ... this represents the situation (hopefully) found in some filtering cap applications - similarly this equation explains the high ripple when larger amounts of current are drawn from a rectifier-fed filter cap ... the same equation is used in analyzing many ramp circuits as well

if you want to analyze what capacitors do in signal processing circuits you can't do it in isolated terms ... also, the idea of frequency (sine waves) doesn't speak for all cases of signal transfer - most people seem to assume that capacitors block DC currents but there are cases were an equivalent DC current will flow through a cap by way of non-linear mechanisms ... in these cases the basic "charge measuring/integrating" capability of the capacitor still holds, and its linear (imaginary phasor) definition starts loosing its usefulness completely

[JKowalski]

For a visual look at how capacitors work, check out this site:

http://falstad.com/circuit/e-index.html

It shows you the voltage and current in each section of the circuit over time on the wires and in the scope (in the scope the current is yellow and the voltage is green)

Very useful. Note that you can change the value of the circuit components (right click, edit) and even build your own circuits (it's actually a simple java SPICE program!)

[welcomb]

wow! thanks R.G.

You know when I started getting into pedal building I tried googling on how exactly capacitors affect freq roll-off, based on the way they function. I never managed to find that information, just people telling me that bigger caps = lower freq. After a while I kinda gave up searching, and now you hit the nail on the head!

Thanks so much!