'Miller' Caps: in a nutshell, what's the story?

[Bucksears]

Before I finish up with completely redesigning my Dr. Boogey PCB with 'Miller' caps (and spaced a little farther apart so the components aren't right on top of each other), I guess I have to ask: what's the concept behind this method? Do they 'round off' some of the treble to make it less harsh, or does it affect the distortion in any way?
I know this has been covered before, but doing a search for 'Miller Caps' in the forum, you get several hits back that just mention it in passing.

Thanks!
- Buck

[Sir H C]

The idea is that when you use a capacitor with voltage gain across the two ends (such as between the base and collector of a transistor in the common emitter configuration), the gain effectively multiplies the value of the capacitor by the gain.  Called the Miller effect, so the capacitors used for this are called Miller capacitors.

[Bucksears]

Thanks, Sir HC.

So, what is the audible difference in this method?

[Sir H C]

Well it is used usually to roll off the highs to keep things from oscillating.  If the gain goes up, the corner frequency for the gain roll-off goes down so that you end up with the same bandwidth for the circuit (or closer).  It is a way to use smaller, cheaper capacitors to get the roll-off frequency.  Also used in ICs because you can get away with a smaller capacitor on the chip (capacitors on ICs take up a lot of real estate and therefore cost).

[R.G.]

To... um... amplify on that a bit:

Assume a circuit where there is a voltage amplifier of gain Vg, with input resistance Rin and some capacitance Cin from the input to ground. The signal source impedance Rs (presumed resistive to a first order for audio) reacts with that input capacitance to form a low pass filter. The input resistance of the amplifier is in parallel with the capacitance to ground.

At frequencies where the capacitor doesn't shunt the signal to ground, the amplifier gain is unaffected by the capacitor. At very high frequencies, the cap to ground acts like a more-or-less dead short, shunting all of the input signal current to ground. The frequency at which this starts to happen can be computed, and for amplifiers which have Rin much larger than Rs is F = 1/(2*pi*Rs*Cin), just the rolloff frequency of the Rs and Cin. If Rin is not much greater than Rs, it can still be computed easily, but you can't ignore Rin.

Cin "eats" some of the signal current by shunting it to ground away from the input terminal. We'll come back to this concept in a minute.

Let's further assume that the amplifier is inverting, and has some feedback capacitance Cf.

The feedback capacitor has a voltage on the output side of -Vg*Vin (the amplifier is inverting) and on its input side of Vin. So the total voltage across it is Vin - (-Vg*Vin) or Vin * (1+Vg).

For AC signals, a current must flow through the feedback cap. That current is the voltage acrosss the cap divided by the cap's impedance, or Icf = Vin * (1+Vg) . This currrent must come out of the input node - the output of the amplifier is sucking current away from its input.

Remember Cin? It too is sucking current away from the input. The current it sucks is Vin/Xcin. The feedback cap sucks (Vin/Xcf)*(1+Vg).

So a feedback cap sucks current away from the input of the same amount as an input capacitor to ground that is the voltage gain plus one times larger. That is,

A feedback cap looks to the circuit like an input capacitor that is the voltage gain times larger. The capacitor has been "multiplied" by the voltage gain of the circuit. It is common to ignore the "1+" because for gains over ten, it makes no significant contribution.

There are other places where voltage gain multiplication of capacitance happens, notably in the Vox Wah circuit - see "The Technology of Wah Pedals" at GEO.

[Bucksears]

Thanks guys.
I think I'm going to socket all of the Miller caps in the Dr. Boogey and Plexizer and see if there is a difference between using all of them vs. using a partial compliment.

- Buck

[Ardric]

In the terrific Fetzer Valve article at ROG, they refer to the 220pF caps from gate to gnd as Miller caps.  I guess this is a bit of a misnomer, as the caps aren't from gate to drain and multiplied by gain.  Tubes and FETS have a small built-in capacitance that does this whether you want it or not.  In the usual tube guitar amps, the tube's own natural Miller capacitance rolls the high end off to good effect.  The JFETs roll off much higher, so the goal is to add a cap to the JFET to simulate how a tube rolls off.  Adding it as a true Miller cap, from gate to drain, would make the proper cap value highly dependent on the gain of the JFET in the circuit, so it should really be a small trimmer cap (!).  Adding it as a low-pass RC filter from gate to ground, with that gate series resistance, allows the correct cap value to be known regardless of the JFET or it's gain.  Right?

[Ardric]

This reminds me of a trick that my father showed me when I was a little kid.  I didn't really understand it at the time, but it might be cool to try now.

He called it a "gimmick" capacitor.  Take two short pieces of insulated wire and twist them together along their length.  Then connect them to grid and plate, or in this case gate and drain.  The wires twisted closely together but not touching forms a very small-value capacitor, perhaps a few pF.  The longer the twisted together section, the higher the value of cap.  The voltage rating is the insulation breakdown rating of the wire (ie, huge).  You can make it longer than you need, then shorten to value.  Instant variable miller cap.

With all the gain we're trying to get out of these amp sims, maybe we should also be looking at inductors or ferrite beads.

[Alex C]

He called it a "gimmick" capacitor.  Take two short pieces of insulated wire and twist them together along their length.  Then connect them to grid and plate, or in this case gate and drain.  The wires twisted closely together but not touching forms a very small-value capacitor, perhaps a few pF.  The longer the twisted together section, the higher the value of cap.

I've heard of this in Craig Anderton's Electronic Projects for Musicians, though I've not tried it.  If I ever run out of low-value caps or feel the urge to tinker, I'll give it a go.

[mojotron]

I think the way that was done (going from gate to ground) in the Fetzer valve write-up is due to not wanting to require a 2pF cap (which I think is hard to find/expensive) from gate to drain.

On the Plexizer, I put these in gate to source as it's a lot easier to layout that way when you know there is a film bypass cap on the source. Note that you really just need C2 and C8 in that circuit: C9 was a 'happy accident' - generally a source follower has unity gain so a Miller C would be just ~2pF - C9 might add some bite (very subjective - not really rational) - but I thought this one could go away. Likewise, C15 and C17 could go away as well - that is not really where the gain happens in that circuit - but they give a slight additional extreme high-end rolloff - I hear a little less shrill when dumpping a bunch of high-end into the front end of this circuit and after building the Dr B I was concerned about squeal so I left them in. That said, when I got it how I liked it I just left it alone and tried to not cost-reduce it as the difference is less than 10 cents.