KISS 125
KISS 125
Fighting capacitances lurking with malicious intent in your amp:
Slew rate current, Miller, stray dogs and bandwidt
by Andre Jute
Just after WW II the PR man at Mahatma Gandhi's ashram was giving a group of American and British journalists the short tour. The Americans were interested in the two nubile virgins the loincloth-clad old sage slept with every evening to keep him warm and to test his willpower. The British, still hungry after war shortages, wanted to know what Gandhi ate.
'Only the simplest food,' the PR man said. 'A little lemon and honey with soda water.'
'Wow,' said the Brits and moved on. (This was before their tabloids became the scummiest in the world.)
Afterwards the Time-Life reporter hung back. 'Aren't lemon and honey and soda water very great luxuries in India?' he asked cynically. 'How can you be so hypocritical as to describe that as simplicity?'
The PR man, who had been an Inner Temple barrister with Gandhi in London a few decades before, knew when he was caught out. 'Quite,' he said smoothly, 'but I never said it didn't cost a fortune to keep Ghandiji in simplicity.'
***
Ultrafi tube amps are like that. The simpler they appear, the greater the mental effort required to win the benefits of that simplicity. There hangs about the apparent simplicity of The KISS Amp 300B a whole miasma of invisible capacitances which can test one's willpower far more than two naked nubile virgins.
Although we commonly say that 'a Class A power tube draws no current on its grid', a power tube requires current from the driver to overcome various capacitance which loiter with malicious intent in your amp. A useful shortcut to half a good answer is slew rate current (which tells us how fast a capacitance is charged up and discharged) and as usual experience provides the other half of the answer. The first half of the answer can be calculated with slew rate formulae and one empirical assumption generously suggested to me by Gordon Rankin (who isn't responsible for what I do with the information) on 15 October 1996 while I was working on an 845 amp:
***
The Slew Rate
SR = 2*Pi*Bandwith*Vmax
Where
Bandwidth = 20kHz or whatever higher frequency your design will pass
Vmax is the maximum voltage the stage will deliver
The input capacitance
Cin = (A + 1) Cgp + Cgc
Where
A = the gain of stage for which the input capacitance is being determined
Cgp is the Capacitance of the Grid to Plate
Cgc is the Capacitance of the Grid to Cathode
The Slew Rate Current
SRC = Cin*SR
Erno Borbely, Jung and Ron Gunzler (according to Gordon Rankin) suggest that the stage current should be 5 times the slew rate current to overcome the input capacitance of the next stage.
The Stage Current
Scur = SRC * K
where
K = 5
***
Bear with me while I put in some numbers:
Desired Stage Current is therefore 5*Cin*SR.
For a 300B,
Cin =9 + (1 + 3.85)*15 = 81.85pf
For a fullrange amp with 80V signal voltage,
Slew Rate = 2*3.14*20000*80 = 10,048,000
(note that to arrive at an irreducible minimum we enter only the audio range)
therefore
Desired Stage Current = 5*81.85*10,048,000
and after moving the decimal we get
4.1mA
***
Mmm. That is of course an absolute minimum requirement. Notice something above? No one has yet counted stray capacitances. In a simple 300B amp strays usually amount to between 15 and 25pf. They too have to dealt with, which is why the constant is a multiple.
We know from experience that a 300B likes more current on the plate of the driver than 4mA. It was the excellent Steve Bench who first suggested to me that 8mA is the right minimum number for a driver for 300B. In fact, this is less of discrepancy between theory and practice than at first appears. We would normally design the amp out to at least 40kHz, not just 20kHz, so the calculated current requirement would match the 8mA from experience without altering the famous constant of 5.
Do the calculations for an 845, which has a difficult signal requirement of around 150V in the more common designs, and you will discover that 20mA is just about a minimum on the driver, which accounts for why some of us laugh when we see designs for 12AX7 driving 845. It also accounts for why I like to drive kilovolt transmitting tubes with a 300B booster amp, or at least a power tube for a driver. The KISS Amp 300B is just such a booster design, requiring only a switch to turn the primary of the output transformer into a choke load on the plate of the 300B and a polyprop cap in series on the output to the grid of the main kilovolt amp. In other words, the 300B is used as a preamp (control amp) tube and as a weapon to absolutely murder Miller.
***
Now we come to the Miller Effect, because we must. Even the exemplary RDH treats this distasteful subject, somewhat akin to removing the nightsoil, less thoroughly than I do here, and believe me, I'm doing the minimum I can get away with and still claim a modest electronic respectability.
Miller is a multiplicatory part of one of three shunt (read "unwanted but unavoidable") capacitances in an amplifier:
Cpc, the output capacitance of the first stage (from plate to cathode)
Cin, the input capacitance of the second stage, which is Cgc (from grid to cathode) augmented by the Miller Effect
Cstray, stray wiring capacitance
These shunt capacitances add up, with the numerals indicating the first and second tubes:
Cs = Cpc1 + Cin2 + Cstray
where
Cin = Ggc2 + Cgp2(A2 +1)
A2 is the amplification factor of the second tube
Cgp2 is the grid to plate capacitance of the second tube.
The Miller Effect is the Cgp2(A2 +1) part of Cin. It is clearly important because the grid to plate capacitance is multiplied by the amplification factor of the tube.
The high frequency rolloff of a stage due to shunt capacitance is
f =1/(2*pi*R’eq*Cs)
where the effective load on the plate is
R’eq = Rg+((Rp*RL)/(Rp+RL))
You can see the important part played by the plate resistance and it isn't rocket science to see that the you should wire tidily and keep leads short to avoid stray capacitances.
***
You can use the capacitances loitering in your computer constructively if you think laterally. For instance, the bandwidth of an amp should be balanced. Any extension below a rather high level, say 50Hz, should be matched by an extension at the top end. Conversely, if the bottom end is being deliberately sloped off early to protect horn drivers (which rapidly become unloaded below Fs), the HF should not be designed out to infinity, whatever the iron may be capable of; it should instead be balanced with the LF you are plotting. One of the tools under your control is the amount of current you put on the driver, and the slew rate concept is your tool to calculate it. That ensures that your amp reaches the bandwidth you design to.
Miller gives you the tools to calculate, with data off the spec sheets for the two tubes and off the schematic of the circuit you have designed, and perhaps to ensure that the amp will not roll off under the bandwidth you are trying to arrange by providing slew current. The calculations are exceedingly tiresome but you can't afford to skip them. Later we will see how to automate all this with a spreadsheet.
***
The question arises, why do you want an amp that has HF extension so far beyond your hearing? What is this 'balance' good for? Does something lie beyond the achievement of 'balance'? The answer is that there is a subjective effect, which ultrafidelista sometimes refer to as 'speed' or the 'fast amp' syndrome, and which novices think is only about undersizing power supply caps. Unfortunately building a 'fast' amp is far, far more complicated than that and definitely requires attention at both ends of frequency scale.
The interrelationships of these factors are not well understood but they are likely to be complicated by the usual difficulties of psychoacoustics. That is one reason I somewhat dislike the sound bite of 'a fast amp' and prefer the more sober phrase 'a responsive amp'.
The implication of this caution is that net gossip that "mo' driva current is betta current" is not necessarily true. There is a correct bandwidth for every speaker/amp combination, and particular correct lower and related correct upper frequencies for each application. If you just throw current at the driver because you have it to spare and the iron can make the frequency, that can easily be as harmful to the sound of your finished amp as not enough current.
Don't skimp. Don't overdo it. Calculate thrice, solder once. An elegant sufficiency will give you the right sound.
THE VOLTAGES IN THIS AMP WILL KILL YOU.
GET EXPERIENCED SUPERVISION IF IT IS YOUR FIRST TUBE AMP
All text and illustration is Copyright © Andre Jute 1996, 2005
and may not be reproduced except in the thread KISS xxx on rec.audio.tubes