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While working on the tube aging page I came across several articles where bandwidth of an amp was discussed. On forums there were discussions as well, mostly of people that commented on others with remarks like: "The output impedance of that stage is far too high", That tube is not suitable for this ..." and "The resulting bandwidth will be far too low", "Don't forget the miller capacitance".
Well, I discovered that while most remarks are made with solid design practises in mind there are not many examples found where people actually prove why they are right. This must be frustrating to others that are too young or unexperienced in this field, and to which these remarks are meaningless without further explanation.
Not that I feel an expert in this field; I picked up on tubes and electronics far too late, but I've read several sources and in order not to make some mistakes again myself I decided to write up this page.
The bandwidth of an amplifier of amplifier stage is the range of frequencies that are transferred from input to output with the right and designed gain. Mostly this is expressed in dB, where the frequency response must be within -3 dB for the amp from the lowest to the highest frequencies. In an audio amp we want frequencies from 20 to 20,000 Hz to pass in the amp, since this is more or less the maximum the humans can hear (we can feel lower frequencies and we notice higher freqs as they interact with lower frequencies and we miss them if they're not there). So, to be on the safe side, we design amps mostly with a desired bandwidth of 5 Hz to 20,000 Hz or more.
Now, we know that most tube amps have a hard time with low frequencies. That is because stages of an amp, and connections between amp are not DC coupled. Therefore, we use capacitors on inputs and/or outputs to prevent DC voltages to enter the next stage. The side effect is that these capacitors and cathode bypass caps must be of such a large value that we do not loose the lowest frequencies. (And we know that they must be of good quality since that affects the sound).
The higher frequencies are affected by the miller capacitance. This is the capacitance between grid and plate of the next tube multiplied by the effective amplification factor of that stage. That capacitance makes that (audio) signals on the grid (AC) are shorted to the plate. And since the plate has a connection to B+ which is grounded for AC signals it means we will loose audio signals as soon as the capacitance is so high that it shorts frequencies high in the audio band.
Bandwidth for high frequencies is defined by the following formula, but only for open loop gain. When feedback is used, normally gain decreases but bandwidth increases.
But as always the exact defnition of the parameter determines whether or not the output of our calculation will be close:
With these valuas it is relatively easy to compute some values.
Nohing we did not knew already, but now with some calculations that support it.