[Radio Wrangler]

The lower device looks at the voltage swings on its grid, cathode and anode. It hasn't got a clue what goes on at nodes it's not connected to. Grid goes up 1 volt, cathode stays still, anode to cathode current goes up Gm mA, anode falls 1 volt. Within that triode's own frame of reference, it sees itself as having a gain of -1. These are the voltages across Cga. Cga sees twice the input voltage across it so we could replace Cga with a capacitance twice as big from grid to ground. Miller factor =2.

The upper triode looks at the voltage swings on its grid, cathode and anode. It too hasn't got a clue what goes on at nodes it's not connected to. It sees its cathode current go up by Gm mA, and its grid stay still, so it has to let its Vc fall by 1v. so that it can carry that current. It pulls Gm mA out of whatever impedance the circuitry is connected to, Ranodeload. So the anode voltage falls by Gm milliamps times Ranodeload. The top triode, as far as it can see is a grounded grid amplifier giving unity current gain, for it cannot do otherwise and it sees signal voltages on its cathode and anode of 1v and Gm*Ranodeload volts. Within the only frame of reference available to it, it thinks it has a personal gain of Gm*Ranodeload. Its Cga acts to load the anode to ground, and Cgc acts to load the cathode to ground. At high frequencies these rob some off the cathode current and some of the current into the load. We have three poles in the response.

If we dump the top triode and connect the anode of the bottom triode to where the anode of the top triode went, quite right, the overall circuit gain at low frequencies is the same as it was with the cascode. And we now have only a single pole, but that pole is at a much lower frequency because it now sees the input signal voltage across it times (1+overall gain) Lorts of Miller factor.

So the cascode is a deal with the devil. It costs you an extra valve structure AND needs cathode-heater isolation AND either low cathode-heater capacitance (or chokes) and it gives you more poles in the response. All you get for these costs is that each of those poles is usefully higher in frequency than the single pole of the plain single triode amplifier would have been.

If you're after high frequency amplification, it's not a bad deal.

If you're not, you don't have to spend the money. AND you can get more anode swing for the same HT.

The cascode really is a 2-stage amplifier. Each stage has clear demarcation of its input and output. We can calculate all the signal voltages and currents. Two divisions and we can calculate the voltage gain in each stage. These are real gains, measurable with an AC voltmeter or scope. They look like ducks, they quack like ducks, and by golly they are ducks.

Yes the bottom stage alone, with the top one removed would give the same LF voltage gain. But in the cascode circuit, the bottom valve is NOT alone. It has its friend above it. The anode voltage swing of the bottom triode is modified by the presence of the top triode. In the cascode circuit, what gain the bottom valve would have had in a different circuit doesn't happen. The bottom valve is in the cascode, not in that other circuit.

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Now, cascodes really come into their own with bipolar transistors. Cbc is the C of a reverse biased diode junction. It is a varactor diode! Ugh! The damned thing is non-linear. So the Miller modified pole isn't just low in frequency, it moves with the signal voltage. Each signal voltage component phase and amplitude modulates each other. Ooooh, Narsty!

So cascoding to shove the pole up out of the way reaps extra benefits.

A few decades ago I designed an audio amp for ultra-low distortion even at full welly, and across the full audio band - both at the same time. Cascoding played a big part in pulling off this stunt. It wasn't needed because of particularly high frequencies being handled, it was needed for its benefits in intermod and harmonic distortion at pedestrian frequencies. This amp was ridiculous... a truly stupid amount of overkill and almost completely pointless, but doing it was great fun and it's sat in my lounge for 38 years. Not quite pointless because I learned a bit doing it and that knowledge got re-used all over the place.

A hobby is also a place where you can play with things which could not be financially justified, or any other sort of justified, at work.

David