This is a simplified schematic of the circuit:
I would much appreciate it if anyone with greater understanding could chime in and settle this once and for all.
The main problem I am having here is how to calculate the input resistance of the cathodyne and this is slightly complicated by the model of an ordinary gain stage that Blencowe uses in Fig.10.3 (page 180) of 'Designing Tube Preamps for Guitar and Bass'.
Aiken in his whitepaper 'What is Negative Feedback?' https://www.aikenamps.com/index.php/wha ... e-feedback discusses how we can calculate the input resistance when there is no physical resistor present...
This is in the context of a discussion about global negative feedback with a description of the Fender AB165 Bassman however, and Blencowe treats the calculation of input resistance differently...In the other case, the feedback is applied to the "signal" side input of the phase inverter. This forms an inverting amplifier configuration, with the gain being set by the ratio of the value of the feedback resistor to the "input" resistor. The input impedance of this type of global negative feedback amplifier is set by the value of the input resistor, so care must be taken in the design of the circuit to avoid loading down the previous stage, as the value of the input resistor usually must be very low in order to get any decent amount of gain with not too large a feedback resistor value. In some cases, there is no input resistor at all, so the effective value of the input resistor is the output impedance of the previous stage. In either case, the overall feedback gain can be set by varying the feedback resistor...
In Blencowe's fixed bias model of the cathodyne in https://www.valvewizard.co.uk/cathodyne.html
or, what we might transpose as Rf || Rg in the simplified Tweedle Dee schematic above. But the fixed bias cathodyne model he uses there is not exactly equivalent either with his R1 attached directly to the HT (above - or before - the plate resistor) and his R2 bypassing Rk all the way to ground. It isn't too far a stretch to imagine the fixed bias model here could be applied in the context of a LNFB net but it's never as straightforward as it seems (it seems!) and in chapter '10.7: Effect on Input and Output Impedance', (page 184) he expresses a formula which demonstrates that when feedback voltage is applied in parallel with the input voltage, that is, when feedback is applied to the input resistance, the input resistance is reduced.The input resistance of the fixed-biased version is R1||R2...
Rin (with feedback) = Rin(1 + Ao) + Rin + Rf/1 + A
When Ao = open loop gain, and A = closed loop gain.
[Edit: I am updating the subject lines of my posts here because Dumble's cathodyne features both a LNFB and variable resistor (trimmer) at the cathode. I could treat the effect of the trimmer separately in its own thread but the NFB and the trimmer are integral to the PI and it makes sense to treat them under the same thread. Please also bear in mind that no-one, to my knowledge, has adequately treated the subject of Tweedle Dee's cathodyne phase splitter before and some of the early mathematical proofs are exploratory. Following the arguments though, the problems are resolved and solutions found.]