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Output impedance of transformer-coupled cathode follower

I want to transformer-couple the final CF stage of a pre-amplifier. 12AU7, 200 V B+, 5 mA, 20 K cathode resistor. Transformer's primary is connected across Rk via coupling capacitor. Transformer's driving impedance is CF's output impedance, something like 200 Ohms. So far so good, everything is straightforward.

Now, remove Rk and capacitor, and wind transformer's primary with high resistance wire, so that its DC resistance is 20 K. What will be transformer's driving impedance with this modification?
 
Another way to frame this question is to ask if the lumped-value model of a transformer, where primary resistance is in series with the indealized "inner transformer", is still accurate at extreme conditions. Very interesting, and I really couldn't predict the outcome.

All good fortune,
Chris
 
It would be very lossy. Probably no high frequency response either. How you would get the DCR that high would be beyond me - it would probably take 1 mil die bond wire (50 AWG), and that normally isn’t enameled. Might not handle the 5 mA when coiled up like that either.

If you want to eliminate the coupling cap maybe drive it differentially. Two k-followers, opposite phase. Use a DC servo to enforce DC balance if you want to eliminate all DC primary current. I was working on a preamp that had low Z balanced outs (pair of 6KV8A) using the power pents as the followers, and the 12AT7-like triodes as an LTP, degenerated to a gain of 2. But I was using output caps.
 
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It would be very lossy.
There is no power transfer involved. Transformer secondary will drive a grid, which is a high impedance load, almost infinite.
Probably no high frequency response either.
Why?
How you would get the DCR that high would be beyond me - it would probably take 1 mil die bond wire (50 AWG), and that normally isn’t enameled. Might not handle the 5 mA when coiled up like that either.
I have Isabellenhutte Heusler 0.04 mm (1.6 mil) enameled manganin wire with additional polyester sheath. 360 Ohm resistance for 1 meter. 5 mA is within its current rating. The whole winding will dissipate 500 mW, so transformer will be slightly warm.

I have a Ferranti interstage transformer whose secondary, wound with 0.03 mm copper wire, has DCR of 17 K. In this case, high resistance is beneficial because it dampens transformer's self-resonance.
If you want to eliminate the coupling cap maybe drive it differentially. Two k-followers, opposite phase. Use a DC servo to enforce DC balance if you want to eliminate all DC primary current. I was working on a preamp that had low Z balanced outs (pair of 6KV8A) using the power pents as the followers, and the 12AT7-like triodes as an LTP, degenerated to a gain of 2. But I was using output caps.
That's a valid approach. More complicated though, as it will require second CF tube, phase inverter somewhere upstream, and dc current equalization circuit.
 
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Transformer's driving impedance is CF's output impedance, something like 200 Ohms. So far so good, everything is straightforward.
Now, remove Rk and capacitor, and wind transformer's primary with high resistance wire, so that its DC resistance is 20 K. What will be transformer's driving impedance with this modification?
Imagine there is a 20K series resistor between the CF and the 'perfect' transformer. Your driving impedance is now 20200 ohms.
 
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There is no power transfer involved. Transformer secondary will drive a grid, which is a high impedance load, almost infinite.
Why in the world would one need a 200 ohm source to drive a grid - through a transformer? Unless you’re trying to do 100:1 or 1000:1 step up. Then you end up with significant power transfer just driving the reflected input capacitance. That makes a voltage divider with the now 20.2K source, and eats into your HF response.
 
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Imagine there is a 20K series resistor between the CF and the 'perfect' transformer. Your driving impedance is now 20200 ohms.
I tend to agree.

Another look at it is figuring series resistance in the primary circuit. This series resistance is the cause of transformer distortion: distorted magnetizing current is converted into distorted voltage in the series resistor, be it output impedance or winding resistance.

There is a rule of thumb about effectiveness of decreasing driver impedance for improving transformer performance: driver impedance lower than transformer's DCR doesn't result in much improvement. From this rule, it doesn't matter that CF output impedance is 200R, because 20K primary resistance swamps it out.
 
Why in the world would one need a 200 ohm source to drive a grid - through a transformer? Unless you’re trying to do 100:1 or 1000:1 step up. Then you end up with significant power transfer just driving the reflected input capacitance. That makes a voltage divider with the now 20.2K source, and eats into your HF response.
The idea was to avoid coupling capacitor at CF output, but, as it turns out, the price is 100-fold increase in output impedance.
 
If there really isn’t a load other than the reflected input capacitance of the tube being driven, the coupling cap won’t really hurt anything. Because at low frequencies there really isn’t much load and the LF corner will depend more on the trafo than the cap.
 
If there really isn’t a load other than the reflected input capacitance of the tube being driven, the coupling cap won’t really hurt anything. Because at low frequencies there really isn’t much load and the LF corner will depend more on the trafo than the cap.
It is same thing with parallel feed interstage transformer, or with coupling capacitor in general. If capacitor is large enough, there is little signal voltage across it, and little signal current through it, so in theory it should not cause distortion. But in practice we know that coupling capacitors do cause coloration.
 
I assume the capacitor is there to block DC current from the winding and core. Your plan stills have DC current, doesn't it?
DC current through transformer is a secondary consideration. The first concern is providing proper DC operating point for the CF tube. If transformer is connected directly across the cathode resistor, it will short it for DC.
 
Since the primary DCR is low, can't you connect cathode to opt primary and then 20K resistor to ground but decoupled with a high value cap? Similar to below?

ciuff3_2.gif


cf-xfmr-schem.jpg
 
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Yes, it can be done this way. But 1 K cathode resistor is too small.
The first schematic was found on the internet just as an example. Plug into whatever value that fits your need. The second schematic is closer to your idea, if direct coupled.

If cap coupled, RK plus the DCR of primary form the bias for the cathode follower.
cf-xfmr-cc-schem.jpg
 
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