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Bootstrapped Gain Stage Theory

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  • #16
    Originally posted by SoulFetish View Post
    in the following two variations, it's obvious that the grid of the first triode is bootstrapped (ie cathode follower), but how would we analyze the cathode input impedance of this example? (again, I'm not trying to increase the voltage gain really. I would need to pad the output down anyway)
    [ATTACH=CONFIG]54391[/ATTACH]
    The left tube in this circuit is an ordinary cathode follower DC coupled to a common grid stage. The cathode follower has low output impedance of maybe 1k. As the cathode output is loaded by the cathode input impedance (also around 1k) of the common grid stage, the common cathode input signal will see around 500 Ohm.

    If you're correct about the "feedback effect" by tying the grid to the top of the tail resistor, maybe it might be useful in this circuit. If I tie the grid of the second triode to the top of the tail, could we not take advantage of the presumed effects of feedback? If it does increase the cathode input impedance, would it also not decrease the output impedance at the plate?
    [ATTACH=CONFIG]54392[/ATTACH]
    I am quite sure about the negative feedback effect from connecting the grid to the tail resistor, so I expect the cathode input impedance of the second tube to rise. But the common cathode input impedance cannot get higher than the internal cathode impedance of the cathode follower.

    If it does increase the cathode input impedance, would it also not decrease the output impedance at the plate?
    Not sure, but there is a chance that plate output impedance actually increases. Generally if the NFB signal is derived from output voltage, output impedance decreases. If the NFB signal is proportional to load current instead, output impedance increases because the NFB tries to keep output current constant. E.g. a common cathode stage with unbypassed cathode cap has higher plate output impedance than with bypass cap. Reason is that the signal (without cap) at the cathode is produced by the cathode current = load current and acts as NFB voltage. (Edit: This is in line with your considerations in post #15)
    Anyway the upper limit for plate output impedance is given by the plate resistor.


    But before further speculating on shaky ground if would prefer that you build at least the single tube circuit and measure input and output impedances with different grid connections. This will show if I am correct so far.

    Unfortunately I am not yet good enough to derive the complete set of circuit formulae in a reasonable time (I am learning from Kuehnel and others). So I don't feel really safe to predict the effects of such modifications.
    Last edited by Helmholtz; 07-20-2019, 03:09 PM.
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    • #17
      Originally posted by Helmholtz View Post
      The cathode follower has low output impedance of maybe 1k.
      The 6111 is a high gm tube, and I would take a quick calculation of the cathode follower Zout to be ≈200Ω or so. I could get a better estimate by looking at the rp and gm in the datasheet for these operating conditions. But that shouldn't be too far off.
      I think I'll set up the circuit this weekend and run some tests.
      Would this be suitable for measuring the results?:
      (V1 = unloaded voltage)

      Zin
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      Zout
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      ...(I am learning from Kuehnel and others)
      I really like Kuehnel's material. I bought "Guitar Amplifier Power Amps" and like it a lot.
      Click image for larger version

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      It's one of the big 3 on guitar amp design, IMO. Along with "Designing Tube Preamps" by Blencowe, and "Guitar Amplifier Overdrive" by Neumann and Irving
      If I have a 50% chance of guessing the right answer, I guess wrong 80% of the time.

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      • #18
        The 6111 is a high gm tube, and I would take a quick calculation of the cathode follower Zout to be ≈200Ω or so. I could get a better estimate by looking at the rp and gm in the datasheet for these operating conditions. But that shouldn't be too far off.
        You're right about high gm. From the tube chart I find rp=5K@4mA and =19@4mA. The exact formula for cathode impedance (rp+RL)/(+1) gives 250 Ohm for the CF and 1k for the grounded grid tube. The values calculated from 1/gm are typically too low, especially when there is a plate resistor.

        Your impedance formulae are correct but the the simplest way to determine

        - input impedance is to wire a variable resistor (of say 5 to 10k) in series with a low impedance signal generator and the circuit input coupling capacitor. Feed 200mV. Vary series resistance until the voltage (wrt ground) after the resistor (at the input) is 50% of the signal voltage before the resistor (generator output). Read/measure resulting series resistance=input impedance,

        - output impedance is to load the circuit (after the coupling cap) with a variable resistor of say 20k. Vary resistance until output voltage is 50% of the no-load output voltage. Read resistance=output impedance.

        The principle should be self-explanatory. The max. values of the variable resistors should be somewhat higher than the max. expected impedances.
        Last edited by Helmholtz; 07-22-2019, 02:28 PM.
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        • #19
          Originally posted by SoulFetish View Post
          [ATTACH=CONFIG]54333[/ATTACH]
          LTSpice says the input impedance of the above circuit is 5.68k
          With the 10k cathode resistor shorted it's down to 186 ohms
          [Assuming I didn't mess it up ]

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          • #20
            Thanks. This seems to confirm my NFB theory. Did you use a 6111 model?
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            • #21
              Originally posted by Helmholtz View Post
              Thanks. This seems to confirm my NFB theory. Did you use a 6111 model?
              Yes, I used a 6111 model with B+ set to 100V

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              • #22
                Originally posted by Dave H View Post
                Yes, I used a 6111 model with B+ set to 100V
                Thanks. Soulfetish showed B+=200V, so I assumed a plate current of 4mA.
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                • #23
                  Originally posted by Helmholtz View Post
                  Thanks. Soulfetish showed B+=200V, so I assumed a plate current of 4mA.
                  I've just run the sim with B+ at 200V and it's nearly the same.
                  The 10k cathode resistor increases the input impedance but it reduces the voltage gain to unity
                  With the 10k shorted voltage gain is 17

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                  • #24
                    If you short the 10k resistor instead of AC grounding the grid while keeping the 10k, the cathode input resistance must be below 240 Ohm.
                    Calculating backwards your result of 186 Ohm means a cathode impedance of 830 Ohm.
                    Last edited by Helmholtz; 07-22-2019, 12:19 AM.
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                    • #25
                      AC grounding the grid (capacitor in parallel with the 10k) is the same 186 ohms.

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                      • #26
                        Originally posted by Dave H View Post
                        AC grounding the grid (capacitor in parallel with the 10k) is the same 186 ohms.
                        That's no real surprize as the cap is more or less an AC short. So the cathode impedance will still appear shunted by the low value 240R.

                        Seems I wasn't clear enough. I meant the comparison to the standard common grid wiring where the grid is AC grounded (via a cap) but connected to the tail bias resistor via a large value resistor (470k or 1M) as in a LTP. In this case cathode impedance will be shunted by the complete tail resistance, which should make the input impedance closer to the actual internal cathode impedance. I would expect an input impedance of 800 to 900 Ohm.
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                        • #27
                          Originally posted by Helmholtz View Post
                          Seems I wasn't clear enough.
                          Correct
                          I didn't think it would be any different with a BFC across the 10k but I thought that was what you were asking.
                          With it wired like a LTP (1M, 100n) I get 744 ohms

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                          • #28
                            Originally posted by Dave H View Post
                            Correct
                            I didn't think it would be any different with a BFC across the 10k but I thought that was what you were asking.
                            With it wired like a LTP (1M, 100n) I get 744 ohms
                            Thanks again. What is a BFC?

                            I kind of envy you for your simulation skills. Don't even understand how to make available/include an additional model .

                            O.K., now we know that the internal cathode impedance of the common grid stage is around 800 Ohm and that connecting the grid to the top of the tail resistor increases the stage's input impedance while strongly reducing gain. All pretty much as I predicted. It means negative feedback.
                            Bootstrapping is different, it is positive feedback between in-phase circuit points and "open loop" gain < 1. It actually increases input voltage and thus gain and doesn't noticeably change output impedance.
                            Last edited by Helmholtz; 07-22-2019, 10:30 PM.
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                            • #29
                              Originally posted by Helmholtz View Post
                              What is a BFC?
                              It's MEF slang for a large capacitor. It stands for Big Fat Capacitor or something like that

                              To add the 6111 model to LTSpice I saved the model text (found at diyAudio) as 6111.inc using Notepad then added the spice directive .INC 6111.inc to the LTSpice schematic.

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                              • #30
                                Originally posted by Dave H View Post
                                It's MEF slang for a large capacitor. It stands for Big Fat Capacitor or something like that

                                To add the 6111 model to LTSpice I saved the model text (found at diyAudio) as 6111.inc using Notepad then added the spice directive .INC 6111.inc to the LTSpice schematic.
                                Thanks for both!
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