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Bootstrapped Gain Stage Theory

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  • #31
    Originally posted by Helmholtz View Post
    Thanks. Soulfetish showed B+=200V, so I assumed a plate current of 4mA.
    I may have made a mistake in the tail resistor/biasing resistor when I drew up the load line. I may not have accounted for twice the bias current from both tubes! lemme go back and double check.

    edit: looks like I took into account the idle current of both triodes, with ≈80V across the 10k resistor at 8mA
    Last edited by SoulFetish; 07-25-2019, 02:27 AM.
    If I have a 50% chance of guessing the right answer, I guess wrong 80% of the time.

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    • #32
      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.
      I signed up on diyAudio, but I can't download attachments yet. Could you post the 6111 model here, Dave? (unless it was written out as txt in a post?)
      If I have a 50% chance of guessing the right answer, I guess wrong 80% of the time.

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      • #33
        Originally posted by Dave H View Post
        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
        This makes sense, since when operating like this, it's essentially running like an unbalanced cathodyne phase inverter. I would think just under 2/3rd (or so) of the voltage at the plate is dropped across the 10k tail resistor (180° difference in phase)
        Still, I would've thought that if shorting the 10k resistor produced a gain of 17, then you would still see a gain of 9-10 as drawn? unless the added negative feedback reduce the already small amount of gain to practically nothing.

        Dave and Helm, appreciate your thoughts and simulations. I had a good hunch that the input impedance could be increased (although I was incorrect as to why). But, the simulations indicate that the input impedance increased x30. I'm still curious how the output impedance is affected. Hopefully I can either try another LTspice sim or take some actual measurements soon
        Last edited by SoulFetish; 07-25-2019, 02:59 AM.
        If I have a 50% chance of guessing the right answer, I guess wrong 80% of the time.

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        • #34
          Bootstrapping can also be employed to increase the gain of an inverting gain stage, as Merlin Blencowe demonstrated in the ‘designing tube preamps for guitars’ books. Works the same way helmholtz describes above: in-phase signal is inserted at the split point of a split plate load resistance, which makes the current through the ‘lower’ load resistor appear greatly reduced (or the load appear infinitely large), which increases the gain of the stage.
          Attached Files
          Last edited by tubeswell; 07-25-2019, 06:02 AM.
          Building a better world (one tube amp at a time)

          "I have never had to invoke a formula to fight oscillation in a guitar amp."- Enzo

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          • #35
            Originally posted by tubeswell View Post
            Bootstrapping can also be employed to increase the gain of an inverting gain stage, as Merlin Blencowe demonstrated in the ‘designing tube preamps for guitars’ books. Works the same way helmholtz describes above: in-phase signal is inserted at the split point of a split plate load resistance, which makes the current through the ‘lower’ load resistor appear greatly reduced (or the load appear infinitely large), which increases the gain of the stage.
            Right. I've been thinking about the difference between increasing the input impedance by bootstrapping the circuit we've been discussing above and the degenerative "grid feedback" as it is drawn.
            I've come up with different circuit with a bipolar supply which would bootstrap the stage using positive feedback into the cathode.
            Here is the simplified grounded grid, single triode with a bootstrapped cathode:
            Click image for larger version

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            I believe this would increase the input impedance, but unsure if it increases the gain of the stage. The value of the feedback resistor off the plate could be adjusted for gain and stability.

            Here is how I would implement it into the dual triode, cathode coupled cascode mixer I posted.
            Click image for larger version

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            edit: scrap this idea. I'm not sure if it's worth a damn after thinking about it some more.
            Last edited by SoulFetish; 07-25-2019, 08:11 AM.
            If I have a 50% chance of guessing the right answer, I guess wrong 80% of the time.

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            • #36
              Originally posted by SoulFetish View Post
              I signed up on diyAudio, but I can't download attachments yet. Could you post the 6111 model here, Dave? (unless it was written out as txt in a post?)
              Here's the 6111 model. I copied the text from post #848 - here

              6111.txt

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              • #37
                I had a good hunch that the input impedance could be increased
                But the cathode input impedance of the complete cascode will still be low. I only expect an increase from about 190 Ohm to 240 Ohm.
                - Own Opinions Only -

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                • #38
                  I'd approach any design aimed at wringing more gain out of a tube, by thinking about how it compares to an efficient loadline in a common cathode amplifier, and then work backwards. So the starting point is to follow the old formula of aiming for a plate idle voltage that is 2/3 HT . With HT = 200, this is 133.2V. The 6111 Pmax = 1.1W. seeing as how rp = 4k, then Rp should be about 8k*. I ran a load line using the Philips datasheet, and this looks about right (see attached).

                  *This follows the other old formula that ideal load resistance is rough equal to 2 x rp. ;-)

                  Splitting this into a cathodyne, that's 4k for each load resistor, with the plate sitting at roughly 166V w.r.t. HT and the cathode sitting at 34V w.r.t. HT.

                  If you want to anchor the grid, then aim for the grid to sit at -4V w.r.t the cathode i.e. 30V w.r.t. HT (or -70V in your dual rail supply). There are several ways of accomplishing that.

                  To implement your simplified circuit, the split load for cathode load resistor would use a pair of 2k2.

                  But if you want the grid to sit at 0V in your dual rail supply, then you need to unbalance the load considerably in order to get the tube to bias adequately, which means reducing the plate load resistance and increasing the cathode load resistance . My hunch is you won't get the cathode to sit where you want it without losing the plate load altogether, at which point there is no point in the feedback mechanism.

                  So... you need to boost the current somehow in order to allow you to progressively increase the (unbalanced) load resistances whilst maintaining enough current to keep the tube 'on'. So maybe you could turn your other triode into current source? (e.g. by substituting it for the plate load resistor in a totem pole arrangement?) It still probably won't enable you to get the grid to sit at 0V though. Sorry for adding to the madness...

                  Edit: with a 42k load and HT=200V, and -1v bias, the plate is sitting at at 50V w.r.t. HT (-50v in your dual rail supply) with s tube current of about 3.5mA. Which still leaves the issue of how to get the grid at 0v in your dual rail supply. And you wouldn’t have much signal headroom
                  Attached Files
                  Last edited by tubeswell; 07-25-2019, 10:11 PM.
                  Building a better world (one tube amp at a time)

                  "I have never had to invoke a formula to fight oscillation in a guitar amp."- Enzo

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                  • #39
                    Did you measure output and input impedances of the cascode variants in the meantime?
                    - Own Opinions Only -

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                    • #40
                      Originally posted by Helmholtz View Post
                      Did you measure output and input impedances of the cascode variants in the meantime?
                      I set up a workable prototype board to wire this up, but got distracted by a project within the project and lost focus.
                      I was going to build myself a Wein Bridge oscillator, because the Velleman signal generator I'm borrowing kind of sucks. But I wasn't sure of a suitable lamp I should use as a ptc stabilizer, and drifted farther and farther into the ether of attention deficit disorder..... But I back now! Thanks for snapping me out of it.
                      I'm going to do some wiring tonight and see how far I can get. In lieu of a proper bench power supply, I'll probably tap of the supply from my amp.
                      If I have a 50% chance of guessing the right answer, I guess wrong 80% of the time.

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                      • #41
                        The prototype board is all set to go.
                        I picked up a Heathkit IG-18 signal generator for free and have been working on it to calibrate it. There are know issues caused by the loading of panel meter connection, so I disconnected the panel from the circuit, and turned the symmetry control fully counter clockwise to kill any signal feeding the square wave generator. I also put pretty much exact spec. cap values in the frequency multiplier switch using tektronix polycarbonate capacitors. The from 1kHz to into the +100kHz range, the sine wave look really clean with a very stable amplitude. (although it take a few cycles to bounce into stability.). The biggest issue left is as i decrease in frequency down from 1kHz, I get some pretty heavy power supply modulation of the output. I'll put a proper regulator circuit and probably replace modify the filtering when I get the chance, and hopefully that will clear things up.

                        I needed to get the IG-18s output impedance to make our circuits input impedance measurements.
                        So, I adjusted the unloaded output voltage to 1.002V RMS (2.833V P-P).
                        Then connected to a load resistor measuring 1.005kΩ, I measured a voltage of 512mV RMS (1.447V P-P).
                        Using the formula I posted earlier for Zout, the output impedance works out to me 961.82Ω.

                        I think it's probably fine to round up and call this a driving impedance of 1kΩ.

                        Here is the exact circuit under test.
                        (note: anticipating a low input impedance possibility, I wanted to extend the bandwidth so the roll off was well below 1kHz into 100Ω. Therefor a 10µF polypropylene coupling cap was used)

                        Click image for larger version

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                        If I have a 50% chance of guessing the right answer, I guess wrong 80% of the time.

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                        • #42
                          I'm going to power this circuit of my amps existing supply. I'm heading out to the garage now, so hopefully I'll be able to post some results a little later on.
                          If I have a 50% chance of guessing the right answer, I guess wrong 80% of the time.

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                          • #43
                            okay. the results are in. stay tuned to find out later on this week.......
                            If I have a 50% chance of guessing the right answer, I guess wrong 80% of the time.

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                            • #44
                              Seems to me there is a lengthy thread about that Heath generator over at DIYAudio forum. People renovating them and updating them, and tweaking them, and making them more accurate, and so on. Might be worth a look.
                              Education is what you're left with after you have forgotten what you have learned.

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                              • #45
                                I'm kidding.

                                With the circuit connected as drawn above, the B+ where I tapped the supply of my amp dropped under load down to about +215V (which is a little closer to 200V I originally designed the circuit for).

                                I connected my meter to the unloaded output of the signal generator and adjusted the voltage to 1.002V RMS.
                                I connected the negative lead to the ground terminal of the 20µF capacitor where the ground return connection was made, and the center conductor to the 10µF coupling capacitor. Bringing up the voltage slowly with my variac, I watched the current draw (nervously) to insure I hadn't inadvertently miswired something, or installed a bum tube.
                                But the DC operating point at all the terminals settled to their expected levels.

                                As the tube began to draw current I watched as the loaded voltage at the cathode input drop to a measured 850mV RMS!
                                That works out to an input impedance of around 5.42MΩ!
                                The input impedance is way higher than anything I expected, so I ran the test again and got the same results.


                                I had so many test leads flying around the bench to test all the voltages and monitoring the current draw to watch for any faults, I wasn't able to check monitor the input and output signals with a scope yet. Plus, I AC ground the grid of the second triode, and measure the results.
                                If I have a 50% chance of guessing the right answer, I guess wrong 80% of the time.

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