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Estimating BIAS voltage for Real World Vs and Vp Voltages

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  • Estimating BIAS voltage for Real World Vs and Vp Voltages

    Tube data sheets give BIAS voltages at industry-standard 250Vp and 250Vs and a few other select voltages, which, unfortunately, seldom coincide with real world values, meaning we have to find some other way of estimating a prioria (in advance) what the BIAS voltage should roughly be...necessary information for both self-biased and fixed bias circuits.

    Below are two slightly different methods for estimating control-grid BIAS voltage, using the tube’s published data sheet parameters:

    1) Transconductance (gm) – Using desired idle plate current (Ip), idle screen (Vs) and plate (Vp) voltages and tube transconductance (gm), and tube amplification factors (mu1(triode) and mu2(pentode)):

    Vg(dc) ≈ %*((3/2)*(Ip/gm)) – (Vs/mu1 + Vp/mu2)...where % ≈ 0.90-0.95

    2) Perveance (G) – Using desired idle cathode current (Ik), idle screen (Vs) and plate (Vp) voltages and tube perveance (G), and tube amplification factors (mu1(triode) and mu2(pentode)):

    Vg(dc) ≈ (Ik/G)^(2/3) – (Vs/mu1 + Vp/mu2)

    Tube perveance (G) is not directly stated in data sheets so it must be determined *from* other data sheet information and is easily backsolved from the tube’s example triode operation data using the “Child-Langmuir 3/2’s Law” equation for triodes:

    Ip = G*(Vg(dc) + Vs/mu1)^(3/2)
    G = Ip/ (Vg(dc) + Vs/mu1)^(3/2)


    Because this perveance value is for triode operation, where screen is connected to plate, it must be reduced slightly for pentode operation(*):

    G(pentode) ≈ %*G(triode) ...where % ≈ 0.88-0.90.

    Now, using either of these equations enables you to reasonably estimate the idle BIAS voltage for ANY combination of screen and plate voltage without having to extrapolate from published curves for voltages that seldom coincide with our real world voltages. Now you don't have to build something before you have a reasonable idea of what the BIAS should be when your real world Vs and Vp voltages don't match the data sheet examples and curves.



    (*) Pentode perveance value could also be directly determined from published pentode operation examples.

    NOTE - Astute readers will realize that the Vp/mu2 values in ALL of the above equations can be omitted causing only moderate reduction in accuracy. And, no electrons were harmed in the generation of this text.
    Last edited by Old Tele man; 07-22-2018, 01:55 PM.
    ...and the Devil said: "...yes, but it's a DRY heat!"

  • #2
    Good thoughts, and an interesting approach.

    I've never approached the question that analytically. My crude approach is to think that bias is like air and water - first, you make sure you have enough, then refine it down. I especially like this approach in a world where the next user of that amp may well jam in a set of 6V6s or EL34s. Even if they use exactly the kind of tubes the amop was designed for, we all know that modern tubes will probably need bias adjustments on a smaller scale, so an adjustment means is necessary.

    If I were designing an amp's output stage, I would generate perhaps -75V to work with, then a means to switch it into the crude area that a tube might need, then some fine adjustment. And in fact, that is what I did with the bias system on the Workhorse amps.

    I like the approach - I just don't trust myself to calculate it well enough a priori.
    Amazing!! Who would ever have guessed that someone who villified the evil rich people would begin happily accepting their millions in speaking fees!

    Oh, wait! That sounds familiar, somehow.

    Comment


    • #3
      Thanks for the kind words.

      I, too, typically started with a very negative bias source (-100Vdc HP) and then dialed the bias voltage up (less negative) until the power tubes idled where I wanted. However, being a 'number-cruncher' at heart, I took an interest in playing with the generic Child-Langmuir 3/2's Law to see what I could learn (and use) from it -- the above article is just one aspect.

      Along the way I learned what Perveance (G or K, depending upon the author) was, since it was a tube value never published...in fact, I've only found it listed in a couple old European rectifier data sheets, although the older RCA manuals at one time had a nomograph for rectifiers that enabled you to make voltage-drop estimations vs. current loads. Of course, after awhile I calculated and made tables of perveance values for all the popular tubes -- can't remember them -- but I can look'em up when needed.

      Here's a brief table I did for another forum I visit:

      Compilation of 6V6, 6L6 & 6BQ5/EL84 tube parameters collected (and derived) from published datasheets.

      ................................|__5881__|__6L6GC_|__758 1A_|__6V6G__|__6V6GT_|6BQ5/EL84|_units___
      Plate dissipation(Ppd)..........|______26|_____30 |_____35 |______12|______14|_______12| Watts
      Screen dissipation(Psd).........|_____3.5|______5 |______5 |_______2|_____2.2|________2| Watts

      Triode transconductance(gm1)....|__0.0047|__0.0047|__0.0047|__0 .0050|__0.0050|___0.0100| A/V
      Triode plate resistance(rp1)....|___1,700|___1,700|___1,700|___1,960| ___1,960|____1,950| Ohms
      Triode amplification factor(µ1).|_______8|_______8|_______8|_____9.8|_____9.8 |__19.5/19| ---
      Triode perveance(G2)............|_0.00106|_0.00106|_0.00106|_0. 00106|_0.00106|__0.00455| A/V^(3/2)

      Pentode transconductance(gm2)...|__0.0060|__0.0060|__0.0060|__0. 0041|__0.0041|___0.0113| A/V
      Pentode plate resistance(rp2)...|__22,500|__22,500|__22,500|__50,000|_ _50,000|___38,000| Ohms
      Pentode amplification factor(µ2)|_____135|_____135|_____135|_____205|_____205| ______429| ---
      Pentode perveance(G3)...........|0.000922|0.000922|0.000922|0.00 0922|0.000922|__0.00327| A/V^(3/2)
      ................................|0.000913|0.000913|0.000 913|0.000901|0.000901|__0.00347| A/V^(3/2)


      Where's that table function when you really need it?
      Last edited by Old Tele man; 07-23-2018, 10:53 PM. Reason: table clean-up
      ...and the Devil said: "...yes, but it's a DRY heat!"

      Comment


      • #4
        The particular equations you show are ideal linear equations ....used for academic purposes and are the classic handbook equations....
        These do not translate into real world operation of tubes.. But good usefull if you are designing new topologies and need to do proof of concept to get you in the ballbark...
        The 250V / 250V standard Class A data sheet test point is actually useful since it is roughly the geometric mean average of a tube operating at roughly twice that voltage in Class AB, B...ie "Large-Signal" gm
        The actual gm of a tube varies greatly during use such as in a output stage amplifier... during the AC conduction cycle the gm varies during the conduction angle...
        So the gm of a tube in a particular circuit is the average over the AC operating cycle....
        For example......you have a P-P amp quiescent point at 500V plate idle at 35mA ....measuring gm at this point would not be useful, since the gm is considered "Small-Signal" gm and would be down in the mud ...even the 3/2 power law equations will show this...

        Comment


        • #5
          You are correct about the "ball-park" usage. And, yes, transconductance (gm) is only an 'average' parameter given for specific operating condition(s); however, most power tube data sheets include triode and multiple pentode configurations, which is why I also collect & compile backsolved values from all the data sheets I can find.

          Also, because amplification factor (mu) is roughly (but not truly) a constant, both gm and dynamic plate resistance (rp) vary as cubic functions of perveance and plate current:

          gm = (3/2)*[G^(2/3)*Ib^(1/3)]

          rp = (2/3)*(mu)/[G^(2/3)*Ib^(1/3)]


          so, you can get an idea of how much variation they'll have at various operating conditions (usually full power). Not exact science, but "close-enuf" science to make educated guessing more accurate.

          Interestingly, that's why I provided both equations -- one using gm and other using G. As you point out, gm varies, but G is far more consistent, but, certainly NOT a hard constant (pentode G < triode G < diode G).
          Last edited by Old Tele man; 07-23-2018, 10:33 PM.
          ...and the Devil said: "...yes, but it's a DRY heat!"

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