Zener Bias "Trick" for Cathode Biased Amps

[jbrrrrr]

Hello, amp tinkerers and tube zealots,

I stumbled across this chunk of a schematic somewhere, but I can't remember the source - it looks like this is a technique used in cathode biased amps with a shared cathode resistor, in order to control the amount of stiffness (or lack thereof) by clamping the cathode voltage at the limit set by the parallel zener(s).  See attachment.

Anyone have any experience using this zener trick as a means to control the 'feel' of a cathode biased output section?  It looks to me like in the 3rd schematic on the right of the 'Zener_bias_trick Squash.gif' file, if you wanted to make it switchable, you could maybe use a DPDT to ground the second series zener with one pole, and parallel in another value for the cathode resistor to make sure the bias sits appropriately in either position using the other pole of the switch.  I could see that being a more impactful modification than just increasing the bypass cap value for a stiffer feel.

Would anyone mind verifying if I'm understanding this correctly?

Regarding any other references to this kind of idea, it looks like tubecad.com might have been an early source for this - Broskie wrote about it here, in the second article on this blog post from 2007.  Paul Ruby is also credited in doing something similar but everything I've read about it seems targeted towards removing "buzz" or crossover distortion, specifically from EL84 tubes. 

[jbrrrrr]

I remembered where the source of this came from - it was from the AX84 archive forum - since it's kind of intermittently accessible and not in a state of maintenance, here's a PDF of the original thread from 2005 - not a whole lot more info here but it does describe using it.  Maybe someone here remembers this or has tried it out?

[kagliostro]

To me it seems an alternative way to obtain a Mixed Bias

----

1.  Fixed Bias

Characteristic: Fixed negative voltage applied to the grid, cathode connected to ground.

Advantages: - Maximum power and efficiency - Greater headroom - Better control of the operating point

Disadvantages: - Requires precise adjustment - Risk of thermal runaway - More sensitive to tube variations

2.  Cathode Bias (self-bias)

Characteristic: A resistor on the cathode automatically generates the bias voltage.

Advantages: - Self-regulating - Increased safety - No adjustment required

Disadvantages: - Lower power - Reduced efficiency - Greater signal compression

3.  Mixed Bias

Characteristic: Combines fixed negative voltage with a cathode resistor.

Advantages: - Good stability - Partial self-compensation - Balance between performance and safety

Disadvantages: - Intermediate efficiency - More complex circuit - Does not reach the performance of pure fixed bias

---

Sound Characteristics Summary

  System         Sound Character
  -------------- ----------------------------------------------------
  Fixed Bias Cleaner, more defined, dynamic, greater headroom


  Cathode Bias   Warmer, softer, more compressed, “spongy” response


  Mixed Bias     Balanced, slightly softer but still well-defined


Franco

[HotBluePlates]

To me it seems an alternative way to obtain a Mixed Bias

Better yet, say it's a way to make Cathode Bias act like Fixed Bias.  Or maybe a little bit like "Applying Negative Feedback" to an amp that has no negative feedback around the power section.


How does Cathode Bias create compression?  Only when driven to distortion (or at least much into Class AB).


The diagrams assume something like a 5E3 tweed Deluxe.  There are no voltages marked on the schematic, but anecdotally they were higher than the 5C3 tweed Deluxe and might have had a voltage across the 6V6 cathode resistor of 21-22v (compared to the 5C3 Deluxe's 18v of bias).

If the amp stays perfectly in Class A, the current draw of one side increases with a positive-going grid signal exactly as much as the current draw of the other side decreases with its negative-going grid signal (except for rise of screen current and/or imperfect matching of tube currents when driven).

Once the Peak Grid Voltage driving the output tubes exceeds the bias voltage across the cathode resistor, the negative-going grid voltage shuts off 6V6 (or close, because it often takes a bit more negative-voltage to shut off the tube).  The tube receiving the positive-going grid voltage now has 1/4 the load impedance at the output transformer primary, so its Rate of Change of Current is 4x what it was when both sides were on.

The side that is Off cannot flow "negative current" to match the other side's current increase, so the Net Current through the Cathode Resistor increases.
The Cathode Resistor has a voltage-drop that is Total Tube Current x Cathode Resistance.
Higher Net Current results in greater voltage drop across the Cathode Resistor, so the Bias Voltage at the cathode increases.

We might usually think simply "this turns down plate current" but think about "bias" in terms of "volts from grid-to-cathode."  A large incoming signal tries to pull higher total tube current, and when only one side is on the voltage across the cathode resistor rises.  For that side, the grid signal is positive-going, but now the cathode is also positive-going by some smaller voltage.  This has the same effect as applying a slightly smaller grid-input voltage because the tube does not feel as-large a grid-to-cathode voltage-change as it would have if the cathode were nailed to a single, steady voltage.

The end result is after the output tubes run into Class AB, some amount of rise of Total Tube Current happens, and it tends to counteract the driving signal that pushed the output tubes into Class AB.  The intensity of the compression effect depends on how large a current-rise happens, and also the resistance of the cathode resistor (and the tube's transconductance).  So we're not necessarily at extreme-squish the moment the Total Tube Current rises above Idle Tube Current.

[HotBluePlates]

What does Fixed Bias do?

With a grid nailed to a single unvarying voltage, the grid-to-cathode voltage stays absolutely steady.  There is no counteracting change of grid-to-cathode voltage in the face of a large driving signal.

At some point, the Peak Input Signal exceeds the Bias Voltage (pretend this Bias Voltage is -22v on the grid).  One side has already long since been driven to cutoff.  However, the remaining side is getting say, +24 volts peak applied to a grid with -22v grid-to-cathode.  +24v + -22v = +2v momentarily on the grid of that output tube.

When the grid goes positive of the cathode, its impedance falls from ∞Ω to some lower impedance (something like 1kΩ seems typical for a 6V6).  The output tube grid tries to pull current from the phase inverter or driver tube (which usually is not designed to supply it), and the sudden low input impedance clamps the drive signal from the driver/phase inverter.  We get an abrupt onset of distortion as the positive-going side of the Grid Input Signal is lopped off.


You know how Negative Feedback is supposed to keep the associated circuit clean?

A Super Reverb has negative feedback around its power section, yet we know a Super Reverb will distort.  What happens is the feedback counteracts the signal applied to the power section (really, all the stuff inside the feedback loop), and causes the amp to behave as if the signal were smaller by a fixed %.  It does this until the drive signal exceeds the amount of gain thrown away as feedback, at which point the feedback stop counteracting drive signal and preventing distortion.

The result is an abrupt transition into distortion for the amp with feedback, as compared to the searlier and more gradual increase of distortion that would happen in the same amp without feedback.


The zener diode across the cathode resistor clamps the Cathode Resistor Voltage (and so Bias Voltage) to a fixed amount.  As the amp transitions into Class AB, the bias cannot rise with increased Total Tube Current as it would have.  If the Peak Input Signal exceeds this fixed value of grid-to-cathode voltage set by the zener, the output tube will attempt to draw grid current, and will clamp the input signal in the same way as happens with Fixed Bias.

We don't have "compression" but we also get an abrupt transition from "clean" to "dirt" the way we would expect with an amp with negative feedback around the power section.

Maybe that sounds like a good option, but we do not get a different benefit of negative feedback:  the bass resonant frequency of the speaker is not damped as it would be with negative feedback.  The low end can sound woofy and uncontrolled, though normally the amp with feedback has lost this control when it is distorting for the same reason it stops keeping the power section clean:  the feedback has run out of gain to use, and the power section is essentially running with no negative feedback (until drive signal is reduced).

[HotBluePlates]

To me it seems an alternative way to obtain a Mixed Bias

Stop thinking in terms of a "Cathode Bias" "Fixed Bias" dichotomy, and think only in terms of grid-to-cathode voltage.

The Left diagram has an adjustable voltage applied grid-to-cathode; it just keeps the cathode tacked to 0v and allows the grid voltage to be changed.

The Right diagram has Zeners to clamp the Cathode to +22v, and tacks the grid to 0v.  But this is non-adjustable.

The middle diagram uses Zeners to keep exactly 22v across the cathode resistor.  However, the ground-side of the cathode resistor is not tacked to 0v but to +15v at the top of a zener to ground.  The grid is not tacked to 0v as with Cathode Bias, but to some point between +15v and something more positive than 0v (due to the 10kΩ resistor to ground).  That allows for adjustment not unlike the biasing arrangement in the Williamson Amplifier.


I wouldn't call the middle diagram "Mixed Bias"... it is 100% "Fixed Bias" but just doesn't have a bias supply derived from a transformer tapping; the fixed bias voltage is created by zener diodes after the tube draws sufficient current to drop volts across the cathode resistor.

[AX84CH]

I have no memory of this.  That's how asleep I was on my own forum.  A neat idea.  You still lose plate voltage due to the cathode being non-zero but sometimes that might be helpful.

Could this also be used in situations where you wanted to run a particular tube but your plate voltage was higher than the tube needed?   A 30v Zener would give back 30 volts to the plate voltage limit and then you could adjust the grid bias to land the biasing where you wanted it?

[jbrrrrr]

This seems useful as a way to allow for more variations of cathode-bias-that-feels-less-cathode-bias-y without having to set up a bias voltage tap.  I tend to prefer the way cathode bias amps feel, but I always get that urge to put an option in to stiffen up the output section, or to change that as part of the voicing structure.

Obviously if you want a fixed bias amp then this is a silly substitute, but it's the range in-between fixed and full cathode bias that I think this could have some use for - if you wanted to have this as a switchable option, you could just shunt the zeners to ground, and switch in the appropriate cathode resistor value for 100% cathode bias.  I think.  I'll have to prototype this on the amp I'm currently working on.

AX84CH - thanks for keeping the archive accessible regardless!  I'm relatively new to the amp building forum world, and I'm always trying to scrounge up forgotten little tidbits that got left by the wayside or weren't as relevant then as they are now.

[HotBluePlates]

This seems useful as a way to allow for more variations of cathode-bias-that-feels-less-cathode-bias-y without having to set up a bias voltage tap.  ...

Obviously if you want a fixed bias amp then this is a silly substitute, but it's the range in-between fixed and full cathode bias that I think this could have some use for ...

If you focus on the self-adjusting nature of cathode bias, then I think you will agree that using the zener creates a fixed-bias supply.  Assuming the tubes pull sufficient current through the cathode resistor, the bias voltage is locked at a single voltage value.  So it behaves as non-adjustable fixed bias.

[passaloutre]

Once the Peak Grid Voltage driving the output tubes exceeds the bias voltage across the cathode resistor, the negative-going grid voltage shuts off 6V6 (or close, because it often takes a bit more negative-voltage to shut off the tube).  The tube receiving the positive-going grid voltage now has 1/4 the load impedance at the output transformer primary, so its Rate of Change of Current is 4x what it was when both sides were on.

I've seen this come up in discussion before, but it always seems to trip me up... Where does the 1/4 load impedance figure come from? Why is it not half, since half the transformer is not doing anything? Or why is the impedance reduced at all?

[pdf64]

The impedance ratio is the square of the turns ratio.
So halving the turns ratio quarters the impedance ratio.
eg if the anode to anode turns ratio is 10:1, when one anode is in cut off, the CT to other anode turns ratio is 5:1.
So the anode to anode impedance ratio is 100:1 and CT to anode is 25:1.

[jbrrrrr]

Is that where the math for using a composite curve of 1/4 the primary and 1/2 the primary is derived from in calculating a push-pull loadline?  i.e. maps to the 1/4 Za-a until the bias point for class B, and then continues on through the 1/2 Za-a loadline for class A?  I just took it for granted that it was written and it must be so - I didn't think about the trafo turns ratio being what was dictating why we use 1/4 and 1/2 specifically.

https://www.valvewizard.co.uk/pp.html

[shooter]

the math

it goes way back, can't recall who came up with inductance, math, but it wasn't any fun cranking out just so I could pass a class

[pdf64]

Is that where the math for using a composite curve of 1/4 the primary and 1/2 the primary is derived from in calculating a push-pull loadline?  i.e. maps to the 1/4 Za-a until the bias point for class B, and then continues on through the 1/2 Za-a loadline for class A?  I just took it for granted that it was written and it must be so - I didn't think about the trafo turns ratio being what was dictating why we use 1/4 and 1/2 specifically.

https://www.valvewizard.co.uk/pp.html

Yes, you've got it, that's it 

[HotBluePlates]

... 1/4 Za-a ... for class B, and ... 1/2 Za-a ... for class A?  ...
https://www.valvewizard.co.uk/pp.html

If there is current pulled through a half-winding then it is "present in the circuit."

   - Class A has current pulled at all times, so both half-windings are "present in the circuit."
   - We get the rated Za-a, and each side sees 1/2 of that Za-a between itself and the power supply.


   - "Class B" (or Class AB once one side has shut off) has no-current through a half-winding part of the time.
   - When no-current flows, that half-winding "doesn't exist."
   - The remaining half-winding has 1/2 turns, and (1/2 turns)² = 1/4 Impedance


We could do a math proof of this using a common output transformer, and recalling that if current flows and there is 1-volt-per-turn on any winding, there is 1-volt-per-turn on every winding of the transformer.

     8kΩ push-pull to 8Ω = 1000 to 1 Impedance Ratio
     √(1000 : 1) = 31.623 : 1 Turns Ratio

     Assume 20w across 4Ω primary.  Volts on Primary and Secondary are:
     Primary:  Volts = √(20w x 8kΩ) = 400v RMS
     Secondary:  Volts = √(20w x 8Ω) = 12.65v RMS
     Volts Ratio = Turns Ratio = 400v / 12.65v = 31.62 : 1

     Both Sides Conducting:  Each side of the Primary sees a load of 4kΩ
     
Now assume there are half the turns on the Primary, because one side is shut off.  The Turns Ratio must also be halved:

     Turns Ratio = 31.623 / 2 = 15.812 : 1

     20w into 8Ω is still Volts = √(20w x 8Ω) = 12.65v RMS
     Primary Volts = Secondary Volts x Turns Ratio = 12.65v RMS x 15.812 = 200v RMS

     Current = Power / Volts, and Impedance = Volts / Current, manipulating gives you Impedance = Volts² / Power
     Impedance = 200v² / 20w = 40,000 / 20w = 2000Ω

     ---> 2000Ω is 1/4 of the original 8000Ω.  We wind up seeing that "Impedance Ratio" fell from 1000:1 to 250:1 when the number of turns was halved.  We could also note that when we calculate Power using known-quantities of Volts, Current and Impedance that the term for either Volts or Current gets squared... and that's where the "squaring" comes from for "Impedance Ratio is the square of the Turns Ratio."