Perfecting Fixed-Bias Cathodyne

[EETStudent]

For my latest build based loosely off a Princeton Reverb, I decided to go with a fixed bias cathodyne. Ive been reading Merlin's article about cathodyne and how to get the most out of them. I followed the schematic he suggests works great with a 12AX7. Im on the right path, but I need some input before I hook up the oscilloscope (which wont be for a couple days). Im taking the B+ from the 3rd filter node, resulting in about 330VDC HT. Im using 100k load resistors (200k total load) for maximum swing. Looking at Merlin's schematic, his is based around 300VDC HT. He suggests applying 50VDC to the grid, and that as a rule of the thumb the grid voltage should be 1/4 HT. That has me confused because 50 is not 1/4 of 300. Am I missing something there? Im currently getting about 53VDC on my grid, which I know is in the ballpark. Im trying to understand more of theory so I'll know how to better tweak things to acheive best balance. Thanks

[Gingertube]

With a Cathodyne (Concertina) Phase Splitter you have to remember that the signals at cathode and anode of the tube are opposite phase. The swing to watch is when the cathode swings positive and the anode swings negative. The voltage across the tube reduces by 2 x the signal swing. This means that you need to run the tube with the cathode at a lower voltage than you might first assume (to leave some "opperating" volts across the tube). 1/4 to 1/5 of the high voltage is what seems to work best. With 300V rail I would therefore expect somewhere between 60 and 75 volts on the cathode. With a 12AX7 that means between 62 to 77 volts at the grid.

You can calculate the maximum swing operating point but I wouln't bother, Remember all tube circuit voltages are (in general) +/- 20% so no need to obsess.

Suggested calc method:
- draw a 200K load line on anode characteristics graph, read off the anode voltage when the line crosses the Vg1 = 0 (the "saturation" voltage )
- subtract that from the B+, that gives you a voltage which is 2 x the peak to peak signal swing
- divide that by 2 to get the peak to peak signal swing
- divide by 2 again to get the peak signal swing
- Use that voltage for the cathode volts, grid will want to be 1 to 2 volts less than that voltage for correct bias.


Cheers,
Ian

[jazbo8]

To save you some time, here are the load lines for the cathodyne, it may appear a bit confusing at first, but if you break it down, then you can see what's going on: the blue line is the total load line for the stage, Rp+Rk (in this case 44K for the 12AU7 in the graph), since the outputs are equally spitted between the plate and the cathode, we can break the combine load line into two, with the green line representing the cathode load of 22K and the orange line representing the plate load of 22K. So looking at the cathode load line you see Ek0=57.9V, now as Ian said, you need to add a few more volts to allow for the input swing (say 6V in the example), so Eg0 = 57.9-6= 51.9V, or ~20%-25% of the supply voltage of 250V.

One more thing to bear in mind though, the output impedance of the plate and the cathode is quite different, so in real life, it is hard to achieve a perfect balance, then again who needs that in a guitar amp anyway...



Jaz

[Gingertube]

Jaz,
With identical laods the output impedance from both anode and cathode is identical adn equal to 1/gm. With non-identical loads which will occur when running into output tube cutoff as part of normal AB1 operation or when overdriven then impedances will vary. The effects of this are well covered in the Wiz's book.
Cheers,
Ian

[jazbo8]

Ian,

I thought so too, and Merlin did reference both Jones and Preisman, but... after reading Ayumi's pages and running the simulation, I came to a different conclusion, please verify the derivations here for yourself to see if you can spot some flaws (it's in Japanese, but you should be able to read the equations). And here is the impedance plot I got from the sim (while not quite the same as the derivations below, but still in the ballpark):



From Ayumi's Lab:

Using 12AU7, with power supply Ebb = 250 V, load resistances Rk = Rp = 22 kΩ, grid bias Eg = -6V, the operating conditions are: Ep = 134.23V, Ip = 2.63mA， So, gm = 1250.99μSiemens, rp = 12.89kΩ, μ = 16.12, then,

|A| = μ*Z/[rp+(2+μ)*Z] = 16.12*22/(12.89+(2+16.12)*22 = 0.86
Zop = Zp//[rp + (1 + μ)Zk] = 22//[12.89 + (1 + 16.12)22] = 20.82 [kΩ]
Zok = 1/[1/Zk + (1+μ)/(rp+Zp)] = 1/[1/22+(1+16.12)/(12.89+22)] = 1.86 [kΩ]

[EDIT] Even some gurus differ on the calculation of the cathodyne output impedances...

Jaz

[EETStudent]

All great responses. Thank you

[Dave H]

Here’s one I prepared earlier. This is what it should look like on the scope (see Cathodyne plot.pdf below). I’ve disconnected and grounded the power tube grids in order to see the full voltage swing available from the PI (as Cathodyne scm). I also have the real amplifier and it performs exactly as the simulation. If you give me your actual circuit values I’ll put those in and run it again.

I forgot to add it's biased at 80V cathode, 220V plate with 300V B+

Cathodyne plot.pdf
Cathodyne scm.pdf

[Dave H]

...I would therefore expect somewhere between 60 and 75 volts on the cathode. With a 12AX7 that means between 62 to 77 volts at the grid.

It's 58 to 73 volts on the grid

[EETStudent]

Dave H,

My circuit follows the fixed-bias circuit on Merlin's page. 100k Rk and Ra, 3M grid bias, 510k grid leak to ground. Just out of curiosity, what programs are you guys using to simulate your circuits? I have no experience with such programs, but it seems like an extremely useful tool when figured out. Thanks again

[EETStudent]

And I should mention that I don't know how to draw my own load lines for my application. I don't know how to generate the actual 'load line', 200k in my case, and where to plot it on the graph. I am capable of simply reading the graph though.

[Dave H]

...Im using 100k load resistors (200k total load) for maximum swing. Looking at Merlin's schematic, his is based around 300VDC HT. He suggests applying 50VDC to the grid, and that as a rule of the thumb the grid voltage should be 1/4 HT. That has me confused because 50 is not 1/4 of 300. Am I missing something there? Im currently getting about 53VDC on my grid, which I know is in the ballpark. Im trying to understand more of theory so I'll know how to better tweak things to acheive best balance. Thanks

I missed this the first time. It should be biased closer to 1/4 of HT (75V) but I think Merlin has it as 1/4 of the 200V across the tube i.e. 50V which won't give max swing.

You can see how it works here without load lines or simulations. The cathode is at 50V so its max undistorted downward peak swing is to 0V (cut off) and the corresponding upward peak swing is to 100V. The plate and cathode resistors are the same so the plate will also swing 100V peak to peak (from 200 to 300V). The cathode swings up to 100V as the plate swings down to 200V so there is a 100V 'gap' between the two which is wasted headroom.

I wouldn’t use the above circuit as it is in your real amp design because it is only ‘theoretical’ as it is not driving a load. Your PR type circuit will be driving the 6V6 grid resistors through coupling capacitors which complicates it a little if you want to set it up for max swing. I’d stick with the 56k plate and cathode resistors in the cathodyne to have more current available to drive the load.

The simulation software was LTspice. It’s a free download from here.
Below is a simulation of the 50V biased cathodyne described above.

Cathodyne 50V.pdf

[Bruce / Mission Amps]

Here’s one I prepared earlier. This is what it should look like on the scope (see Cathodyne plot.pdf below). I’ve disconnected and grounded the power tube grids in order to see the full voltage swing available from the PI (as Cathodyne scm). I also have the real amplifier and it performs exactly as the simulation. If you give me your actual circuit values I’ll put those in and run it again.

I forgot to add it's biased at 80V cathode, 220V plate with 300V B+

[ATTACH]22740[/ATTACH]
[ATTACH]22741[/ATTACH]

Sims are cool but here is what I get when actually driving it hard...

[EETStudent]

Dave H, thank you for your assessment. My ultimate goal is to achieve maximum swing without any of the ugly artifacts common to cathodynes. I think Im understanding it better, but still not entirely sure exactly what to be looking for in determining the best balance. Dave H, your suggestion is to stick with 56k plate and cathode resistors to have more current available to drive the 6v6s (im actually 7591's, but the drive requirements are very similar). Its my understanding that higher Rp/Rk will yield higher current capabilities. I can see how 56k would be a suitable choice in my application, but Im still unsure of what the grid voltage should be. I will be experimenting with the software. In the meantime, additional input is much appreciated

[Dave H]

Sims are cool but here is what I get when actually driving it hard...[ATTACH=CONFIG]22748[/ATTACH]

Bruce, My sim didn’t do that because I had disconnected the power tube grids from the PI to make it show the full PI output swing. Below is a sim with the grids connected. I also sometimes use a 'scope

Cathodyne 6V6.pdf

[pdf64]

'Sims are cool but here is what I get when actually driving it hard..'
The blip is due to power tube grid conduction, hence Dave specified that the power tubes were out of circuit.
The key thing being that the cathodyne has more voltage output swing available, beyond the point that the power tube grids clip it (as shown in that scope shot).
Pete