Unimportant Details Dept: Bias and 1-ohm cathode resistors

I've raved here about how great it is to fit 1-ohm resistors between cathode and ground to directly measure plate current in fixed-bias amps. Except of course you're actually measuring *cathode* current, which includes both plate and screen current.

Luckily, of course, the difference is small, and as noted the other day in a nearby thread, it's in the *safe* direction -- the actual bias will be a little cooler than you calculate. And we should bias by ear -- so if you end up at 60% when you think you're at 65%, it still *sounds* good and the exact number doesn't matter.

But Rob pointed out there he lists his formulas on his bias calculator, and I'm the first to say I love that page and use it all the time. He also (typical Rob generosity) has a link to his Excel spreadsheet, which (typical Rob attention to detail) must have been a ton of work.

So, just for curiosity, I took the 5.5% (arbitrary/approximate) offset he uses elsewhere for screen current and applied it to the 'plate current' section of the calculator. I simplified mine since he has a ton of power features, like a lookup table for dozens of tube types.

How big is the difference in terms of scale? Here're some made-up numbers in my baby version that includes the offset:



So a 5.5% offset to the current measurement results in a *less than 5%* difference in terms of percent dissipation (though note this is simply a result of comparing proportions; in fact 8.1/7.7 = 1.05). So folks smarter than me wouldn't need to do all this calculating.

In any case, I can live with that -- at least if 5.5% is a reasonable estimate of the offset for screen current.

Back at the ranch, Rob's bias method 'Using Cathode Resistor Voltage Drop' *includes* the 5.5% offset for screen current; a little thought tells us we can use this method with 1-ohm resistors, too, if we scale the units and recall we're now measuring for just one tube. In fact his "if triode" calculation does what I did above and shows the 'uncorrected' bias value...

 

Right: Good old rounding error.

But, LLC, help me out. Is 5.5% some accurate and universal figure? I assumed the actual difference varied from circuit to circuit and tube to tube, and that 5.5% was just a 'useful, typical estimate.'

At this point, I recalled I have an old Eurotubes bias probe that directly measures actual plate current. On my 5G9, the 1R-derived cathode current was 22mA, and measured plate current was 20mA, so at least for this amp, the screen current looks like 9–10% of the total cathode current. (Though, even so, my calculated percent max dissipation only drops from 67% to 61% -- not a huge difference.)

Or am I just adding good old measurement error (and imprecision) to the rounding error problem?

EDIT: I shoulda said I'm grateful to LLC for reminding me in the first place that cathode current is *not* exactly the same as plate current.

 

Thanks! And good, I was gonna be weirded out if 5.5% was some kinda tube-amp equivalent of Planck's constant...

 

Yeah, "Rob's constant." Hey, at least it's not 6.02*10^23...

Actually, all my circular math aside, the fun thing I learned here is when I measure current (as mV=mA) across my 1-ohm resistors, I could use Rob's "Cathode Resistor Voltage Drop" and see the both the 'corrected' (estimated plate) and uncorrected results (in the 'if triode' last line).

Notes:

1. I already did the first section, with tube type and plate voltage (in fixed bias, plate V = plate-to-cathode V)
2. Then, '1' tube, current in volts (mV/1000), and '1' ohm for your resistor....

 

You're right. I've always used 1R 1% ½ W Dales -- 1% is just nice, and the 1/2W makes them big enough to, like, see -- and clip your grabbers on. But lets say you used 5% tolerance resistors and measured 20.9 or 23.1 instead of 22 -- a full ±5% error. The result in % max dissipation would be 63% to 69% instead of 66% -- not enough to likely change your 'safety zone' calculations -- but hey not as precise as it could be.

And of course if you happened to have only 2ohm or 10ohm resistors, you could do the Ohm math -- or just plug into Rob's cathode resistor calculator above.