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Cathode Current Biasing Error

From ashinma–(at)–hem.ucalgary.ca Mon Apr 28 10:53:36 CDT 1997
From: Scott Hinman
Newsgroups: alt.guitar.amps
Subject: Cathode Resistor Bias Ponderables
Date: Sun, 27 Apr 1997 15:19:58 +0000
Mime-Version: 1.0
Content-Transfer-Encoding: 7bit
Xref: geraldo.cc.utexas.edu alt.guitar.amps:47268

Howdy Folks
Sometime back I promised to make some measurements regarding
the errors associated with the cathode resistor bias method.
About a week ago somebody actually posted a question about
the magnitude of screen currents to expect when using this
method. I didn’t see any replies to that post (maybe I missed
some?) so I figured maybe I should quit procrastinating.
So…… The cathode resistor method refers to measuring
the voltage drop across a resistor (commonly one ohm) inserted
between cathode and ground, and calculating bias current from
Ohm’s law. That current actually is the sum of the plate current
and the screen current, assuming you can ignore grid current
(which you should be able to, unless somebody got inside and
ate the beans off your plate. I’ve got a question about this
for the gurus later). Aside from the screen current, there
are difficulties associated with accurately measuring the
resistance of small value resistors. Resistors first. I took
a handful (thats ten, right?) of 2% one-ohmers and another of
5% one-ohmers, and measured their resistance with a Hewlett Packard
model 3468A multimeter. I did this both in two-wire mode, which
is what would be available to the majority of DIYer’s, as well
as in 4-wire mode, which eliminates errors due to lead and contact
resistance. Data:
5% quarter watt carbon film:
individual values
2-wire:1.092,1.105,1.093,1.095,1.083,1.090,1.092,1.082,1.081,1.080
4-wire:0.987,0.980,0.982,0.982,0.982,0.975,0.985,0.974,0.982,0.974

2% half watt carbon film:
individual values
2-wire:1.083,1.089,1.077,1.079,1.083,1.094,1.084,1.081,1.086,1.077
4-wire:0.978,0.981,0.982,0.991,0.994,1.009,1.001,0.990,0.990,0.985

Note that the two-wire method is always about 10% too high with this
meter. A Fluke model 8000A invariably gave values of 1.1 or 1.2 ohms.
Same thing for a cheapy radio shack. On the other hand, the 4-wire
meter readings indicate the 5% resistors are all within about 2.5% of
the stated value, although they are all a little low (Average = 0.980).
The 2% resistors didn’t offer that much improvement in precision,
(although they’re all essentially in spec if we don’t quibble about
the 0.978 guy), but the average value (0.990) is closer to the nominal
value than the 5%. Lesson – if you measured 1.2 ohms with your
Radio Shack meter, you’re out 20% to start with. You’re far better
off to just buy semi-precision resistors and use the nominal value.
(Yeah, I know. You already knew that.)
Next thing I did was to solder a one ohm resistor in between the
plate and the transformer so I could measure the plate current as
the voltage drop across the resistor. (This is a Robert Fries
suggestion, for which I thank him. I didn’t like the idea of
doing a series current measurement here with the plate supply wire
not physically held in place by anything other than an alligator
clip.) I also soldered a one-ohm resistor between cathode and ground,
and got an accurate measurement of the screen resistor. Hooked the
Hewlett Packard across the cathode resistor, Fluke 8000A across the
plate resistor, and my faithful Radio Shack across the screen resistor,
allowing simultaneous measurement of plate, screen, and cathode
currents (Yes, I do have three eyes ). I did this for three
different tubes and, for two of them, at three different bias levels.
The amp is ’69 Pro Reverb put to BlackFace specs.

More data: (this would be easier with a spread sheet)

Fender Special Design 6L6GC (mid 70’s, made in USA. Sylvania I think).
Plate mA 31.2 36.0 42.0
Screen mA 1.72.0 2.3
Cathode mA 32.6 37.7 44.0
% error 4.54.7 4.8
RCA 6L6GC (mid 70’s, made in _Japan_, didn’t know they did that).
Plate mA 27.6 36.9 41.7
Screen mA 1.31.8 2.0
Cathode mA 28.6 38.3 43.4
% error 3.63.8 4.0
NOS Sylvania 5881 (USA)
Plate mA 36.5
Screen mA 1.6
Cathode mA37.8
% error 3.6
(The % errors were calculated as 100*(Cathode – Plate)/Cathode)

>From this, I’d have to guess that typical screen currents are in
the 1 to 2 mA range. Its also apparent that the screen current
will differ with the tube (comparing the three mid-bias range
screen currents, for instance, Fender> RCA > Sylvania 5881) but
I can’t say whether the variation is typical of the type/make (eg RCA vs
Sylvania) or whether different tubes of the same type would show
similar variations. Also note that the screen current and error
associated with the cathode resistor method increase as you bias
your amp hotter. (I hadn’t expected that). Anyway, the errors are
all less than 5%, and they’re on the safe side (ie measured current
is larger than actual plate current, so you’re biased colder than
you think). By way of comparison, the error inherent with the
transformer shunt method gives you an apparent plate current that
is smaller than the actual plate current. Unlike the cathode resistor
method, the error in the xfrmer shunt method is independent of the
actual bias point (at least theoretically). Had I used a Fluke meter
with an internal resistance of 5 ohms (which is all the Flukes I’ve
checked), and given that the DC resistance of my xfrmer primary is
70 ohms, the error with the xfrmer shunt method would be -6.7%.
The xfrmer shunt can give you larger errors than this if you’ve got
higher meter resistance or smaller xfrmer resistance (we went through
this stuff before in a.g.a – if your curious e-mail me. I’ve
got the original post on that still). So I guess Father Mark
was right when he told us that this could well be the case.
(Annoying, how he’s always right, in’t ). Now, some of you astute
persons will have noticed that in the above data, the sum of the plate
and screen currents is always greater than the cathode current by
about 0.3 mA. I’m writing that off at present to some systematic
error with the experiment. (Different meters used in a non-random
fashion, maybe I wrote a resistance value down incorrectly, or even
measured one wrong, lots of possibilities.) But to you more
thermionically informed persons, 0.3 mA couldn’t possibly be grid
current, could it? Okay, sorry for going on so long. Hope somebody
finds this useful.
Regards
Scott H.
(Oh yeah, PLEASE don’t show this post to Mark Garvin. He has bad
dreams when he hears about thermionic novices playing with high
voltage ). (Jocularity aside, thanks to Mark for suggesting I
do this. I learned alot).

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