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Pentode Screen Resistance (rs) Estimation Example



 
 
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  #1  
Old January 31st 16, 05:26 PM
John L Stewart John L Stewart is offline
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Smile Pentode Screen Resistance (rs) Estimation Example

John L Stewart Jan 2016

In the Heathkit UA-1 12W Amplifier we see a 0.1 microF capacitor bypassing a one Meg resistor supplying the screen current. We might think that we can simply take that RC time constant & easily estimate the low frequency rolloff. But we would be dead wrong & get a result with a gross error.

The actual R the supply resistor is driving into is the screen resistance, analogous to a plate resistance of a triode. So the R in the RC time constant then becomes the parallel resistance of the screen & supply resistances. The problem is complicated by the lack of any published data with regards to screen resistance.

Fred Terman (And Wm. Hewlett) tell us that screen resistance for a pentode can be estimated as follows-

rs = ( ( Ib + Ic2 ) / Ic2 ) * Rp

From this we need to know 6AN8 triode Rp, another spec not published for the 6AN8. For the attached 6AN8 pentode plate family draw a line from the origin to the intersection of the Ec1 zero bias curve where Ec2 & the plate are at equal voltage. In this example that would be at 150 plate volts.

Triode plate Rp for the pentode section at zero bias is approximately as follows-

Rp ~ Change of Eb / Change of Ib

From the 6AN8 Average Transfer page, Change of Eb = 150 Volts
& Change of Ib ~ 28mA (plate) + 9mA (screen)
So triode Rp ~ ( 150 / 37 ) K or 4.05K

Aside from the scale factors of voltage & current all triode plate families look very much the same. As an example refer to the 6BQ7 plate family. When G1 bias is increased plate resistance increases. As an educated guess we can assume Rp for a triode connected 6AN8 pentode section to be something like 10K at the operating point.

Using the typical operating currents split on the 6AN8 pentode we get-

rs ~ ( ( 9 + 2.8 ) / 2.8 ) * 12K
or rs ~ 42.1K

That is the number we need to compute the rolloff frequency of the amplifier front end.

The R in the RC calculation now becomes rs in parallel with one M.

R ~ 40.4 K, a factor of about 20 times different than where we started.

RC = 0.0040 sec F = 0.159 / RC Hz 39.4 Hz

Looks like it is a step built in as part of the NFB stabilization circuits.

Note 1- Wm Hewlett & David Packard of HP were Fred Termanís Graduate Students at Stanford U.

More to come
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  #2  
Old January 31st 16, 06:15 PM
John L Stewart John L Stewart is offline
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Posts: 301
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Measurement of Screen Resistance Example John L Stewart Jan 2016

When designing or building an ordinary vacuum tube audio amplifier with a pentode front end we can for the most part ignore the screen supply resistance. Simply set it to be in the range of 3-4 times the plate resister & the circuit will perform satisfactorily. As long as the screen resister is adequately bypassed there are no significant problems.

That all changes when the intention is to use NFB. Most folks would assume that the RC time constant is simply the screen resister times the screen bypass capacitor. That can lead to problems since the screen supply resister is actually in parallel with the resistance of the screen grid itself as seen looking into the tube. Some calculations using the available published tube data indicates the screen resistance of common audio voltage amplifier pentodes to be in the range of 40K.

This simple setup makes measurements leading to the incremental screen resistance of the pentode section of a 6U8 vacuum tube while in operation. The tube is connected to a plate supply of 300 volts. The screen is fed from this supply thru a total of 730K resistance. But interposed on that is a means of applying an interfering One KHz test signal. Any audio transformer of high impedance primary & secondary can be used to couple the audio signal generator to the high voltage on the screen. I used an old Hammond 447 Interstage Transformer.

Just two measurements are required. Using a differential probe the AC voltage drop across the 730K is measured, then the AC voltage from common to screen.

The results are as follows-

First Pass- Drop across 730K was 0.9V

So Ig2 is 0.9 V / 0.73 M, 1.23 microA And Eg2 measured 0.043V

So rs is delta E / delta I rs = (0.043V / 1.23 microA)K or 35.0K

2nd Pass- Drop across 730K was 2.83V

So Ig2 is 2.83 V / 0.73 M, 3.88 microA And Eg2 measured 0.133V

So rs is delta E / delta I rs = (0.133V / 12.83 microA)K or 35.0K
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  #3  
Old January 31st 16, 09:56 PM
John L Stewart John L Stewart is offline
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Measure Step Size caused by the Screen Bypassing Network
John L Stewart Jan 2016

This paper covers measurements made to determine the frequency response step size caused by the screen bypass circuit in a voltage amplifier pentode.

Two similar circuits were used in this trial. Neither is optimized. In one circuit the screen grid is supplied DC in the ordinary way from the plate supply. In the alternative circuit a screen DC connexion thru a suitable resistance back from the following cathode of a DC coupled split load phase inverter is used. Each has certain advantages & problems. Refer to the schematics.

The signal generator is direct connected to grid one of the 6U8 pentode section. There is no capacitor in order that there be no other RC time constant in circuit that might cause errors during the tests. Notice the screen bypass capacitor is rather low capacity. The test equipment would take a very long time while operating at low frequency in order to acquire the data. Shifting the frequency by using a smaller RC time constant eliminates that problem. The resulting step remains the same size.

The Pico Technology Scope/ Spec A has a max input of +/- 20 volts. With the X10 Differential Probe that becomes +/- 200 volts. So the gain measurements are all taken off the cathode of the triode section of the 6U8. If taken off the plate connexion of the 6U8 pentode the probe would need to be set to X100 which would result in less measurement resolution. The experimenter needs to know as much about what his equipment will not do as what it will.

For the ordinary circuit- in out Gain Gain db


Bypass cap connected 100 mV 12.54 V 125 42
Bypass cap disconnected 100 3.59 35.9 31
Step is ~ 11 db


Bypass cap disconnected 182 mV 6.14 V 33.7 30.6
Bypass cap connected 182 18.8 102.2 40.2
Step is ~ 10 db almost clipping

For the CF to G2 circuit- in out Gain Gain db

Bypass cap disconnected 99 mV 2.11 V 21.2 26.5
Bypass cap connected 103 7.89 76.6 37.7
Step is ~ 11 db overloaded


Bypass cap connected 50 mV 4.87 V 97.4 39.8
Bypass cap disconnected 48 1.04 21.7 26.7
Step is ~ 13.1 db almost clipping

Terman reports phase shift for screen steps in this range have maximums of 25-40 degrees.
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  #4  
Old January 31st 16, 10:54 PM
John L Stewart John L Stewart is offline
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Here are the measurement results with the formatting still intact.

Cheers to all, John L Stewart
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  #5  
Old February 1st 16, 06:15 AM posted to rec.audio.tubes
Big Bad Bob
external usenet poster
 
Posts: 366
Default Pentode Screen Resistance (rs) Estimation Example

On 01/31/16 13:56, John L Stewart so wittily quipped:
> Measure Step Size caused by the Screen Bypassing Network
> John L Stewart Jan 2016
>
> This paper covers measurements made to determine the frequency response
> step size caused by the screen bypass circuit in a voltage amplifier
> pentode.
>
> Two similar circuits were used in this trial. Neither is optimized. In
> one circuit the screen grid is supplied DC in the ordinary way from the
> plate supply. In the alternative circuit a screen DC connexion thru a
> suitable resistance back from the following cathode of a DC coupled
> split load phase inverter is used. Each has certain advantages &
> problems. Refer to the schematics.
>
> The signal generator is direct connected to grid one of the 6U8 pentode
> section. There is no capacitor in order that there be no other RC time
> constant in circuit that might cause errors during the tests. Notice the
> screen bypass capacitor is rather low capacity. The test equipment would
> take a very long time while operating at low frequency in order to
> acquire the data. Shifting the frequency by using a smaller RC time
> constant eliminates that problem. The resulting step remains the same
> size.
>
> The Pico Technology Scope/ Spec A has a max input of +/- 20 volts. With
> the X10 Differential Probe that becomes +/- 200 volts. So the gain
> measurements are all taken off the cathode of the triode section of the
> 6U8. If taken off the plate connexion of the 6U8 pentode the probe would
> need to be set to X100 which would result in less measurement
> resolution. The experimenter needs to know as much about what his
> equipment will not do as what it will.
>
> For the ordinary circuit- in out Gain Gain db
>
>
> Bypass cap connected 100 mV 12.54 V 125 42
> Bypass cap disconnected 100 3.59 35.9 31
> Step is ~ 11 db
>
>
> Bypass cap disconnected 182 mV 6.14 V 33.7 30.6
> Bypass cap connected 182 18.8 102.2 40.2
> Step is ~ 10 db almost clipping
>
> For the CF to G2 circuit- in out Gain Gain db
>
> Bypass cap disconnected 99 mV 2.11 V 21.2 26.5
> Bypass cap connected 103 7.89 76.6 37.7
> Step is ~ 11 db overloaded
>
>
> Bypass cap connected 50 mV 4.87 V 97.4 39.8
> Bypass cap disconnected 48 1.04 21.7 26.7
> Step is ~ 13.1 db almost clipping
>
> Terman reports phase shift for screen steps in this range have maximums
> of 25-40 degrees.
>
>
> +-------------------------------------------------------------------+
> |Filename: Screen Decoupling in DC NFB Version 6W.jpg |
> |Download: http://www.audiobanter.com/attachment.php?attachmentid=427|
> |Filename: Screen Decoupling in Ordinary Version 6W.jpg |
> |Download: http://www.audiobanter.com/attachment.php?attachmentid=428|
> |Filename: Keep-On-Truckin-T-Shirt-(8395).jpg |
> |Download: http://www.audiobanter.com/attachment.php?attachmentid=429|
> +-------------------------------------------------------------------+
>
>
>


I would expect screen resistance to change based on G-K volts, according
to some kind of general curve, and it's probably NON-linear at that,
based on the actual screen volts, plate volts, plate current, blah blah
blah.

But yeah, get it wrong and you howl and screech like a poorly configured
regenerative receiver.


  #6  
Old February 1st 16, 06:10 PM
John L Stewart John L Stewart is offline
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First recorded activity by AudioBanter: Jan 2011
Location: Toronto
Posts: 301
Smile

I would expect screen resistance to change based on G-K volts, according
to some kind of general curve, and it's probably NON-linear at that,
based on the actual screen volts, plate volts, plate current, blah blah
blah.

But yeah, get it wrong and you howl and screech like a poorly configured
regenerative receiver.

------------------------------------------------------------------

OK Bob, you bring up a good point. But things are not as ominous as that. See below-

Termanís Explanation of Change of rs with Change of Screen Current

Translated it looks like this-

If Ig2 the screen current increases by 25% we would take the 3rd root of 1.25

(1.25)^(1/3) = 1.077

Then the reciprocal 1 / 1.077 = 0.928

If the screen resistance rs was 40K then at the new current it is 0.928* 40K

rs = 37.1 K at the new current

Fortunately the test setup is relatively simple. It is easy to make measurements under any set of conditions. If one has an ordinary scope there is no need for a differential probe as I have used. Just need two channels set for AC in, x10 probes & A-B to measure the difference resulting.

Some measurements are a long way off ground with large DC offsets so be sure to set AC inputs. With x10 probes the circuit loading will be 20M so in most cases that will not have to be taken into account.

I gave my analogue scope away several years ago. The Pico Tech provides a lot more information. And that can go right to a file for further use. But I forget to check the diff probe input Z, it is 4M. So I would need to go back & take that into account for the measurements across the 730K resister in the example. That is easy on an HP Calculator running RPN. So the 730K screen resister in the example becomes 617.3K & on from there. But the basic procedure is the otherwise the same.

The step in frequency response provided by the partially bypassed screen is a convenient adjustment one can make to get LF stability in a NFB amplifier. If it were a triode front end then a partially bypassed cathode resister could perform the same function. For the HF something else needs doing.

Cheers to all the Faithful still on here, John L Stewart
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  #7  
Old February 1st 16, 07:28 PM posted to rec.audio.tubes
Big Bad Bob
external usenet poster
 
Posts: 366
Default Pentode Screen Resistance (rs) Estimation Example

On 02/01/16 10:10, John L Stewart so wittily quipped:
> I would expect screen resistance to change based on G-K volts,
> according
> to some kind of general curve, and it's probably NON-linear at that,
> based on the actual screen volts, plate volts, plate current, blah blah
> blah.
>
> But yeah, get it wrong and you howl and screech like a poorly
> configured
> regenerative receiver.
>
> ------------------------------------------------------------------
>
> OK Bob, you bring up a good point. But things are not as ominous as
> that. See below-
>
> Termanís Explanation of Change of rs with Change of Screen Current


(etc.)

this probably plays a big role in determining the series resistance
needed for a proper ultra-linear config. As for me, I think I prefer
using a fixed and well regulated (and short-circuit protected) voltage
for G2 in the power stages. It also tends to give you a bit more power
out of the same tubes, with somewhat higher distortion depending on the
amplifier configuration [if you're doing AB2, it's probably less
significant, and G1 current probably becomes the primary source of
distortion and whatnot]. My focus is normally on 'final stage' beam
power and power pentodes.

In low power amplification stages with pentodes, this is a completely
different thing.

Biggest problems with pentodes overall is the nonlinearity. It's great
for mixer stages, great for frequency synth in radios, great for IF with
AGC, not so good for audio amplification. Basically, a pentode can act
as nonlinearly as a bipolar transistor. Correcting for this in audio
circuits requires lots of negative feedback, and so you point out the
problems with feedback and G2 series resistors and bypass capacitors [etc.].

Most pentode tube usage I've seen is in RF, not AF, and RF is where they
do the best, particularly the 'sharp cutoff' variety [a side effect of
their nonlinearity] for AGC and similiar circuits.

I'm not a fan of using them in AF circuitry. A dual triode typically
gives you as much open loop amplification using 2 stages, with
significantly lower distortion.

Anyway, this whole thing about G2's biasing and filtering could become
the topic of an entire series of articles or even a book.


  #8  
Old February 2nd 16, 10:03 PM
John L Stewart John L Stewart is offline
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First recorded activity by AudioBanter: Jan 2011
Location: Toronto
Posts: 301
Smile

Biggest problems with pentodes overall is the nonlinearity. .



I'm not a fan of using them in AF circuitry. A dual triode typically
gives you as much open loop amplification using 2 stages, with
significantly lower distortion.

``````````````````````````````````````````````````

Are your conclusions based on hearsay or did you make some measurements to back up your opinion? If you have some comparison data perhaps you could post it here.

Thanx, John
  #9  
Old February 4th 16, 02:43 PM
John L Stewart John L Stewart is offline
Senior Member
 
First recorded activity by AudioBanter: Jan 2011
Location: Toronto
Posts: 301
Smile

Biggest problems with pentodes overall is the nonlinearity. It's great
for mixer stages, great for frequency synth in radios, great for IF with
AGC, not so good for audio amplification. Basically, a pentode can act
as nonlinearly as a bipolar transistor. Correcting for this in audio
circuits requires lots of negative feedback, and so you point out the
problems with feedback and G2 series resistors and bypass capacitors [etc.].

Most pentode tube usage I've seen is in RF, not AF, and RF is where they
do the best, particularly the 'sharp cutoff' variety [a side effect of
their nonlinearity] for AGC and similiar circuits.

I'm not a fan of using them in AF circuitry. A dual triode typically
gives you as much open loop amplification using 2 stages, with
significantly lower distortion.

--------------------------------------------------------

For sure a pair of triodes will get more gain than a pentode. But the 2nd triode of the pair amplifies all the distortion of the first as well as the fundamental resulting in several even higher order harmonics, not exactly what we need.

As it turns out a pentode does have lower D than it does as a triode over a useful section of its output voltage range. Refer to the attached work done many years ago.

That range corresponds to the region where most hi G power pentodes such as EL34, KT66, 6550 & son on can be driven to full power. And running thru a split load phase invertor can easily drive a PP pair to full power, something Dyna & others took advantage of. Fewer stages translates to fewer high order harmonics before NFB is applied. And much better stability margin & reliability.

In the normal listening range the pentode looks much better than it does hooked up as a triode.

Cheers to all, John L Stewart
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  #10  
Old February 4th 16, 07:22 PM posted to rec.audio.tubes
Big Bad Bob
external usenet poster
 
Posts: 366
Default Pentode Screen Resistance (rs) Estimation Example

(I said)
> Most pentode tube usage I've seen is in RF, not AF, and RF is where
> they
> do the best, particularly the 'sharp cutoff' variety [a side effect of
> their nonlinearity] for AGC and similiar circuits.
>
> I'm not a fan of using them in AF circuitry. A dual triode typically
> gives you as much open loop amplification using 2 stages, with
> significantly lower distortion.
>


then, On 02/04/16 06:43, John L Stewart so wittily quipped:
>
> For sure a pair of triodes will get more gain than a pentode. But the
> 2nd triode of the pair amplifies all the distortion of the first as well
> as the fundamental resulting in several even higher order harmonics, not
> exactly what we need.


yeah, that's somewhat unavoidable. so you suggest that single stage has
lower overall distortion? Hard to tell, but I suppose it would depend
on the overall circuit design, operating range, etc.. and whether you're
using 'mu factor' gain or an unbypassed cathode resistor to provide a
small amount of negative feedback in the stage.

[my favorite includes partial bypass to give you proper cathode bias but
still control the gain, maybe 1/2 or 1/3 of the mu factor per stage]

> As it turns out a pentode does have lower D than it does as a triode
> over a useful section of its output voltage range. Refer to the attached
> work done many years ago.


saw that, measured IM distortion but for the same tube [not an actual
triode, just triode-configured pentode]. But it doesn't address the
higher noise typically found in pentode amplifiers due to the additional
grids, etc..

So maybe it makes the case for a pentode at the mid-point, then? Low
signal input levels sort of demand a triode to improve S:N (and high
quality low noise grid resistors with values below ~200k).

> That range corresponds to the region where most hi G power pentodes such
> as EL34, KT66, 6550 & son on can be driven to full power.


OK - that would make sense. dual pentodes driving power output tubes,
maybe, or single-ended pentode driving a phase-split transformer. Since
off-the-shelf pentodes typically run at higher currents than triodes,
AB2 amplifiers would possibly work better.

> In the normal listening range the pentode looks much better than it does
> hooked up as a triode.


I'd still like to see the noise measurements, comparing actual triodes
to pentode, maybe 12AX7 [which would be the typical triode to use for
low level signals]. I suppose I'd run my own o-scope test for that one,
if I had any pentodes laying about to test. There are a number of
things to look at, from grid resistor values to capacitor materials to
power supply rejection. Those would have to be factored out somehow for
a fair comparison.


 




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