Tidbit from a nice old book "Radio Transmitters"

[Opcom]

To improve linearity in Tetrode RF amplifiers, an "i.p. improver" is used.

A resistance effective only at audio frequencies is placed from cathode to GND, by means of an inductor as explained in the text. It is bypassed for RF. A rheostat is placed across the inductor to adjust the effect. It's said to make a few dB reduction in distortion. See the page on it fairly used. Has anyone experimented with this technique?

"Radio Transmitters, R F Power Amplification" by V.O. Stokes (Van Nostrand, "Marconi" series, 1970). A good read and explains distributed rf power amps, a 1KW case is given, and in general quite higher/professional power levels are discussed. The book seems kind of rare and or costly at $311 for the last known copy. Sad because it's very enlightening. Mine was 'withdrawn' from the public library. Previously, I was the only one to check it out in a 5 year period, this in Dallas TX! ahem what's wrong with the people in this city?!?!?!

[W7TFO]

'Ats what ya' gets fer messin' wit tubes havin' mor'en one grid, boy!

Nice pussies, by the by.

73DG

[K1JJ]

Very interesting.

I have a few tetrode linear amps here and have tried various resistances in the cathode in an attempt to improve linearity thru cathode negative feedback. Each trial failed cuz the bias was shifting with plate current, thus causing distortion.  It works FB with a class A stage, but not with a class AB/B stage with varying plate current.


However, this approach may solve that problem, I dunno.  I can easily hook it up and run some tone tests to see how the IMD improves.  But I wonder if ANY variation in bias voltage at ANY frequency will cause distortion at that frequency?


Let me send this link to my RF engineer friend and see what he thinks before I spend any time with it.

Tnx.

T

[w4bfs]

Very interesting.

.......Let me send this link to my RF engineer friend and see what he thinks before I spend any time with it.

Tnx.

T

ah so ..... mr Vu keeping expert on retainer ....velly smart

[AB2EZ]

Opcom
Tom

I'm assuming that we are talking about a "linear" RF amplifier.

In the case of an ideal, grounded cathode, class B RF amplifier (i.e. without the added cathode circuitry): the cathode current will consist of half-cycle, sinusoidal-shaped pulses... that repeat at the RF rate. The amplitudes of these half-cycle pulses will be proportional to the amplitude of the RF signal that is applied to the grid.

If you expand waveform (current vs. time) of the cathode current in a Fourier series (don't worry about what that is, if you are not familiar with the concept), it consists of:

A) Amplitude modulated sine waves at the fundamental RF frequency and harmonics of the fundamental RF frequency

plus

B. An audio frequency component that corresponds to the upper envelope of the input RF signal

Now, returning to the added components in the modified circuit.

The grid-to-ground input signal will continue to be an amplitude and/or phase modulated RF signal at the fundamental RF frequency

All of the RF, amplitude modulated components (mentioned in A. above) of the cathode current will pass through the cathode bypass capacitor.

The average value (i.e. DC) of the audio frequency component of the cathode current (that previously* corresponded to the upper envelope of the input RF signal) will pass through the choke.

*We will say, shortly, why the words "previously" and "approximately" have been added to this section of this post.

The time varying portion of the audio frequency component of the cathode current will pass through the cathode resistor... to produce a time varying, audio frequency voltage between the cathode and ground that follows (approximately) the envelope of the modulated input signal between the grid and ground.

But, what this audio frequency, time varying voltage is really following is: the time varying envelope of the amplifier's output signal. That is... to a very good approximation... the envelope of the modulated sine wave that is produced at the output of the amplifier will track the time varying, audio component of the waveform of the cathode current.  

Therefore, what is different in the modified design is that an audio frequency voltage is added between the cathode and ground, which follows (approximately) the time varying amplitude (envelope) of the amplifier's modulated, RF output signal.

This added, audio frequency, cathode-to-ground voltage will have the effect of modulating the grid-to-cathode bias of the tube in such a way as to:

a. Increase (make more negative) the grid-to-cathode bias when the pulses of cathode current are larger in amplitude (actually, when they are larger in area)

b. Decrease (make less negative) the grid-to-cathode bias when the pulses of cathode current are smaller in amplitude (actually, when they are smaller in area)

Strictly speaking... this corresponds to a version of  "feed forward" or "adaptive pre-distortion" compensation rather than negative feedback, because the compensation (i.e. changing the cathode-to-ground bias) reacts at audio frequencies, rather than at RF frequencies:

https://smartech.gatech.edu/bitstream/handle/1853/11652/sperlich_roland_200508_phd.pdf

If the amplitude of the incoming, modulated RF grid drive signal increases, then the cathode current will increase... and the cathode-to-ground bias voltage produced by the cathode resistor will increase (become more positive). This will increase the grid-to-cathode bias voltage (making it more negative)... thereby reducing the area of each pulse of cathode current (i.e. the tube will turn on for a smaller portion of each RF cycle, and the amplitude of each pulse of cathode current will also decrease).

Therefore, the modulated RF drive will not be directly converted into cathode current by the (non-linear) transconductance of the tube(s). Rather, it is the modulated grid-to-ground RF drive - a compensating cathode to ground voltage (varying at audio frequencies) that is converted into cathode current by the (non-linear) transconductance of the tube(s).

This is analogous to (but not the same as) the "adaptive pre-distortion" approach being used in Apache Labs' SDR transmitters.

Therefore, in summary, the added cathode circuitry is producing feed-forward type compensation, with an audio frequency time constant, to linearize the behavior of the overall amplifier. It is doing this by adjusting the bias, and, therefore, the fraction of each RF cycle that the tube conducts, as well as amplitude of each pulse of cathode current.

Stu

[K1JJ]

Interesting.

[Opcom]

That is an interesting expansion on the article, good explanation of what is going on there. The approximate resistance value in the text, 1 Ohm for the inductor, was chosen so that "DC" bias would not be upset excessively and the circuit acts only on the audio current.

What is missing from the textbook and context is what size of amplifier the technique applies to. The chapter is 'Class B Applications' with statements about Tetrodes being more available for (commercial amplifier/transmitter stage) powers up to 10KW, and class B Tetrode discussion followed by Triode discussion (conventional and GG), and the cited page is then given as a means of linearizing a Tetrode. From datasheets it is not so clear where the practical line is drawn between class AB and class B, regardless of the strict definitions.

With the low-ish currents drawn by ham level tetrode amps, usually less than 1A (in contrast to tubes with which the book is possibly more concerned like the 4CX5000 or -10000 with 2 to 3A plate current), the DCR of the inductor could possibly be more than the 1 Ohm value without ruining the effect. I'm curious also if a higher inductance value is acceptable, as long as the rheostat is there to reduce the inductor's effect, and the DCR is low (0.5 to 1 Ohm per amp?). Just saying a 2 Ohm DCR choke in the return of a 4-1000A or 4CX1000 is at worst adding 1.2-1.5V of unwanted 'averaged' DC cathode bias, comparing this to the actual -60 to 70V grid bias, a 1% addition.

[AB2EZ]

Opcom
et al.

With respect to values:

I think that it would be sufficient to have the value of the choke large enough to produce an impedance that is 2x the resistance of the added cathode resistor... at the lowest intended AM audio modulation frequency. I think it would be sufficient if the resistance of the choke were less than 5% of the value of the added cathode resistor.

Example:

The plate current (at carrier) is 300mA. The peak (not RMS) value of the input RF signal, at carrier, is 100V. The lowest audio modulation frequency of interest is 50Hz.

The maximum value of the added adjustable/selectable cathode resistor that I would chose (at least to experiment with) is: 100V/300mA = 333 ohms.

[Note: this maximum value of the added cathode resistor will reduce the AM modulation index at the output of the amplifier to approximately half of the AM modulation index at the input of the amplifier... because the pre-distortion responds to only the time varying part of the envelope of the cathode current. If you eliminate the choke, then the pre-distortion will not reduce the modulation index at the output of the amplifier (vs. the modulation index at the input of the amplifier)... but you will then require (in this example) approximately 2x the RF input voltage (i.e. 4 x the RF input power)... and you will have to adjust the fixed bias to compensate for the DC value of the added cathode-to-ground voltage*.]

I would choose an inductor whose impedance is (at a minimum) 660 ohms at 50Hz => approximately 2H

I would require the DC resistance of the choke to be less than 5% of the maximum added cathode resistance = 16.7 ohms. The fixed bias needs to be re-adjusted (as you suggest), so that the tube is operating close to the desired class B or class AB1 operating point.

I.e., if the target plate current, at carrier, is 300mA, and the added cathode choke has a resistance of 16.7 ohms... then I would re-adjust the fixed bias voltage to be 5V less negative than the value it would have with the added cathode choke bypassed with a wire.

*An improvement in this approach would be to measure the DC (average) value of the cathode-to-ground voltage with an op-amp... and use that to adjust the fixed grid-to-ground bias, via a feedback loop. If done properly... this feedback-loop-based approach would eliminate the need for the choke.  

[Note: this is a larger value of series resistance than what the author of the book recommended... even taking into account the relatively low plate current at carrier... but it is a more practical value for a moderately priced/moderate size 2H choke... at least for initial experimentation with this approach. The consequence, of allowing a larger value of choke resistance, is the need to re-adjust the fixed bias]

Stu
 

[Opcom]

I would agree about a higher choke resistance, however Mr Stokes cautions against a high DCR, saying it would add materially to bias and act like a cathode resistor, because he claims it would ruin linearity by changing grid bias at the audio rate.

I mis-stated by suggesting/interpreting it to mean about 0.5 to 1 Ohm per amp, it ought be an inverse function there, like the Ampere-Ohm, which is the Volt. So in Volts dropped across L, some percentage of bias, say 2-3V in a -300V arrangement with a 4CX10000, or less than 1V in a -60V arrangement as with a 4-1000.

For experimenting, a 16.7 Ohm choke might affect, or would affect, the result. I'm afraid too much. I appreciate the cost of things. There is a choke from a 4KV 3A klystron supply, perhaps 2 Ohms or so, have to go look at it again. It's not big, perhaps the size of a 250W power transformer. I'm not sure what to apply it to around here. The only Tetrode amp is an NCL-2000 running a pair of 8122's at 2KV and "1KW input" in AM mode. Would this be a type of amp to try it on? Ad it and increase the bias from AB1 to closer to B and see what the scope looks like? Negative points of that amp as part of an experiment are that it's a pretty big amp for a first experiment, and has two tubes likely not matched. -extra variable there.

From that page being in the class B chapter, he must be aiming more toward linearizing a tetrode operated more Class-B-ish-ly than AB1-ish-ly. Near cutoff, Triodes have more linear curves than most Tetrodes.  -his point, then, on what to do with tetrodes.

In the overall book, efficiency is mentioned many times for the sake of the broadcaster, thus the class B Tetrode discussion. I have no foolproof way to measure the smaller improvements, only basic instruments up to a spectrum analyzer, if that would do.

[AB2EZ]

Opcom

You wrote:

"I would agree about a higher choke resistance, however Mr Stokes cautions against a high DCR, saying it would add materially to bias and act like a cathode resistor, because he claims it would ruin linearity by changing grid bias at the audio rate." and "For experimenting, a 16.7 Ohm choke might affect, or would affect, the result. I'm afraid too much."

I respectfully disagree with the statement that you attribute to Mr. Stokes.

The resistance of the choke is in series with the inductance of the choke. Since the choke will represent a high impedance at audio frequencies of interest... the current through the choke will not vary significantly at audio frequencies in interest... and the voltage drop across the choke will, therefore, not vary significantly at audio frequencies. The audio component of the cathode current almost entirely flows through the added resistor, not the choke.

Therefore:

Will the cathode-to-ground portion of the bias vary at audio frequencies? Yes... but this effect will be totally dominated by the added cathode resistor... while the series resistance of the choke will have a negligible effect. The series resistance of the choke will primarily affect the DC cathode-to-ground voltage, and therefore the cathode-to-ground portion of the fixed bias.

Stu

I would agree about a higher choke resistance, however Mr Stokes cautions against a high DCR, saying it would add materially to bias and act like a cathode resistor, because he claims it would ruin linearity by changing grid bias at the audio rate.

I mis-stated by suggesting/interpreting it to mean about 0.5 to 1 Ohm per amp, it ought be an inverse function there, like the Ampere-Ohm, which is the Volt. So in Volts dropped across L, some percentage of bias, say 2-3V in a -300V arrangement with a 4CX10000, or less than 1V in a -60V arrangement as with a 4-1000.

For experimenting, a 16.7 Ohm choke might affect, or would affect, the result. I'm afraid too much. I appreciate the cost of things. There is a choke from a 4KV 3A klystron supply, perhaps 2 Ohms or so, have to go look at it again. It's not big, perhaps the size of a 250W power transformer. I'm not sure what to apply it to around here. The only Tetrode amp is an NCL-2000 running a pair of 8122's at 2KV and "1KW input" in AM mode. Would this be a type of amp to try it on? Ad it and increase the bias from AB1 to closer to B and see what the scope looks like? Negative points of that amp as part of an experiment are that it's a pretty big amp for a first experiment, and has two tubes likely not matched. -extra variable there.

From that page being in the class B chapter, he must be aiming more toward linearizing a tetrode operated more Class-B-ish-ly than AB1-ish-ly. Near cutoff, Triodes have more linear curves than most Tetrodes.  -his point, then, on what to do with tetrodes.

In the overall book, efficiency is mentioned many times for the sake of the broadcaster, thus the class B Tetrode discussion. I have no foolproof way to measure the smaller improvements, only basic instruments up to a spectrum analyzer, if that would do.

[Opcom]

Stu, I am trying to understand this.

You said:
"Will the cathode-to-ground portion of the bias vary at audio frequencies? Yes... but this effect will be totally dominated by the added cathode resistor... while the series resistance of the choke will have a negligible effect. The series resistance of the choke will primarily affect the DC cathode-to-ground voltage, and therefore the cathode-to-ground portion of the fixed bias."

By "added cathode resistor", do you mean the variable resistor R1 from the cathode to GND?
My thought was that the resistor in the original circuit was of a higher value (20-100x) than the choke and is used to adjust the relative amount of audio developed across the choke, and acts like the cathode resistor for audio, whereas the DCR of the choke is the item acting like an unwanted cathode resistor for DC. LTSpice chould help me out there.

[AB2EZ]

Opcom

You wrote:

"By 'added cathode resistor', do you mean the variable resistor R1 from the cathode to GND?"

Yes... the variable resistor, R1 in the author's diagram, is what I was calling "the added cathode resistor".

You also wrote:

"My thought was that the resistor in the original circuit was of a higher value (20-100x) than the choke and is used to adjust the relative amount of audio developed across the choke, and acts like the cathode resistor for audio, whereas the DCR of the choke is the item acting like an unwanted cathode resistor for DC. "

Yes.. that is exactly what is happening. In my previous post I was disagreeing with the statement that you attributed to Mr. Stokes:

"Mr. Stokes cautions against a high DCR, saying it would add materially to bias and act like a cathode resistor, because he claims it would ruin linearity by changing grid bias at the audio rate"



Best regards
Stu

[Opcom]

I must have not understood Mr. Stokes and mis-wrote what I thought he meant.

[K4RT]

I must have not understood Mr. Stokes and mis-wrote what I thought he meant.

Perhaps you should take more care in posting.

[Opcom]

I must have not understood Mr. Stokes and mis-wrote what I thought he meant.

Perhaps you should take more care in posting.

No, I wrote precisely what I thought he meant, which was based on an incorrect understanding of the writing. Thank you for your contribution.

[WBear2GCR]

Just thinking about this a little...

the bypass resistor is going to introduce some bias voltage, but since the choke is lower in DCR, it is swamped. Ok. But as the DCR of the choke goes up, so does the bias voltage effect at DC. Above DC, and at low freqs there might be some "pumping" where (or if) the DCR and the impedance start to look similar.

I don't see how this meets the criteria of "feed forward" at all. It's simply a bandpass filter in a standard cathode feedback arrangement. In fact the cap in parallel with an inductor, shunted by a resistor is a bandpass filter, and the R adjusts the "Q".

Otoh it is an interesting way to do things.

Why would it not be applicable to tubes other than tetrodes?

[AB2EZ]

Bear

The more I think about it, the more I agree, with you, that this method is best described as a method to make the amplifier's output envelope more linearly proportional to the amplifier's input envelope... by employing a form of negative feedback... using the short-time-averaged cathode current to estimate the audio frequency envelope of the output RF signal, and to modulate the amplifier's bias voltage at those audio frequency rates. I.e. if the fidelity between the output RF signal's envelope, and the input RF signal's envelope is all you really care about, then this method can be considered to be an example of the use of "negative feedback" (although, as is discussed below, what you are subtracting from the input is not an RF signal)

In each of: the "feed forward", "adaptive pre-distortion",  and the "negative feedback" approaches, you are comparing a sample of the output that is being produced now (or something else that you believe to be proportional to the output that is being produced now), to what you would like it (ideally) to be... and then making adjustments of one kind or another. The adjustments might include: adding a correction signal to the input signal... in order to make the output signal more closely match what you would like the output signal to be; or adjusting one or more parameters of the amplifier chain to make the output signal more closely match what you would like the output signal to be; or adding a correction signal to the output signal, in order to make the output signal more closely match what you would like the output signal to be.

In the case of "negative feedback", the adjustments are made quickly enough so that the output being produced now is corrected in "real time". To achieve this, the delay associated with: obtaining a sample of the present output, or an estimate of the present output (not necessarily from the output itself), then determining what the "error" is between the sample or estimate of the present output and the desired output, and then applying the correction, must be less than the time it takes for the output to change significantly. The traditional "negative feedback" approach (as Harold Black invented it) is: to subtract a portion of the amplifier's output signal from the amplifier's input signal. Some might argue that the terminology "negative feedback" should only be used in a case where a correction signal is subtracted from the input, and that correction signal is the same type of signal as the input signal (i.e. an RF signal in this case).   

In the case of "feed forward", or "adaptive pre distortion" the delay associated with: obtaining the sample of the present output or an estimate of the present output (not necessarily directly from the output itself), then determining what the "error" is between the sample or estimate of the present output and the desired output, and then applying the correction, can be longer than the time it takes for the output to change significantly. In that case, one is attempting to make future outputs (that result from future inputs) more faithfully resemble what you want them to be... not to make further corrections to the present output. Perhaps this method should always be called "adaptive pre-distortion", which is what Apache Labs calls the linearization method they employ on their transceivers... because only future outputs are affected, based on corrections that are computed from present (and past) outputs.

Note: There is one version of the feed forward method (also invented by Harold Black), that does not quite fit the above, generalized definition of "feed forward". The present output is sent to a delay line to produce a delayed output. A correction signal is added to the delayed output, in order to make the corrected, delayed output closer to what you want the output to be. The delay of the delay line has to equal the delay between the sampling of the present output (not the delayed output) and the production of the correction signal. I believe that the earliest examples of "feed forward" linearization, that I saw in the late sixties, employed this approach. Perhaps the name "feed forward" should only apply to this version of the approach, and all other versions should be called "adaptive pre-distortion"

In the particular case we are discussing here, the RF signal, that we are trying to make corrections to, is a signal that has a frequency of (for example) 3.8MHz; and, therefore, 45 degrees of phase shift corresponds to 0.033 microseconds of delay. But the bias is being adjusted at audio frequency rates... so the delay times associated with obtaining the corrections are in the range of: 0.1 to 10 milliseconds.

If you think of this method as trying to make the RF output waveform more linearly proportional to the RF input waveform... then this is an example of the "feed forward method" (or, alternatively, "adaptive pre-distortion")

If you think of this method as trying to make the envelope of the RF output waveform more linearly proportional to the envelope of the RF input waveform, then this can be considered an example of the negative feedback method... although (again) the correction signal, being subtracted from the input to the amplifier, is not an RF signal.

Of note: this method would also work if the amplifier was being operated as a frequency doubler. In that case, the RF output of the amplifier would be an amplitude modulated sine wave at twice the RF frequency of the input to the amplifier... so, in that sense, the output would definitely not be linearly proportional to the input. Nevertheless, the envelope of the RF output signal would (more or less) linearly track the envelope of the RF input signal.

I don't agree with your analysis of how the circuit works... but that is what makes horse races. I have already posted my analysis, in some detail... so I won't repeat it here. In summary, a negative feedback approach is being used to adjust the bias (at audio frequency rates) in order to make the RF output envelope more linearly proportional to the RF input envelope.

I do agree, however, that one needs check what the resonant frequency and the Q of the RLC circuit are (ignoring, for simplicity, the series resistance of the inductor). For example, if L=2H, and the RF bypass capacitor (C) is chosen to be .01uF (4.2 ohms of reactance at 3.8MHz), then the resonant frequency is 1125Hz. This is right in the middle of the range of audio frequencies of interest. But, the Q at this frequency would be R/(14.2k ohms)... which is very low, for values of R less than 1000 ohms. So, the resonant peak associated with this RLC circuit will be negligible, in terms of its effect on the behavior of this circuit.

I.e.

At DC, the impedance between the cathode and ground will be the series resistance of the choke (instead of zero ohms, in the unmodified circuit)

At audio frequencies, the impedance between the cathode and ground will be the value of R1 (the adjustable parallel resistor)

At RF frequencies, the impedance between the cathode and ground will be the reactance of the bypass capacitor.

Stu  

[WBear2GCR]

Seems about right, Stu!

The adaptive feedforward is a "thing".

Classic (if it can be called classic) feedforward is realtime in as much as it often takes a
separate signal path in parallel with the main path to "inject" the correction signal forward of the input to the two paths.

In one early case the design was actually two paralleled power amplifiers, one provided the correction signal only... expensive of course.

But one thing that I wonder about, is this only applicable to tetrodes? If so, why?
Are triodes inherently more linear so there is no real benefit, or are triodes and pentodes not generally used for high power RF service?

                    _-_-

PS. thanks for figuring the Q and the resonant freq!

[AB2EZ]

Bear

I can think of only one reason why this method would not work with a triode. I can't think of any reason why this method would not work with a pentode. Maybe there is a reason that I'm not "seeing". See my question below.

I think this method could work even better with a triode... because, in a triode, the cathode current does not split between plate current and screen current. Therefore the variations in the audio frequency component of the cathode current (which is producing the feedback signal) would more closely track the audio frequency variations in the amplitude of the fundamental RF frequency component of the plate current.

However, there is one thing, in this regard, that I am not sure of:

In a class B linear RF amplifier application: as the grid-to-cathode voltage varies through each RF cycle, with various peak amplitudes (corresponding to the amplitude modulation of the input signal)... does the differential output impedance [dv/di] of the tube itself (in the case of a triode) vary too much... as a function of the instantaneous plate current (i) and the instantaneous grid-to-cathode voltage? If it does, then the amplitude of the fundamental RF frequency voltage across the output of the tube will not be proportional to the amplitude of the fundamental RF frequency component of the plate current. I.e. the RF load impedance (through which the RF portion of the plate current flows) is: the output impedance of the tube in parallel with the input impedance of the pi network.

Checking a few points on the published specification sheet for an Eimac 3-500Z, the plate resistance (dv/di), at various fixed values of grid-to-filament voltage, varied between 7000 ohms and 8750 ohms. Since the recommended "resonant" RF load impedance is around 3000-5000 ohms (depending upon the DC plate voltage), it appears that the combined (in parallel) plate impedance and load impedance will vary too much to consider the RF output voltage at the fundamental frequency as being proportional to the fundamental RF frequency component of the plate current... at least in the context of this linearization approach.  

In the case of a tetrode or a pentode, the output impedance of the tube is usually much larger than the input impedance of the pi network... so the output impedance of the tube has only a small effect on the impedance of the parallel combination.

Stu

[John K5PRO]

Interesting discussion here. I got my copy of Stoke's book online a few year ago, it smells like it sat in a damp basement and I was never able to remove that by drying it, sitting it in a bag with baking soda, etc.

The biggest Pentode (of US make) that I am familiar with is the 5CX3000A. Trying to align a third grid in a large diameter radial beam tube is challenging in larger tube than this. The biggest triode that is still in production is probably the RCA/Burle/Photonis 7835. It is rated for 300 kW plate dissipation and comes from a family of triodes that work(ed) up to 400 MHz or more. Grid current is huge in a tube like this. We use them at pulsed at work and the DC cathode current is 400 amps. They are self biased with a cathode resistor of 0.25 ohms, giving 100 volts of bias when driven with RF.

However, most or all of the new super high power tubes are tetrodes now. The screen and control grid are aligned closely so that electrons don't intercept the screen much, and they use pyrolytic graphite instead of wire grids. The TH628 from Thomson/Thales is easily able to make 1.5 MW CW at HF, while the Eimac 4CM2500KG can do a bit more. Cathode currents are hundreds of Amps.

Back to the topic though, these techniques (in Stokes) are not going to make a tremendous difference are they?