Calculating modulator impedances

[W8ACR]

Well, I have spent a lot of time reading technical manuals the past few days but to no avail. I thought I had things figured out, but when I start to do the math, things just don’t make sense.

Here is the question that I am trying to answer: if I know the optimal impedance for a modulator to work into at a certain set of parameters, can I figure out, mathematically, the optimal impedance at a new set of parameters?

For example, 811A’s with 1500V on the plates, will deliver 340 watts of audio into an optimal impedance of 12400 ohms plate to plate. These numbers are from the published RCA tube data. However, in my home brew transmitter, the 811A’s are running with 1400V and need only deliver 225 watts of audio. What is the optimal plate to plate impedance at the new settings? It seems like this should be a straightforward mathematical conversion, but maybe I’m wrong. FWIW, the modulated rf stage is running at 2000V and 200mA. I have a multi tap modulation transformer so I can get a good match once I know what the match needs to be. I’d appreciate any help.

Thanks, Ron w8acr

[KA2DZT]

Most all multi-match mod xfmrs have a slight step up (or down) from the whole winding on one side to the other side.  You can find what side is what by applying a low AC voltage to one side and then measure the voltage on the other side.  Each side has two windings each with a tap.  The tap is not in the center of the windings.  Most likely you'll need a slight step down from the modulators to the PA.  Best to use the entire winding on the modulator side and then use a portion or the whole winding on the PA side.

2KV and 200ma plate voltage and current results in a 10K PA impedance.  Those impedance charts are nice to look at but it's the turns ratio that counts.  The PA load sets the load reflected back to the modulators.  First find which side of the xfmr has the higher number of turns.  Do that with the low AC voltage test (probably you may be able to see this by looking at the impedance charts).  From the voltage readings you can find the overall turns ratio.  The impedance ratio is the square of the turns ratio.

BTW what mod xfmr do you have??

Fred

[w8khk]

Ron, I think you could just go with 12400 ohms on the primary and 10000 ohms on the secondary as a starting point.  I am not sure there is anything to be gained by trying to calculate an exact impedance for that power level.  You could always tune it in by changing taps after your initial testing.  I did the same thing with my PP 810s modulating PP 250THs using a Stancor A3899 modulation transformer.  Running slightly lower than design impedance provided optimal results regarding headroom and distortion.

I attached the 811A RCA document I am referring to, and a snip of the Class B specifications for both CCS and ICAS.

As you can see, they provide parameters for 12400 ohms for CCS at 1250 volts and for ICAS at 1500 volts.  As you said, max output for ICAS is 340 watts, and for CCS at 1250 volts it is 235 watts.  Modulating your final RF amplifier at 400 watts requires a minimum of 200 watts, and I believe you specified you need 225 watts of audio, this allows 25 watts loss in the modulation transformer and other components, but this figure does not provide any headroom for positive peaks greater than 100 percent.

If you were to increase the primary impedance (because you have excess plate voltage and excess power) then you could potentially reduce the maximum power output to your goal of 225 watts, and, at the same time, you would be running a higher peak voltage on the transformer primary (with inherent breakdown risks), and you would have no headroom for positive peaks.

Running with 1400 volts is so close to 1500 that it does not seem to be necessary to calculate a different impedance, even though you have excess power available.  I think there are other, more important considerations than just matching the impedance for your exact power goal.  Looking at the curves on the last two pages of the 811A document, you can see the maximum harmonic distortion values.  It appears to me that on the 1500 volt curve, running 12400 ohms primary, gives you the least harmonic distortion at 250 watts output.  Drive voltage is about the same, but drive power is lower with the higher plate voltage and higher impedance than other options.  Around 4 volts negative bias is needed, compared to zero bias when running at 1200 volts.  As you can see, you have more headroom with this configuration than changing the impedance to limit your power output to 225 watts.

Your configuration will run the 811s conservatively, and also limit the voltage on the primary of the transformer, as compared with calculating a higher load impedance, thus preserving headroom.  As Fred said, try to use all of the two highest turns windings for the center tapped primary, and use what is necessary of the other windings to achieve a turns ratio close to the desired impedance ratio.   It has been my experience that close is good enough, and it has seemed best to err on the lower impedance side with regards to the primary, for the reasons stated above.  It is true that you might be able to get your desired power from the pair of 811As at a lesser plate current if you run a higher impedance primary, but this benefit does not outweigh the disadvantages.  At 250 watts, the 811As are running well within their design ratings.   Hope this helps.

[W8ACR]

Thank you Fred and Rick. Full disclosure: I have gotten excellent audio reports so far, so I must be close, or at least close enough. But I have two issues. First, I am somewhat of a perfectionist, so I want to do this audio impedance matching thing as correctly as possible. Secondly, I really do want to understand the physics of what is occurring during the modulation process, and it bugs me that I am just guesstimating, even though I have apparently guesstimated well.

Fred, I am currently using a UTC S-22 mod transformer. I have obtained a UTC CVM-4 but have decided to stick with the S-22 for now. I also have some large RCA broadcast mod iron and will soon be the proud owner of a genuine UTC LS-66 as well. More on that later. I think I have a pretty good grasp on the concepts of final amplifier plate impedances, turns ratios, and reflected impedances to the mod iron primary. I am just trying to figure out if there is a way to calculate the optimal plate to plate impedance for a given pair of modulator tubes operating at a given set of parameters. I know it can be done, I just haven’t figured it out yet, and that bothers me. If I understand it correctly, for any pair of modulator tubes operating at a specified plate voltage and power output, there is an optimal plate to plate impedance that the tubes would like to see. I want to know how to calculate that optimal impedance

Rick , thank you for taking the time to write a lengthy reply. It sounds like you have done about what I have done so far - guesstimate impedance ratios based on published tube data, and then make an educated guess on what is likely to be close. I agree that anywhere in the ballpark is likely to work ok, and so far for me it has. Again, I want to really understand this stuff, but so far, I don’t. The 225 watt figure I came up with is simply a ballpark figure to modulate 400 watts input allowing for some losses. Perhaps 250 Watts would have been a better number to use. I do monitor my modulation on an oscilloscope using a trapezoid waveform so I can see my modulation characteristics in real time. I am not interested in modulating to 150% on positive peaks or anything like that. I just want clean audio modulated close to 100%.

Getting back to that LS-66 mod transformer. It is designed specifically for 805 or 838 modulator tubes. I’d like to hear opinions on which tubes are better as modulators, 805’s or 838’s. My next home brew transmitter is going to be a single band transmitter using either 810’s or 8000’s modulated by 805’s or 838’s. What would you do?

[KA2DZT]

Ron,

Yes, I figured you probably already knew everything I was telling you.  I didn't know the answer to the question you actually asked so I figured that I would fill the page with a bunch of useless info.

Although, it may end up being helpful to some other readers.

Fred

[W8ACR]

Thanks again Fred, it’s not useless info. I really appreciate your input. I don’t know why things like this bug me so much. I should just be happy that my educated guess seems to be working well.

Thanks again, Ron W8ACR

[w8khk]

Fred, none of this is useless information.  Sometimes practical and experience is more valuable than the theoretical.  I as well shared what worked for me and why.

I think one of the important things is that we build conservatively and sometimes calculating to allow for overhead, etc, is better in the long run for reliability and best performance.  If we calculate exactly what we need, then extreme situations present problems.

A case of the optimist says a glass is half full, the pessimist says the glass is half empty, and the engineer says the glass is fifty percent larger than required.

As Ron says, the goal is to calculate the actual impedance necessary for a proper match with a given tube and set of parameters.  My approach is to evaluate the various curves, and attempt to extrapolate the values needed for my specific case, but in this instance the difference between 1400 and 1500 volts was not enough of a variance to get me in a different ballpark.  HI HI. 

If we calculate the optimum impedance for the tube, voltage, and power we are working with, then add a reserve to handle headroom and circuit losses, I think we will be approaching what Ron is looking for.  Maybe a trip back to the radiotron designer's handbook is needed to derive the formulae rather than extrapolate from the tube characteristic graphs.  Then we will be able to deal with any of the situations we are presented.  But we must not focus on efficiency solely; we must also look at linearity and distortion, and designing with a conservative approach allows these issues to be addressed at the same time we arrive at a reliable and efficient solution.  Maybe Stu, AB2EZ will chime in with his regular wisdom and expertise???  This is a valuable learning experience for all of us!

[KL7OF]

Yes...I am enjoying this thread....I've gained some understanding.....

[KD6VXI]

Yes...I am enjoying this thread....I've gained some understanding.....

I second this.


--Shane
KD6VXI

[W8ACR]

What got me going on this was that I was reading that Taylor tube manual and they seemed to make a big deal of getting the correct impedance presented to the modulator tubes. They discuss the mathematics pretty well, and the math wasn’t too complicated, but when I plug in numbers from my own situation, I get answers that can’t be correct. I have three different RF decks that I can put into my transmitter, and I can operate the finals anywhere from 1000V to 2500V and up to 300mA. The impedances presented to the modulator tubes must be varying quite a bit as well. I thought that maybe I could put a variac on the primary of the modulator plate transformer and vary the plate voltage to get optimum conditions for the tubes at any given setting of RF plate voltage, current, and audio power requirements. My assumption was that if I know the optimum plate to plate impedance at one set of parameters as given in manufacturers tube tables, I would have enough information to calculate the optimum impedance at another set of operating parameters. It seems intuitive that this would be so, but I think it takes more than ohm’s law and simple algebra. Maybe I should just chill and be happy with good audio reports and forget about optimum impedances.😛

[KA2DZT]

Ron

Good idea, this way your xmtr will continue to run less than optimum which allows my HB xmtr to continue to be the best sounding xmtr on the air

Fred

[DMOD]

You might also check out:

http://n4trb.com/AmateurRadio/RCA_Ham_Tips/issues/rcahamtips1304.pdf


Phil - AC0OB

[Steve - K4HX]

Plate-to-plate load impedance is calculated as follows

Rl = 4Ep/Imax (1- Emin/Ep)

where, Ep is plate voltage,
Imax is the maximum current during a sine wave cycle for a single tube, or DC current x pi,
Emin is the minimum plate voltage during a cycle.


So for an 811A we get something like


4 x 1500/0.45 x (1 - 100/1500)

13333 x (1- 0.0667)

13333 x (0.93)

12444 Ohms


I made some guesstimates on the numbers above, but it should be close. Actual Emin could be measured or obtained from the characteristic curves.

So, you should be able to make some calculations based on 1400 volts on the plate and a lower plate current to get close. Or you can just play with the taps on the mod tranny until things look right on the scope and the meters (like Fred said).

[W8ACR]

Thank you Steve. That is what I was looking for. In all my reading, I have never seen that equation before. That really helps. Ron