Advice Needed on calculating input and output impedance of a 3-500z Triode

[K9MB]

I need some input on doing some calculations for a medium power 3-500z amp I am working on.

Firstly- The plate impedance data that Eimac published over and over do not even come close to the values that are published on other web pages that I have trusted.

The parameters I am looking at for the 3-500z are:

Plate voltage- 1500volts
Plate current- 400mA peak

Eimac has published data on this exact setup over many years thus: (see first phot below:

Note that they show a resonant load resistance of 1600 ohms.

Now, compare this to the standard formula for estimating load impedance.

(From K4RFE)

“RL =Ep/KxIp
ClassAOperation(K=1.3~1.4):RL =Ep/(1.3~1.4)xIp ClassABOperation(K=1.5~1.7):RL =Ep/(1.5~1.7)xIp ClassBOperation(K=1.8~1.9):RL =Ep/(1.8~1.9)xIp ClassCOperation(K=2.0):RL =Ep/2.0xIp”

Using these formulae, we have:

1500/(1.6 x 0.4) = 1500/0.64 = 2343 ohms



First question is how did Eimac come up with a 1600 ohm resonant load resistance here?
Is this caused by definitions being different fir terms or is EIMAC wrong or are these two venerable engineers wrong.
Seems like the answer must be that I am wrong, but need help figuring out this conundrum…


Second question:
Subject- Calculation of input impedance of a Grounded Grid Amp.
I see that Eimac has published that the input impedance of a 3-500z is either 90 or 100 ohms.

I tried to find a way to calculate this figure, and found a formula that I do not understand because I do not know what each entry means.

The formula is (from W8JI site):

“The input impedance of the stage, neglecting capacitances, is Zin = Eg / Ip =  Rp + Zload / µ + 1

Thus the input impedance is the total plate circuit impedance (rp + Zload) divided by µ+1.”

My problem here is that this formula sums rp and Zload and then divides that sum by mu+1

mu for a 3-500z is 130, so mu +1 = 131 - right?

If I assume that the published input impedance estimate for a 3-500z is close to 90-100 ohms, then rp+Zload should be 100*(130+1) = 13000.

If plate resistance changes with plate voltage from 2300 ohms at 1500 volts to 4600 ohms at 3000 volts, then it would seem that rp +Zload should also change, but the input impedance is estimated at between 90 and 100 ohms and no adjustment is made for plate voltage changes.

It is perfectly obvious to me that I do not understand this at all, but I would love to understand it thoroughly.
I am missing something(s). What is(are) they?

Any assistance will be greatly appreciated. All my Google searches have not helped so far…Thanks in advance.

73, Mike K9MB

[K9MB]

Bump- I am not sure if the questions are unclear or if they are just dumb questions, since nobody has commented.
Has anyone else noticed a difference between published Eimac data and values calculated by standard formulas?
Eimac said 1600 ohms and the value calculated at 2300 ohms. Big difference, though not sure how much that affects efficiency…

[KD6VXI]

110 ohms for a 500Z always gets me very close.

This is relative to how hard you are driving the cathode, but using this as a ballpark number will 'get you there'....

As to the output, I use Ian's spreadsheet.  It will figure in your parasitic suppressor, strays, effect of lead lengths, etc.

I've used it from a hundredish watts to the output network on a modified shortwave xmitter currently plugging away at near 55kw carrier.

G3SEK SPREADSHEET in Google will get it to you.


--Shane
WP2ASS / ex KD6VXI




As to why eimacs are put to lunch?  Good question.

[WD5JKO]

We must remember that in Class B (biased near cutoff), the cathode only passes current in one direction with respect to the driving waveform. With an untuned input, that means the driver is loaded only on one side. This is not a big deal if the driver has a resonant tank on the output circuit, or if an intermediate tuner is used between the exciter, and the final. I recall back in the days when G-G linear amplifiers were new, some of the articles used a vacuum diode to load the other half of the cycle to have a more even load on the driver. These days with a tuned input, a low Q is generally recommended to cover the entire band with one adjustment. Is this convenience optimum when the driver resonant tank is getting 1/2 wave rectified?

How do the input Z formulas deal with the cathode load only passing current in one direction?

Jim
Wd5jko

[K9MB]

110 ohms for a 500Z always gets me very close.

This is relative to how hard you are driving the cathode, but using this as a ballpark number will 'get you there'....

As to the output, I use Ian's spreadsheet.  It will figure in your parasitic suppressor, strays, effect of lead lengths, etc.

I've used it from a hundredish watts to the output network on a modified shortwave xmitter currently plugging away at near 55kw carrier.

G3SEK SPREADSHEET in Google will get it to you.


--Shane
WP2ASS / ex KD6VXI




As to why eimacs are put to lunch?  Good question.

Thanks Shane. I just joined the Group and will download the program amd run some numbers to compare to my other calculations.
also, thanks for the 3-500z impedance. Eimac published the input impedance as between 90 and 100 ohms.
I am using pinets to transform 50 ohms to 100 ohms and anything from 90-110 will not make much difference.
The reason for wanting to get it close is to minimize 3rd order IMD caused by mismatch non-limearities.
I have always made those networks at a Q of 2, but read that a Q of at least 4 is needed to provide enough energy to make it all symmetrical…
Of course, a higher Q means that the match will shift with big movements in frequecy.
Thsnk you for the tips. I wish that I could decifer that input impedance formula based on plate and load impedance and mu though….
I am missing something because I cannot tell the difference between plate resistance and load impedance if they are not the same thing in a matched system..
73, Mike

[K9MB]

We must remember that in Class B (biased near cutoff), the cathode only passes current in one direction with respect to the driving waveform. With an untuned input, that means the driver is loaded only on one side. This is not a big deal if the driver has a resonant tank on the output circuit, or if an intermediate tuner is used between the exciter, and the final. I recall back in the days when G-G linear amplifiers were new, some of the articles used a vacuum diode to load the other half of the cycle to have a more even load on the driver. These days with a tuned input, a low Q is generally recommended to cover the entire band with one adjustment. Is this convenience optimum when the driver resonant tank is getting 1/2 wave rectified?

How do the input Z formulas deal with the cathode load only passing current in one direction?

Jim
Wd5jko

Hi Jim,
Apparently a high C to L parallel circuit or pinets with minumal Q provide the flywheel effect needed to symmetrically stabilize the load that is seen.
The operating angle for these data on the 3-500z look like AB2 to me amd close to cutoff for lower plate voltages.
I suppose that the plate circuit looks the same with pulses added to the parallel circuit that turns it into sine waves…
Thanks for your help. I still cannot figure out the input impedance formula I copied.

I also womder why Eimac has published resonant plate impedances for output designs that are far different than what I get from published formulas…
73, Mike

[KD6VXI]

The trick to lowering imd is to put the C of the input circuit AT THE CATHODE! 

If you want to further increase efficiency, make it a third harmonic trap!

--Shane
WP2ASS / ex KD6VXI

[K1JJ]

For the cathode input:  To avoid the calculations, estimates and bandwidth limitations, just use a fully variable C-L-C input.  (like a pi-network)

To cover as low as 160M, use a 2000pF variable to ground, a small roller inductor in series and another 2000 pF variable to ground at the cathode.   Those ganged 365pF receiver AM broadcast variables work fine when the sections are strapped in parallel. Test it using clip leads and an appropriate cathode load resistor first.

I use this on my big linear and it covers the bands FB with a 1:1 input swr and decent Q.   I used fat copper strap for all connections for best efficiency and stability.

T

[K9MB]

For the cathode input:  To avoid the calculations, estimates and bandwidth limitations, just use a fully variable C-L-C input.  (like a pi-network)

To cover as low as 160M, use a 2000pF variable to ground, a small roller inductor in series and another 2000 pF variable to ground at the cathode.   Those ganged 365pF receiver AM broadcast variables work fine when the sections are strapped in parallel. Test it using clip leads and an appropriate cathode load resistor first.

I use this on my big linear and it covers the bands FB with a 1:1 input swr and decent Q.   I used fat copper strap for all connections for best efficiency and stability.

T

Hi Tom,
Great idea. I actually have several 4x550pf variables I have purchased over the years. The best ones were in old HP generators.
Probably a 10uH roller from a viking II would serve for the inductor.
I will strongly consider it for my 2x4K big amp.
Trouble is that pile of components is bulky and my space limited…
Another option I figure is to band switch a piece of B&W inductor by shorting turns and put one of those old HPs across it and pad the things to get 160 in and fine tune with the double two section. This cheat is tempting because a pair of 4Ks will be close to 50 ohms. I have a two deck 11 position switch that can handle the drive.
Thanks again, Tom.

[K9MB]

The trick to lowering imd is to put the C of the input circuit AT THE CATHODE! 

If you want to further increase efficiency, make it a third harmonic trap!

--Shane
WP2ASS / ex KD6VXI

Interesting comment. In his article on grounded grid input circuits, WiJI says that when he took a contract with Heathkit in the 70s or 80s, he tried to put the matching networks some distance from the cathodes and the IMD was seriously degraded. He says that keeping the matching networks as close as possible is advised, though he discovered that when he replaced the 50ohm coax he had been using with 18 ohm coax, the IMD was restored to good values.
I suppose that one could hook in a bundle- three equal length pieces of rg-316 in parallel to give a 17 ohm coax 9f one must extend the leads a bit. I plan to do this very thing, though I expect to have my connections within 6 inches.

Shane, on another subject, I downloaded the G3SEK spreadsheet and it is very nice.
I do have some confusion, however, about the fact that it gives two different load impedances for a given set of plate voltage, current, and operating mode and they are not close.
The higher value is the same value I got with the formula I have been using and the second is much lower. Very confusing to me…

Also, I saw that G3SEK gave a link to Duncans Amps power supply software.
I was interested in getting that program, so I joined the group and logged in and attempted to download the PSUD2 program here:

http://www.duncanamps.com/psud2/download.html

I was unable to get it to download anything, so I cannot figure out why…
Does this program work?
I need some hints on how to get this software.
Can you advise me on this? Tnx.
73, Mike

[K9MB]

Just got assistance from WZ5Q on PSUD.
Many thanks, Mike.
I am always impressed by the immense knowledge and willingness to share on this forum.
73, MB

[KD6VXI]

PSUD is great.  I've been using it.....  Man, it's old enough to drink now. 

If you read the fine print on the spreadsheet you'll see the explanation for the two different Z and how they come to the number.   One uses just volts, amps and K factor.  Thr other hs s power output and other variables.

I'll usually use one of the numbers, then I'll compare with the other derived number.  Use that as a sanity check.

If the two plate load Z are wildly off, then double check your work.  If they are within a couple hundred owhms (maybe ten percent is a good fudge factor), then I didn't worry about it.  Just make sure you keep all inputs correct when doing this, or the number comparison will be meaningless.

Welcome to the rabbit hole of these cool programs.  Now you need to go waste time on Tonnes website.  Good lord I can't tell you howany what if nights these programs have spawned!

--Shane
WP2ASS / ex KD6VXI

[w9jsw]

I am in the SimSmith and EZNEC rabbit hole now.

[DMOD]

Looking at the Eimac data sheet with a Vp of 2000V, the resonant load impedance is 2750 ohms for a Single Tone Ip of 400mA.

I ran my MatLab routine using the Weigand equations with 1500Vp and 400mA Ip and it calculated a resonant load impedance of 2,300 ohms.

Phil

[K9MB]

Looking at the Eimac data sheet with a Vp of 2000V, the resonant load impedance is 2750 ohms for a Single Tone Ip of 400mA.

I ran my MatLab routine using the Weigand equations with 1500Vp and 400mA Ip and it calculated a resonant load impedance of 2,300 ohms.

Phil

Yes, you are right, Phil, I get the same value:

2000/(1.7*0.4) = 2000/0.68 = 2940 ohms which is close assuming a K of 1.7
2000/(1.8*0.4) = 2000/0.72 = 2800 ohms.
It appears to be ok for a K of 1.8 (class B)

The Eimac datasheet for 1500 volts, shows a plate impedance of 1600 ohms at 400mA , but assuming a K of 1.8 again, we have:
1500/(1.8*0.4) = 1500/=0.72= 2080 ohms, not 1600 ohms.
The Eimac Data for 1500volts seems to be wrong. The interesting thing is that this data sheet was published in 1968, 1970 and 1973.
I guess nobody ever caught it…Seems weird.
73, Mike

[KD6VXI]

Stop using the plate V for the calculation.

You'll never achieve 100 pct plate swing.

If you run 1950(1.8*.400)=2708.

Asduming a plate swing of 1900 volts with wknon the plate and Eimac is spot on.

A linear amp, unless run as a switch (and then it's not a linear amp.......) isn't going to run rail to rail.

--Shane
WP2ASS / ex KD6VXI

[K9MB]

Stop using the plate V for the calculation.

You'll never achieve 100 pct plate swing.

If you run 1950(1.8*.400)=2708.

Asduming a plate swing of 1900 volts with wknon the plate and Eimac is spot on.

A linear amp, unless run as a switch (and then it's not a linear amp.......) isn't going to run rail to rail.

--Shane
WP2ASS / ex KD6VXI

Excellent point.
I knew better than this. 😳😬🤪
I will get the chart and run some load lines to determine the minimum and calculate dynamic voltage range.
Always do this for class B triodes for modulators to calculate load impedance.
Thanks for pointing this essential point out, Shane.
Feel free to slap me (metaphorical) back to consciousness any time… 😉
73, Mike

[KD6VXI]

It'd all good man.  I've had to have the reality slap myself.

Sadly, the older I get I seem to be having to do it more?


Lol.

And yeah, it didn't dawn on me at first either hahaha

I always wanted to incorporate a tap to watch what happens with the rf, watch what changes do when you tune at different q levels, etc.  Would also be nice to see exactly the plate V swing.  I know a lot of places make assumptions as to how far the tube will go before shutoff.....  But is that really accurate?


--Shane
WP2ASS / ex KD6VXI

[K9MB]

It'd all good man.  I've had to have the reality slap myself.

Sadly, the older I get I seem to be having to do it more?


Lol.

And yeah, it didn't dawn on me at first either hahaha

I always wanted to incorporate a tap to watch what happens with the rf, watch what changes do when you tune at different q levels, etc.  Would also be nice to see exactly the plate V swing.  I know a lot of places make assumptions as to how far the tube will go before shutoff.....  But is that really accurate?


--Shane
WP2ASS / ex KD6VXI

😂😂😂.
Yeah- every body who has not been only in CMOS logic knows that you cannot drive the plate lower than the grid….😬🤪
My wife and I will be married 50 years in April and I will be 75 in May.
We decided that we had to keep going because two half-wits can act like parallel finals and keep the vintage equipment going. 😉
After designing and building for 60 years and clearing some smoke from the room in the past, this is why I spend a lot of time thinking and calculating before I get out tue hole saws, nibblers and soldering irons. Never walk into a strange dark room without turning on the lights and both physically and mentally, my “lights can be dimmed and need more focus and thinking three times-not twice, so if I am an ass, at least it did not cost a valuable tube or transformer that may be hard to replace…
Glad that other guys like you actually know when a man is heading toward a hole in the floor amd let him know…😉
Just printed the curves on the 3-500z. They are pitiful for detail, but a quick visual shows them saturating at about 250-300 volts.
I will plot my points based on about 80- 400mA plate current , 120mA grid current and 2400vdc on the plate and see if I can get better than the visual estimate of about 2100 volts for my more “intelligent” plate impedance calculations.
73, Mike

[K9MB]

Shane, please check me- it has been a while since I plotted a load line and never on triode in grounded grid.
I attempted to plot using:

Vp- 2500 volts
Imax -400mA
Igrid max 120mA

What I saw was that this triode -at least the data sheet does not have a nice vertical diode line like-say- a 811A- so I had to guess that the diode line was at about 250volts.

When I plotted 400mA plate current and 120mA grid current, the voltage was close to 500 volts, so that was one end point.
I decided to use about +6volts on the cathode to make the quiescent close to 70mA, so the intercept of 2500volts and 70mA was my other end of the load line.

This means that my calculations should be:

Rp = 2000/(1.8*0.4) = 2000/0.72 =2780 ohms
Eimac says 2750 ohms, but they are pushing it to 130mA of grid current in the datasheet plus they are operating at zero biad. Close enough I think-finally.
Please correct me, though- if you see errors…😉
73, Mike

PS: the reason that I am putting buas in the cathode is to lower the quiescent to 70mA.
I noticed that in the datasheets, whenever the quiescent was lower (at 1500v, 300-,3500v), the 3rd order IMD was notoeably better across the board.
They have not provided a plot of that function, so just have those finite poimts as reference. It may mean that the transfer curve is more linear closer to Class B.
Comments? MB
Tom, please add comments on this crazy notion based on a guess…😉
Anyone else as well.

[KD6VXI]

Your numbers pass a sanity check.

I've always liked biasing the 500z tube down.  I think it's a great tube even at say 50 mils at 3.x KV.  Other tubes don't handle this as cleanly, but the 500z just runs.

There are other tube data sheets by other mfg.  You may find a better plot, maybe not.  The Amoetex tubes are a whole different 500Z tube, though....  So I'd not use them.

--Shane
WP2ASS / ex KD6VXI

[K9MB]

Your numbers pass a sanity check.

I've always liked biasing the 500z tube down.  I think it's a great tube even at say 50 mils at 3.x KV.  Other tubes don't handle this as cleanly, but the 500z just runs.

There are other tube data sheets by other mfg.  You may find a better plot, maybe not.  The Amoetex tubes are a whole different 500Z tube, though....  So I'd not use them.

--Shane
WP2ASS / ex KD6VXI

Hi Shane,
Thanks for the comments.
It is very interesting to look at the IMD figures published by Eimac.
The best 3rd order IMD figures are at 1500 volts on the plate -48dB
The second best figures are at 3kv and 3.5kv (-40dB)
The next after that is 2kv (-38dB)
The lowest figures published are at 2500 volts (-33dB)

What I suspect from these data is that the plate voltage is irrelevant.

What really sticks out is the relationship between quiescent current and IMD.

1500 volts -48dB - quiescent current 60mA
2000 volts -38dB- quiescent current 95mA
2500 volts -33dB - quiescent current 130mA
3000 volts  -40dB - quiescent current  62mA
3500 volts -40dB - quiescent current 53mA

The worst IMD is at 2500 volts with zero bias resulting in a very high grid current

One might think that it is the zero bias setup that degrades 3rd order IMD, but the 1500 volt data is zero bias and the 2kv is very good at -38dB, but it also a moderately low IMD at zero bias, though the 95mA grid current mirrors the median performance and median IMD.

The 3kv and 3.5kv plate voltage is better -40dB than either the 2kv or 2.5kv plate voltage data.

The very best predictor of better IMD is clearly keeping quiescent current between 53 and 60mA no matter what the plate voltage is, based on this very limited data set.

Shane, I now read a post by you, in which you say you like the idea of quiescent current down neat 50mA is better, in your experience.

The head scratcher here is not that you have discovered an important fact about the running of the 3-500z for best IMD, but that Eimac published these figures in 1968 that prove (evidently) that calling this tube a zero bias triode is a stupid title above 2kv on the anode.

Rather, anybody that publishes an article about a 3-500z linear amplifier should never call the tube “zero bias”, but instead, the writer should say that cathode bias should be made adjustable to -6 to -8 volts to give a quiescent current of 50-70mA for linear SSB operation and values up to -30 to -35  below cutoff for CW operation in hard class B or for cutoff on standby and also -12 to -15vdc for AM operation to loser dissipation and increase output.

Ironically, commercial amps like the SB220 and L4 had 7.5volts cathode bias, so why the zero bias talk when it is a very bad idea at all but very low voltages?

All of this knowledge seems to have application even on tetrodes like 4-1000a when operated as a grounded grid triode if stabilized screen voltage is used and large strings of power supply diodes to allow the quiescent current to be adjusted to a sweet spot for best IMD when coupled with correct loading, etc.
The operating point and current range for best IMD and efficiency have nothing to do with zero bias, whether it is a 3-500z or a 4-1000a that is strapped as a zero bias triode. In both cases, the performance is mediocre, so why do this and produce very powerful noise makers that make enemies of all your neighbors on the bands?

I appreciate guys like you, Shane and Tom and others on AMfone who set a standard of expectation of excellence and speak up to help others work toward those standards.
73, Mike