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[Articles Home]  [Add Article]  

Measuring a Solid-State PAs Zs

from Mike Perks, ZS6BIM on February 8, 2012
View comments about this article!

Measuring a solid-state PAs Zs:

Measuring the output impedance (Zs) of solid-state broadband HF amplifiers operating in class AB.

A daunting or perhaps impossible task considering the following:

Output impedance (Zs) can only be defined for linear systems that obey Thevenins theorem and amplifiers biased in class AB, although referred to as linear amplifiers, are not linear in the above sense.

However although it may be difficult or even impossible to define Zs for non linear systems it may be possible to measure Zs or at least an average value for Zs at a number of frequencies and power levels.

Before proceeding it might be prudent to mention:

Broadband solid-state HF amplifiers, for radio communications equipment, are not normally designed to have a specific output impedance, say 50 Ohms, although it is possible to design an amplifier to have a 50 Ohm output impedance.

In radio communications equipment the broadband RF power amplifiers output matching network is usually designed to transform the load, normally 50 Ohms, to a collector or drain load resistance needed to develop the required output power and linearity. RF power devices are chosen accordingly.

To measure the Zs of two solid-state HF power amplifiers available to me (125W / 24V and a 100W / 12V) I used the ingenious method proposed by G3UUR (see: http://www.eham.net/ehamforum/smf/index.php/topic,79068.0.html.)

Both amplifiers were operated without ALC or harmonic filters and the Zs measuring point was positioned within 10cm of the amplifiers output network.

The output matching network of both amplifiers uses transmission line transformers.

Push-pull HF-28-220 and MRF421 RF transistors are used in the 24V and 12V amplifiers respectively.

I had problems, yet to be resolved, in getting meaningful results for Zs at 10MHz and above using G3UURs method. These problems arise partially from having to drive the amplifiers into reactive loads so no >10MHz data are currently shown.

The Zs measured results are shown graphically below.

What I find really interesting is how close to 50 ohms Zs appears to be, < 2:1SWR over the measured frequency range.

Also interesting is that the measured Zs appears to represent a magnified view of the transfer function of the amplifiers with the data showing the 24V amplifier to be generally more linear than the 12V amplifier; as expected.

Zs also remains fairly constant with output power over a wide range; this is also to be expected from a linear amplifier.

At very low power levels, <1W, Zs can be seen to change rapidly with power level possibly reflecting the cross-over region of the class AB push-pull amplifier.

To confirm this assumption I increased the quiescent bias current level substantially and found the rapid Zs change at low power levels to be significantly reduced. See below.

I believe nonlinearity at the crossover region of a push-pull amplifier contributes significantly to the higher order IMD products.
To check my theory the higher order IMD products of the 24V amplifier were measured at 125W PEP output with the bias set to the nominal 250mA and then to 2A.
To emphasize the higher order products a notch filter (also shown on the spectrum analyzer display) has been included in the measurement path.

As suspected there is a significant reduction in higher order products at the higher bias current.
This may be a useful observation considering the current initiative for cleaner amplifiers.

Another interesting observation is that with the amplifier biased at 2A the measured Zs over the power range, where the amplifier is effectively running in class A, is virtually the same as that for the amplifier driven into the class B region.

An amplifier biased in class A is a linear system allowing Zs to be calculated from the component parameters.
Could these results then indicate that the Zs of a class AB amplifier is in fact very similar to that of the equivalent class A design?

In conclusion, the findings using G3UURs methods for determining Zs were also compared to those obtain using the load variation method.
A surprisingly good agreement was obtained between the two methods, at least between 2MHz and 7MHz!

73
Mike
ZS6BIM

Member Comments:
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Measuring a Solid-State PAs Zs  
by ZS5WC on February 8, 2012 Mail this to a friend!
Hi Mike,

Thanks for a fantastic TECH. article!..
I have always wondered if the use of an active bias system (where the bias currents effectively follow the modulation envelope)would not be great to use in a new SS amp design.
Obviously the crossover products will be reduced and and in band splatter minimised.
Down side is Heat and reduced output.

I hear so many NEW rigs where the IMD performance is a LOT worse than for example a 40 year old Collins--the rig designers' TX departments seems to be short staffed of late.

Keep up the good work!..
73 De William
ZS4L
 
RE: Measuring a Solid-State PAs Zs  
by KE5JPP on February 8, 2012 Mail this to a friend!
Two thumbs up! Very interesting article. We need more like this.

Gene
 
Measuring a Solid-State PAs Zs  
by K8QV on February 8, 2012 Mail this to a friend!
Finally! A real article! Thanks.
 
RE: Measuring a Solid-State PAs Zs  
by KA4KOE on February 8, 2012 Mail this to a friend!
I haven't heard the word "Thevenin" used in a sentence since college!

Philip
 
Measuring a Solid-State PAs Zs  
by N6RK on February 8, 2012 Mail this to a friend!
Why would I want to know the output impedance of an amplifier?
 
RE: Measuring a Solid-State PAs Zs  
by KZ1X on February 8, 2012 Mail this to a friend!
If you were going to design a filter, you'd want to know the input and output impedance for the filter.
 
Measuring a Solid-State PAs Zs  
by WA0ZZG on February 8, 2012 Mail this to a friend!
Mike;
I love these kind of articles. I am 63 years old. My first job, out of school was working for Collins Radio in Cedar Rapids. I still think having a ham license had some impact on getting hired. I didn't work on the amateur line but in the same building which led to some wandering in that area. KWM-2's were being built for Viet Nam. Spectrum analyzers were custom build affairs that took up an entire seven foot rack with a large TV screen and were used in the final test area to set distortion. With a pair of 6146's they were doing -56db. It sometimes took some tube swaping and bolt tightning but it got there.
Dave....
 
RE: Measuring a Solid-State PAs Zs  
by W9PMZ on February 9, 2012 Mail this to a friend!
"Why would I want to know the output impedance of an amplifier? "

Well, probably to provide the correct matching... The complex conjuate match provides maximum power transfer.

73,

Carl - W9PMZ
 
RE: Measuring a Solid-State PAs Zs  
by W5DXP on February 9, 2012 Mail this to a friend!
Electric power generation plants are more worried about efficiency than conjugate matching. Why shouldn't we amateur radio operators be more worried about efficiency than about conjugate matching?

Except for efficiency, what does it matter if a source, that is delivering 100 volts of RF to a 50 ohm load, has a source impedance of 5 ohms, 50 ohms, or 500 ohms? I vote for the 5 ohm source that is 99% efficient.:)
 
RE: Measuring a Solid-State PAs Zs  
by AI7RR on February 9, 2012 Mail this to a friend!
I am very appreciative of the effort you took to share your research and findings. Thank you.

73, Roger
 
RE: Measuring a Solid-State PAs Zs  
by KB4QAA on February 9, 2012 Mail this to a friend!
Doesn't the conjugate match provide the most efficient transfer of power?
 
RE: Measuring a Solid-State PAs Zs  
by W5DXP on February 9, 2012 Mail this to a friend!
> KB4QAA wrote: Doesn't the conjugate match provide the most efficient transfer of power? <

Of course not! Maximum transfer of power in a linear system ensures that the efficiency is limited to 50%. If electric power generating plants operated into a conjugate match, their generators would melt. Why on earth would amateur radio operators want their transmitters to melt?
--
73, Cecil, w5dxp.com
 
RE: Measuring a Solid-State PAs Zs  
by NO6L on February 10, 2012 Mail this to a friend!
W5DXP,
First, regarding a 5 ohm source looking into a 50 ohm load, there is no way you will get 99% efficiency for two reasons; First, there is no amplifier that is that efficient in the first place. Second, the voltage to deliver a given power at 5 ohms is 1/10 that required for 50 ohms.

Second, please explain to us all just how a conjugate match "melts" a transmitter.

Seeing as how you hold an Extra Class amateurs license, this should not be a problem for you.

73
 
RE: Measuring a Solid-State PAs Zs  
by W5DXP on February 10, 2012 Mail this to a friend!
> NO6L wrote: First, there is no amplifier that is that efficient in the first place. <

That's why there's a smiley face attached. OTOH, there is no such thing as a lossless transmission line - required by the conjugate matching theorem. Seems the best that we mere mortal hams can do is a Z0-match point at the tuner input.

> NO6L wrote: Second, please explain to us all just how a conjugate match "melts" a transmitter. <

Here one possibility:

Assume a fixed 150 volt, 50 ohm source designed to deliver 100 watts to a 100 ohm load (100v at 1a). The source dissipates 50w but we have designed the source to tolerate a dissipation of 60w so all is well. But it is not conjugately matched so we change the load to 50 ohms. The current jumps to 1.5 amps, the source dissipation jumps to 112.5 watts, almost double the designed-for dissipation, and that melts the transmitter.
--
73, Cecil, w5dxp.com
 
RE: Measuring a Solid-State PAs Zs  
by W9PMZ on February 10, 2012 Mail this to a friend!
"and that melts the transmitter."

You need to start using devices that are tolerant to any load... ;)

73,

Carl - W9PMZ
 
RE: Measuring a Solid-State PAs Zs  
by K1ZJH on February 10, 2012 Mail this to a friend!
[quote]by W5DXP on February 9, 2012 Except for efficiency, what does it matter if a source, that is delivering 100 volts of RF to a 50 ohm load, has a source impedance of 5 ohms, 50 ohms, or 500 ohms? I vote for the 5 ohm source that is 99% efficient.:)
[/quote]

And also the source impedance has no effect on the SWR.

Pete :)
 
RE: Measuring a Solid-State PAs Zs  
by W5DXP on February 10, 2012 Mail this to a friend!
> K1ZJH wrote: And also the source impedance has no effect on the SWR. <

Yes, all voltage, current, and power conditions will be identical external to the three sources (if all of the sources are putting out a steady 100 volts of RF). Yet only one of the systems is conjugately matched while the other two systems are conjugately mismatched. In fact, one of the conjugately mismatched systems is putting out the same power at a higher level of efficiency than the conjugately matched system.

If all conditions external to the source are identical, what difference does it make if the system is conjugately matched or not? Between a Z0-match and the antenna, exactly the same conditions exist as if a conjugate match exists. Therefore, IMO, a Z0-match is just as good as a conjugate match. Note that a Z0-match blocks reflected energy from reaching the source.
 
RE: Measuring a Solid-State PAs Zs  
by AA1LL on February 10, 2012 Mail this to a friend!
This article is a great effort at understanding the workings of a class AB or other amplifier made from nonlinear devices. But still, determining the impedance looking into the amplifier output at a given frequency would not seem to help us do a lot (except have fun on eham.net). If this impedance is nonlinear it won't be constant vs. amplitude so how do you design a filter for it? Determining Output power can be dealt with by the Reike diagram which specifies the output power of a device (usually microwave) for a given R+jX load on the Smith chart. Who wants to deal with that??

Maybe the confusion is, the amplifier is linear in the sense that its transfer function behaves linearly but its terminal impedances do not follow the rules at high power levels. Better to spend our time designing a matching network that transforms a (linear) antenna impedance to the rated load for the amplifier.

73, AA1LL
 
RE: Measuring a Solid-State PAs Zs  
by NO6L on February 11, 2012 Mail this to a friend!
W5DXP,
First item, about the 5 ohms/99%/smiley emoticon thing, whatever.

Second: A "...50 ohm source designed to deliver 100 w to a 100 ohm load..."? Within your first sentence the whole rebuttle falls completely apart. Or, you just forgot one of those smiley things...

Whatever the case, 73.
 
RE: Measuring a Solid-State PAs Zs  
by N0CU on February 11, 2012 Mail this to a friend!
W5DXP: I am admittedly a little slow sometimes, so please bear with me.
"Yes, all voltage, current, and power conditions will be identical external to the three sources (if all of the sources are putting out a steady 100 volts of RF)." Unlike with power companies, ham transmitters are not designed to be constant votage (or current) generators. Depending on how you design you energy source (or transmitter), a conjugate match will not necessarily give you the best overall (ie, System) efficiency, but it will give you the best transfer of the energy coming from the transitter output to the load.

"IMO, a Z0-match is just as good as a conjugate match." No! A conjugate match is a subset of a Zo match. You can't have a Zo match without also having a conjugate match. You can however, have a conjugate match without a Zo match.
"Note that a Z0-match blocks reflected energy from reaching the source." With the use of solid state transmitters today (all of which use SWR shut down protection circuits), this is one of the main reasons for using an antenna tuner and strive for a conjugate match. If, in addition to the conjugate match, additional steps are also taken to acheive a Zo match , then the additonal power lost in the transmission line due to an SWR>1.0 will no longer be lost and will be delivered to the load.
So, with all that has been said, I am still not clear on what your point is: are you saying hams should stop wasting their time and money using antenna tuners??

Bill N0CU
 
RE: Measuring a Solid-State PAs Zs  
by W5DXP on February 11, 2012 Mail this to a friend!
> NO6L wrote: Second: A "...50 ohm source designed to deliver 100 w to a 100 ohm load..."? Within your first sentence the whole rebuttle falls completely apart. Or, you just forgot one of those smiley things... <

"falls completely apart"??? I chose those values for illustration purposes in order to to make the math easy to understand. (100w into 100 ohms is 100v at 1a). If I had a 100 ohm full-wave loop antenna fed with 100 ohm parallel feedline, I might design such a source myself. I could have just as easily chosen a 25 ohm source designed to drive a 50 ohm load - the conceptual results and conclusions would have been the same.

The point is that many sources are not designed to be conjugately matched and are simply designed to drive a particular load impedance. Satisfying that design load impedance ensures that reflected energy is not flowing back into the source and in that case, except for efficiency, the source impedance is irrelevant. Identical external conditions can exist in two systems one of which is not conjugately matched so exactly what is the big deal about conjugate matches?

What do you think would happen to your stereo amplifiers if they were conjugately matched?
--
73, Cecil, w5dxp.com
 
RE: Measuring a Solid-State PAs Zs  
by W5DXP on February 11, 2012 Mail this to a friend!
> N0CU wrote: Depending on how you design you energy source (or transmitter), a conjugate match will not necessarily give you the best overall (ie, System) efficiency, but it will give you the best transfer of the energy coming from the transitter output to the load. <

The point is that many sources are not designed to be conjugately matched - they are designed to linearly drive a specified load impedance and many designs are more attuned to linearity and efficiency than to maximum power transfer. One can always increase the maximum power output of an amplifier while risking the generation of illegal harmonics and/or failure of the amp.

> N0CU wrote: You can't have a Zo match without also having a conjugate match. You can however, have a conjugate match without a Zo match. <

A system-wide conjugate match requires zero losses in the system between the source impedance and the load impedance. Therefore, a system-wide conjugate match is impossible in the real world. A Z0-match is not system-wide, occurs at a single point, and is easy to obtain in the real world. In fact, a Z0-match IS a conjugate match but only at the Z0-match point.

> N0CU wrote: So, with all that has been said, I am still not clear on what your point is: are you saying hams should stop wasting their time and money using antenna tuners?? <

Nope, actually the opposite. the point is: Be happy with that Z0-match point effected at a tuner input. To achieve a conjugate match point at the source would require another network inside the source. To achieve a conjugate match point at the antenna would require yet another network at the antenna feedpoint. And even then, a system-wide conjugate match would still not exist in the real world. The best we can do in a low loss system is to achieve a near-conjugate match by implementing our old friend, the Z0-match, using a tuner.

Why not just present the source with its designed-for load impedance, achieved by an antenna tuner, and enjoy operating one's ham radio? What good has been accomplished by the source impedance argument that has now spanned at least two decades of two centuries and caused such ill feelings with no answers in sight?

Here's some information on conjugate matching. Please note the lossless requirement.

The Conjugate Theorem also shows that in a sequence of matching networks it is necessary to match at only one junction if (*AND ONLY IF*) the networks are non-dissipative."

Theorem If a group of four-terminal networks containing *ONLY PURE REACTANCES* [includes *LOSSLESS* transmission lines] are arranged in tandem to connect a generator to a load, then if at any junction there is a conjugate match of impedances, there will be a conjugate match of impedances at every other junction in the system.

http://www.w2du.com/Appendix09.pdf
 
RE: Measuring a Solid-State PAs Zs  
by N0CU on February 11, 2012 Mail this to a friend!
I don't understand why some folks get so focused on the fact that the actual values needed to achieve a conjugate match in the real world (ie, with losses) are slightly different from what they would be in an ideal lossless system. It seems no different than what happens when designing a pi net matching network- the actual values will be slightly different with real (lossy components) than what would be predicted with ideal components. But who cares?- the physics don't change. We are still adjusting a match network for maximum energy transfer, which to me means a conjugate match.
 
RE: Measuring a Solid-State PAs Zs  
by W5DXP on February 11, 2012 Mail this to a friend!
> N0CU wrote: I don't understand why some folks get so focused on the fact that the actual values needed to achieve a conjugate match in the real world (ie, with losses) are slightly different from what they would be in an ideal lossless system. <

Trouble is, those "actual values" can be proven mathematically not to achieve a conjugate match in the real world. To the best of my knowledge, nobody has ever defined how close to a conjugate match something must be to earn the title - within 2%, 10%, 20%, 50%?

Once upon a time, Steven Best proved that, in real world systems with losses, a conjugate match established at the source cannot result in a conjugate match at the antenna so maximum power transfer cannot be occurring at the antenna.
--
73, Cecil, w5dxp.com
 
RE: Measuring a Solid-State PAs Zs  
by N0CU on February 11, 2012 Mail this to a friend!
Ok Cecil, I follow your argument now. But it still seems strange to me that the concept of conjugate match is singled out in this way. After all, I have never heard anyone claim that a bandpass filter is something other than a bandpass filter when low Q components are used and the final values don't end up close to what they would have been if high Q components have been used. Thanks for sharing your thoughts- it has been interesting.

Bill N0CU
 
RE: Measuring a Solid-State PAs Zs  
by W5DXP on February 12, 2012 Mail this to a friend!
> N0CU wrote: ... I have never heard anyone claim that a bandpass filter is something other than a bandpass filter when low Q components are used and the final values don't end up close to what they would have been if high Q components have been used. <

The difference is in the definition. If someone told you they had developed a "perfect ideal bandpass filter" with zero losses, would you believe them?

A conjugate match, using a lossless transmission line, is *defined* as lossless between the source and the load. Lossless transmission lines are a useful conceptual tool but they cannot exist in reality. A conjugate match is a useful tool but it cannot exist in reality.

I use the term "near conjugate match". Walter Maxwell uses the terms "one-way conjugate match" and "maximum *available* power transfer".

Again, if reflected energy is prohibited from entering a source by a Z0-match (or Zg-match) then, except for efficiency, IMO the source impedance is irrelevant. If *all* conditions outside of two different sources, one conjugately matched and the other not, can be identical while the non conjugately matched source is more efficient, what does a conjugate match buy us?
--
73, Cecil, w5dxp.com
 
RE: Measuring a Solid-State PAs Zs  
by W5DXP on February 13, 2012 Mail this to a friend!
> W5DXP wrote: A conjugate match is a useful tool but it cannot exist in reality. <

I apologize. This statement is false without a specified context so let me add the context to the statement.

A system wide conjugate match is a useful concept but it cannot exist in the real world using only one matching network (e.g. one antenna tuner).
 
RE: Measuring a Solid-State PAs Zs  
by W5DXP on February 18, 2012 Mail this to a friend!
> W5DXP wrote: A system wide conjugate match is a useful concept but it cannot exist in the real world using only one matching network (e.g. one antenna tuner). <

Again I apologize. Someone pointed out that a system-wide conjugate match can be achieved in the real world by terminating a transmission line with the conjugate of its characteristic impedance. So please change "cannot exist" to "unlikely to exist" in my above assertion. Argggghhhhhh!:)
--
73, Cecil, w5dxp.com
 
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