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Network theory: travelling waves vs power waves

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mtwieg

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My network theory is self-taught, so maybe there are some basic answers to this, but while writing my thesis this keeps coming up:

Why aren't power waves (as defined by Kurokawa's scattering matrix paper) see more use than travelling waves in research and literature? Seems to me that the power wave reflection coefficient s has more utility than the travelling wave reflection coefficient Γ, especially at circuit junctions where the impedance looking in both directions is complex. Perhaps it is because it is much more difficult to measure power waves than travelling waves with a VNA? Is there even a method to experimentally measure s at a junction with arbitrary impedances?
 

Why aren't power waves (as defined by Kurokawa's scattering matrix paper) see more use than travelling waves in research and literature?
You are misunderstanding.
Power Wave formulation is most used in RF world.
For example, S-parameters of Keysight ADS are based on Power Wave formulation.

See https://www.designers-guide.org/Forum/YaBB.pl?num=1266403928/#10

Perhaps it is because it is much more difficult to measure power waves than travelling waves with a VNA?
For real value reference impedance, there is no difference between Power Wave and Voltage Wave formulations.
VNA can treat only real value reference impedance.
 

Well do a google search for reflection coefficient and you'll see almost nothing but the travelling wave equation. Even in IEEE I almost never see s, always gamma.

Yes, for real valued terminating impedance, they are identical, so when connecting to a VNA the reflection coefficient looking into the VNA's own ports is the same for both types of waves. But even if the VNA's reference impedance is zero, there must be some way to measure s at a junction with arbitrary impedances? Perhaps by embedding directional couplers at the junction?
 

Well do a google search for reflection coefficient
and you'll see almost nothing but the travelling wave equation.
Even in IEEE I almost never see s, always gamma.
What do you search ?
See http://wikis.ua.pt/MTT-11/index.php/S-Parameters_and_VNA_Calibrations#Power_waves

Also see "Kurokawa" in the following.
http://en.wikipedia.org/wiki/Scattering_parameters
S-parameter in Wikipedia is Power Wave Formulation.

S-parameters of Keysight ADS are also based on Power Wave formulation.
See page-9 of http://literature.cdn.keysight.com/litweb/pdf/5989-9273EN.pdf

Perhaps by embedding directional couplers at the junction?
Assume reactive(lossless) matching network for R+j*X to 50Ohm, it ihas to be conjugate matching, so it is power wave definition, Sqrt(Gamma_P) not Gamma_V.

Port Impedance=R+j*X
(1) Load=R+j*X
(2) Load=R-j*X

Then calculate S11 using RF simulator.
Which case do you think you can get S11=0 ?
 
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Assume reactive(lossless) matching network for R+j*X to 50Ohm, it ihas to be conjugate matching, so it is power wave definition, Sqrt(Gamma_P) not Gamma_V.

hi pancho_hideboo,
can you please explain this? thanks.
 

See attached diagram.
 

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Again, Power Wave formulation is most used in RF world.
I don't disagree, but I find it strange that I've never seen the term "power wave" at any conference I've attended, and have had people ask me what a power wave is when I use the term.

I think people use the power wave formulation without knowing it, since they almost always measure their systems at points connected to Z0 and just say "reflection coefficient," which in itself is okay. But then I see people referring to other points in the system (like in between a matching network and the gate or drain of a FET), but still just say "reflection coefficient." That's where ambiguities arise, because at such an observation point the travelling wave and power wave reflection coefficients will not necessarily be equal, but I have never seen the distinction made in any literature I've come across.
 

but I find it strange that I've never seen the term "power wave" at any conference I've attended
What community do you attend ?

Term of "Power Wave" is very common in IEEE MTT and IEEE AP which have been existed since IEEE was named as IRE.

Even Mode and Odd Mode.
Common Mode and Differential Mode.

RF people use former.
 
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What community do you attend ?
MRI hardware (ISMRM). Also MTT, but less of the latter.

- - - Updated - - -

And it doesn't help that stuff like this pops up on the first page of google results for "power waves and the scattering matrix."
 

Modern MW engineering uses travelling waves, like S11 = B/A where B is the reflected traveling wave, and A is the incident travelling wave. B and A are moste like E Fields, or "voltages", so to see the power in them you have to square the quantities.

But old school MW engineering, like the type done 40 years ago, involved a lot of directional couplers and thermistor power meters...so Power waves, if you want to call them that, were more en vogue. Of course, even back then there were slotted lines and standing wave meters...measuring voltage standing waves.....
 

Modern MW engineering uses travelling waves, like S11 = B/A where B is the reflected traveling wave, and A is the incident travelling wave. B and A are moste like E Fields, or "voltages", so to see the power in them you have to square the quantities.
But power waves are proportional to E and B fields, and are linear. Really the only difference is the conjugate terminating impedance.

But old school MW engineering, like the type done 40 years ago, involved a lot of directional couplers and thermistor power meters...so Power waves, if you want to call them that, were more en vogue. Of course, even back then there were slotted lines and standing wave meters...measuring voltage standing waves.....

I think it's clear that any instrument that terminates the waves with a real impedance (virtually all of them) cannot distinguish power waves from traveling waves. I don't know if swr meters can distinguish an impedance match vs a conjugate match, interesting to think about...

My question is more about why power waves aren't commonly explicitly referred to when analyzing RF systems in literature. Are they not taught at universities anymore? My university doesn't even have an RF/MW curriculum, but when I look at lecture slides from other universities I never see them mentioned except for maybe a background slide here or there.
 

Are they not taught at universities anymore? My university doesn't even have an RF/MW curriculum, but when I look at lecture slides from other universities I never see them mentioned except for maybe a background slide here or there.

Our university teaches conjugate matching for power electronics, but in the RF lecture the wave stuff is always explained in terms of purely ohmic reference impedance.

We talk about "waves" and standing waves and in the lab we measure voltage standing wave ratio with a voltage probe in a slotted line, for different loads. It might be a language thing, but "power waves" is a term I haven't heard about in our RF education.
 

Modern MW engineering uses travelling waves, like S11 = B/A where B is the reflected traveling wave, and A is the incident travelling wave.
B and A are moste like E Fields, or "voltages", so to see the power in them you have to square the quantities.
No.
Commercial RF simulator such as "Keysight ADS" gives S11=0 at conjugate matched condition.
Generalized S-parameters are defined by "Power Wave".

I don't know about Cadence Spectre.
I can't believe Cadence Spectre with complex impedance port at all.
See http://www.designers-guide.org/Forum/YaBB.pl?num=1231076499/13#13

b=S*a, here S means S-matrix.
but "power waves" is a term I haven't heard about in our RF education.
If so, what do you call "|a|^2" and "|b|^2" ?

Have you seen all references I showed in #4 of this thread ?
http://wikis.ua.pt/MTT-11/index.php/S-Parameters_and_VNA_Calibrations#Power_waves
http://en.wikipedia.org/wiki/Scattering_parameters
http://literature.cdn.keysight.com/litweb/pdf/5989-9273EN.pdf

You can see term of "power wave" even in Wikipedia.

We call "|a|^2" as "incident power wave" and "|b|^2" as "reflected power wave".

Both "a" and "b" are neither voltage nor current.

I call "a" as "root(incident power wave)" and "b" as "root(reflected power wave)", however these names are not general.

Strictly speaking, "a" and "b" are root(power) not power.
However we often call "a" and "b" as power simply.

But power waves are proportional to E and B fields, and are linear.
Really the only difference is the conjugate terminating impedance.
Right.
Are they not taught at universities anymore?
I think so.
I can not see any reference of generalized s-parameters where port impedances are complex value in current many text books.

I think the following is a standard text book on microwave engineering.
**broken link removed**

However there is no reference of "Power Wave" and " generalized s-parameters where port impedances are complex" even in this famous text book.

I think it's clear that any instrument that terminates the waves with a real impedance (virtually all of them) cannot distinguish power waves from traveling waves.
Right.
My question is more about why power waves aren't commonly explicitly referred to when analyzing RF systems in literature.
From practical point of view, s-parameters with complex value reference impedance are not needed at all.

As far as my opinion, generalized s-parameters where port impedances are complex value are no more than mathematical extension.

My university doesn't even have an RF/MW curriculum,
but when I look at lecture slides from other universities I never see them mentioned except for maybe a background slide here or there.
I think it is recent trend, since there is no practical need for generalized s-parameters where port impedances are complex value.
 
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No.
Commercial RF simulator such as "Keysight ADS" gives S11=0 at conjugate matched condition.
Generalized S-parameters are defined by "Power Wave".
Well as we said at a VNA's ports, Zi is real so power waves and traveling waves are the same.

As for the S matrix, S is defined under the assumptions that all ports are terminated with real Zi, so S is the same for power and traveling waves. The difference emerges when one or more ports are not terminated in a real impedance, and thus you get reflection coefficients which differ depending on whether you consider power or traveling waves.

If so, what do you call "|a|^2" and "|b|^2" ?
I have actually seen material where traveling waves are referred to as a and b.

We call "|a|^2" as "incident power wave" and "|b|^2" as "reflected power wave".

Both "a" and "b" are neither voltage nor current.

I call "a" as "root(incident power wave)" and "b" as "root(reflected power wave)", however these names are not general.

Strictly speaking, "a" and "b" are root(power) not power.
However we often call "a" and "b" as power simply.
Never seen the term "root" power wave, Kurokawa originally called a and b power waves (even though they do not have unit watts).
 
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Commercial RF simulator such as "Keysight ADS" gives S11=0 at conjugate matched condition.

Sure. There wasn't any doubt about that.

Generalized S-parameters are defined by "Power Wave"..

As I already mentioned, it might be a language thing or you might teach RF differently .... we discuss wave and standing waves all the time, but the word "power waves" is not common in RF education over here.

All that S-parameter and Smith chart stuff is teached with real system impedance.
 

From practical point of view, s-parameters with complex value reference impedance are not needed at all.
I agree in the case of s parameters, but it matters with regards to reflection coefficients.

For example when I'm seeing a talk on RFPA design and someone suggests that reflection coefficient Γ at the gate of a FET should be zero, and shows the equation Γ=(Zs-Zin)/(Zs+Zin), they're just wrong. I see terms like "impedance matching," "conjugate matching," and "power matching" thrown around as if they're all identical, and it drives me a little crazy.
 

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