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29th June 2018, 00:42 #1
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Reflection Coefficient when conjugate matching
I have a question about the conjugate matching.
When we calculate the reflection coefficient of the circuit, we use Γ=(ZLZg)/(ZL+Zg).
What if Zg is conjugate matching we ZL which means Zg=ZL*, and Zg=R+jX, ZL=RjX?
The Γ is not 0.
I think the conjugate matching make sure that there is no power reflect back to source generator so the Γ should be 0. I know why we need the conjuagate matching. All I need is to solve this math problem.
Thanks

29th June 2018, 05:04 #2
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Re: Reflection Coefficient when conjugate matching
Your calculations are right, Γ is not 0. Here is most interesting links I've found to help with your question:
1. http://www.analogrf.com/match.shtml
2. http://www.thefullwiki.org/Maximum_power_theorem
3. http://www.ece.rutgers.edu/%7Eorfanidi/ewa/ch13.pdf
From [1]:
Complex conjugate matching produces the maximum small signal transfer of power from a source that is not a transmission line to a load at the sacrifice of:...
Maximizing power transfer versus power efficiency
The theorem was originally misunderstood (notably by Joule) to imply that a system consisting of an electric motor driven by a battery could not be more than 50% efficient since, when the impedances were matched, the power lost as heat in the battery would always be equal to the power delivered to the motor. In 1880 this assumption was shown to be false by either Edison or his colleague Francis Robbins Upton, who realized that maximum efficiency was not the same as maximum power transfer. To achieve maximum efficiency, the resistance of the source (whether a battery or a dynamo) could be made close to zero. Using this new understanding, they obtained an efficiency of about 90%, and proved that the electric motor was a practical alternative to the heat engine.
Conjugate matching is not the same as reflectionless matching, which refers to matching the load to the line impedance,ZL=Z0, in order to prevent reflections from the load.

29th June 2018, 05:39 #3
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Re: Reflection Coefficient when conjugate matching
Thanks Georgy.
I am thinking another way to explain this is situation. If we think about the wave theory, P_{L}=P_{+}P_{}. P_{+}= V_{+}^2/R and P_{}= V_{}^2/R. The V_{+}could have higher level than voltage at the output of generator, where v+ is at insert voltage the load and v is reflect voltage at the load. therefore, even Γ is not zero, there are still half of the power transmitted to the load.

29th June 2018, 07:43 #4
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Re: Reflection Coefficient when conjugate matching
A simple example of conjugate matching is a RL series load. Conjugate matching can be achieved by placing a series C to the generator with same amount R of real impedance. Means you put the capacitor in resonance with the load L. At the load terminals you have a large reflection coefficient, most energy in the system is circulating between L and C although the generator R is perfectly matched to the load R.
Reflection coefficient is no useful parameter to describe conjugate matching.
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29th June 2018, 15:21 #5
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Re: Reflection Coefficient when conjugate matching
This is a reflection coefficient for Voltage Wave.
Reflection coefficient for Voltage Wave is not zero.
Reflection coefficient for Power Wave is zero.
Port Impedance=R+j*X
(1) Load=R+j*X
(2) Load=Rj*X
Then calculate S11 using RF simulator.
Which case do you think you can get S11=0 ?
Gamma_V = {Zin  Zref} / {Zin + Zref}
Gamma_P = {Zin  conjugate(Zref)} / {Zin + Zref}
Power Wave formulation is most used in RF world.
For example, Sparameters of Keysight ADS are based on Power Wave formulation.
RF simulator give Gamma_P as S11.
See followings.
https://www.edaboard.com/showthread.php?347861#4
https://www.edaboard.com/showthread.php?347861#7
Wrong.
This is a reflection coefficient for Voltage Wave.
Reflection coefficient in Power Wave formulation is useful parameter to describe conjugate matching.
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29th June 2018, 23:25 #6
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Re: Reflection Coefficient when conjugate matching
More information see "Microwave Network Design Using the Scattering MatrixJanusz A. DobrowolskiARTECH HOUSE pp7577

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30th June 2018, 11:11 #7
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Re: Reflection Coefficient when conjugate matching
Like others mentioned in the linked previous thread https://www.edaboard.com/showthread....vspowerwaves, the terms "power wave" and "power wave reflection coefficient" aren't commonly used in the majority of RF text books.
I see that they have been apparently introduced in the 1965 IEEE paper Power Waves and the Scattering Matrix by Kurokawa. They are surely useful when calculating power transfer with complex termination. Thanks for sketching the concept.

11th July 2018, 17:55 #8
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Re: Reflection Coefficient when conjugate matching
S11 is {Zin  conjugate(Zref)} / {Zin + Zref}
in RF simulator or internal post processing in VNA(Vector Network Analyzer).
It is never {Zin  Zref} / {Zin + Zref}
Many people don't know this.
Code://**************************************************************************** /*BEGIN_DOC FUN_NAME:zin() FUN_DESCRIPTION: Given a reflection coefficient and the reference impedance, this measurement returns the input impedance looking into the measurement ports. RETURNED_VALUE: Integer, real or complex CATEGORY: SParameter SYNTAX: z = zin(Sii, Z) EXAMPLE: zIN = zin(S11, 50.0) ARGUMENT ARG_NAME: Sii ARG_DESCRIPTION: complex reflection coefficient. ARG_DEFAULT: None ARG_RANGE: (inf:inf) ARG_TYPE: Complex ARG_REQUIRED: YES ARGUMENT ARG_NAME: zRef ARG_DESCRIPTION: reference impedance ARG_DEFAULT: 50.0 ARG_RANGE: (inf:inf) ARG_TYPE: Integer, real or complex ARG_REQUIRED: NO DEFINED IN: $HPEESOF_DIR/expressions/ael/network_fun.ael SEE ALSO: vswr(), yin() EXTERNAL: yes AUTHOR: Agilent Technologies DATE: Unknown VERSION_CREATED: ADS 1.0 END_DOC*/ //**************************************************************************** defun zin(sii,zRef) { decl zi = if (zRef == NULL) then 50.0 else zRef; return (conj(zi)+zi*sii)/(1sii); }
Last edited by pancho_hideboo; 11th July 2018 at 18:01.

11th July 2018, 18:29 #9
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11th July 2018, 18:36 #10
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Re: Reflection Coefficient when conjugate matching
ADS2016 give S11 as VoltageReflection Coefficient ?
Until ADS2009U1 since MDS, S11 was PowerReflection Coefficient.
When did it change ?
This might be due to trend of current ADS target application, SI(Signal Interity) or High Speed Data Transmission.
Conjugate matching is not important in such applications.
I'm very curious about other simulators such as Microwave Office, Eagle, dead GoldenGate etc.Last edited by pancho_hideboo; 11th July 2018 at 18:54.

11th July 2018, 19:05 #11
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12th July 2018, 13:54 #12
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Re: Reflection Coefficient when conjugate matching
Power Wave Formulation in ADS is well known in FAQ.
See attached document(https://www.edaboard.com/attachment....9&d=1531391256).
SParameters in both Agilent ADS2009U1 and Cadence Spectre(Version 17.1.0.270) are defined by Power Wave Formulation.
S11 is {Zin  conjugate(Zref)} / {Zin + Zref}
Show me result of "zin(0.0, 50+j*50)" in Data Display Window.
If function zin() of measurement expression is also defined by Voltage Wave formulation, it has to give 50+j*50.
I don't have valid support contract now, so I can not access Keysight EEsof Knowledge Center.
If you can access Keysight EEsof Knowledge Center, search any change or update about Sparameter definition for complex Zref.

12th July 2018, 16:35 #13
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Re: Reflection Coefficient when conjugate matching
Here it is ...
"Given a reflection coefficient and the reference impedance, this measurement returns the input impedance looking into the measurement ports."
I wonder what the highlighted section really means. It doesn't say this is the impedance of the DUT, the wording is a bit strange.
But anyway, I've been a happy RF/µW engineer for decades now without power wave reflection coefficient definition, using real impedance reference values with the nonconjugate equation from textbooksLast edited by volker@muehlhaus; 12th July 2018 at 16:47.

12th July 2018, 19:37 #14
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Re: Reflection Coefficient when conjugate matching
I noticed that your usage of "S1P_Eqn" is wrong in https://www.edaboard.com/attachment....5&d=1531330031
Z[1] is a "Port reference impedance" not input impedance.
S[1,1]=Blank and Z[1]=50j*50 for "S1P1".
So input impedance is 50+j*50 not 50j*50.
Power Wave formulation is used here.
Sparameters are defined by Power Wave Formulation even in ADS2016.
Confirm it by using "Z1P_Eqn" instead of "S1P_Eqn".
See https://www.edaboard.com/attachment....1&d=1531400101
zin() is surely for Power Wave formulation even in ADS2016.
See code in https://www.edaboard.com/showthread.php?378353#8
Power Wave Formulation are used for both simulation and postprocessing even in ADS2016.Last edited by pancho_hideboo; 12th July 2018 at 19:53.

12th July 2018, 21:20 #15
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13th July 2018, 02:16 #16
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Re: Reflection Coefficient when conjugate matching
Last edited by pancho_hideboo; 13th July 2018 at 02:26.

13th July 2018, 08:33 #17
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Re: Reflection Coefficient when conjugate matching
Maybe that topics is teached differently in Japan, due to Kurokawa's efforts? FvM and I have been doing our PhD at the same university in Germany where voltage/current waves were teached.
I haven't used the power waves concept, so I can't estimate the practical value. Here's a publication from IEEE micrwave magazine where the author is a bit sceptal:
"Much like a lava lamp, the power waves are comforting to look at, but do not offer the engineer the tools required for analytic design."
https://www.nist.gov/sites/default/f...eoryproof.pdf
But I agree that i seems to solve the discrepancy from post #1, so thanks for poiting to this topic!

13th July 2018, 18:31 #18
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Re: Reflection Coefficient when conjugate matching
I've also seen this. They suggest that Pseudowaves "have long been a cornerstone of microwave circuit theory" but I've only found a couple publications that mention pseudowaves or pseudo s parameters (aside from the author's other works), and the first use of the term came 27 years after Kurokawa's paper. Meanwhile they refer to power waves as a "new addition" to network theory. It looks to me like Williams is pushing a pet theory. If he weren't affiliated with NIST, I'd assume he's a hack.

14th July 2018, 03:19 #19
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Re: Reflection Coefficient when conjugate matching
No.
Generalized Sparameters where port impedances are complex value are not taught at all even in Japan.
For example, see the following standard text book on microwave engineering.
https://www.wiley.com/ensg/Microwav...9780470631553
Many people don't know difference between Power Wave Formulation and Pseudo Wave Formulation even in Japan.
From practical point of view, Sparameters with complex value reference impedance are not needed at all.
As far as my opinion, generalized Sparameters where port impedances are complex value are no more than mathematical extension.
See https://www.edaboard.com/showthread.php?347861#17
However important fact is that Generalized Sparameters are defined by "Power Wave Formulation" in almost all commercial RF Circuit Simulators.
They give S11=0 at conjugate matched condition.
Internal post processing in actual VNA(Vector Network Analyzer) also use "Power Wave Formulation".
We can see descriptions of "Power Wave Formulation" in any vendor's documents.
Keysight
Anritsu
Wiltron(Now Anritsu)
Advantest(Now Rohde & Schwarz)
Many people don't know this fact.
Attached are results of Agilent GoldenGate4.3.8
SParameters of Agilent GoldenGate4.3.8 are also defined by Power Wave Formulation.
No.
You can see many references about "Pseudo Wave Formulation" in EM simulation therory books.
Keysight Momentum use "Power Wave Formulation" as sama as ADSsim.
But Keysight EMPro use "Pseudo Wave Formulation".
Almost all circuit simulators use "Power Wave Formulation".
But this is not true for EM simulator.Last edited by pancho_hideboo; 14th July 2018 at 03:40.

26th July 2018, 11:01 #20
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Re: Reflection Coefficient when conjugate matching
"Microwave Engineering" Written by David M. Pozar
1st Edition : Published in 1990
2nd Edition : Published in 1998
3rd Edition : Published in 2005
4th Edition : Published in 2012
I have 1st and 3rd Editions.
I saw 4th Edition recently.
There was no description about "Power Wave Formulation" until 3rd Edition.
However descriptions about "Power Wave Formulation" are added in 4th Edition.
See "Power Waves and Generalized Scattering Parameters" at pp.185188 in 4th Edition.
Adding descriptions about "Power Wave Formulation" seems to be a request from many teacher or instructors in world wide who use previous three editions.

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