The Designer's Guide Community Forum - How to plot "input reflection coefficient" in ADS

DoYouLinux

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How to plot "input reflection coefficient" in ADS
Feb 17^th, 2010, 2:52am

Hi all,

I am just wondering .... I am trying to simulate a single transistor with two 50-ohm ports connected at the base and collector in ADS.

From theory, if the output is terminated with a 50-ohm load, the input reflection coefficient looking into the base is equal to S11. How ever, if the output is terminated with some impedance other than 50 ohm (Gamma_L is not zero), we need to calculate the input reflection coefficient (Gamma_in) as a function of "Gamma_L"

My question is, how could we plot "Gamma_in" in ADS ??? Do we need to edit the equation of Gamma_in by ourselves ? Or, there exists some predefined function ?

Thanks a lot in advance (I will put my schematic soon)

DYL ;D

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pancho_hideboo

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Re: How to plot "input reflection coefficient" in ADS
Reply #1 - Feb 17^th, 2010, 3:17am

Assume following.
ZL ; Load Impedance.

Z01 ; Port1 Impedance=Reference Impedance for Port1
Z02 ; Port2 Impedance=Reference Impedance for Port2

You can calculate Gamma_in by various methods.

If {S(1,1),S(1,2),S(2,1),S(2,2)} are evaluated under condition of Z02==conj(ZL), S(1,1) is Gamma_in you want.

If {S(1,1),S(1,2),S(2,1),S(2,2)} are evaluated under condition of Z02!=conj(ZL), use "stos()" function.
http://edocs.soco.agilent.com/display/ads2009/stos%28%29

Scorrected = stos(S, PortZ, {PortZ(1),conj(ZL)})

You can get Gamma_in as Scorrected(1,1).
Here PortZ(1)=Z01, PortZ(2)=Z02.

Of course, you can also calculate Gamma_in by the following.
Gamma_L=(ZL-conj(Z02))/(ZL+Z02)
Gamma_in=S(1,1)+S(1,2)*S(2,1)*Gamma_L/(1-S(2,2)*Gamma_L)

You can define your custom functions in Agilent ADS post processing environment which are commonly usable in ADS native, RFDE and GoldenGate.

See http://www.edaboard.com/viewtopic.php?t=371902

Source codes of original prepared functions exist in "$HPEESOF_DIR/expressions/ael".
You can create your custom function easily by modifying them.

Code:

defun  my_gamma_in(S, ZL, Z02)
{
	  decl  gammaL = (ZL-conj(Z02))/(ZL+Z02);
	  decl  gamma_in=S(1,1)+S(1,2)*S(2,1)*gamma_L/(1-S(2,2)*gamma_L);
	  return gamma_in;
}

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« Last Edit: Feb 17^th, 2010, 6:14am by pancho_hideboo »

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DoYouLinux

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Re: How to plot "input reflection coefficient" in ADS
Reply #2 - Feb 17^th, 2010, 7:18am

Hi pancho_hideboo,

Thank you so much again for your great reply. However, I am still confused at some points.

1) For the load reflection coefficient (Gamma_L), is it not calculated by "(ZL-Z02)/(ZL+Z02) ? Why is the numerator in your reply equal to "ZL-conj(Z02)" ? From what I understand, your reflection coefficient is a general form. For example, as seen from the attached figure, if Z0 is complex and if ZL is a complex conjugate of Z0, the two impedances are conjugately matched and there will be no reflection at the reference plane. Do I understand correctly ??

However, in ADS, the reference impedance becomes Z0 of the "term" element, not that of the transmission like shown in the figure anymore. Hmmmm .... so where is the reference plan that we can define the "reflection" ???

2) As you can see from another attached figure, if I changed Z0 of "Term 2" to be, for instance, 10 + j20 instead of 50. Now does my load become 10 + j20 ohm and the reference impedance of Term 2 is 10 Ohm.

I am quite confused about reference impedance in ADS and reference impedance used in several text books now >:(

However, thank you very much again for your nice post

DYL

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DoYouLinux Community Member Offline Posts: 63	Re: How to plot "input reflection coefficient" in ADS Reply #3 - Feb 17^th, 2010, 7:19am Oh, forgot another figure. Here it is.
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pancho_hideboo

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Re: How to plot "input reflection coefficient" in ADS
Reply #4 - Feb 17^th, 2010, 7:30am

See http://en.wikipedia.org/wiki/S-parameters
a1=0.5*k*(V1+Z01*I1), b1=0.5*k*(V1-conj(Z01)*I1), k=1/sqrt(real(Z01))
Gamma=b1/a1=(V1-conj(Z01)*I1)/(V1+Z01*I1)=(Zin-conj(Z01))(Zin+Z01), Zin=V1/I1

DoYouLinux wrote on Feb 17^th, 2010, 7:18am:

1) For the load reflection coefficient (Gamma_L), is it
not calculated by "(ZL-Z02)/(ZL+Z02) ?
Why is the numerator in your reply equal to "ZL-conj(Z02)" ?

Try to run 1 port s-parameter analysis using Agilent ADS under Z of "Term1" is 50+j*50 and Zload=20+j*30.
Confirm S11 which ADS gives is (Zload-conj(Z))/(Zload+Z) not (Zload-Z)/(Zload+Z).

DoYouLinux wrote on Feb 17^th, 2010, 7:18am:

For example, as seen from the attached figure, if Z0 is complex and if ZL is a complex conjugate of Z0, the two impedances are conjugately matched and there will be no reflection at the reference plane.
Do I understand correctly ??

Not correct. Reflection regarding "Voltage Wave" exists even if this reflection coefficient is zero.
This reflection coefficient is for maximum power transmission. That is no reflection for sqrt(Power Wave).
Not for non-distortion(non reflection regarding Voltage Wave) transmission condition.

Definition of reflection coefficient for non reflection regarding Voltage Wave is (Zload-Z)/(Zload+Z) not (Zload-conj(Z))/(Zload+Z).

DoYouLinux wrote on Feb 17^th, 2010, 7:18am:

However, in ADS, the reference impedance becomes Z0 of the "term" element,
not that of the transmission like shown in the figure anymore.
Hmmmm .... so where is the reference plan that we can define the "reflection" ???

Signal source having source impedance of Z0 is connected to left of transimission line in your attatched figure.
Consider Tevenin equivalent circuit seeing left from Ref. plane in your attached figure.
If you consider Tevenin equivalent circuit, it is very clear that reference plane is point you showed.

DoYouLinux wrote on Feb 17^th, 2010, 7:18am:

2) As you can see from another attached figure,
if I changed Z0 of "Term2" to be, for instance, 10 + j20 instead of 50.
Now does my load become 10 + j20 ohm and the reference impedance of Term 2 is 10 Ohm.

Not correct.
The reference impedance of "Term2" is (10+j*20)ohm not 10ohm.

If you use AC analysis for evaluation of Zin, Z of "Term2" must be ZL.

But if you use SP analysis for evaluation of Zin and Z of "Term2" is conj(ZL),
Gamma_in which you want is given as S11.

DoYouLinux wrote on Feb 17^th, 2010, 7:18am:

I am quite confused about reference impedance ADS and reference impedance used in several text books now

Treatment of complex impedance of "Term" in Agilent ADS is very correct.
There are very few books which describe definition of S-parameters when reference impedances are complex number, although I don't know what text books you read.

In Agilent ADS, "SP_Probe" is available for evaluation of Zs,Zin,Zout and ZL.
http://edocs.soco.agilent.com/display/ads2009/SP+Probe+%28S-Parameter+Probe%29

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« Last Edit: Feb 18^th, 2010, 3:17am by pancho_hideboo »

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Frank Wiedmann

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Re: How to plot "input reflection coefficient" in ADS
Reply #5 - Feb 18^th, 2010, 2:07am

pancho_hideboo wrote on Feb 17^th, 2010, 7:30am:

There are very few books which describe definition of S-parameters when reference impedances are complex number, although I don't know what text books you read.

The article http://www.mtt.org/measurements/GENERWGCT.PDF is the best reference for this subject I know of. The discussion at http://www.designers-guide.org/Forum/YaBB.pl?num=1251245633 might also be interesting regarding the definition of S-parameters.

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pancho_hideboo

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Re: How to plot "input reflection coefficient" in ADS
Reply #6 - Feb 18^th, 2010, 2:29am

When reference impedance is real number, definition of s-parameter is very easy.
See http://www.designers-guide.org/Forum/YaBB.pl?num=1266168115/1#1

Frank Wiedmann wrote on Feb 18^th, 2010, 2:07am:

The article http://www.mtt.org/measurements/GENERWGCT.PDF is the best reference for this subject I know of.

This is based on "Electro-Magnetic Wave Circuit Theory".
So I think it is very difficult to understand for people who are not microwave theory experts.

Most important issue is understanding "Power Wave formulation" based on "Kaneyuki Kurokawa's formulation".

When reference impedance is real number, sqrt(power wave) is same as voltage wave except for scalar multiplication existing between them.

But when reference impedance is complex number, sqrt(power wave) is different from voltage wave completely.

This board is "Simulators".
So I move back to issue of "Simulators".

I have confirmed that treatment of complex impedance of "Term" in Agilent ADS's SP analysis is very correct.

However I have not confirmed whether treatment of complex impedance of "port" is correct or not in SP analysis of both Cadence Spectre and Agilent GoldenGate.

Cadence Spectre claims supporting "port" with complex impedance at least for small signal analysis.
http://www.designers-guide.org/Forum/YaBB.pl?num=1231076499/5#5

Is there anyone who confirmed treatment of complex impedance of "port" in SP analysis of both Cadence Spectre and Agilent GoldenGate ?
Can they give correct S11 and S21 when both Z01 and Z02 are complex numbers ?

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« Last Edit: Feb 18^th, 2010, 4:32am by pancho_hideboo »

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Frank Wiedmann

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Re: How to plot "input reflection coefficient" in ADS
Reply #7 - Feb 18^th, 2010, 5:06am

pancho_hideboo wrote on Feb 18^th, 2010, 2:29am:

Frank Wiedmann wrote on Feb 18^th, 2010, 2:07am:

The article http://www.mtt.org/measurements/GENERWGCT.PDF is the best reference for this subject I know of.

This is based on "Electro-Magnetic Wave Circuit Theory".
So I think it is very difficult to understand for people who are not microwave theory experts.

The summary at http://wikis.ua.pt/MTT-11/index.php/S-Parameters_and_VNA_Calibrations might be more accessible.

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DoYouLinux

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Re: How to plot "input reflection coefficient" in ADS
Reply #8 - Feb 18^th, 2010, 6:54am

Hi Pancho_Hideboo,

I have just finished my homework, proving your reply. Wow, you are correct about the definition of reflection coefficient that is used by ADS. I attached what I did in ADS and the results here.

Now I am trying to understand the definitions of reflection coefficients you mentioned (I still don't know exactly how to use Quote, sorry about this):

--------------------------------------------------------------------------------
-------------------
Reflection regarding "Voltage Wave" exists even if this reflection coefficient is zero.
This reflection coefficient is for maximum power transmission. That is no reflection for sqrt(Power Wave). Not for non-distortion(non reflection regarding Voltage Wave) transmission condition.

Definition of reflection coefficient for non reflection regarding Voltage Wave is (Zload-Z)/(Zload+Z) not (Zload-conj(Z))/(Zload+Z)
--------------------------------------------------------------------------------
-------------------

Why do we have two definitions: (Zload-Z)/(Zload+Z) and (Zload-conj(Z))/(Zload+Z). As I have proved in ADS, the latter definition is correct, while the first one is not correct :-/

Thank you very much for your explanation again,

DYL

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DoYouLinux Community Member Offline Posts: 63	Re: How to plot "input reflection coefficient" in ADS Reply #9 - Feb 18^th, 2010, 6:55am Oh, forgot the results.
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pancho_hideboo

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Re: How to plot "input reflection coefficient" in ADS
Reply #10 - Feb 18^th, 2010, 7:18am

DoYouLinux wrote on Feb 18^th, 2010, 6:54am:

Why do we have two definitions: (Zload-Z)/(Zload+Z) and (Zload-conj(Z))/(Zload+Z).
As I have proved in ADS, the latter definition is correct, while the first one is not correct

Both reflection coefficients are correct.
They depend on wave which we have interest in.

First one is based on Voltage Wave.
Second one is based on sqrt(Power Wave).

For complex reference impedance, you have to distinguish S11 from Γ_V(=Voltage Wave Refelection Coefficient).

At power matching(=conjugate matching) condition, output waveform is distorted unless input signal is single frequency sinusoidal.

Assume source impedance is Zs=Rs//Cs=1/(1/Rs+j*ω*Cs) and Load impedance is ZL.

If ZL=conj(Zs)=1/(1/Rs-j*ω*Cs)=1/(1/Rs+1/(j*ω*Leq)), (Leq=1/(ω²*Cs)), output waveform is distorted
because we can never realize broadband conjugate matching.

If ZL=k*Zs, (k is real number), output waveform is never distorted.
Here we can realize ZL=k*Zs=(k*Rs)//(Cs/k) over relative wide frequency band.
k=1 is no more than no reflection condition for Voltage Wave.

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« Last Edit: Feb 18^th, 2010, 9:32am by pancho_hideboo »

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pancho_hideboo

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Re: How to plot "input reflection coefficient" in ADS
Reply #11 - Feb 19^th, 2010, 1:47am

pancho_hideboo wrote on Feb 18^th, 2010, 2:29am:

I have confirmed that treatment of complex impedance of "Term" in Agilent ADS's SP analysis is very correct.

However I have not confirmed whether treatment of complex impedance of "port" is correct or not in SP analysis of both Cadence Spectre and Agilent GoldenGate.

Cadence Spectre claims supporting "port" with complex impedance at least for small signal analysis.
http://www.designers-guide.org/Forum/YaBB.pl?num=1231076499/5#5

Is there anyone who confirmed treatment of complex impedance of "port" in SP analysis of both Cadence Spectre and Agilent GoldenGate ?
Can they give correct S11 and S21 when both Z01 and Z02 are complex numbers ?

I have confirmed treatment of complex impedance of "port" in SP analysis of both Cadence Spectre and Agilent GoldenGate.

Both Cadence Spectre and Agilent GoldenGate can give same S11 and S21 as Agilent ADSsim when both Z01 and Z02 are complex numbers.

But Cadence OCEAN functions, "zm()" and "zref()" can't give correct values. "zref()" ignores imaginary part.

I've not confirmed other Cadence OCEAN functions related to SP analysis.
If you will use Cadence Spectre, you should confirm their validity for complex reference impedance case.

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« Last Edit: Feb 19^th, 2010, 7:49am by pancho_hideboo »

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DoYouLinux Community Member Offline Posts: 63	Re: How to plot "input reflection coefficient" in ADS Reply #12 - Feb 23^rd, 2010, 6:17am Hmmm Pancho_Hideboo, I actually am reading it, from the beginning .... I will come back with some results of my homework soon DYL
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pancho_hideboo

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Re: How to plot "input reflection coefficient" in ADS
Reply #13 - Feb 23^rd, 2010, 9:13pm

pancho_hideboo wrote on Feb 17^th, 2010, 3:17am:

If {S(1,1),S(1,2),S(2,1),S(2,2)} are evaluated under condition of Z02==conj(ZL), S(1,1) is Gamma_in you want.

If {S(1,1),S(1,2),S(2,1),S(2,2)} are evaluated under condition of Z02!=conj(ZL), use "stos()" function.
http://edocs.soco.agilent.com/display/ads2009/stos%28%29

Scorrected = stos(S, PortZ, {PortZ(1),conj(ZL)})

I have mistakes.
Correctly these have to be : Quote:

If {S(1,1),S(1,2),S(2,1),S(2,2)} are evaluated under condition of Z02==ZL, S(1,1) is Gamma_in you want.

If {S(1,1),S(1,2),S(2,1),S(2,2)} are evaluated under condition of Z02!=ZL, use "stos()" function.
http://edocs.soco.agilent.com/display/ads2009/stos%28%29

Scorrected = stos(S, PortZ, {PortZ(1),ZL})

pancho_hideboo wrote on Feb 17^th, 2010, 7:30am:

But if you use SP analysis for evaluation of Zin and Z of "Term2" is conj(ZL),
Gamma_in which you want is given as S11.

I have mistakes.
Correctly this has to be : Quote:

But if you use SP analysis for evaluation of Zin and Z of "Term2" is ZL,
Gamma_in which you want is given as S11.

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DoYouLinux Community Member Offline Posts: 63	Re: How to plot "input reflection coefficient" in ADS Reply #14 - Feb 24^th, 2010, 7:06am Hi Pancho_Hideboo, Thank you for the correction. However, is Gamma_L still the same: Gamma_L=(ZL-conj(Z02))/(ZL+Z02) ?? DYL
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