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

pancho_hideboo

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Re: How to plot "input reflection coefficient" in ADS
Reply #15 - Feb 24^th, 2010, 7:10am

DoYouLinux wrote on Feb 24^th, 2010, 7:06am:

However, is Gamma_L still the same:
Gamma_L=(ZL-conj(Z02))/(ZL+Z02)

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

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)

Gamma_L might be (Z_L-Z₀₂)/(Z_L+conj(Z₀₂)) in the above.

But I use AC analysis for evaluation of Γ_in. I don't use SP analysis.
So I have not confirmed this for complex reference impedance case.

I use custom interstage impedance probe with conventional AC analysis and master large signal steady state analysis followed by small signal AC analysis.
See the followings.
http://www.designers-guide.org/Forum/YaBB.pl?num=1221012939
http://www.designers-guide.org/Forum/YaBB.pl?num=1240334878/18#18
http://www.designers-guide.org/Forum/YaBB.pl?num=1218635777/5#5

Also see http://www.edaboard.com/viewtopic.php?t=380636

Again see the following. This is also interstage impedance probe, although this gives reflection coefficients not impedances.
pancho_hideboo wrote on Feb 17^th, 2010, 7:30am:

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

Back to original topics of this thread.

Γ_P=(Z_in-conj(Z₀₁))/(Z_in+Z₀₁)
Γ_V=(Z_in-Z₀₁)/(Z_in+Z₀₁)

If Z₀₁ is real number, Γ_P=Γ_V.
Is Z₀₁ real number in your evaluation of Γ_in ?

If Z₀₁ is complex number, which type of reflection coefficient is required as Γ_in, Γ_P or Γ_V.

When Z₀₁ is complex number, results of SP analysis are all Γ_P type not Γ_V type.

I think the followings are proper in sqrt(Power) wave formulation, although I have not confirmed.

Γ_S=(Z_S-Z₀₁)/(Z_S+conj(Z₀₁))
Γ_in=(Z_in-conj(Z₀₁))/(Z_in+Z₀₁)

Γ_out=(Z_out-conj(Z₀₂))/(Z_out+Z₀₂)
Γ_L=(Z_L-Z₀₂)/(Z_L+conj(Z₀₂))

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« Last Edit: Feb 24^th, 2010, 9:27am by pancho_hideboo »

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pancho_hideboo

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Re: How to plot "input reflection coefficient" in ADS
Reply #16 - Feb 25^th, 2010, 3:54am

pancho_hideboo wrote on Feb 24^th, 2010, 7:10am:

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

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)

Gamma_L might be (Z_L-Z₀₂)/(Z_L+conj(Z₀₂)) in the above.

I confirmed this.

Gamma_L has to be (Z_L-Z₀₂)/(Z_L+conj(Z₀₂)).

Attached figure is a testbench schematic for AC analysis.

The followings are netlists of DUT. Here I used netlist of Cadence Spectre syntax directly in Agilent ADSsim.

"FBP_1.scs": Code:

simulator lang=spectre
global 0

include "~/RFDE/FBP_1.sub"

I1 (in out) bpf

"FBP_1.sub": Code:

simulator lang=spectre

// Star-Hspice Manual, Release 1998.2 at page.9-21
// Bandpass Netlist: Star-Hspice Network Analysis Results
// References
// Goyal, Ravender. "S-Parameter Output From SPICE Program", MSN & CT,
// February 1988, pp. 63 and 66.

// FILE: FBP_1.SP
// BAND PASS FILTER

subckt bpf ( in out )
c1 ( in 2 ) capacitor c=3.166p
l1 ( 2 3 ) inductor l=203n
c2 ( 3 0 ) capacitor c=3.76p
c3 ( 3 4 ) capacitor c=1.75p
c4 ( 4 0 ) capacitor c=9.1p
l2 ( 4 0 ) inductor l=36.81n
c5 ( 4 5 ) capacitor c=1.07p
c6 ( 5 0 ) capacitor c=3.13p
l3 ( 5 6 ) inductor l=233.17n
c7 ( 6 7 ) capacitor c=5.92p
c8 ( 7 0 ) capacitor c=4.51p
c9 ( 7 8 ) capacitor c=1.568p
c10 ( 8 0 ) capacitor c=8.866p
l4 ( 8 0 ) inductor l=35.71n
c11 ( 8 9 ) capacitor c=2.06p
c12 ( 9 0 ) capacitor c=4.3p
l5 ( 9 10 ) inductor l=200.97n
c13 ( 10 out ) capacitor c=2.97p
ends bpf

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test_FBP_1_AC.png

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pancho_hideboo Senior Fellow Offline Posts: 1356 Real Homeless	Re: How to plot "input reflection coefficient" in ADS Reply #17 - Feb 25^th, 2010, 4:15am Attached figure is a testbench schematic for SP analysis.
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pancho_hideboo Senior Fellow Offline Posts: 1356 Real Homeless	Re: How to plot "input reflection coefficient" in ADS Reply #18 - Feb 25^th, 2010, 4:19am Attached figure is a result.
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pancho_hideboo Senior Fellow Offline Posts: 1356 Real Homeless	Re: How to plot "input reflection coefficient" in ADS Reply #19 - Feb 25^th, 2010, 4:20am Attached figure is a result as "pdf" format for detail view.
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DoYouLinux

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Re: How to plot "input reflection coefficient" in ADS
Reply #20 - Apr 21^st, 2010, 8:35pm

Hi pancho_hideboo,

Thank you very much again for your great post. I am trying to understand the given example. One thing that is still not clear to me is Gamma_L, why is it defined as "Gamma_L=(ZL-Z02)/(ZL+conj(Z02))" ??

Should it be defined as "Gamma_L=(ZL-conj(Z02))/(ZL+Z02)" ??

Thank you very much,

DYL

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pancho_hideboo

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Re: How to plot "input reflection coefficient" in ADS
Reply #21 - Apr 22^nd, 2010, 10:08am

DoYouLinux wrote on Apr 21^st, 2010, 8:35pm:

Should it be defined as "Gamma_L=(ZL-conj(Z02))(ZL+Z02)" ??

No.

It has to be Gamma_L=(Z_L-Z₀₂)/(Z_L+conj(Z₀₂)).
See equations in http://www.designers-guide.org/Forum/Attachments/test_FBP_1.pdf

Derive Gamma_out and Gamma_L from definition in http://en.wikipedia.org/wiki/S-parameters.

As direct thought, simply consider "complex conjugate matching condition" as reflection coefficient expressions, Gamma_out and Gamma_L.

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« Last Edit: Apr 23^rd, 2010, 2:27am by pancho_hideboo »

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DoYouLinux

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Re: How to plot "input reflection coefficient" in ADS
Reply #22 - May 6^th, 2010, 8:01am

Hi pancho_hideboo,

Thank you very much for the explanation, again. Let me take some time to prove and understand them.

However, as I tried to follow the given example to plot Gamma_in (the BPF example), but here I used a transistor as a test vehicle. I found from the result that, in the plot of Gamma_in using "stos" function, if I defined the function as:

S_new=stos(S, PortZ, {Zo1, Zload}),

then S_new(1,1) will be identical to Gamma_in I defined using an equation. However, if I replaced Zo1 in the S_new function by Zsource as:

S_new=stos(S, PortZ, {Zsource, Zload}),

then S_new(1,1) will not be identical to Gamma_in function. How come ?

To my understanding "S_new=stos(S, PortZ, {Zsource, Zload})" should be correct because we changed the reference impedance to be Zsource and Zload (here in my case, my Zo1 is not equal to Zsource, as in your example).

Could you clarify more on this point, please ?

Thank you very much in advance,

DYL

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sch_test.JPG

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DoYouLinux Community Member Offline Posts: 63	Re: How to plot "input reflection coefficient" in ADS Reply #23 - May 6^th, 2010, 8:02am Here is the result:
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pancho_hideboo

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Re: How to plot "input reflection coefficient" in ADS
Reply #24 - May 6^th, 2010, 8:16am

Gamma_in is not correct for your case since you change Z01.
On the other hand, S_new(1,1) is correct.

Equation for Gamma_in has to be modified if Z01 is changed.

You can derive modified equation for Gamma_in_corrected valid for changing Z01.

Calculate Zin from Gamma_in=(Zin-conj(Z01))/(Zin+Z01).
Next calculate Gamma_in_corrected as (Zin-conj(Zs))/(Zin+Zs).

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« Last Edit: May 7^th, 2010, 12:57am by pancho_hideboo »

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DoYouLinux

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Re: How to plot "input reflection coefficient" in ADS
Reply #25 - May 8^th, 2010, 10:39am

Hi pancho_hideboo,

Thank you for your further explanation. However, I think that I am still confused about the expression "S_new" using "stos" function of ADS.

As explained also in the attached figure, to my understanding, the "PortZ" argument represents the default set of reference impedances, which are Zo1 and Zo2 as shown in the schematic. In my example, Zo1 and Zo2 imply the reference impedances used for characterizing the default S parameters of the transistor.

Then, the transistor was assume to be terminated with another set of impedances at the source side and the load side, which are "Zsource" and "Zload" in this example. This new termination is defined in the "S_new" expression as "{Zsource, Zload}". So, "Zsource" will be a new termination for port 1 (source side) and "Zload" will be a new termination for port 2 (load side).

Then, I compared "S_new(1,1)" with the "Gamma_in" expression given in the previous reply. The "Gamma_in" expression uses "my_Sxx" to represent the default set of S parameter based on Zo1 and Zo2 reference impedances. "Gamma_L" in "Gamma_in" expression represents the load reflection coefficient due to termination using "Zload".

From my understanding described above, I expected that "S_new(1,1)" and "Gamma_in" would be identical. But this was not the case. However, when I changed the new reference impedance in the "stos" function of the "S_new" expression to be "{Zo1, Zload}", the expressions "S_new" and "Gamma_in" were identical. Why when I replaced "Zsource" with "Zo1", the results were identical ?
"Zo1" is not a new reference impedance at the source side (it is the default reference impedance at the source side instead), in my understanding, "Zsource" should be the correct variable.

Would you mind to explain me further about this please ? I really want to understand as clear as I can.

Thank you very much again,

DYL

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S_new.JPG

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pancho_hideboo

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Re: How to plot "input reflection coefficient" in ADS
Reply #26 - May 8^th, 2010, 10:46am

I can't understand what you want to mean at all.

"stos()" is very clear and straightforward.
If you have any doubt about it, see its definition in "$HPEESOF_DIR/expressions/ael/network_fun.ael".

=======================================================================
PortZ={Z01, Z02}

Zs!=Z01, ZL!=Z02

S_Z01_ZL=stos(S, PortZ, {Z01, ZL})
S_Z01_ZL(1,1)==Gamma_in

S_Zs_ZL=stos(S, PortZ, {Zs, ZL})
S_Zs_ZL(1,1)!=Gamma_in
S_Zs_ZL(1,1)==Gamma_in_corrected

Zin is unique regardless of {Z01,Z02} values.
Zin is determined by only ZL.

Gamma_in is a reflection coefficient defined for Zin and Z01.
Gamma_in_corrected is a reflection coefficient defined for Zin and Zs.
=======================================================================

Again see http://www.designers-guide.org/Forum/YaBB.pl?num=1266403928/24#24
Try to calculate Gamma_in_corrected.
Show me plot result of this Gamma_in_corrected and S_new(1,1).

I think you can't understand S-parameters and Reference impedances at all.
I think you should not use S-parameter formulation.
You had better use AC analysis, although there are no difference between AC and SP analyses for me,
since they are both linear analysis.

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« Last Edit: May 8^th, 2010, 2:10pm by pancho_hideboo »

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DoYouLinux

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Re: How to plot "input reflection coefficient" in ADS
Reply #27 - May 10^th, 2010, 9:21am

Hi pancho_hideboo,

Thank you very much again for your explanation. I really appreciated it. I think perhaps I am confused about the definition of the "input reflection coefficient" and also confused about the expression of "stos" function. Therefore, I tried to summarize again in the attached figure.

In the figure, what I understood is, please correct me if I were wrong,:

1) A 2-port was first characterized with reference impedances Zo1 and Zo2. From these reference impedance, the default S parameter set was obtained and the input reflection is S11. The reference impedance is defined as "portZ" in the "stos" function.

2) Then, assuming that the reference impedance on the load side was changed to "Zload", now the input reflection coefficient was not equal to S11 anymore (since Gamma_L is not zero). In this configuration, the new reference impedance was defined as "{Zo1, Zload}" in the "stos" function (Zo1 remains but Zo2 replaced by Zload). Then, "Gamma_in" can be found from S_new(1,1).

Did I understand correctly ?

Thank you in advance again,

DYL :)

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Gamma_in.JPG

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pancho_hideboo Senior Fellow Offline Posts: 1356 Real Homeless	Re: How to plot "input reflection coefficient" in ADS Reply #28 - May 10^th, 2010, 9:24am DoYouLinux wrote on May 10^th, 2010, 9:21am: Did I understand correctly ? Correct
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DoYouLinux Community Member Offline Posts: 63	Re: How to plot "input reflection coefficient" in ADS Reply #29 - May 27^th, 2010, 6:43am Hi Pancho_Hideboo, After I repeat the simulation in ADS again, I got correct results. Thank you very much again for your explanation about Gamma_in topic. DYL
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