See
http://en.wikipedia.org/wiki/S-parametersa1=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 17th, 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 17th, 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 17th, 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 17th, 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 17th, 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