I'm trying to learn how to correctly calculate (cascade==RF system cascading) the connection of 2-port networks, taking into account mismatch losses. For example There is a first 2-port network, its S parameters at 10GHz, And a second 2-port network. They are shown in the pictures below. If you try to add them up as an RF system (!!!not adding S parameters via ABCD or T matrices!!!) - you have to add their insertion loss ((-0.577)+ (- 0.895) = -1.472 ). So the total insertion loss should be 1.472 - only if the 2-port networks themselves are matched by exactly 50 ohms (perfect impedance matching). But in fact, as you can see in the picture in ADS and ADSimRF - the insertion loss is 1.508. My question is this. If I know the input and output impedance of the 2-port networks (s11 and s22 impedance on SmithChart) how do I need to account for mismatch losses to get the same results in ADS and ADSImRF ? I think I need to calculate the mismatch loss between port 1(50 ohms) - and the first 2-port network (46.999+j16.888), then between network 1(46.999+j16.888) and network 2 (55.2+j2.594) and finally between network 2(55.2+j2.594) and port 2.
I tried to use the formula
MismatchLosses = -10log(1-Г^2)
but either I calculated something wrong, or it does not fit.
I will be grateful for any help or advice
Hi, Your calculation is almost correct. Note, in the above first GT -equation, there is a typo; it should read GT1 (not GT2 ). Your values (at the top right) of 0.895 and 0.577 are dB-Values; actually, they should be negative because 10log(|s21|2)=–0.895dB for NET1; and 10log(|s21|2)=–0.577dB for NET2. They represent the Power Transducer Gains of NET1 and NET2, respectively; and the values apply under the condition of perfect match, i.e., s22=0 of NET1 (or ΓS=0 in GT2 for NET2), and s11=0 of NET2 (or ΓL=0 in GT1 for NET1). So, the cascade (total) Power Transducer Gain is –0.895dB – 0.577dB = –1.472dB for this perfect matching, being a reference case or benchmark. Considering now the mismatch, your calculated linear values of 0.866 and 0.783 for GT1 and GT2, respectively, are correct; and the corresponding product of 0.678 is also ok. However, then we need to take 10log(0.678) which is –1.688dB. Note the Transducer Gain refers to Power, (not voltage or current). Therefore, the values |s21| appear as squared in the GT -equations. In conclusion, the mismatch between NET1 and NET2 imposes a penalty, or additional power loss of 0.22dB in your example case. It occurs that cascade programs (a) neglect the denominator in the GT -equations, and sometimes (b) assume implicitly the source as matched (ΓS=0 ). If we assume both (a) and (b), the resulting cascade (total) Transducer Gain becomes –1.49dB in the example. I hope the above clarifies the issue. Jens`
Yes, I saw the typo about GT and about the negative dB(S21) values for network 1 and 2.
And still I can't understand you -
"However, then we need to take 10log(0.678) which is -1.688dB." - Yes it is, but where is the similarity with the values calculated in ADS? In ADS = -1.508dB. -1.688 is not equal to -1.508.
How do I get 1.508 ? or the difference is the interstage loss ? 1.508 (total of 2 nets) 1,472 (total value if adding up the values separately) 1.508 minus 1.472 = 0.036 dB
I do not see anywhere even close to a value of 0.036
"In conclusion, the mismatch between NET1 and NET2 imposes a penalty, or additional power loss of 0.22dB in your example case." - 0.036 does not equal 0.022 again
"It occurs that cascade programs (a) neglect the denominator in the GT -equations, and sometimes (b) assume implicitly the source as matched (ΓS=0). If we assume both (a) and (b), the resulting cascade (total) Transducer Gain becomes -1.49dB in the example." What is it mean? You mean EDA Keysight ADS or ADISimRF counts wrong or what? Then why do they both add up?
Let me explain what I need it for. If you try to calculate cascade P1dB with nets AS IF matched at 50 ohms each - you get one value. But, if you take mismatch losses into account - you will get the total P1dB higher, because mismatch losses - will increase the cell losses - accordingly if you look at the cascade P1dB formula - you will see that this leads to an increase in the total P1dB. I wrote in more detail here in a similar question and explained the reasons (https://www.edaboard.com/threads/how-to-take-to-account-impedance-mismatch-losses-when-cascading-2-port-networks-as-rf-system.398650/)
So - I still don't understand how do I calculate the interstage mismatch loss (get the total dB(S21) of the two networks = 1.508 as in ADS) AND/OR then - how much should I change the cell loss to get a more accurate total P1dB value.
Excuse me for my misunderstanding.