Regarding GTUMAX computed value vs handcalculated value

[hptrivedi95]

Hi QucsStudio community,

I am Het Pranav Trivedi, an enthusiastic RF Engineer. I have been working with QucsStudio (u-Simmics-5.8) for the past 2 months.

Recently, while simulating a circuit, I found that it yielded a max_ulgain_dB of 42.8 dB, which, to the best of my understanding, indicates the maximum unilateral transducer gain. When I hand calculate it using S-parameters, I get 32.8 dB gain. I am attaching an image of the circuit and an image of the .s2p file. The transistor used is from a special transistor library>>atf3413 low noise pHEMT

The formula I use for hand-calculation is as follows:
GTU,MAX = GAU,MAX = GPU,MAX = [(1/(1 – |ГS|^2))]*[|S21|^2]*[(1/(1 – |ГL|^2))] (This formula is referenced from – Microwave Transistor Amplifier Analysis Design, 2nd Edition by Guillermo Gonzalez )

GTU,MAX dB = 10log10(GTU,MAX)

S12 = 0 is assumed for GTU and then ГS = S11*, ГL = S22* gives the GTUMAX as to my understanding. This way it only depends on S – parameters and not on source and load impedances, as they are assumed to be conjugate as described above. So, |ГS| = |S11*| = |S11| , |ГL| = |S22*| = |S22| in the above formula.

GLUMAX = 0.16 dB, GSUMAX = 10.438 dB , GD = 22.064 dB

GTUMAX = 10.438 + 22.064 + 0.16 = 32.662 dB

Now, agreeably at 1 GHz, K < 1 and Δ < 1, along with |S12| ≠ 0 or < 0.005 (Considering |S21| < 40), thus unilateral gain merit cannot be applied here, although, as I understand it can still be computed assuming |S12| = 0. GMSG hand calculation aligns well with max_gain_dB.

Kindly help me figure out what I am missing.

PFA
Best Regards
Het (KJ5BEI)

 

Attachments:

1. 

   RF_Char_circuit_atf3413_special_transistor.png
   

2. 

   s2p_@1GHz_S_parameters.png
   

[Max1499]

Hello Het,

In the directory where uSimmics is installed there is a subdirectory named “doc” in which you find the file “technical.pdf”. This contains a detailed description of all calculations used in uSimmics. The calculation you are interested in is on page 38 under “4.6.2 Gain”. I am not sure if your own calculation is different.
In a first step I recommend in this case not to use the s2p-file to get S-parameter values but to use a diagram to plot all parameters and set markers. Moreover, for doing hand calculations I suggest to use uSimmics itself. In a diagram you can plot a graph defined by your own equation and add a second graph with the max_ulgain_dB(S) function for comparison. That makes it easy to check if your own formula is different from the one used by uSimmics. I did not define an equation in the attached simulation but you certainly get the idea.

Regards

Max

 

Attachments:

1. 

   simulation.png
   

[hptrivedi95]

Hi Max,

Please view the attached image, which reports the maximum unilateral transducer gain from equations computed in QucsStudio using S-parameters as 32.8 dB (equations are also visible). This is because the image of .s2p file I attached was extracted directly from the schematic. The formula given in the technical document reduces to the one that I mentioned in the previous post under the conditions of a unilateral maximum approach to gain. It is also mentioned in chapter – 3 page 230 of Microwave Transistor Amplifier Analysis Design, 2nd Edition by Guillermo Gonzalez.

I am where I started. However, thank you for your prompt response and debug suggestion.

PFA
Best Regards
Het (KJ5BEI)

Attachments:

1. 

   Equations_and_response_QucsStudio.png
   

[hptrivedi95]

Hi Max and QucsStudio community,

The document in the link below is helpful in resolving my query. In short, the Mason’s unilateral gain function in QucsStudio plots the inherent gain of device which is independent of matching networks while including stability factor and does not fix |S12| = 0.  This makes it invariant and important FoM.  The GTUMAX which I hand calculated is different as it assumes  |S12| = 0 and conjugate match at input and output.

https://ieeexplore.ieee.org/document/137392

Thanks
Best Regards
Het (KJ5BEI)

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