# Gain when amplifier is in compression

Question asked by sergiodibello on Apr 4, 2019
Latest reply on Apr 12, 2019 by Dr_joel

Hi All

My question is regarding the section 6.2.4.3 ("Calibration in Compression Measurements") of the book "Handbook of Microwave Component Measurements" that is usually taken as reference for Microwave measurements with VNA.

In the next line I paste some line taken from the book. If it is not allowed to paste the text of the book for copyright reasons, please remove it.

For easier understanding of people who do not have the book, I paste here the text I am referring to "One important point to note is that for gain compression measurements, the error correction math of Eq. (3.3) does not strictly apply. The concern about this math function is that the input reflection errors are not properly accounted for when an amplifier is in compression. Take the extreme case of an amplifier in saturation. The output power is limited at a fixed level by the saturation. If there is mismatch ripple at the input which causes the incident source power to be greater than that of a matched source, there will be no corresponding increase in the output power. However, the error-correction function of Eq. (3.3) supposes that an increase would occur (S21 being linear in the assumption) and so the corrected gain and output power (which is sometimes computed as input power times gain) are reduced by the input mismatch error.
In fact, the input mismatch error causes no change at all in the output power (the amplifier being saturated), and thus the gain will show ripple which it does not really have. Therefore one should not use normal error correction for amplifiers tested in their non-linear mode of operation."

Eq.3.3 refers to the application of the calibration--> how to find [S],A (Actual S-Parameter of the DUT) starting from [S],M (Measured S-parameter of the DUT) and the error coefficients of the 12 terms error model.

Usually for measuring an amplifier, even if in compression, I was always using the S21.
1) In the Bold line, when it is mentioned the "incident source power" it is not clear if it is referred to the "power measured by the Reference Receiver" or the "power delivered to the DUT".
From my understanding it should be the "power measured by the reference receiver". In this case makes sense that the S21 will get smaller because the output power (measured on receiver B) is constant and the input power (measured on receiver R1) is increasing. Right?

2) This means that using S21 for compression measurements, is accurate only if the S11 of the DUT is well matched?

3) Regarding the Italic line. I know S-parameter should be used only in case of linear DUT (that is not the case of amplifier in compression). But I do not understand why this assumption (S21 being linear) is the problem in ths case. Can you try to explain with other words or another example?

4) Instead of using the S21, the book suggest to use the ration between match-corrected output power and match corrected input power. In practice B,1/R1,1 or b,2/a,1.
I read the chapter Receiver calibration and how the match corrected receiver Calibration (included in the SmartCal) takes into account the mismatch of the Power Sensor (during Source and Receiver power calibration) and mismatch of DUT (during measurements). It is clear why in order to perform Receiver Calibration with match correction, is necessary to perform also S-parameter correction.
Here the question: In case of Match corrected Reference receiver calibration, the power that I read on the R1,1 trace corresponds to the power absorbed by the DUT (delivered power to the DUT)?
For example if the Input Power of the DUT is -10dBm (calibrated with Source power calibration at the input of the DUT) and I read S11=-1dB, I would expect that the power absorbed by the DUT (delivered to the DUT) is -16.87dBm. After Match-corrected Reference receiver Calibration, should I expect to read -16.87dBm at the R1,1 trace? (of course without using any leveling).