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Design >> RF Design >> Mason's Invariant or Unilateral Power Gain?
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Message started by aaron_do on Apr 15^th, 2010, 8:42pm

Title: Mason's Invariant or Unilateral Power Gain?
Post by aaron_do on Apr 15^th, 2010, 8:42pm

Hi all,

In Spectre S-parameters form, we can plot Gumax which is supposed to be the maximum unilateral power gain, and it's definition seems to be the same as in

R. Ludwig, P. Bretchko, "RF Circuit Design"

page 467, equation (9.12). However, I thought this was supposed to be the same as Mason's Invariant, but they do not appear to be the same at all. Mason's Invariant can be found here:

http://en.wikipedia.org/wiki/Mason's_invariant

Can somebody please enlighten me on the difference?

thanks,
Aaron

BTW spectre's version of Gumax is found by taking the transducer gain and simply setting S12=0 and is dependent on the characteristic impedance setting. Mason's invariant is independent of Z0 and is an inherent property of a device.

Title: Re: Mason's Invariant or Unilateral Power Gain?
Post by RFICDUDE on Apr 16^th, 2010, 8:48pm

A nice lengthy discussion on Mason's Invariant and its application in microwave circuits can be found in

Gupta, M.S.; , "Power gain in feedback amplifiers, a classic revisited," Microwave Theory and Techniques, IEEE Transactions on , vol.40, no.5, pp.864-879, May 1992

The specific answer to your question (from the above paper) seems to be that the maximum power gain is related to Mason's Invariant as

Gumax = (2U-1)+2*sqrt(U*(U-1))

where U is Mason's Invariant. The comment was made that "U is not a gain maximum unless the device is first unilateralized by the
embedding network."

Hope this helps?

Title: Re: Mason's Invariant or Unilateral Power Gain?
Post by aaron_do on Apr 17^th, 2010, 7:35am

It helps a lot. Thanks! Actually I just started reading that paper, but it may take more than one read before I can fully grasp the meaning behind power gain.

cheers,
Aaron

Title: Re: Mason's Invariant or Unilateral Power Gain?
Post by aaron_do on Apr 18^th, 2010, 6:39pm

Hi RFICDude,

the expression,

(2U-1)+2*sqrt(U*(U-1))

does not appear to be the same as Gumax. In the paper you referenced, the author says, "in the special case where the fourport embedding network consists of two decoupled ports", i.e. just an input and an output matching network. The value Gumax which I was talking about involves setting S12=0...

Also, I tried to trace back the derivation of the above formula and I reached a road block. In the paper you referenced, the author references the following:

A. Singhakowinta, A. R. Boothroyd, "On linear twoport amplifiers", IEEE Trans. Circuit Theory, vol. CT-11, no.1, p.169, Mar 1964.

In the above paper, the formula is stated without proof, and is referenced to a future publication by the same authors. Well I looked for a future publication by the same authors and found only 1 published two years later:

"On Analysis and Representation of Two-Port", IEEE Trans. Circuit Theory, vol. 13, no. 1, 1966, pp. 102-103.

And the paper above simply referenced their original publication in 1964. i.e. the two papers cite each other, and neither of which actually derive the equation. Sounds like instability due to positive feedback to me.

Do you have any idea where I can find a derivation of the formula?

thanks,
Aaron

BTW, Gumax from spectre is dependent on Z0 while (2U-1)+2*sqrt(U*(U-1)) is not. BTW according to my simulations, Gumax is a very close approximation of U.

Title: Re: Mason's Invariant or Unilateral Power Gain?
Post by aaron_do on Apr 18^th, 2010, 9:11pm

OK, I went over the derivation myself and it seems that Gumax = Umax as long as Z0 is real. At least this seems to be the case. Correct me if i'm wrong.

cheers,
Aaron