[SI-LIST] Re: Convergence problem after inserting detailed connectormodel
- From: "Scott McMorrow" <scott@xxxxxxxxxxxxx>
- To: yu_liu@xxxxxxxxxxxxx
- Date: Fri, 20 Feb 2004 18:44:57 -0800
Yu
Yes, that is correct. This is what the following matlab code does.
mineigv = min(real(eig(eye(size(S))-S*S')))
It computes the minimum real eigenvalue of I - S*S'
scott
Yu Liu wrote:
>Hi, Scott,
>
>I thought it is the product of S-matrix's conjugate and itself, and
>compare to the identity matrix. Consider a one-port network, with
>incident wave "a", and reflection wave "b", the power consumption of the
>network is
>
> p = (a* a - b* b) / R
>
>where "a*" is the conjugate of "a", "b*" is the conjugate of "b", "R" is
>the port resistance. By S-parameter definition,
>
> b = S a
>
>you can put the above relation to the power equation, that gives
>
> p = a* (I - S* S) a / R
>
>if the network is passive, then we require (I - S* S) > 0. And of
>course, the product of a complex number with its conjugate is real.
>
>
>Regards,
>
>
>Yu
>===
>
>Scott McMorrow wrote:
>
>
>
>>Michael and Ray,
>>First of all, I am not as smart as I sometimes sound. I had a good
>>friend of mine, Rob Hinz, develop the code for passivity checking and
>>passivity correction based upon some of my simple thoughts on the
>>subject . We use what we call the "Wack a Mole" method for correction
>>of non-passive s-parameters. You can imagine from that name what we
>>might do.
>>
>>You will want to compute the minimum real eigenvalue of Identity matrix
>>- Smatrix * Smatrix' on the complex data.
>>
>>In matlab this is done as follows
>>
>>mineigv = min(real(eig(eye(size(S))-S*S')))
>>
>>
>>The matrix is passive the value is positive real
>>THe matrix is conditionally passive if the value is zero
>>The matrix is non-passive if the value is negative.
>>
>>
>>The original reference is:
>>
>>R. A. Rohrer, "Lumped network passivity criteria," IEEE Trans. Circuit
>>Theory, vol.
>>CT-15, no. 1, pp24-29, March 1968
>>
>>
>>At this time, no one has developed a mathematiclly rigorous method for
>>passivity correction that I am aware of.
>>
>>
>>regards,
>>
>>scott
>>
>>
>>
>>
>>
>>
>>Mirmak, Michael wrote:
>>
>>
>>
>>>To echo Raymond (forgive the questions from the matrix-impaired):
>>>
>>>Scott,
>>>
>>>If I have an 8-port S-parameter measurement (S11, S28, etc.), from a
>>>Touchstone or CITI file for example, would the given equation apply to
>>>the complex data or just to eh magnitudes?
>>>
>>>More specifically, taking the equation literally, my eigenvalues are
>>>calculated as:
>>>
>>>Identity matrix (8x8) - Smatrix * Smatrix'
>>>
>>>Where Smatrix is an 8x8 matrix of complex S-parameter values, Smatrix'
>>>is its transpose, and the identity matrix is just that, an 8x8 matrix
>>>filled with zeros on the off-diagonals and ones on the diagonals. Is it
>>>still correct to say that a complex result from that calculation, if
>>>having a negative real part, indicates non-passivity?
>>>
>>>More specifically still, I get an 8x8 matrix result of "eigenvalues"
>>>
>>>
>>>
>>>from your equation. However, if I request eigenvalues from Matlab using
>>
>>
>>
>>>the same 8x8 Smatrix, I get a result which is 8x1 only. Why the
>>>difference?
>>>
>>>Thanks!
>>>
>>>- MM
>>>
>>>
>>>
>
>
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--
Scott McMorrow
Teraspeed Consulting Group LLC
2926 SE Yamhill St.
Portland, OR 97214
(503) 239-5536
http://www.teraspeed.com
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