FreeLists / si-list / [SI-LIST] Re: Using W-element in HSPICE

[Nirmal Jain <nirmalj@xxxxxxxxxx>]

>
>
>For readability, I will post the lossless solution explicitly. As 
>always, verification of algebra is encouraged...
>
>Zeven = sqrt((L+Lm)/(C-Cm))
>Zodd = sqrt((L-Lm)/(C+Cm))
>
>Z11 = Z22 = Zeven + Zodd
>Z12 = Z21 = Zeven - Zodd
>
Hi Steve,

I think there's some error in above equations. From the above equations 
we get

Zeven = (Z11+Z12)/2
Zodd =  (Z11 - Z12)/2   and hence
Zdiff  = 2 * Zodd = Z11-Z12 which is not right.

The correct expressions for a symmetrical transmission line is

Zodd = Z11-Z12
Zeven = Z11+Z12
 
&
Zdiff = 2*Zodd = 2*(Z11-Z12)

Hope that makes sense.  Best Regards

Nirmal



>
>1. Note again that C is the 'Maxwellian' capacitance as described in an 
>earlier post.  That is, the total capacitance from that conductor to 
>every other conductor, including ground, in the system.
>
>2. If you are operating in the presence of loss, you can replace all L's 
>with R+jwL and all C's with G+jwC.  This includes the mutual L's and 
>C's, of course.
>
>
>We also have:
>
>Zcommon = Zeven/2
>Zdiff = Zodd*2
>
>I will mention that smart people disagree on the definition of Zcommon, 
>since some don't like the factor of two.  The main thing is to be self 
>consistent in your own usage, and of course to be clear in using the 
>term with others.  Maybe some day a de facto standard will stick.  We 
>avoid using Zcommon altogether, and go with Zeven which is unambiguously 
>defined.
>
>Finally, I neglected to mention in my prior post that due to sign 
>conventions in the propagation constants, it is necessary to choose the 
>square root with the positive real part, to ensure that the voltage 
>waves decay as they move along the transmission line.  This is 
>straightforward, and arguably obvious, in the scalar math given above, 
>but requires a certain amount of care when computing the matrix square root.
>
>   -- Steve
>
>-------------------------------------------
>Steven D. Corey, Ph.D.
>Time Domain Analysis Systems, Inc.
>"The Interconnect Modeling Company."
>http://www.tdasystems.com
>
>email: steve@xxxxxxxxxxxxxx
>phone: (503) 246-2272
>fax:   (503) 246-2282
>-------------------------------------------
>
>


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