question about symmetric in function: rlgc2s

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kuan zhang 2024-9-21，6:35

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https://ww2.mathworks.cn/matlabcentral/answers/2154460-question-about-symmetric-in-function-rlgc2s

回答： Vinay 2024-9-23，7:13

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I found there is a symmetrize at the end of matlab funciton:rlgc2s, code as below.

s_params(1:num lines，1:num lines,m) = 0.5*(S11 + S11.');

I wonder the physical meaning of this option?

For a symmertric differential transmission, this option will make S12 = S21, but it missed S11 = S22.

For a symmertric transmission with 3 lines, this option will make S12 = S21, but I think S12 should equals S32 rather than S21.

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Answer 1

Vinay 2024-9-23，7:13

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Hi Kuan,

The symmetrize is used at the end of the function to ensure the individual s parameter of the network are symmetric.

For a 2 – port symmetric reciprocal network, the conditions s12 = s21 and s11 = s22 holds

This is due to the reciprocal nature of the network, which ensures that the ABCD parameters satisfy

(AD - BC = 1), leading to ( s12 = s21). The symmetric network condition requires (A = D ) in the ABCD parameters, which makes the numerators of s11 and s22 identical, as defined below:

s11 = (A + B./z0 - C.*z0 - D)/den

s22 = (-A + B./z0 - C.*z0 + D)/den

This ensures the s11 = s22 and s21= s12 for a 2-port network.

In case of 3 transmission line the reciprocal network ensures sij = sji so s21 = s12 follows. However, the parameters s12 and s32 are independent and do not necessarily equal each other.

Kindly refer to the below documentation of “rlgc2s” for more details:

https://www.mathworks.com/help/rf/ref/rlgc2s.html

I hope this helps!