ABCD transformation to S matrix (RF Engineering)

Discussion in 'Homework Help' started by Ledwardz, Apr 27, 2014.

  1. Ledwardz

    Thread Starter Member

    Oct 31, 2010
    Hey guys,

    the question is on the attachement. I am a little stuck on part b

    my answers to part a for the ABCD is

    A = 1
    B = 0
    C = 1/Z
    D = 1

    and for the S parameters i have

    S11 = S22 = -Y/ 2 + Y
    where Y, the admittance is normalised - i.e. it is Y = yZ0 = Z0/Z
    S12 = S21 = 2/2+Y

    anyways, moving on to part b.

    I think the question wants me to show the derivation from ABCD to S parameters. i have done this for S11 and S22 which is also shown in the attachements. My question is how do i do this for S12 and S21??

    I also dont know what the question is getting at when it asks for the impedance and power loss advantages and disadvantages seperately, mayb i am reading the question wrong? it isn't very well worded? I assume this refers to transduer and insertion losses which can both be calculated in terms of ABCD and S parameters??? soooo yeh no idea what this wants?

    anyways, any help appreciated.


  2. t_n_k

    AAC Fanatic!

    Mar 6, 2009
    This may provide some insights

    Also one could consider what 's' parameters mean in each case.

    For example s21 is the forward transmission coefficient and is useful in relation to comparative power transmission ....

    \text{{|s_{\small{21}}|}^{\ \small{2}}=\frac{Power \ delivered \ to \ port2}{Power \ delivered \ by \ V_{gen}}}

    What might one say about s12 in a similar context?
    Last edited: Apr 27, 2014
  3. Ledwardz

    Thread Starter Member

    Oct 31, 2010
    Cheers, the link is similar to the answers i wrote on the second attachement (left hand side) although i still have no idea how this relates to impedance and power loss... unless its saying scattering relies on attenuation which i guess is like a power loss? and ABCD is relying on impedance prameters?

    ya cheers, so S12 the reverse transmission coefficient. i guess my question should of been i only know the input and output reflection coefficients in terms of ABCD so what is s21 in terms of the output and input coeffecients then i can convert to ABCD. i think.