# ABCD transformation to S matrix (RF Engineering)

Thread Starter

#### Ledwardz

Joined Oct 31, 2010
37
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.

Thanks,

Lee.

#### t_n_k

Joined Mar 6, 2009
5,455
anyways, moving on to part b.

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?
This may provide some insights

http://www.home.agilent.com/agilent/editorial.jspx?ckey=1000002126:epsg:faq&id=1000002126:epsg:faq&nid=-11143.0.00&lc=eng&cc=AU

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:
Thread Starter

#### Ledwardz

Joined Oct 31, 2010
37
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.

This may provide some insights

http://www.home.agilent.com/agilent...0002126:epsg:faq&nid=-11143.0.00&lc=eng&cc=AU

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?

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