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- 22nd May 2012, 03:25 #1

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## relationship between transmission and reflection coefficient

I'm working on a project on calibration,

i would like to find out whether my results are logical or not.

are the following statements true?

S11 = reflection coefficient

S21 = transmission coefficient

-20log10 (S11) = return loss

-20log10 (S21) = insertion loss

**now how is the return loss related to insertion loss?**

or how is the reflection coefficient relates to the transmission coefficient?

i've read this thread,

Transmission and Reflection coefficient from S parameter

one member says that

Transmission coefficient = 1**-**ΓL

but in RF circuit design text book page 85,

equation 2.86 says that

To = 1**+**Γo

so...i'm thoroughly confused.

please help me.

thanks

- 22nd May 2012, 03:25

- 22nd May 2012, 04:42 #2

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## Re: relationship between transmission and reflection coefficient

http://home.sandiego.edu/~ekim/e194rfs01/sparm2.pdf

http://course.ee.ust.hk/elec518/lect4.pdf

http://www.docstoc.com/docs/84241212...ave-Amplifiers

These answers should be best response.

All that is not transmitted is reflected.A good design question lists your overall requirements™ The best question deserves a better answer. ™

... Tony Stewart EE since 1975

- 22nd May 2012, 04:42

- 22nd May 2012, 06:03 #3

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## Re: relationship between transmission and reflection coefficient

Those definitions are true. As for the return loss and insertion loss, you need to measure both, you can't necessarily determine one from the other. For a passive device, some of the incident power is reflected, some is transmitted, and some is absorbed (turned to heat). For an active device you have those effects, plus possibly amplification of the signal.

- 22nd May 2012, 06:03

- 22nd May 2012, 06:43 #4

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## Re: relationship between transmission and reflection coefficient

Really? there's no relationship between these two?

then i have been mistaken.

i have measured both S11 and S21,

and applied some calibration calculations to them.

giving another S11 and S21, i thought there were some relationship between them,

that i can use it to verify whether the calibrated S11 and S21 are logical or not.

was wondering which one is correct.

To = 1 + Γo

To = 1 - Γo

but if there is no relationship between To and Γo, then i will forget about this checking procedure.

thanks for your answer

- 22nd May 2012, 08:39 #5

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## Re: relationship between transmission and reflection coefficient

Quoting formulas without telling about the described system is pointless.

If you read the linked Edaboard thread where you took the*To = 1 - Γo*expression thoroughly, you should have seen the critical comments. It has been clarified that a lossless system would enforce conservation of energy, instead of To + Γo = 1, you get To² + Γo² = 1. So in a short, there are different equations describing different situations.

In most cases, there is a relation between transmission and reflection coefficient. You can't avoid to analyze the system details to know how exactly.

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