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Transfer S-parameters

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New for July 2016.  This info came from Hadrien, thanks!

 

Transfer S parameters are a convenient way to express S parameters in a way that allows to easily cascade blocks. They have the same principle as ABCD parameters: they express all relevant input quantities in function of all relevant output quantities, contrary to normal S parameters which express all scattered waves in function of all incident waves, and are messy when cascading blocks. They are sometimes more convenient than ABCD parameters, because they work with wave quantities instead of voltages and current, which are very difficult to measure at high frequencies.

It is very counter-intuitive, but expressing input in function of output and not the inverse allows to deal with unilateral blocks, what the other convention doesn’t allow. They are most often defined in the following way:

Eq1

Be careful! Another convention exists, with a and b inverted. Some people even express output in function of the output. So, pay attention to the used convention when reading calculations from other people!

With the definition used in this page, the transfer parameter matrix of a chain of elements can be calculated as follows:

Eq2

And, be careful, this is the inverse order as one expects. Yes, matrix multiplication is very convenient but sometimes crazy!

The following formulas can be used to pass from regular to transfer S parameter:

 
 Eq3  Eq4
 Eq5  Eq6
 Eq7  Eq8
 Eq9  Eq10

 

 

 

Author : Hadrien Theveneau

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