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# Directional Coupler calculate directivity from S-Parameters (VNA)

#### izsurk

##### Newbie level 6
Hi guys,

maybe I am asking a stupid question.
I have a *.s4p 4 port measurement performed with a 4 port VNA and now I'd like to know the directivity of my coupler FROM S-PARAMETERS. Can't find a single source telling me how. Am I missing out something obvious?

Thanks

#### albbg

With respect to the figure you posted usualy the coupled port is represented close to the input while the reverse is the one near the output of the directional coupler. In any case from the S-parameter you can see (if Port 1=input, Port 2=output, Port 3=forward, Port4=reflected):

return loss of port "x" as Sxx
insertion loss as S21
Coupling factor as S31
Isolation S31-S41

Isolation is a positive number.
The network is reciprocal so Sxy = Sxy, for instance S21=S12

Furtermore the directional coupler is usually bidirectional, so you can exchange input <-> output and then forward <-> reflected. In this case:

return loss of port "x" as Sxx
insertion loss as S21
Coupling factor as S41
Isolation S41-S31

#### izsurk

##### Newbie level 6
Hi albbg,

thanks you for your answer. I am looking for the directivity which is stated in nearly every coupler's datasheet (e.g. https://www.minicircuits.com/pdfs/ADC-6-10-75+.pdf). Maybe I am missing something ... is directivity even calculatable / estimatable from S-Parameters?

#### albbg

Sorry, i wrote isolation instead of directivity. By the day, isolation is simply S41

#### izsurk

##### Newbie level 6
Sorry, i wrote isolation instead of directivity. By the day, isolation is simply S41
So you're proposing directivity = S31-S41 ?

#### izsurk

##### Newbie level 6
Hmm I am really confused. I had a quick look into trusty Pozar "Microwave Engineering", 4th edition, Chapter 7.1 "Basic Properties of Dividers and Douplers" : "Four-Port Networks (Directional Couplers)" p.323

"The directivity of a coupler generally cannot be measured directly ..."
See the section attached.