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Cascaded RL Calculations? - RF Cafe Forums

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Amateur Radio | Antennas | Circuits & Components | Systems | Test & Measurement


Yup
Post subject: Cascaded RL Calculations?
Unread postPosted: Wed Aug 11, 2004 5:13 pm
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Lieutenant

Joined: Wed Aug 11, 2004 5:11 pm
Posts: 2
I’m trying to characterize the return loss of a cascaded path. The path elements are very simple… cables, attenuators and switches. I have SWR and insertion loss data for each element, but am unsure how to calculate the return loss or SWR of the entire path. Do you know of a tool or method that may be useful?

Thank-you very much, any help would be greatly appreciated.


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Vuk Borich
Post subject:
Unread postPosted: Thu Aug 12, 2004 12:49 pm

Do you have (complex) s-parameter data for the components? If so, the s-parameters of the cascade can be computed by converting the s-parameters of each of the elements to their ABCD matrices, then computing the ABCD matrix of the system by multiplying the individual ABCD matrices, then converting back to s-parameters.

A math package can be very helpful for this type of calculation. There is also free MW software that will compute this easily, though I've never used it.


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Post subject: Itay
Unread postPosted: Thu Aug 12, 2004 2:06 pm

Greetings:

If your elements are cascaded then you should multiply the SWR of each element and you will get the cascaded SWR. From this it is easy to obtain the relflection coefficient and RL, as follows:

SWR=1+rho/1-rho (rho- Reflection Coefficient)

RL=20 log |rho|

Hope this helps,
Itay


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Guest
Post subject:
Unread postPosted: Thu Aug 12, 2004 2:14 pm

Thanks for your replies!

I have already calculated the cascaded VSWR and RL using the RSS method (very similar result to simply multiplying each components VSWR as Itay mentioned), but the problem is that the result is not even close to the measured value of return loss. The calculated value is MUCH worse. I am using the specified max VSWR for each device which would of course cause the resulting calculated VSWR to be higher than would typically be measured. My paths are also up to 12 devices long which is compounding the errors due to the assumptions made in the RSS method.

I think part of the problem, if I understand this method correctly, is that it assumes no device losses and only looks at the 1st order reflections. In this model the reflected waves do not experience any attenuation because device losses have not been considered. This results in much larger SWRs and much smaller return loss values than would actually occur.

Of course the RSS method calculates the absolute max possible VSWR only. I will use the information on http://www.rfcafe.com/references/electr ... smatch.htm to calculate the minimum...hopefully my measurements are somewhere between the two ;-) Otherwise I suppose I’ll need to get a hold of the complex s-parameters for each device from their manufacturers and try Vuk Borich's suggested method.


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Guest
Post subject:
Unread postPosted: Thu Aug 12, 2004 4:09 pm

Why make your life complicated? Use a VNA to measure exactly the Return Loss/VSWR at the wanted frequency range for each element in your cascade (don't meaure it outside the frequency band you are using). Then apply the method you named, which is similar to the one I noted before. If you start to convert ABCD matrices to S-parameters you will end the calculation next year ... long and winded calculations are prone to errors. :!:

Also check that all your elements are in good shape, a cable that is faulty might give you a short circuit or an open circuit and then of course you will end with a wrong measurements. Check that the insertion losses of the cables are in the range and that the cables are matched to 50-ohm (Use the Smith Chart for that).

Good luck,
Itay


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Yup
Post subject:
Unread postPosted: Thu Aug 12, 2004 6:54 pm
Offline
Lieutenant

Joined: Wed Aug 11, 2004 5:11 pm
Posts: 2
I'm actually trying to determine the limits that a measured result should be between. I'm more or less satified with my current results. The RSS method is providing a maximum SWR (minimum RL) and the method of deviding the larger VSWR by the smaller VSWR thought the cascade (used here http://www.rfcafe.com/references/electr ... smatch.htm) is providing the min SWR (max RL).

Anyone have any details of the theory behind this min VSWR calculation?


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