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If system 1 has 10 dB return loss and system 2 has 20 dB return loss then what is the overall return loss of cascaded system of 1&2 ?

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2 Answers 2

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  • \$\begingroup\$ Please format your answer using text or the MathJax feature of SE. While hand-drawn diagrams may be easier to complete, having the math+text be typed makes answers more readable and able to be searched. \$\endgroup\$ Jun 30, 2016 at 19:22
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Assuming the simplest case where system 1 is a cable with nominally zero loss (cannot be exactly zero with a non-zero reflection), then the reflection loss of the whole system will be somewhere between -8dB (when the reflections add in phase) and -14dB (when they add out of phase).

In the more general case, it depends on the magnitude and phase of the returned signals (S11) of both systems, and the transmission gain and phase (and even output match) (S21, S12 (and even S22)) of the first system cascaded.

To do it properly and exactly, look up S parameters in wikipedia here, and go to section 'S-parameters in amplifier design', where it gives the expression for how to determine the total reflection coefficient of a cascade of two systems from their S-parameters. It's shown in the context of the first system being an amplifier, and the second a load, but plug in the right values for the S parameters, and it all works.

Beware that all the terms are complex numbers, so if you don't understand those, you will have some preparatory homework to do.

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  • \$\begingroup\$ Actually no information is given regarding S-parameters. I got this question in exam. The answer given was 9.63dB. \$\endgroup\$
    – Aparna B
    Jun 13, 2016 at 10:31
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    \$\begingroup\$ Unless the exam question gave you more information on the gain of system 1, and the phases of the reflections, the answer is undefined. If system 1 is a 40dB attenuator, then the return loss is essentially -10dB, as it 'masks' the S11 of system 2 by 80dB. If system 1 is a cable, then it's between 8 and 14dB. \$\endgroup\$
    – Neil_UK
    Jun 13, 2016 at 13:23

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