Converting magnitude ratio to complex form

Question

I want to inquire as to how we can convert a magnitude ratio, given in dB, to complex form, in real and imaginary form, provided of course that we have the phase given as well.

Eg. Suppose I have an S-parameter reading as -11dB with a phase of 1.4 radians

How would I go about a situation like this? I wish to use this formula to create touchstone (.s1p) files from a list of input reflection coefficient (S11) values.

Did the answer resolve your question? – DanielSank Apr 10 '18 at 19:47 — DanielSank, Apr 10 '18 at 19:47

score 2 · Accepted Answer · answered Apr 10 '18 at 18:07

S parameters are supposed to be a ratio of two voltage phasors, e.g. $$S_{21} = \frac{V_2}{V_1}$$ where $V_2$ and $V_1$ are complex numbers. However, when S parameters are reported in dB, you are actually getting the dB form of the square of the S parameter. To be specific, if someone tells you that $S_{21}$ has a value of "X dB", then what they mean is this: $$10 \cdot \log_{10} \left( \left \lvert \frac{V_2}{V_1} \right \rvert^2\right) = X$$ This is a ridiculous abuse of language that is unfortunately very common in engineering. Rearranging the equation, we find $$\left \lvert \frac{V_2}{V_1}\right \rvert = 10^{X/20} \, .$$ From there you can add in the phase, if you know it, to get the complex voltage ratio.

Straight and to the point. Thanks a bunch! And I am guessing to get the real and imaginary values I would just have to use [X * cos(phase) = real] and [X * sin(phase) = imaginary]? — C Vith, Apr 11 '18 at 05:53

Converting magnitude ratio to complex form

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