[SOLVED] A very basic problem?

[saq_kaleem]

Is it possible to compute equivalent resistance at a particular frequency from given reflection and transmission coefficient?
S11 -33.062dB
S21 -0.049dB
f 1GHz
delay @1GHz 56.53psec

regards,
saqib

 

[enjunear]

Is it possible to compute equivalent resistance at a particular frequency from given reflection and transmission coefficient?
S11 -33.062dB
S21 -0.049dB
f 1GHz
delay @1GHz 56.53psec

regards,
saqib

Here are some equations you can use.
VSWR to Return Loss Conversion Equations Formulas - RF Cafe

If you assume, Z0 = 50 ohms:
S11 = -33.062 dB
then we can find |Γ| = 0.0222798
if |Γ| = 0.0222798, then ZL = 52.27333 or 47.82556 ohms.

If this is a 50 ohm system, then a series resistor would need to be ~2.27 ohms, or a shunt resistor with a value of 1100 ohms.

From S21, if you assume R is a series device, then you'll need a voltage divider that will give you an output voltage -0.049 dB from the input level. Working backward, we find the voltage ratio is 0.994375 V/V. Then, going through a simple voltage divider equation gives you Rseries = 0.28286 ohms (using R2 = 50 ohms)

From the math, it's difficult to say what your part really is. If this is a real component, then at 1 GHz you will be seeing effects of the parasitic inductance and capacitance of the part.

Here's an example of a parasitic model for SMT chip resistors.

From this paper

I'm not sure if any of that helps, you, but those are the equations/methods I used to back out a resistance value given the datapoints provided (which, at 1 GHz, is highly unlikely to be purely resistive).

 

[saq_kaleem]

Thanks and appreciation for enjunear for sharing his reply.
Actually, this problem could easily be solved by using following forumula derived from two-port network theory.

R=50*2*(1/abs(S21)-1)

50 is only a normlization factor.

regards,
saqib