# Impedance of an antenna

I need to calculate input impedance of an antenna. What I've got is frequency, SWR magnitude, phase, return loss and impedance of transmission line. As far as I know, as a result I should get complex number. I used SiteMaster S331 and my example parameter measurements are:

f[Mhz]    SWR   rho   phase
450    2,802  0,47  10,4
841    2,017  0,34  -76,2
510,1  2,231  0,38  -55,6
531,4  1,77   0,28  59,8


I'm aware of correlation between input impedance and SWR $$SWR = \frac{Z_{0}}{Z}$$ and $$\rho = \frac{Z - Z_{0}}{Z + Z_{0}}$$but still can't figure this out, how to get the result as complex number. I know I should use phase, but don't know which formula to use.

• – Tony Stewart Sunnyskyguy EE75 Oct 19 '16 at 17:49
• It all depends what you mean by phase. If phase is the phase of the reflection coefficient, and rho means the magnitude of the reflection coefficient, then you just have $\Gamma=\rho\left(\cos\phi + j\sin\phi\right)$. – The Photon Oct 19 '16 at 17:49
• What I mean is, you said you measured "phase" but you didn't say what you measured the phase of. – The Photon Oct 19 '16 at 17:50
• Also, the formula $\rm{SWR}=\frac{Z_0}{Z_L}$ only applies when $Z_0$ and $Z_L$ are real, in which case you already know the phase of $Z_L$. – The Photon Oct 19 '16 at 17:55
• Based on the content of my lecture, I figured out that having rho and phase, I can calculate the exponential form and then go with $$Z = Z_{0} \cdot \frac{1+S_{11}}{1-S_{11}}$$, as a result I'll get my desired result. Am I right? – PotatoBox Oct 19 '16 at 18:21