# 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.

• 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 $\Gamma=\rho\left(\cos\phi + j\sin\phi\right)$. 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. 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 $Z_L$. 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? Oct 19 '16 at 18:21

I need to calculate input impedance of an antenna.

Different antennas have different impedances and the same antenna has widely different impedances depending how long it is relative to the radio frequency it emits or receives.

For instance, a quarter wave monopole has an impedance like this: -

So, when used as a classic quarter wave monopole, the impedance is purely resistive (about 37 ohms). When used at 0.47 wavelengths it is also purely resistive but nearer 2500 ohms.

Monopoles are often used "short" and typically at a length of 0.05 wavelengths it will look like a capacitor having an input impedance of about -j1000 ohms.

So, decide what antenna you are referring to, then decide what effective length the antenna is then try and find a graph like the above.