# Given is Tolerable Percent Reflected Power, Calculate Bandwidth of Antenna. Relation?

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#### zia.newversion

##### Member level 5 Hello there...
I am taking a course of Antenna Theory and was looking around for some material for self study where I came across this problem.

It gives a table of Freq vs. Impedance (Imaginary and Real). Asks to plot on MATLAB. That was easy. Done!

Then tells to plot Voltage Reflection Coefficient by taking Z0=150 Ω. I figured it'd be
Γ = (ZL-Z0)/(ZL+Z0), while ZL is the Impedance given in the table. Done!

Then Power Reflection Coefficient... I think that must be square of magnitude of Voltage Reflection Coefficient. Done!

Then it says to plot VSWR. I searched over the internet and found on Wikipedia that
VSWR = (1+ρ)/(1-ρ) where ρ = |Γ|... That's done, too!

Then S11, which in my opinion should be 20log(Γ)... I did it that way. So that's over...

Now there is this last part that is bothering me.
It lists percent tolerable reflected powers (as 10%, 20% etc.) and asks to calculate bandwidth of antenna for each of these values... Now here is where I got lost. I can feel there is some relation, but I can't actually see it. Square root of percent reflected power should give magnitude of percent reflected voltage, but what next... How do I calculate bandwidth of antenna from there?

I need your help to find an answer to that problem as well as let me know if any of the previous concepts are wrong. Please help. Thank you.

#### Kohi_boy

##### Full Member level 4 Do you have an estimate of the Q factor of the antenna?

If you do, then, the Q factor can be related to the VSWR and fractional BW. Refer to Balanis antenna theory 3rd on microstrip antenna.

#### zia.newversion

##### Member level 5 I have Balanis Antenna Theory. In fact it is my text book. But we haven't studied microstrip antennas yet. We are only halfway through the course. And I haven't studies Q-factor yet, either. Is it possible to find an answer to the problem using only the information that I already have? Or do I really have to go ahead and dive into more complex concepts (which might be a little difficult for me to understand right now).

Thank you very much for replying.

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