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

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Member level 5
Mar 28, 2010
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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.

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.

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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