How to make an impedance matched circuit for fabbed antenna?

Okay I have developed an antenna for a system and need to create an impedance matching circuit. The theory of conjugate matching is simple, but actually implementing it is something I can't find explained anywhere. For example, do I use the network analyzer to first find the real and imaginary impedance at a desired frequency with the smith chart, and THEN I can take S11 measurements?

I have access to a network analyzer and a spectrum analyzer. Please take me through the step-by-step process of creating an impedance matching circuit.

• what's your frequency? – ivan Apr 19 '16 at 21:36

The first step, as it looks like you guessed is to measure the complex impedance R+jX at the frequency of interest. I'm guessing it's some real value materially less than 50 ohms and some imaginary value which could be just about anything (negative or positive).

Next verify that your source is actually 50 ohms if necessary.

You have some choices at this point, but I'll tell you what I've done.

Calculate a value of parallel capacitance that gets you from 50 ohms (real) down to the real part of the antenna's impedance. $$\frac{1}{\frac{1}{50}+jwC}=R$$

That parallel capacitance will change the source impedance to R-jX2. Now in the very unlikely event that X1 = X2, you are miraculously done. However, if there is a difference simply subtract X2 from X1. If this is a positive number, add a series capacitor to cancel the reactance, and if it is a negative number, add a series inductor to cancel the reactance.

• Thank you! So, now next step.. I assume that would give us accurate s-parameter measurements for the antenna itself. But the load the antenna will ultimately be attached to is not a 50 ohm load like the network analyzer is. So I guess what I'm asking is, is the matching circuit only to ensure accurate antenna measurements at the frequencies of interest? – anduril16 Apr 14 '16 at 0:00
• Ahhh, excellent point - if the load attached to the antenna is not 50 ohms, then use that complex impedance instead of 50+j0, in the calculations above. You definitely want to match to the specific load, not an arbitrary 50 (which I had assumed was the load)! – MikeP Apr 14 '16 at 14:11
• Got it! And now just to confirm so I have a fundamental understanding, the S-parameter results from the spectrum analyzer will be incorrect without a matching circuit. After I make a matching circuit for the frequency of interest, THEN I can take accurate S-parameter values? – anduril16 Apr 19 '16 at 16:25
• Yes, s-parameters are only 'correct' for the specific characteristic impedance under which they are tested. So if you have a 50 ohm network analyzer you only get 50 ohm s-parameters. If you've matched the antenna to a 30 ohm load, the 50 ohm s-parameters will be incorrect. – MikeP Apr 21 '16 at 12:45