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[trobe]

Hello guys,

I'm doing a project for school in which I designed and build a 15dBi Yagi antenna. I'm currently trying to calculate the complex impedance. I've got the return loss values (in dB). How do I calculate these to the complex impedance?

S11 = 10^(RL/-20)
in which RL is the return loss in dB

Then use S11 in this formula:

Zin = [(1+S11)/(1-S11)]*Z0
In which Z0 = 50 ohm and Zin is the complex impedance

Is this correct? I tried to verify this by using the theoretical values in my design.

I hope you guys can help me out with this. Thanks in advance!

[bigSteve]

When you say S11=-15 dB, you really mean the magnitude of S11 is -15 dB. To be able to calculate complex impedance, you also need to know the phase of S11.

Then you convert S11 to linear units (which will be something like S11=0.2+i*0.1), and then use the formula for Zin you mentioned.

So you need more information to get the complex impedance

[trobe]

S11 = Zin-Z0/Zin+Z0

Using this formula, it actually gives the correct answer. Is this not a complex value-formula?

[Schubert]

You don't know if you have the "right" answer. Note that:

|S11| = gamma = | (zL - z0)/(zL + z0) |

Now, let's say S11 = -20 dB (0.1 in linear units), so then you use your formula and calculate Zin:

Zin = (1+.1)/*1-.1)*50 = 61.111

Then you check using the first equation above and find |s11| = 0.1, and therefore you believe you have the correct answer.

But what if Zin = 40.9? Then:

|s11| = | (40.9 - 50)/(40.9+50) | = 0.1 = -20 dB

So they both work. And actually, when you start allowing complex impedances, like z = x + i*y, then there are an infinite number of solutions for impedance, all that give the same value for |s11|

[trobe]

Thanks for your reply. I don't know whether I have the associated phase info. If I don't take the phase info into account, would it still give a good indication on how the complex impedance would look like?

Thanks again for your reply

[trobe]

Alright, turns out I do have the phase info. Now I need to know how to do a division with complex numbers...

[Schubert]

Here is an intro to complex numbers page:
http://www.thefouriertransform.com/math/complexmath.php