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If you build a microstrip on a silcon wafer, connected by picoprobes via SMA connector and cables to a VNA, what is actually a good match of the impedances of the cables and the waveguide. Is there a formula (if I understand correctly, the Smith Chart can answer this, I'm still trying to understand it completely) to calculate the losses.

Say you are able to structure your waveguides on the silicon by lithography with a tolerance/accuracy of 10%. So the impedance can vary by this 10%. So you might get 55 Ohm instead of the wished 50 Ohm that typical SMA cables are set up to. How much signal loss will this cause?

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  • \$\begingroup\$ The question is unclear because we don't know what you are trying to achieve, which is what dictates "a good tolerance". (1) This is a digital signal and I must maintain an eye height at the receiver better than 50%. (2) This is a trellis coded signal with 8 levels (64 codes) and the eye height must be better than ...% (5%?) (3) This is my antenna input and my noise budget allows 1dB for loss (4) This is my transmitter output and my output stage can tolerate xxx mismatch without overheating. As it goes, the Photon's answer is good, but may not answer the real question. \$\endgroup\$ – Brian Drummond Feb 5 '13 at 18:39
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The reflection at the end of a transmission line is given by

\$ \Gamma = \dfrac{Z_L - Z_0}{Z_L + Z_0}\$

Where Z0 is the line's characteristic impedance and ZL is the load impedance.

So if you have a 55 Ohm line and you terminate it with 50 Ohms, you're looking at about 5% reflection.

If you have a 50 Ohm line, followed by a short length of 55 Ohm line, terminated with 50 Ohms, you're going to get about 5% reflection from the mismatch between the two lines, and 5% reflection from the end termination.

But...these two reflections will interact with each other. Depending on your operating frequency and the length of the mismatched line, they could interfere with each other constructively or destructively. You could have anywhere from 0 to +/-10% reflection from this structure.

But this is about the voltage signal (or travelling wave) reflection. If you're talking about "losses" you probably want to convert this to power terms. If you know the signal reflection, that would correspond to \$(1-|\Gamma|)^2\$ fraction of the power transmitted to the load. For 10% reflection, that's about 81% power delivery or 0.9 dB of loss.

To find out the exact reflection for your situation, you'd need to either run a simulation, or do a pen-and-paper analysis with a Smith Chart, which we've discussed a little bit in a previous question. The simulator is probably the easier way to go, though, and it will enable you to do things like sensitivity analysis more quickly.

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