Effect of Q on impedance matching

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Effect of Q on impedance matching

Post by Sam » Thu Aug 05, 2010 2:31 pm

I did some playing with RFSim99 to see what effect inductor Q has on the accuracy of impedance matching with the low pass topology, which on the input side of a filter is a series inductor followed by a shunt capacitor. An SMT inductor at 10.7 MHz probably has a Q no higher than 30 and possibly as low as 15. So I assumed a middle value of 22.

I matched 50 ohms to 2 kohms. With Q of 22, the input impedance actually came out to 64 ohms, and the impedance seen by the filter (i.e. the output impedance of the matching circuit) came out to 1.6 kohms.

To get the correct impedance as seen from the filter, I had to tell RFSim99 to match 50 ohms to 2.75 kohms. That fixed half the problem, but the input impedance went up to about 85 ohms. Fortunately, the IF amp does not care that much what impedance it sees. With this design, the loss is only a tiny bit higher (about 0.2 dB higher) than that for matching 50 ohms to 2 kohms, and it should make the filter happier.

The effect of inductor Q is somewhat more dramatic if matching to 3 kohms, and less dramatic if matching to 1 kohms.

My conclusion is that when designing a typical match to a crystal filter, you may have to raise the target filter impedance by 20-40% to deal with typical SMT inductor Q values. Once Q gets to 50, the effect on the impedance match is about 10% (when matching to 2 kohms), so Q can probably be ignored.

Hand-wound inductors can certainly achieve higher Q values, mainly because they can use bigger wire. I'm curious about the Q values for mine, which were wound with skinny wire (#28 or so). One of these days, I'll have to test one. (I probably should have done that before building my filters!)

Sam W.

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