Why is a high-Q circuit difficult to match?

Question

People in the microwave/RF field constantly talk about how it is "difficult" to match a high-Q circuit (ie. a CS amp with very little gate resistance and no degeneration). Why is that?

The problem is made slightly more confusing for me by the multiple quality factor definitions. If I consider the fractional bandwidth definition, it kind of makes sense that a circuit having a very narrow bandwidth would be more adversely affected by the addition of any parasitics. Thus tuning a matching network to resonate at such a narrow frequency might prove tricky. Am I going in the right direction with this?

Answer 1

For high Q systems, the impedance of the circuit changes very rapidly when you change the frequency. The circuit driving the high-Q system is designed for a specific impedance, and if the impedance is different performance will suffer. In an antenna, it means that much energy sent to it is actually reflected back to the amplifier, instead of being converted into radio waves.

Therefore the impedance of the amplifier needs to be carefully matched to the impedance of the antenna for high-Q systems, at the frequency being transmitted.

Special measuring equipment is needed to determine how much energy is reflected. Also, while making the adjustment the impedance is often affected by the proximity of your hand or tool, meaning you will have to make small changes and observe the results.

Also it may not be clear which part of the system needs to be tuned. Especially with microwaves, every part of the system transporting the wave may need to be tuned.

Answer 2

As you suspect, the problem is the definition of Q.

For example, a band pass filter can have a very high Q, where Q = F0/BW, but if its input impedance is reasonable, it can be quite easy to match to.

In the context of impedance matching, Q is defined as the ratio X/R, the reactive part of the impedance over the real part. Using this definition, high Q impedances are those out near the edge of the Smith Chart, and indeed, these are difficult to match to a real impedance.

Remember that impedance matching is all about obtaining maximum power transfer. The problem with a high Q impedance (primarily reactive) is that it dissipates very little power. Thus, in essence, you are trying to transfer power to a circuit that can't accept it. Of course, if the Q is high enough, pure reactance, then it is strictly impossible to match to it using lossless elements. In other words, its impossible to transfer power to it.