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Component Q: what a real inductor does to your match

Most free matching calculators assume perfect components. Real inductors have a Q somewhere between 15 and 150, and the difference does not just cost you power, it moves your match.

Two things go wrong, not one

A real inductor is an inductor with a resistance in series with it. The ratio of the two is Q, at the frequency you are working at. Put one into a matching network and:

• Some of your power turns into heat in that resistance.
• That resistance is part of the circuit, so the impedance the network presents is not what you designed.

The second one surprises people. Here is a matched L-network, 5 ohms to 50 ohms at 100 MHz, with the inductor Q swept and nothing else changed:

At a Q of 15 the match has drifted from 1.0005 to 1.20 and you are down 0.83 dB. Neither number is catastrophic, but if you designed for a perfect 1.0 and measured 1.2 on the bench, you would spend an afternoon looking for a mistake that is not there.

The loss depends on the network's Q, not just the part's

This is the rule worth carrying around. A higher Q network circulates more reactive current for the same delivered power, so the same imperfect component dissipates more.

Same load, same 100 MHz, same inductors. The only change is the topology:

Same parts, three times the loss, because the network stores more energy for the same throughput. So the useful figure of merit is the ratio of your network's loaded Q to your components' unloaded Q. Keep the network Q well below the component Q and the loss stays small. Let them approach each other and it does not.

This is the hidden cost in the Pi and T article. A high Q network buys you selectivity and comfortable component values, and it charges you in dissipation.

What Q to actually use

Q is frequency dependent and part dependent, so the honest answer is to look at the datasheet curve at your frequency. As a starting point:

• Wirewound chip inductors, VHF: 40 to 90.
• Multilayer chip inductors: 15 to 40. Cheap, small, lossy.
• Air wound coils, made properly: 150 to 300. This is why transmitter output networks still use them.
• C0G/NP0 capacitors: 1000 and up. High enough that you can usually leave capacitors ideal and only worry about inductors.
• X7R capacitors: don't, not in a matching network.

That last pair is why the examples above only degrade the inductor. In most RF matching networks the inductor is the lossy part by an order of magnitude, and modelling the capacitor as perfect costs you almost nothing in accuracy.

Putting it in the model

Every component slot in QuickSmith carries its own Q. Double-click a component, or drop a new one, and the dialog has a Q field. The default is 1000000, which is ideal in all but name.

Set it to something real and everything downstream follows: the node moves, the insertion loss appears in the readout, the response sweep changes shape. The regression suite has a case for this, because it is easy to get wrong in a way that hides: a series part round-trips through the solver exactly regardless of its Q, since loss does not touch reactance, but a shunt part lands about 1/Q away from where an ideal one would.

One more place it bites

Example 5 is a five pole low-pass filter, and it is the clearest demonstration of what component Q does to a design that is not a match at all. The published design asks for 60 dB down at 100 MHz. With the real Q values on the parts, it gives 53.25 dB, and about 0.75 dB of loss through the passband that an ideal design would not have.

Nobody did anything wrong. That is just what the parts cost.