# Impedance matching vs LC filter

I have noticed in many papers, publications and in general application the use of LC filter for impedance matching. I wonder why this is the case? How is it that by using an LC filter, it can be used for impedance matching? How is it that an LC filter is both a filter and an impedance match? I know these may be trivial questions, but I'm trying to explain it to myself and I can't (I also know that for example "pi filters" can be also used for impedance matching).

Example of an impedance matching configuration using an LC filter:

• This power matching is only valid within a limited bandwidth. The idea is that this L and C in combination with the complex input impedance of the amplifier resonate at a certain frequency and at that frequency (and frequencies that are close to that frequency) the input impedance becomes close to 50 ohms meaning the impedance is matched. Commented Mar 3, 2021 at 10:08
• What @Bimpelrekkie is an answer: it's not "A vs B", but "A by means of B". Commented Mar 3, 2021 at 10:13
• It all comes from basic electrotechnicsâ€¦ the reactance turn the phase and aid the match (at a given frequecy). For multifrequency matching you use transformers and resistors (with various compromises). The difference is that a resistor match has a power loss while a resonant match doesn't (in principle) since the energy goes back and forth Commented Mar 3, 2021 at 10:16
• @MarcusMüller What Bimpelrekkie is an answer Thanks, but was lazy and waited for a nice answer from Andy, he didn't disappoint, see below :-) Commented Mar 3, 2021 at 10:31

You have shown a high pass LC circuit (an L-pad). That L-pad will have an input resistance that is purely resistive at one particular frequency. That input resistance will be lower than the output resistance of the load. Here's an example and a calculator you can use for determining the matching components: -

Picture and calculator can be found here. On that page you will find full derivations for the formulas.

In simple terms, the C and L form a high pass filter that have a natural resonant frequency but, when loaded with a particular value of resistance, the input impedance is purely resistive at a frequency a little bit higher than the natural resonant frequency.

In the example above you can see that the natural resonant frequency is 9.1287 MHz but, at 10 MHz (an enterable quantity) the impedance is a pure match. It is also loss-less i.e. power entering the capacitor is transferred without loss to the load.

And, if you look a little more on pages around the link I gave you'll see how two of these L-pads can form a pi-filter impedance matching network. There are several examples given.

This is a 2nd order HPF around 1GHz with low Q. with -6dB in the passband and -9dB at cutoff.

This example looks like a rookie design without specs .

The clue is a resonance around 350 MHz, where the impedance is much lower than 50 Ohms, hence overdamped with the 50 Ohm source now pushing the HPF breakpoint up to 1GHz dominated by L/R.

The other clue is Mickey Mouse Cap symbol.

So it's not really an L pad or a refined Bessel HPF, just a sloppy 2nd order HPF with a 180 deg phase shift that spans >3 decades instead of >2.

• Can you clarify what you mean with "-6dB in the passband and -9dB at cutoff". I thought cutoff was the point where the gain was -3dB?
– Carl
Commented Mar 3, 2021 at 11:02
• The source is 50 Ohms and load is 50 so I modelled that as -6dB with load @Carl relative to a 0 OHm source Commented Mar 3, 2021 at 11:25