LC filter

Harmonics don't belong in the antenna

Besides the frequency you transmit on, every power amplifier also produces multiples of it: the harmonics. Transmit on 7.1 MHz without a filter and you also radiate on 14.2, 21.3 and 28.4 MHz, right in other bands or just next to them. How far they have to be suppressed is set by the regulations, and it's measured at the antenna connector. A push-pull stage already gives little second harmonic, but the third stays strong.

A low-pass filter passes everything below its cut-off frequency and attenuates above it. It sits between the amplifier and the antenna, and because it carries the full power, it's not just the curve that counts but also what the parts can take. The table under the schematic shows that.

Low-pass, high-pass, band-pass

The low-pass is the harmonic filter. The high-pass keeps low frequencies out, for example strong medium wave broadcasters away from the receiver input when you want to listen on 160 m. The band-pass only lets one range through, say 2 m in front of a preamp or one band in a multiband receiver.

Here all three are calculated from the same basic circuit: the normalised low-pass prototype. Its values (the g values) are in tables, and with the cut-off frequency and characteristic impedance they turn into real parts. For the high-pass, inductors and capacitors swap places; for the band-pass, every part becomes a resonant circuit on the centre frequency.

Pi or T

The same curve works with two forms. Pi starts at the transmitter with a part across to ground (a capacitor for the low-pass), T with a part in the line (an inductor). For the low-pass, Pi needs fewer inductors, and inductors are what you have to wind and what gets warm. That's why most harmonic filters are Pi filters.

The filter is calculated for 50 Ω at both ends. With an antenna at high SWR the curve no longer holds, so it belongs between the amplifier and the tuner, not after it. What the filter shows at its input you can see on the Smith chart via the button by the schematic.

Butterworth: as flat as possible

A Butterworth filter has no ripple at all in the passband. In return the curve falls off slowly: at the cut-off it's already 3 dB down, and beyond that each order adds 6 dB per octave of slope. Good when you want an even response over a wide range.

Chebyshev: steeper, but with ripple

A Chebyshev filter allows a little ripple in the passband, say 0.1 dB, and buys a much steeper skirt with it. At the same order it attenuates harmonics a lot more. The cut-off here is the point where the curve reaches the ripple level for the last time, not the 3 dB point.

More ripple means a steeper skirt, but also more mismatch in the band: 0.1 dB ripple equals an SWR of up to 1.36, 0.5 dB up to 1.98, 1 dB up to 2.66. For transmitter filters 0.01 to 0.1 dB is usual, so the amplifier sees a clean 50 Ω load.

Odd order only

A Chebyshev filter of even order needs a different resistance at the output than at the input. Between two 50 Ω ports you therefore only get 3, 5, 7 and 9 here. Butterworth works with any order.

Which order?

Try it with the harmonic markers. For a 40 m low-pass with 0.1 dB ripple, fifth order brings the second harmonic to about −32 dB and the third to about −52 dB. Seventh order adds a good 20 dB more, but costs one more inductor, one more capacitor and a little loss.

On the Smith chart

How the input impedance of a filter moves with frequency, looping around the ripple circle, is shown under Over frequency, also as a curve you can rotate in 3D.

Q

A real inductor has a loss resistance besides its inductance: the copper and, on a toroid, the core material. The Q factor says how much smaller this resistance is than the reactance: R = ωL / Q. Iron powder toroids reach about 100 to 250 on HF, good air-core coils more. NP0/C0G or mica capacitors have such high Q that you can usually ignore it; by default they're ideal here.

What the losses cost

The through loss in the values is everything that doesn't reach the load: mismatch and heat. For a fifth-order low-pass with Q = 150 it's a few tenths of a dB in the band. Sounds like little, but at 100 W, 0.2 dB is already 4.5 W ending up in two inductors. The Loss column shows where.

Voltage and current

For the stress, the page assumes a transmitter delivering the set power into 50 Ω. Into 50 Ω, 100 W is a peak voltage of 100 V and a current of 1.41 A. Inside the filter it can be more, especially in the middle and near the cut-off. Capacitors are checked against the chosen rated voltage: up to half is fine, up to 80 % is tight. With high SWR at the antenna, voltage and current rise further, so allow some margin.

Does the core get warm?

The page estimates toroid heating with the core makers' rule of thumb: ΔT ≈ (loss in mW / surface in cm²)^0.833 in kelvin. Below 25 K the core is fine, up to 50 K it gets warm, above that it's too small. With iron powder on HF, heat is the limit, not saturation. The turns come from the A_L value, and the wire is the thickest that fits in one layer around the inner circumference. Mix 2 (red) for 1 to 30 MHz, mix 6 (yellow) up to 50 MHz.

The calculation assumes a continuous carrier, as with FT8 or RTTY. On SSB the average power is a quarter to a third, on CW about half: a core that's red here may still be enough then. Lower the power in the design to see by how much. That's why the 100 W presets use T106; smaller cores get hot on long overs.

Tolerances and standard values

Parts have tolerances. The tolerance band shows where the curve ends up if every part is randomly off by up to ± that many percent (40 runs, always the same ones, so the picture stays the same on reload). “As built” uses the standard capacitor values and the inductances from whole turns. With “E12, 2 in parallel” two capacitors get you closer to the calculated value.