Tools / Low-pass filter and L-network calculator

Low-pass filter and L-network calculator

Design a harmonic filter for a transmitter: choose the cutoff, the number of poles and the response, and get every component value with the attenuation at each harmonic. Below that, an L-network calculator matches any load to 50 Ω.

Low-pass filter

Set it a little above the top of the band
PartExact valueNearest E12Toroid turns
FrequencyMHzAttenuation

L-network matching

Matches a load to the source impedance at one frequency. Enter the load's resistance and reactance (positive is inductive).

SolutionNext to the sourceNext to the loadType

Why a transmitter needs a low-pass filter

Every transmitter produces some harmonics, signals at two, three and more times the operating frequency. A home-built QRP transmitter, especially one with a class C or class E output stage, can produce strong harmonics that land in other bands and services. A low-pass filter passes the wanted frequency with almost no loss and attenuates everything above its cutoff. For a typical single-band QRP rig, a 5- or 7-pole filter brings the harmonics comfortably below the levels in the licence.

How the values are worked out

The calculator uses standard normalised low-pass prototypes, scaled to your cutoff and impedance. The filter starts and ends with a capacitor to ground (a pi or capacitor-input layout), with series inductors between them:

Ck = gk ÷ (2π fc Z)
Lk = gk × Z ÷ (2π fc)

The g values come from the Chebyshev or Butterworth equations. For a Chebyshev filter, the cutoff is the edge of the ripple band, where the loss first reaches the ripple figure. A 0.1 dB ripple Chebyshev gives a much steeper roll-off than a Butterworth with the same number of parts, and the ripple adds a return loss of about 16 dB, an SWR of about 1.36, at worst in the passband.

Set the cutoff 10 to 20% above the top of your band, so the whole band is well inside the passband but the second harmonic of the bottom of the band is well into the stopband.

Building it

Use stable, low-loss capacitors: silver mica or C0G (NP0) ceramic, rated for the voltage at your power. Wind the inductors on red mix 2 iron powder toroids for HF, and check each one with an LCR meter or NanoVNA if you can, adding or removing a turn to get close. Spread or squeeze the turns slightly to fine-tune. Nearest E12 capacitor values are usually close enough; for a closer match, combine two capacitors in parallel. Check the finished filter's response with a NanoVNA before using it.

L-networks

An L-network is the simplest matching network: one series and one shunt component. It can match any resistive load to any source, and cancel the load's reactance at the same time. There are usually two solutions. The low-pass version, with a series inductor and a shunt capacitor, also helps to reduce harmonics, so it's usually the better choice for a transmitter. An L-network is narrowband, so it's designed for one frequency.

Questions

What cutoff frequency should I use for a 20m low-pass filter?

About 16 MHz, 10 to 15% above the top of the band at 14.35 MHz. That passes the whole band and attenuates the second harmonic at 28 MHz strongly.

How many poles does my filter need?

Five poles is usually enough for a QRP transmitter with a reasonably clean output stage. Seven poles gives about 20 dB more attenuation at the second harmonic.

Chebyshev or Butterworth?

Chebyshev filters roll off much faster for the same number of parts, at the cost of a small ripple in the passband. For harmonic filters, a 0.1 dB Chebyshev is the usual choice.

Which capacitors should I use?

Silver mica or C0G/NP0 ceramic, with a voltage rating well above the peak RF voltage. At 5 W in 50 Ω the peak voltage is about 22 V, and at 100 W it's 100 V.