Low-pass filter designer
A low-pass filter passes the operating frequency and attenuates the harmonics above it. Pick a band, shape the response, and get part values, winding counts and the voltage each part must handle.
Filter design
Band presets start the cutoff 20 percent above the band's top edge. Move it and watch the passband and the harmonics.
- Filter response
- Operating range
- Spurious emission limit
- Dots: worst case of each harmonic
- Worst loss in the operating range
- 0.10 dB
- Worst SWR at the transmitter
- 1.36 : 1
- 2nd harmonic reduced by
- 23 dB
- 3rd harmonic reduced by
- 44 dB
The filter alone reduces the second harmonic by 23 dB. For the whole station the rules require 43 dB (47 CFR 97.307(d), for transmitters installed after January 1, 2003), so the transmitter's own suppression must make up the rest, or use a sharper filter. At 100 W PEP the parts carry the stresses listed below.
| Part | Placement | Value | How to make it | Worst case at 100 W PEP |
|---|---|---|---|---|
| C1 | To ground | 417 pF | Capacitor | 103 V peak |
| L1 | In series | 1.25 µH | 18 turns on a T-50-6 | 1.67 A rms |
| C2 | To ground | 718 pF | Capacitor | 113 V peak |
| L2 | In series | 1.25 µH | 18 turns on a T-50-6 | 1.93 A rms |
| C3 | To ground | 417 pF | Capacitor | 98.9 V peak |
Values are exact; a nearby standard capacitor value shifts the response slightly. Each winding link opens the inductor in the coil winder. Stresses are the largest anywhere in the operating range, for ideal parts.
Open this filter in the circuit bench to try standard part values or add a matching network.
Try this
A 5-part Butterworth filter with its cutoff 20 percent above 40 m. It reduces the 14 MHz second harmonic by only about 20 dB, and because a Butterworth response already sags near its cutoff, the transmitter sees an SWR above 2:1 at the top of the band.
The same 5 parts stay flat closer to the cutoff: the worst SWR drops to about 1.4:1 and the second harmonic falls a few dB further. Raise the ripple and rejection improves again, but the SWR climbs; 1 dB of ripple allows up to 2.7:1.
Seven parts reach about 41 dB at the second harmonic, with a better match than five. Each extra inductor and capacitor steepens the slope.
A 5-part, 0.1 dB Chebyshev filter that only stops signals above the HF bands passes the 7 MHz second harmonic of an 80 m signal almost untouched, about 0.1 dB down. Harmonics of the lower bands need a cutoff close to each band.
Apply it
- Below 30 MHz, spurious emissions from transmitters installed after January 1, 2003 must be at least 43 dB below the fundamental (47 CFR 97.307(d)). From 30 to 225 MHz they must be at least 60 dB below; a transmitter of 25 W mean power or less must instead keep each spurious emission at or below 25 µW and at least 40 dB down, but need not reduce it below 10 µW (47 CFR 97.307(e)). The filter's attenuation adds to whatever harmonic suppression the transmitter already has.
- The rules use mean power. For a steady carrier it equals the PEP (General question G5B11); for unprocessed SSB voice the PEP is about 2.5 times the mean (Extra question E8A06). The check here uses the PEP you enter, so it is exact for a steady carrier and otherwise stricter than the rule.
- Check the finished station with a spectrum analyzer, the instrument the exams name for displaying spurious signals.
- Use capacitors rated well above the peak voltage shown for each part. Wind the inductors on iron powder, which Micrometals rates for high Q up to 40 MHz, and measure each one before installing it: spreading or squeezing the turns on a toroid changes the inductance a little.
- An RF switching amplifier needs a filter at its output to remove harmonic content, as the Extra exam notes.
How it works
- Part values come from the normalized Butterworth prototype, g = 2 sin((2k - 1)π / 2n), and the Chebyshev prototype formulas, scaled to the cutoff and system impedance: L = g Z0 / 2πfc and C = g / (2πfc Z0).
- The response, the SWR the transmitter sees and the stress on each part are computed from the circuit itself with ideal, lossless parts. A Butterworth filter is 3 dB down at its cutoff (the half-power point), and a Chebyshev filter loses exactly its ripple there.
- A Chebyshev filter with the same source and load impedance needs an odd number of parts; even orders need unequal terminations.
- A pi network puts capacitors from the line to ground at the input and output with an inductor between them. A Chebyshev filter trades ripple in the passband for a sharper cutoff.
- Below 30 MHz, spurious emissions from transmitters installed after January 1, 2003 must be at least 43 dB below the fundamental. From 30 to 225 MHz they must be at least 60 dB below; a transmitter of 25 W mean power or less must instead keep each spurious emission at or below 25 µW and at least 40 dB down, but need not reduce it below 10 µW.
- The rules use mean power. The check uses the PEP you enter, which equals the mean power of a steady carrier and is about 2.5 times the mean power of unprocessed SSB voice, so it is never less strict than the rule.
Learn more: Electronics basics
Sources: Microwave and RF Design: Modules, 2.7 Butterworth and Chebyshev Filters (Michael Steer, NC State University (LibreTexts)); Microwave and RF Design: Modules, 2.4 The Maximally Flat (Butterworth) Lowpass Approximation (Michael Steer, NC State University (LibreTexts)); Microwave and RF Design: Modules, 2.5 The Chebyshev Lowpass Approximation (Michael Steer, NC State University (LibreTexts)); Microwave and RF Design: Modules, 2.9 Filter Transformations (Michael Steer, NC State University (LibreTexts)); 47 CFR 97.307, Emission standards (eCFR); 2023-2027 General question pool (G5B11, G7C12) (NCVEC Question Pool Committee); 2024-2028 Extra question pool (E1C10, E4A03, E7B03, E7C01, E7C05, E8A06) (NCVEC Question Pool Committee)
Practice the exam questions: G7 Practical Circuits (General), E7 Practical Circuits (Amateur Extra)
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