Filters

What it is

A filter passes some frequencies and blocks others. Radios use them everywhere: to pick one signal out of a crowded band, to keep a transmitter's harmonics off the air, and to smooth the ripple out of a DC supply.

Four shapes

Shape	Passes	Typical use
Low-pass	below the cutoff	transmitter harmonic filter, audio smoothing
High-pass	above the cutoff	at a TV or FM receiver's antenna input, to keep HF transmissions out
Band-pass	a band around the centre	IF and receiver front-end filters, repeater duplexers
Band-reject (notch)	everything except a narrow band	removing one interfering tone or carrier

How a filter works

A capacitor's opposition to AC, its reactance, falls as frequency rises (Reactance and impedance). In a low-pass filter the capacitor sits across the output: low frequencies find it almost an open circuit and pass; high frequencies find it almost a short and are shunted to ground. At the cutoff the capacitor's reactance equals the resistance and the output is 0.707 of the input voltage, which is half the power or −3 dB. Swap the two parts and you have a high-pass filter. With 1 kΩ and 0.1 µF the cutoff is 1.59 kHz.

One RC section only falls 6 dB per octave, far too gentle for radio. Real filters use inductors and capacitors, which store energy and can resonate (Resonance and Q), and cascade several sections. Each extra section adds 6 dB per octave of skirt:

Sections (order)	Loss at twice the cutoff (Butterworth)
1	7 dB
2	12 dB
3	18 dB
5	30 dB

Shape, steepness and cost

A steeper skirt always costs something. Butterworth keeps the passband flat but falls gradually; Chebyshev falls faster at the price of ripple in the passband; elliptic is steepest, with ripple and notches. More sections also mean more insertion loss (power lost in the passband) and more phase distortion.

A narrow filter also needs a high Q. A 2.4 kHz SSB filter at 9 MHz has a Q of about 9 MHz ÷ 2.4 kHz = 3750, far beyond what a coil can give. That is why receivers use crystal, ceramic or mechanical filters for selectivity, and why DSP, which filters with arithmetic, is so attractive (Digital signal processing).

In practice

• Terminate filters properly. A filter is designed for a specific source and load impedance, usually 50 Ω; connect it to something else and its response changes.
• Match the width to the signal. Narrower than the signal loses audio, wider lets in noise; see Filters in radios.
• Filters can stop interference at either end. A low-pass in the transmit line stops harmonics (Harmonics and spurious emissions); a filter at a victim receiver stops strong out-of-band signals (Filters and ferrites for RFI).
• Active filters use op-amps with resistors and capacitors, so they need no coils, and suit audio frequencies.

Related

• Resonance and QTuned circuits, bandwidth and selectivity.
• Filters in radiosRoofing, crystal, mechanical and DSP filters.
• Crystals and resonatorsPiezoelectric frequency references and filters.
• Digital signal processingFiltering and demodulating with maths instead of components.
• Harmonics and spurious emissionsCleaning up your transmitter.
• Filters and ferrites for RFITreating the problem.