E7C

Filters and matching networks

Tell low-pass from high-pass networks, name filter types by their response, and pick the right filter for a job.

11 pool questions1 on the exam

Syllabus: Filters and matching networks: types of networks; types of filters; filter applications; filter characteristics; impedance matching

Series inductors and shunt capacitors pass low frequencies

An inductor blocks high frequencies in the signal path; a capacitor to ground shorts high frequencies away. A capacitor in the path blocks low frequencies; an inductor to ground shorts them away.

Capacitor to ground at input and output, inductor between.

Pi (low-pass): capacitor to ground at input and output, inductor between.
Pi-L: a Pi network plus an extra series inductor at the output. The extra element gives greater harmonic suppression.
T with series capacitors and a shunt inductor: high-pass.

RememberSeries L + shunt C = low-pass. Series C + shunt L = high-pass. Pi-L = Pi plus output inductor, for more harmonic suppression.

A matching network cancels reactance and sets the resistance

A load is often complex: resistance plus reactance. A network adds the opposite reactance to cancel the reactive part, and also transforms the resistive part to the value the source wants.

A matching network does two jobs: cancel the reactance, then set the resistance.

RememberMatch = cancel the reactance, change the resistance to the desired value.

Filter names tell you the shape of the response

Same cutoff, different trade-offs. Flat passband gives a gentle skirt. Allow ripple in the passband and the skirt steepens. Add notches in the stop band and it steepens further.

Same cutoff, three shapes (elliptical is a sketch). Ripple buys a steeper skirt; notches the steepest.

Filter	Passband	Cutoff
Butterworth	maximally flat, no ripple	gradual
Chebyshev	ripple	sharp
Elliptical	ripple	extremely sharp, with notches in the stop band

RememberRipple + sharp cutoff = Chebyshev. Sharpest with stop-band notches = elliptical.

Shape factor measures how steep the skirts are

Shape factor compares the filter's width far down (60 dB) with its width near the top (6 dB). A smaller number means steeper skirts, so a signal on the next channel is rejected better.

Shape factor = width at −60 dB ÷ width at −6 dB. Lower is better.

Filter sections (more = steeper skirts)6

Shape factor2.89

RememberShape factor = adjacent-channel rejection ability. Lower is better.

Match the filter to the job

Cavity filters let one antenna share transmit and receive.

Filter	Used for
Helical	band-pass or notch in VHF and UHF transceivers
Crystal lattice	low-level signals; built from quartz crystals
Cavity	repeater duplexer on 2 m; very sharp and handles power

RememberVHF/UHF transceiver: helical. Quartz, low level: crystal lattice. Repeater duplexer: cavity.

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