Network topologies
The names describe the shape the components make on a schematic.
How are the capacitors and inductors of a low-pass filter Pi-network arranged between the network’s input and output?
A capacitor is connected between the input and ground, another capacitor is connected between the output and ground, and an inductor is connected between the input and output
Two shunt elements with a series element between: the shape of the Greek letter Pi.
What is the frequency response of a T-network with series capacitors and a shunt inductor?
High-pass
A T has two series elements with a shunt between them. Reason it out rather than memorise: series capacitors block low frequencies, and a shunt inductor shorts them to ground. Both actions reject low frequencies, so it is high-pass.
The general rule works for every case: series inductors and shunt capacitors pass low frequencies; series capacitors and shunt inductors pass high ones.
Which describes a Pi-L network?
A Pi-network with an additional output series inductor.
What is the purpose of adding an inductor to a Pi-network to create a Pi-L-network?
Greater harmonic suppression
The extra series inductor adds another low-pass section, so the response falls off faster above cutoff. This is why serious tube amplifiers use Pi-L output networks rather than plain Pi: the same matching, with better harmonic rejection.
What a matching network actually does
How does an impedance-matching circuit transform a complex impedance to a resistive impedance?
It cancels the reactive part of the impedance and changes the resistive part to the desired value
Two jobs, always. Cancel the reactance — the resonance idea again — and transform the resistance to the value you want. Any matching network you meet is doing both, and understanding that makes the topologies interchangeable rather than arbitrary.
Filter responses
The response name describes the shape of the curve, independent of how the filter is built.
| Response | Character |
|---|---|
| Butterworth | maximally flat passband, gentle cutoff |
| Chebyshev | ripple in the passband, sharp cutoff |
| Elliptical (Cauer) | extremely sharp cutoff with one or more notches in the stopband |
| Bessel | flat group delay, gentlest cutoff |
Which filter type has ripple in the passband and a sharp cutoff?
A Chebyshev filter.
The trade is explicit: you buy steepness with passband ripple. An elliptical filter goes further still, buying an even sharper edge with stopband notches — deep nulls at specific frequencies, with the response rising again between them.
Which is right depends on the job. For rejecting a specific interfering carrier, an elliptical’s notch is ideal. For a receiver’s IF, passband flatness matters more.
Which of the following measures a filter’s ability to reject signals in adjacent channels?
Shape factor.
The ratio of the −60 dB bandwidth to the −6 dB bandwidth. A perfect brick-wall filter would have a shape factor of 1.0; a good crystal filter reaches about 1.5; a cheap one is 3 or worse. Lower is better, and it is a far more informative specification than bandwidth alone.
Filter technologies
The physical construction, chosen by frequency and required performance.
| Technology | Use |
|---|---|
| Crystal lattice | low-level signals, quartz crystals — receiver IF filters |
| Cavity | VHF/UHF duplexers, e.g. a 2 metre repeater |
| Helical | band-pass or notch filtering in the 150 to 450 MHz range |
| LC | HF and below, and any low-Q application |
What is a crystal lattice filter?
A filter for low-level signals made using quartz crystals.
Quartz has a Q in the tens of thousands — far beyond any LC circuit — so a crystal lattice gives the sharp skirts an SSB or CW receiver IF needs. Low-level: these handle milliwatts, not transmitter power.
Which of the following filters is used in a 2-meter band repeater duplexer?
A cavity filter.
A duplexer must let a repeater transmit and receive simultaneously on frequencies 600 kHz apart, with the transmitter perhaps a hundred million times stronger than the signal being received. Nothing but a resonant cavity — a tuned metal box with very high Q and high power handling — will do it.
Which of the following is most frequently used as a band-pass or notch filter in VHF and UHF transceivers?
A helical filter
A helical resonator is a coil inside a shielded cavity: much of a cavity’s Q in a fraction of the volume, at frequencies where a full cavity would be inconveniently large.
Check yourself
- A network has series inductors and a shunt capacitor. Topology and response?
- Why does a repeater duplexer need cavity filters rather than LC ones?
- Two crystal filters, both 2.4 kHz wide, with shape factors of 1.5 and 3.0. Which rejects an adjacent signal better?
Answers
- Two series elements with a shunt between them is a T; series inductors and a shunt capacitor pass low frequencies, so low-pass.
- It must separate signals 600 kHz apart with the transmitter vastly stronger than the received signal — that needs a cavity’s very high Q and power handling.
- 1.5. Shape factor is the −60 dB bandwidth over the −6 dB bandwidth, and lower means steeper skirts.