Bandpass and band-rejection filters

One teaching approach: cascade a high-pass and a low-pass so only the middle survives. Another: use a series resonant branch that presents low impedance at fr so that frequency passes to the load, while off-resonance the branch blocks.

At resonance of a series LC in the pass path, Z is minimum → signal couples through. Away from fr, reactance rises → attenuation.

A common approach uses a parallel resonant tank that goes to high impedance at fr in series with the signal, blocking that frequency, or a series resonant short across the signal at fr that steals that band away from the load.

Notch filters are how you carve out an interfering tone without killing everything else.

High-Q circuits make narrow pass or notch bands (sharp). Low-Q circuits make wider bumps and valleys. Component resistance and inductor Q set how selective the filter feels.

• Rejecting a stubborn harmonic
• Passing a modem or carrier frequency
• Audio feedback notches
• Instrumentation isolating a measurement band

Even if you never tune a radio IF can, the words “passband” and “notch” appear in drive and EMI literature.

1. Pick fr with L and C: fr = 1/(2π√(LC)).
2. Decide pass vs reject topology (series vs parallel resonant placement).
3. Adjust R / Q for width.
4. Verify on a scope or analyzer that the wanted signal survives.

Power-level notches and harmonic traps carry real current. Treat them like any power LC — fuses, heating, and voltage ratings still apply.

Pick fr first: fr=1/(2π√(LC)). Then choose topology:

• Want to pass fr → series resonant path (low Z at fr)
• Want to kill fr → parallel resonant block or series resonant short across the node

Q sets width. If interference sits 50 Hz from your carrier, you need a narrow notch — high Q, careful tuning.

Spectrum first, solder iron second. Guessing fr wastes parts.

A signal notch uses small energy. A harmonic trap on a 400 A bus is a power device — fusing, heat, and fault duty apply. Same physics, different PPE and ratings.

Situation. A building automation link fails only when a large chiller VFD runs at a certain speed. A technician installs a notch filter tuned to the interfering frequency on the signal line; communications return.

What happened. A band of noise sat on the carrier. Rejecting that band restored SNR without redesigning the whole network.

Applied lesson. Band-rejection is surgical. Measure the offender frequency before you tune L and C.

### Teaching pause — say this out loud

Before you leave this lesson, explain the main idea to an imaginary first-month helper in under one minute. If you need the book open to do it, reread How it works once more. Field diagnosis only helps after the concept is yours.

Also sketch the key diagram from memory (triangle, wye/delta, filter shape, or charge curve — whichever this lesson used). Labels beat artistic skill.

### Why this lesson matters on Monday morning

Bandpass and band-rejection filters is not trivia. You will meet it when a meter reading looks “impossible,” when a replacement part is almost right, or when a helper asks why the book uses √3 or lead/lag. Master the model here so the next call is pattern recognition, not panic.

Common Monday uses: verify a nameplate against clamps, explain a PF or capacitor change to a customer, or catch a miswired series/parallel or wye/delta assumption before energizing.