15.1 Filters — Low Pass, High Pass, Band Pass, Band Stop

15.1 Filters — Low Pass, High Pass, Band Pass, Band Stop

Quick Answer: A filter selects frequencies. Low-pass → DC/low through, highs attenuated. High-pass → highs through, lows blocked. Band-pass → one mid-band through. Band-stop (notch) → one band rejected. Cut-off is often the −3 dB point. Aircraft uses: radio/audio, bus ripple/EMI suppression, sensor signal conditioning.

CAAS SAR-66 Module 3 topic 3.16 Filters follows transformers (3.15) and precedes AC generators (3.17). You already know that inductive reactance rises with frequency (X_L = 2πfL) and capacitive reactance falls (X_C = 1/(2πfC)). Filters exploit that frequency dependence so a network can prefer some frequencies and reject others. Module 3 expects recognition of the four classic types, how they behave, and where they appear in aircraft electrical and avionics practice—not deep filter-design calculus.

What a Filter Does

A filter is a two-port (or multi-port) network whose transfer from input to output depends on frequency. Ideal textbooks draw brick-wall responses; real filters roll off gradually. For exam language:

Why filters exist on aircraft. Generators and converters produce ripple and switching noise. Radios and audio need clean bands. Sensors and ADC front-ends need anti-alias or noise rejection. Bonding and shielding help, but intentional RLC networks implement the frequency selection Module 3 names.

Low-Pass Filters (LPF)

A low-pass filter passes DC and frequencies below cut-off and attenuates frequencies above cut-off.

Operation intuition

• Series inductor + load: at low f, X_L is small → series drop small → output follows input. At high f, X_L rises → more voltage dropped in L → output falls.
• Shunt capacitor across the load (series resistor feeding it): at low f, X_C is large → capacitor does little; at high f, X_C is small → capacitor shunts AC to ground/return → output falls.

Classic first-order RC low-pass: series R, shunt C to return. Cut-off:

f_c = 1 / (2πRC)

At f = f_c, capacitive reactance equals R in magnitude for this topology, and magnitude response is about 0.707 of the DC gain.

Worked example 1. RC low-pass with R = 1.6 kΩ, C = 0.1 µF.

f_c = 1 / (2π × 1600 × 1×10⁻⁷) ≈ 1 / (1.005×10⁻³) ≈ 995 Hz ≈ 1 kHz.

A 100 Hz tone (well below f_c) passes; a 10 kHz tone is strongly reduced.

Applications and uses (LPF)

Aircraft link. After rectification in a TRU or power supply, capacitor and choke arrangements act as low-pass networks so the DC bus sees reduced ripple. On a scope, remaining ripple is the incomplete stop-band rejection of the filter under load.

High-Pass Filters (HPF)

A high-pass filter attenuates DC and frequencies below cut-off and passes frequencies above cut-off.

Operation intuition

• Series capacitor + load: at low f, X_C is huge → series impedance blocks; at high f, X_C falls → signal couples through.
• Shunt inductor to return with series feed resistor: at low f, X_L is small → shunt shorts low frequencies; at high f, X_L rises → shunt less effective → highs appear at output.

Classic first-order RC high-pass: series C, shunt R to return. Cut-off again:

f_c = 1 / (2πRC)

Worked example 2. Same R and C as example 1 but wired as high-pass: f_c still ≈ 1 kHz. A DC bias is blocked; a 10 kHz tone passes; a 50 Hz hum is attenuated.

Applications and uses (HPF)

Exam trap. “Capacitor in series with the signal” does not automatically mean low-pass. Series C is the hallmark of high-pass coupling; shunt C across the load is the hallmark of simple low-pass.

Band-Pass Filters (BPF)

A band-pass filter passes a band of frequencies between a lower cut-off f_L and an upper cut-off f_H, and attenuates both below f_L and above f_H.

Operation intuition

Conceptually: high-pass cascaded with low-pass (high-pass sets f_L; low-pass sets f_H), or a tuned RLC circuit near resonance.

For a series RLC driven from a source, current (and voltage across R) peaks near resonance:

f_0 = 1 / (2π√(LC))

Bandwidth relates to how sharp the resonance is (Q factor). Module 3 needs the idea: only a mid-band gets through efficiently.

Worked example 3. A simple cascade wants pass from about 300 Hz to 3 kHz (voice band training figure). Implement approximate HPF with f_c ≈ 300 Hz and LPF with f_c ≈ 3 kHz. Frequencies near 1 kHz pass; 50 Hz and 20 kHz are reduced.

Applications and uses (BPF)

Aircraft link. Navigation and communication receivers rely on tuned (band-pass) stages so a weak wanted carrier is preferred over nearby frequencies—conceptually the same Module 3 band-pass idea scaled into RF practice.

Band-Stop / Notch Filters (BSF)

A band-stop (also band-reject or notch) filter attenuates a chosen band between f_L and f_H and passes frequencies below f_L and above f_H.

It is the logical complement of band-pass: reject the middle, keep the sides.

A sharp notch might target a single nuisance frequency (for example 400 Hz aircraft AC hum pickup in an audio or instrumentation path, or a known interference tone).

Applications and uses (BSF)

Worked concept. An audio monitoring circuit on an aircraft picks up a strong 400 Hz tone from the AC bus magnetically. A notch centred at 400 Hz reduces that tone while voice frequencies above and below remain usable.

Four-Type Comparison (Exam Table)

Reactance Reminder Tied to Filters

Order and steepness. A first-order RC rolls off at about 20 dB/decade beyond cut-off. Cascading stages (higher order) steepens the skirt. Module 3 rarely asks dB/decade arithmetic, but knowing that real filters are gradual—not brick walls—prevents over-claiming “complete” rejection in fault stories.

Practical Technician Notes

1. Loading matters. Cut-off formulas assume a defined source/load. A much lower load resistance than design can shift the response.
2. Electrolytic capacitors used in power low-pass filters are polarity-sensitive; reverse voltage destroys them.
3. Inductors have winding resistance and core losses—real choke filters are not pure L.
4. Safety. Filters on power lines must be rated for voltage, current, and fault conditions; never treat a random RC breadboard network as an approved aircraft EMI fix.
5. Diagnosis. If a low-pass smoothing capacitor opens, ripple rises; if it shorts, the supply may collapse or trip protection—link symptoms to filter function.

Section Synthesis

Memorise the four behaviours, the series-C vs shunt-C trap, f_c ≈ 1/(2πRC) for first-order RC, and aircraft examples (smoothing, EMI, radio/audio, 400 Hz notch). Topic 3.17 next builds the AC generators that often create the frequencies these filters manage.