7.5 Filter Networks

Why This Matters for the Exam

Aircraft electrical and electronic systems operate in a highly dense electromagnetic environment. A single aircraft contains alternating current generators, high-power radar transmitters, VHF/UHF communication radios, digital flight computers, and delicate audio buses. The high-power AC system operates at 400 Hz, which can easily induce an audible "hum" in cockpit communications systems. Furthermore, alternating currents generated by alternators must be rectified to DC for battery charging and avionics, which introduces AC ripple voltage.

To prevent electromagnetic interference (EMI), ensure clear communications, and smooth out rectified DC voltages, technicians must understand and maintain filter networks. For the EASA Part-66 Module 3 exam, you need to understand how resistors (R), inductors (L), and capacitors (C) are combined to form passive filter networks, how their impedances react to varying frequencies, how to calculate their cutoff frequencies, and how to identify their response curves.

---

Passive Components in Filter Networks

Passive filters rely on the frequency-dependent behavior of inductors and capacitors.

1. Resistors (R)

A resistor's resistance (R) is constant and does not change with frequency. Its impedance is simply Z = R.

2. Inductors (L)

An inductor resists changes in current by generating a back EMF. Its opposition to AC is called inductive reactance (XL):

XL = 2 x pi x f x L

Where:

• f = Frequency in Hertz (Hz)
• L = Inductance in Henrys (H)
• Frequency Response: At DC (f = 0), XL = 0 (acts as a short circuit). As frequency increases, XL increases linearly. Inductors block high frequencies and pass low frequencies.

3. Capacitors (C)

A capacitor stores energy in an electrostatic field and blocks DC while passing AC. Its opposition to AC is called capacitive reactance (XC):

XC = 1 / (2 x pi x f x C)

Where:

• f = Frequency in Hertz (Hz)
• C = Capacitance in Farads (F)
• Frequency Response: At DC (f = 0), XC is infinitely high (acts as an open circuit). As frequency increases, XC decreases towards zero. Capacitors pass high frequencies and block low frequencies.

---

Filter Configurations

By combining these components, we can build four primary types of filter networks:

1. Low-Pass Filter

A low-pass filter allows low-frequency signals (from DC up to a specific cutoff frequency) to pass with minimal attenuation, while blocking (attenuating) high-frequency signals.

• RC Low-Pass Filter: A series resistor (R) followed by a parallel capacitor (C) connected to ground.
  • Operation: At low frequencies, XC is very high, so the output voltage across the capacitor is nearly equal to the input voltage. At high frequencies, XC drops to a very low value, shunting the high-frequency signals to ground.
  • Cutoff Frequency (fc): fc = 1 / (2 x pi x R x C)
• RL Low-Pass Filter: A series inductor (L) followed by a parallel resistor (R).
  • Operation: At low frequencies, XL is low, allowing the signal to pass. At high frequencies, XL becomes very high, blocking the signal from reaching the output.
  • Cutoff Frequency (fc): fc = R / (2 x pi x L)

2. High-Pass Filter

A high-pass filter blocks low-frequency signals (including DC) and allows high-frequency signals to pass.

• RC High-Pass Filter: A series capacitor (C) followed by a parallel resistor (R) to ground.
  • Operation: The series capacitor blocks DC and low frequencies because XC is high. High-frequency signals pass easily because XC is low, developing a voltage across the output resistor.
  • Cutoff Frequency (fc): fc = 1 / (2 x pi x R x C)
• RL High-Pass Filter: A series resistor (R) followed by a parallel inductor (L) to ground.
  • Operation: The parallel inductor shunts low frequencies to ground because XL is low. High frequencies are forced to the output because XL is very high.
  • Cutoff Frequency (fc): fc = R / (2 x pi x L)

3. Band-Pass Filter

A band-pass filter allows a specific range (band) of frequencies to pass while attenuating all frequencies below and above this band.

• Construction: Can be created by placing a high-pass filter in series with a low-pass filter (provided their cutoff frequencies overlap) or by utilizing LC resonant circuits.
• LC Band-Pass: A series resonant LC circuit placed in the signal path has minimum impedance at resonance (fr = 1 / (2 x pi x sqrt(L x C))), allowing that frequency to pass. Alternatively, a parallel resonant LC circuit placed in parallel to ground has maximum impedance at resonance, preventing the resonant frequency from being shunted to ground.

4. Band-Stop (Band-Reject or Notch) Filter

A band-stop filter blocks a specific band of frequencies while allowing all frequencies outside that band to pass.

• Aviation Application: Commonly used as a 400 Hz notch filter in aircraft communications and audio systems to eliminate the electrical hum induced by the 115V AC 400 Hz power distribution lines.
• LC Band-Stop: A parallel resonant LC circuit placed in series with the signal path has infinite impedance at resonance, blocking the target frequency. A series resonant LC circuit placed in parallel to ground shunts only the resonant frequency to ground, leaving other frequencies unaffected.

---

Filter Response Curve Terminology

• Cutoff Frequency (fc): The boundary frequency at which the output power drops to 50% of the input power (also known as the -3 dB point or half-power point). At this frequency, the output voltage is 1 / sqrt(2) (or approximately 70.7%) of the input voltage.
• Passband: The range of frequencies that pass through the filter with minimal attenuation.
• Stopband: The range of frequencies that are heavily attenuated by the filter.
• Roll-off: The steepness of the filter's transition from the passband to the stopband. A single-pole (first-order) RC or RL filter has a roll-off rate of -20 dB per decade (or -6 dB per octave). Adding more reactive stages (poles) increases the roll-off steepness.

---

Worked Exam Calculation Scenarios

Scenario 1: RC Low-Pass Filter Cutoff Frequency

An aircraft avionics technician needs to install a low-pass filter to eliminate high-frequency noise from a sensor signal wire. The filter consists of a 1.2 k-ohm resistor and a 0.047 microfarad capacitor.

1. Calculate the cutoff frequency (fc): fc = 1 / (2 x pi x R x C) fc = 1 / (2 x 3.14159 x 1200 x (0.047 x 10^-6)) fc = 1 / (7.5398 x 10^-5) = 2821.9 Hz The filter will allow frequencies below approximately 2.82 kHz to pass, while attenuating noise above this frequency.

Scenario 2: RL High-Pass Filter Design

You are tasked with designing an RL high-pass filter to block low-frequency engine vibrations below 150 Hz in a cabin microphone line. You have a 150 ohm resistor.

1. Calculate the required inductor value (L): Since fc = R / (2 x pi x L): L = R / (2 x pi x fc) L = 150 / (2 x 3.14159 x 150) = 150 / 942.48 = 0.159 H An inductor of 0.159 H (or 159 mH) is required.