4.3 Filters, Oscillators, and Multivibrators

4.3 Filters, Oscillators, and Multivibrators

Frequency selection, waveform generation, and pulse timing are essential operations in aircraft navigation, communication, radar, and digital flight control systems. This section covers frequency-selective filter networks, sinusoidal LC and quartz crystal oscillators, and regenerative multivibrator circuits.

Passive Filter Networks in Avionics

Electrical filters are frequency-selective circuits designed to pass signals within specific frequency ranges while attenuating signals outside those ranges. In aircraft avionics, filters process radio frequencies (RF), audio signals, and telemetry data.

Low-Pass, High-Pass, Band-Pass, and Band-Stop Topologies

1. Low-Pass Filter (LPF): Passes all frequencies from DC (0 Hz) up to a designated cut-off frequency ($f_c$) while attenuating higher frequencies. LPFs eliminate high-frequency engine alternator noise from audio interphone systems and smooth rectified DC voltages in power supplies.
2. High-Pass Filter (HPF): Attenuates frequencies below the cut-off frequency ($f_c$) while passing higher frequencies without attenuation. HPFs block 400 Hz aircraft power hum while passing high-frequency audio or RF signals.
3. Band-Pass Filter (BPF): Passes a specific band of frequencies bounded by a lower cut-off frequency ($f_{c1}$) and an upper cut-off frequency ($f_{c2}$), attenuating all frequencies below $f_{c1}$ and above $f_{c2}$. BPFs are used in VHF communication receivers to isolate specific 25 kHz radio channels.
4. Band-Stop (Notch) Filter: Attenuates a narrow band of unwanted frequencies while passing all frequencies above and below the rejection band. Notch filters eliminate specific interference tones, such as removing 1020 Hz VOR identification tones from navigation voice channels.

Filter Cut-Off Frequency & Resonance Mathematics

Filter performance is governed by reactive component behavior ($X_C = \frac{1}{2\pi f C}$ and $X_L = 2\pi f L$).

Reactance and the -3 dB Frequency Formula

For a single-pole passive RC filter, the cut-off frequency ($f_c$) (also called the half-power or half-voltage point) occurs at the frequency where capacitive reactance equals resistance ($X_C = R$): $f_c = \frac{1}{2\pi R C}$

At $f_c$, the ratio of output voltage to input voltage is: $\frac{V_{out}}{V_{in}} = \frac{1}{\sqrt{2}} \approx 0.707$

This voltage drop corresponds to a power attenuation of -3 dB. The output signal experiences a $45^\circ$ phase shift relative to the input. A single-pole first-order filter exhibits a attenuation roll-off rate of -20 dB per decade (-6 dB per octave).

In LC resonant circuits, resonance occurs when inductive reactance equals capacitive reactance ($X_L = X_C$). The resonant frequency ($f_r$) is given by: $f_r = \frac{1}{2\pi \sqrt{L C}}$

The sharpness of filter selectivity is defined by the Quality Factor ($Q$): $Q = \frac{f_r}{BW}$ where $BW = f_{c2} - f_{c1}$ is the 3 dB bandwidth. Higher $Q$ values yield narrower, more selective filter passbands.

Worked Formula: VHF Navigation Audio Low-Pass Filter Calculation

An avionics technician needs to select component values for a single-pole RC low-pass filter to attenuate high-frequency noise above a cut-off frequency $f_c = 1591.5\text{ Hz}$ in a VOR navigation audio circuit. Given a precision capacitor value $C = 0.01\ \mu\text{F} = 1.0 \times 10^{-8}\text{ F}$, calculate the required resistor value ($R$).

1. Rearrange Cut-Off Frequency Formula for Resistance ($R$): $f_c = \frac{1}{2\pi R C} \implies R = \frac{1}{2\pi f_c C}$

2. Substitute Known Values: $R = \frac{1}{2 \times 3.14159265 \times 1591.55\text{ Hz} \times (1.0 \times 10^{-8}\text{ F})}$

3. Compute Denominator and Result: $\text{Denominator} = 6.283185 \times 1591.55 \times 10^{-8} = 1.0 \times 10^{-4}$ $R = \frac{1}{1.0 \times 10^{-4}} = 10,000\ \Omega = 10\text{ k}\Omega$ The technician selects a standard $10\text{ k}\Omega$ precision resistor.

Oscillator Circuits and Feedback Principles

An oscillator is an active electronic circuit that converts DC power into a continuous, self-sustaining periodic AC signal (sinusoidal or non-sinusoidal) without needing an external AC input signal.

Barkhausen Criteria, LC Topologies, and Quartz Crystals

To maintain continuous unattenuated oscillations, a circuit must satisfy the Barkhausen Stability Criteria:

1. The magnitude of the closed-loop gain must equal unity ($|A\beta| = 1$).
2. The cumulative phase shift around the feedback loop must equal $0^\circ$ or an integer multiple of $360^\circ$ at the desired frequency.

Common sinusoidal oscillator topologies in avionics include:

• Hartley Oscillator: Features an LC tank circuit utilizing a tapped inductor (or two series inductors) in parallel with a tuning capacitor. The inductor tap forms a inductive voltage divider to feed back a fraction of the output signal to the active device in proper phase.
• Colpitts Oscillator: Utilizes an LC tank circuit containing a capacitive voltage divider (two series capacitors in parallel with a single inductor). The junction between the two capacitors provides the feedback signal. Colpitts oscillators offer superior high-frequency frequency stability compared to Hartley oscillators.
• Quartz Crystal Oscillators: Replace the mechanical LC tank with a synthetic quartz crystal wafer operating on the piezoelectric effect (mechanical deformation generates electrical charge, and applied electrical voltage induces mechanical vibration). Quartz crystals exhibit extremely high Quality Factors ($Q > 10,000$ up to $100,000$), delivering exceptional frequency stability for aircraft VHF radio transmitters, TCAS transponders, and GPS receivers.

Multivibrator Circuits and Digital Pulse Generation

Multivibrators are two-state regenerative circuits widely used in digital clock generation, timing delays, and binary data storage.

Astable, Monostable, and Bistable Architectures

1. Astable Multivibrator (Free-Running): Possesses no stable electrical states. It continuously alternates between two quasi-stable states, generating a continuous square-wave clock output. The output frequency is dictated by internal cross-coupled RC timing networks. Astable circuits function as master system clock generators for flight control computers.
2. Monostable Multivibrator (One-Shot): Possesses one stable state and one quasi-stable state. When triggered by an external pulse, the circuit switches to its quasi-stable state for a fixed duration determined by an RC timing network ($T \approx 1.1 R C$) before automatically returning to its stable state. Monostable circuits stretch short pulses and generate precise radar trigger delays.
3. Bistable Multivibrator (Flip-Flop): Possesses two stable states. The circuit remains in its current state indefinitely until driven to the opposite state by an external SET or RESET pulse. Bistable multivibrators serve as basic 1-bit binary memory cells and pulse frequency dividers.

Avionics Traps & Maintenance Considerations

• Crystal Thermal Drift & Mechanical Shock: Severe physical vibration or extreme temperature swings in unconditioned avionics bays can crack quartz crystal wafers or shift resonant frequencies outside strict FAA/ICAO channel tolerances, causing radio off-frequency transmission.
• Filter Phase Shift Degradation: In synchro/resolver aircraft navigation systems, subtle component value drift in filter capacitors introduces phase shifts that manifest as directional heading errors on Horizontal Situation Indicators (HSI).

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Active vs Passive Power-Supply Filters (NCATT Standard)

NCATT distinguishes power-supply filter classes by gain:

• Active filters produce a current or voltage gain (typically op-amp or transistor-based regulation/filtering stages).
• Passive filters produce no gain—they use only R, L, and C networks and always attenuate or reshape without amplifying.

Frequency-sensitive filter topologies (low-pass, high-pass, band-pass, band-reject) may be built as passive LC/RC networks or as active circuits. Cutoff frequency is where attenuation begins to increase rapidly. In avionics power supplies, a passive LC pi-filter after a rectifier is the classic no-gain ripple smoother; an active voltage-regulator stage that also filters is an active filter path.

Exam cue: If the question asks whether a filter produces gain, answer using the active (gain) vs passive (no gain) distinction—not merely low-pass vs high-pass.