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Chapter 12 Glossary

Term Definition
First-order filter A filter with exactly one reactive element (one capacitor or one inductor), producing a transfer function with a single pole. Magnitude rolls off at −20 dB/decade in the stopband with a maximum phase shift of 90°. The simplest building blocks for audio and signal processing: RC low-pass, RC high-pass, RL low-pass, RL high-pass.
Second-order filter A filter with two reactive elements, producing a transfer function with two poles (and possibly zeros). Rolls off at −40 dB/decade in the stopband. Can exhibit resonance, peaking, or very selective band-pass behavior. Characterized by center frequency \(f_0\), quality factor Q, and bandwidth BW = \(f_0/Q\).
RC low-pass filter An RC circuit with series resistor R and shunt capacitor C, with output across the capacitor. Transfer function: \(H(j\omega) = 1/(1 + j\omega RC)\). Cutoff frequency: \(f_c = 1/(2\pi RC)\). Attenuates high-frequency signals while passing low-frequency and DC signals. Used for anti-aliasing and noise removal.
RC high-pass filter An RC circuit with series capacitor C and shunt resistor R, with output across the resistor. Transfer function: \(H(j\omega) = j\omega RC/(1 + j\omega RC)\). Same cutoff frequency as the RC low-pass with the same R and C: \(f_c = 1/(2\pi RC)\). Removes DC offset and low-frequency hum from signals.
RLC band-pass filter A second-order filter using a series or parallel RLC combination that passes a band of frequencies centered on the resonant frequency \(f_0 = 1/(2\pi\sqrt{LC})\). The bandwidth BW = \(f_0/Q = R/(2\pi L)\) for series RLC. Used in radio tuners, audio equalizers, and communications channel selection.
Passive filter A filter built exclusively from passive components (resistors, capacitors, inductors) without active devices (transistors, op-amps). Maximum gain is unity (0 dB). Inductors at audio frequencies are large and expensive, making passive filters less popular than active designs for audio applications.
Active filter A filter using op-amps (or other active devices) together with R and C components. Can achieve gains greater than unity, eliminates the need for inductors at audio frequencies, and cascades without loading because of low output impedance. Standard topology at audio frequencies.
Filter design The process of selecting topology and calculating component values to meet a frequency-response specification. Given a target cutoff frequency \(f_c\), resonant frequency \(f_0\), and quality factor Q, design equations yield R, L, C values: \(f_c = 1/(2\pi RC)\), \(Q = f_0/\text{BW} = \omega_0 L/R\).
Audio tone control A filter circuit that allows the user to boost or cut audio signals in specific frequency regions. Bass tone control boosts or attenuates signals below ~300 Hz (shelving filter). Treble tone control boosts or attenuates signals above ~3 kHz. Used in amplifiers, mixers, and consumer audio equipment.
Decibels in audio The standard unit for expressing audio signal levels, gains, and losses. \(0\text{ dBV} = 1\text{ V RMS}\) is the consumer reference. \(0\text{ dBu} = 0.775\text{ V RMS}\) (\(= 1\text{ mW}\) into 600 Ω) is the professional reference. Voltage ratios: \(20\log_{10}(V_2/V_1)\). 6 dB ≈ double voltage; 20 dB = 10× voltage; 40 dB = 100× voltage.
Headroom The difference in decibels between the operating signal level and the clipping level (maximum undistorted output). Expressed as a positive number of dB. Higher headroom means the system can handle transient peaks without distortion. Professional audio equipment typically has 18–24 dB of headroom above 0 dBu.
Dynamic range The ratio in decibels between the loudest undistorted signal and the noise floor of a system. \(DR = \text{Max level} - \text{Noise floor}\). CD audio: ~96 dB. Professional digital audio: ~120–130 dB. Determines the fidelity with which a system can reproduce both loud and quiet signals simultaneously.
Amplifier gain The ratio of output signal amplitude to input signal amplitude, expressed in decibels as \(A_v = 20\log_{10}(V_{out}/V_{in})\). For cascaded stages, gains in dB add: \(A_{total} = A_1 + A_2 + \cdots\). This additive property is a primary reason decibels are used throughout audio engineering.
dBV A logarithmic voltage level measured relative to 1 V RMS: \(L_{dBV} = 20\log_{10}(V/1\text{ V})\). Consumer audio standard. A CD player output of 2 V RMS = +6 dBV. A microphone at 1 mV = −60 dBV. Used in consumer equipment datasheets and specifications.
dBu A logarithmic voltage level measured relative to 0.7746 V RMS (the voltage that produces 1 mW in 600 Ω): \(L_{dBu} = 20\log_{10}(V/0.7746)\). Professional audio standard. Nominal line level in professional equipment is +4 dBu. Used in studio consoles, outboard gear, and professional amplifiers.