Figure 1.1. (a) The pressure exerted by a gas is due to countless elastic collisions between gas molecules and the walls of
the container. (b) If the wall moves against the gas pressure, the rebound velocity increases. (c) Motion with the gas pressure
reduces the particle velocity.
Figure 1.2. Wavelength is defined as the distance between two points at the same place on adjacent cycles. Wavelength is inversely
proportional to frequency.
Figure 1.3. (a) A periodic signal repeats after a fixed time and has a simple spectrum consisting of fundamental plus harmonics.
(b) An aperiodic signal such as noise does not repeat and has a continuous spectrum. (c) A transient contains an anharmonic
spectrum.
Figure 1.4. The structure of the human ear. See text for details.
Figure 1.5. The malleus tensions the tympanic membrane into a conical shape. The ossicles provide an impedance-transforming
lever system between the tympanic membrane and the oval window.
Figure 1.6. (a) The cochlea is a tapering spiral cavity. (b) The cross section of the cavity is divided by Reissner’s membrane
and the basilar membrane. (c) The basilar membrane tapers so that its resonant frequency changes along its length.
Figure 1.7. Having two spaced ears is cool. (a) Off-center sounds result in a phase difference. (b) The distant ear is shaded
by the head, producing a loss of high frequencies. (c) The distant ear detects transient later.
Figure 1.8. A real acoustic event produces a pressure step. The initial step is used for spatial location; equalization time
signifies the size of the source. (Courtesy of Manger Schallwandlerbau.)
Figure 1.9. Contours of equal loudness showing that the frequency response of the ear is highly level dependent (solid line,
age 20; dashed line, age 60).
Figure 1.10. The basilar membrane symbolically uncoiled. (a) Single frequency causes the vibration envelope shown. (b) Changing
the frequency moves the peak of the envelope.
Figure 1.11. The critical bandwidth changes with SPL.
Figure 1.12. Impulse response of the ear showing slow attack and decay as a consequence of resonant behavior.
Figure 1.13. Perceived level of tone burst rises with duration as resonance builds up.
Figure 1.14. (a) Result of adding two sine waves of similar frequency. (b) Spectrum of (a) to infinite accuracy. (c) With
finite accuracy, only a single frequency is distinguished whose amplitude changes with the envelope of (a) giving rise to
beats.
Figure 1.15. Why frequency response matters. (a) Original spectrum determines the timbre of sound. If the original signal
is passed through a system with a deficient frequency response (b), the timbre will be changed (c).
Figure 1.16. Nonlinearity of the transfer function creates harmonies by distorting the waveform. Linearity is extremely important
in audio equipment.
Figure 1.17. (a) A perfectly linear system will pass a number of superimposed waveforms without interference so that the output
spectrum does not change. (b) A nonlinear system causes intermodulation where the output spectrum contains sum and difference
frequencies in addition to the originals.
Figure 1.18. A sine wave is one component of a rotation. When a rotation is viewed from two places at places at right angles,
one will see a sine wave and the other will see a cosine wave. The constant phase shift between sine and cosine is 90° and
should not be confused with the time variant phase angle due to the rotation.
Figure 1.19. The displacement, velocity, and acceleration of a body executing simple harmonic motion (SHM).
Figure 1.20. (a) Ohm’s law: the power developed in a resistor is proportional to the square of the voltage. Consequently,
1 mW in 600 Ω requires 0.775 V. With a sinusoidal alternating input (b), the power is a sine-squared function, which can be
averaged over one cycle. A DC voltage that delivers the same power has a value that is the square root of the mean of the
square of the sinusoidal input to be measured and the reference. The Bel is too large so the decibel (dB) is used in practice.
(b) As the dB is defined as a power ratio, voltage ratios have to be squared. This is conveniently done by doubling the logs
so that the ratio is now multiplied by 20.
Figure 1.21. (a) For a sine wave the conversion factor from peak to rms is . (b) For a square wave the peak and rms voltage
are the same.
Figure 1.22. (a) The logarithm of a number is the power to which the base (in this case 10) must be raised to obtain the number.
(b) Multiplication is obtained by adding logs, division by subtracting. (c) The slide rule has two logarithmic scales whose
length can be added or subtracted easily.
Figure 1.23. (a) The Bel is the log of the ratio between two powers, that between two powers, that to be measured, and the
reference. The Bel is too large so the decibel is used in practice. (b) As the decibel is defined as a power ratio, voltage
ratios have to be squared. This is done conveniently by doubling the logs so that the ratio is now multiplied by 20.
Figure 1.24. (a) Traditional impedance matched source wastes half the signal voltage in the potential divider due to the source
impedance and the cable. (b) Modern practice is to use low-output impedance sources with high-impedance loads.
Figure 2.1. Voltage and power relationships in a circuit.
Figure 2.2. Conversion of dB from logarithmic form to exponential form.
Figure 2.3. Power in dB across a load versus available input power.
Figure 2.4. Relationship of spherical surface area to radius.
Figure 2.5. Ohm’s law nomograph for AC or DC.
Figure 2.6. Typical A-weighted sound levels as measured with a sound level meter. (Courtesy of GenRad.)
Figure 2.7. Typical power and LW values for various acoustic sources.
Figure 2.8. Chart used for determining the combined level of uncorrelated noise signals.
Figure 2.9. The 10log10 x chart.
Figure 2.10. The 20log10 x chart.
Figure 2.11. Voltage, electrical power, Pw, and sound pressure compared.
Figure 2.12. Sine wave voltage values. The average voltage of a sine wave is zero.
Figure 2.13. Volume indicator instrument circuit.
Figure 2.14. Volume indicator instrument scales.
Figure 2.15. Examples of commercial-type VI instrument panels.
Figure 2.16. Relationship between circuit impedance and dB correction value.
Figure 2.17. Equal loudness contours.
Figure 2.18. Audible frequency range.
Figure 2.19. Measurement of harmonic distortion.
Figure 2.20. Methods of measuring distortion.
Figure 2.21. Male speech, normal level 2 ft from the microphone.
Figure 2.22. Ambient noise levels.
Figure 3.1. Predicted atmospheric absorption in dB/100 m for a pressure of 1 atm, temperature of 20°C, and various values
of relative humidity.
Figure 3.2. Absorption of sound for different frequencies and values of relative humidity.
Figure 3.3. Excess attenuation for different frequencies and distances from the source.
Figure 3.4. Effect of temperature differences between the ground and the air on the propagation of sound.
Figure 3.5. Calculating relative levels of reflections.
Figure 3.6. Absorption, reflection, and transmission of boundary surface areas.
Figure 3.7. Effect of thermal gradients in a room.
Figure 3.8. Sound in an open field with no wind.
Figure 3.9. Sound from an orchestra enclosure in an open field with no wind.
Figure 3.10. Sound from an orchestra enclosure with an audience.
Figure 3.11. Sound sources and audiences on a hill.
Figure 3.12. Means of eliminating noise and weather while preserving outdoor conditions.
Figure 3.13. Sound paths in a concert hall.
Figure 3.14. Time relationship of direct and reflected sounds.
Figure 3.15. Vivid proof that there is a fundamental difference between a small reverberant space and a large reverberant
hall.
Figure 3.16. Comparison of direct, early, and reverberant sound fields in an auditorium (reflection adjusted for purposes
of illustration).
Figure 3.17. Graphic representation of near field, free field, and reverberant field.
Figure 4.1. Fixed resistor and potentiometer.
Figure 4.2. Resistors in series and resistors in parallel.
Figure 4.3. Disc and electrolytic capacitors.
Figure 4.4. Capacitors in series and capacitors in parallel.
Figure 4.5. Axial and radial capacitor types.
Figure 4.6. Diode symbol and bias conditions.
Figure 4.7. Transistor terminals.
Figure 4.8. Integrated circuit package outline.
Figure 4.9. Switch terminals.
Figure 4.10. Different switch applications.
Figure 4.11. One-pole, four-way rotary switch.
Figure 4.12. Jack socket conventions.
Figure 4.13. An example of a normally closed jack socket.
Figure 5.1. Full-wave rectifier systems.
Figure 5.2. Simple shunt regulators.
Figure 5.3. Simple series regulators.
Figure 5.4. Series-stabilized PSU.
Figure 5.5. Stabilized PSU (one-half only shown).
Figure 5.6. s/c-protected PSU.
Figure 5.7. Trip circuit.
Figure 5.8. Rotel rhb10 PSU (only one channel shown).
Figure 7.1. Common DIN connector configurations.
Figure 7.2. The phono connector.
Figure 7.3. The RIAA record/replay characteristics used for 33/45 rpm vinyl discs.
Figure 7.4. Circuit layouts that will generate the type of frequency response required for RIAA input equalization.
Figure 7.5. Ortofon MCA-76 head amplifier.
Figure 7.6. The Naim NAC 20 moving coil head amplifier.
Figure 7.7. Braithwaite RAI4 head amplifier. (The output stage is shown in a simplified form.)
Figure 7.8. Head amplifier using a LM394 multiple transistor array.
Figure 7.9. Cascode input moving coil head amplifier.
Figure 7.10. Very low-noise, low-distortion, symmetrical MC head amplifier.
Figure 7.11. Moving coil/moving magnet RIAA input stage in a Technics SU-V10 amplifier.
Figure 7.12. The “Quad” ultralow noise input circuit layout.
Figure 7.13. Bipolar transistor-operated shunt switching. [Also suitable for small-power metal–oxide–semiconductor field-effect
transistor (MOSFET) devices.]
Figure 7.14. Junction FET input switching circuit.
Figure 7.15. Typical diode switching circuit, as used in RF applications.
Figure 7.16. Use of DC blocking capacitors to minimize input switching noises.
Figure 7.17. Typical chip cross section of NPN and PNP silicon planar epitaxial transistors.
Figure 7.18. Typical transfer characteristic of a silicon transistor.
Figure 7.19. Transistor amplifier waveform distortion due to transfer characteristics.
Figure 7.20. Relationship between signal distortion and output signal voltage in a bipolar transistor amplifier.
Figure 7.21. Output current/voltage characteristics of a typical silicon bipolar transistor.
Figure 7.22. Transistor voltage amplifier using a long-tailed pair circuit layout.
Figure 7.23. Circuit effect of stray capacitance.
Figure 7.24. Influence of circuit stray capacitances on stage gain.
Figure 7.25. Gate voltage versus drain current characteristics of field-effect devices.
Figure 7.26. Chip cross section and circuit symbol for lateral MOSFET (small signal type).
Figure 7.27. Chip cross section and circuit symbols for (bipolar) junction FET.
Figure 7.28. Power MOSFET constructions using (a) V and (b) T configurations. (Practical devices will employ many such cells
in parallel.)
Figure 7.29. Thermal noise output as a function of circuit impedance.
Figure 7.30. A two-stage transistor voltage amplifier.
Figure 7.31. A practical two-transistor feedback amplifier.
Figure 7.32. Improved two-stage feedback amplifier.
Figure 7.33. Transistor constant current source.
Figure 7.34. Two-transistor constant current source.
Figure 7.35. Two-terminal constant current source.
Figure 7.36. Load impedance increase by boot-strap circuit.
Figure 7.37. Simple form of a current mirror.
Figure 7.38. Improved form of a current mirror.
Figure 7.39. Use of circuit elaboration to improve the two-stage amplifier of Figure 7.32.
Figure 7.40. Circuit layout of Texas Instruments TL071 op-amp.
Figure 7.41. Method of fabrication of components in a silicon-integrated circuit.
Figure 7.42. Intermodulation distortions produced by the effect of a nonlinear input/output transfer characteristic on a complex
tone.
Figure 7.43. Simple HF two-tone intermodulation distortion test.
Figure 7.44. Two-tone intermodulation distortion test rig.
Figure 7.45. Effect of amplifier slew-rate saturation or transient intermodulation distortion.
Figure 7.46. Typical amplifier layout causing slew-rate saturation.
Figure 7.47. Transient “ringing.”
Figure 7.48. Circuit design aspects that may cause slew-rate limiting.
Figure 7.49. Input HF limiting circuit to lessen slew-rate limiting.
Figure 7.50. Standard gain control circuit.
Figure 7.51. Improved gain control using a multi-pole switch.
Figure 7.52. Bass and treble lift/cut tone control.
Figure 7.53. Slope control.
Figure 7.54. Clapham junction type of tone control.
Figure 7.55. Parametric equalizer control.
Figure 7.56. Graphic equalizer response characteristics.
Figure 7.57. Circuit layout of passive tone control.
Figure 7.58. Negative feedback type tone control circuit.
Figure 7.59. Layout and frequency response of a simple bass-cut circuit (high pass).
Figure 7.60. Layout and frequency response of a simple treble-cut circuit (low pass).
Figure 7.61. Modified bass-cut (high-pass) RC circuit.
Figure 7.62. A modified treble-cut (low-pass) RC circuit.
Figure 7.63. Active RC treble-lift or bass-cut circuit.
Figure 7.64. Active RC treble-cut or bass-lift circuit.
Figure 7.65. The Quad tilt control.
Figure 7.66. Clapham junction tone control.
Figure 7.67. Parametric equalizer circuit.
Figure 7.68. Circuit layout for a graphic equalizer (only four sections shown).
Figure 7.69. Negative feedback type channel balance control.
Figure 7.70. Circuit for producing enhanced or reduced stereo channel separation.
Figure 7.71. Simple stereo channel blend control.
Figure 7.72. Channel separation or blending using matrix addition or subtraction.
Figure 7.73. Steep-cut filter circuits.
Figure 7.74. Characteristics of circuits of Figures 7.73(a) and 7.73(b).
Figure 8.1. Input impedance (load) variation in a typical, simple unbalanced power amplifier input stage.
Figure 8.2. A typical unbalanced input stage.
Figure 8.3. Impedance variation in a typical unbalanced power amplifier input stage as the amplifier warms up.
Figure 8.4. Impedance variation in a typical unbalanced power amplifier’s input stage as the gain control is swept.
Figure 8.5. Most of the common mode noise that CMR defends against is either RF and 50/60 Hz fundamental intercepted in cabling
(Vcml) or 50/60 Hz hum+harmonics caused by magnetic loop, eddy, and leakage currents flowing in the safety ground wiring between
any two equipment locations (Vcm2).
Figure 8.6. Typical high-pass (subsonic protection) filter circuitry.
Figure 8.7. High-pass filter capacitor positions. The potential locations of DC blocking/HPF capacitors in the signal path
of conventional transistor power amplifiers, assuming that gain blocks (the triangles) are internally direct coupled.
Figure 8.8. Direct current servo circuits cause at the very least the same phase and delay error as using a DC-blocking capacitor
conventionally. The upper graph shows the frequency response of a standard two pole servo (2×{1 M.O×470 nF}). The lower graph
shows the phase shift, which is clearly nonlinear below 85 Hz—place a ruler against the line. The curvature indicates a frequency-dependent
signal delay, hence smearing (after Deane Jensen). An alternative, custom three-pole compensating type (C3P) is plotted. This
overcomes the smearing, as the phase shift is much less than 0.1º above 5 Hz, but the amplitude (upper) is now peaking below
1 Hz.
Figure 8.10. Gain pot settings. Shown are six ways of looking at any power amplifier’s gain control; in this instance the
simplest and most familiar “volume” control type. The final knob labeled “input clip volts (pk)” scale is for peak levels
and is correct only for an amplifier that clips at 900 mV rms. In reality, the point would depend on speaker loading, mains
voltage, the program, etc. The constant 9.6-V peak reached at lower levels shows where the input stage clips or where zener-based
input-protection clamping is operating. Courtesy of Citronic Ltd.
Figure 8.11. The family tree of electronically controllable gain and attenuation devices.
Figure 8.12. A typical soft clip circuit as used in the Otis Power Station amplifier. Copyright Mead & Co. 1988.
Figure 9.1. BJT nonlinearity.
Figure 9.2. Decrease in hfe with frequency.
Figure 9.3. Comparative characteristics of valve, germanium, and silicon based BJTs.
Figure 9.4. Biasing circuits.
Figure 9.5. NPN/PNP feedback pair.
Figure 9.6. Grounded base stage.
Figure 9.7. Cascode layouts.
Figure 9.8. Long-tailed pair layouts.
Figure 9.9. Emitter–follower.
Figure 9.10. Compound emitter–follower.
Figure 9.11. Darlington pair.
Figure 9.12. Bipolar breakdown limits.
Figure 9.13. Simple JFET biasing system.
Figure 9.14. Bipolar/FET cascode.
Figure 9.15. FET/FET cascode.
Figure 9.16. Drain current characteristics of junction FET.
Figure 9.17. Current source layout.
Figure 9.18. Power MOSFET.
Figure 9.19. Diode gate protection.
Figure 9.20. Power MOSFET SOAR limits.
Figure 9.21. MOSFET characteristics.
Figure 9.22. MOSFET design styles.
Figure 9.23. MOSFET symbols.
Figure 9.24. Constant current sources.
Figure 9.25. Current mirror circuits.
Figure 9.26. Circuit oddments.
Figure 9.27. Cause of slew rate limiting.
Figure 10.1. The three-stage amplifier structure. There is a transconductance stage, a transadmittance stage (the VAS), and
a unity-gain buffer output stage.
Figure 10.2. The two-stage amplifier structure. A voltage-amplifier output follows the same transconductance input stage.
Figure 10.3. Class-G-series output stage. When the output voltage exceeds the transition level, D3 or D4 turn off and power
is drawn from the higher rails through the outer power devices.
Figure 10.4. A Class-G shunt output stage, composed of two EF output stages with the usual drivers. Vbias3,4 set the output
level at which power is drawn from the higher rails.
Figure 10.5. A conventional double emitter–follower output stage with emitter resistors Re shown.
Figure 10.6. The extra distortion generated by an 6800-μF electrolytic delivering 40 W into 8 Ω. Distortion rises as frequency
falls, as for the small-signal case, but at this current level there is also added distortion in the midband.
Figure 10.7. Distortion with and without a very large output capacitor, the BHC Aerovox 100,000 μF/40 V (40 watts/8 Ω). Capacitor
distortion is eliminated.
Figure 10.8. Distortion with and without an “audiophile” Cerafine 4700-μF/63-V capacitor. Midband distortion is eliminated
but LF rise is much the same as the standard electrolytic.
Figure 11.1. Valve cathode styles.
Figure 11.2. Control grid construction.
Figure 11.3. Triode valve characteristics.
Figure 11.4. A simple valve amplifier.
Figure 11.5. Construction of a beam tetrode.(Courtesy of RCA.)
Figure 11.6. An audio amplifier block diagram.
Figure 11.7. A simple valve amplifier.
Figure 11.8. Output arrangements.
Figure 11.9. A simple 20-W amplifier.
Figure 11.10. A simple phase inverter.
Figure 11.11. A floating paraphase circuit.
Figure 11.13. A split load phase splitter.
Figure 11.14. A simple headphone amplifier.
Figure 11.12. A long-tailed pair circuit.
Figure 11.15. Equivalent circuits of idealized coupling transformer.
Figure 11.16. A magnetization curve.
Figure 11.17. (a) Power output vs THD. (b) Power output curve.
Figure 11.18. An anode dissipation curve.
Figure 12.1. Block diagram of system for SPICE stability testing.
Figure 12.2. SPICE results in the time domain. As Cdom increases, the response V(7) becomes slower and the error (g1) declines
more slowly. The input is the step-function V(3) at the bottom.
Figure 12.3. SPICE simulation in the frequency domain. As the compensation capacitor is increased, the closed-loop bandwidth
decreases proportionally.
Figure 12.4. Adding a second pole P2 causes overshoot with smaller values Cdom, but cannot bring about sustained oscillation.
Figure 12.5. The frequency responses that go with the transient plots of Figure 12.4. The response peaking for Cdom=50 pF
is very small compared with the transient overshoot.
Figure 12.6. Manipulating the P2 frequency can make ringing more prolonged but it is still not possible to provoke sustained
oscillation.
Figure 12.7. Adding a third pole makes possible true instability with an exponentially increasing amplitude of oscillation.
Note the unrealistic voltage scale on this plot.
Figure 13.1. A grounding system for a typical power amplifier.
Figure 13.2. Pitfalls of adding a “technical ground” to a system that is already grounded via the mains.
Figure 13.3. A poor cable layout in the PSU at the left wraps a loop around the transformer and induces ground currents.
Figure 13.4. The injection of mains current into the ground wiring via transformer interwinding capacitance.
Figure 13.5. If ground current flows through the path F′FGG′, then the relatively high resistance of the PCB tracks produces
voltage drops between the internal circuit blocks.
Figure 13.6. The correct method of dealing with ground currents; they are diverted away from internal circuitry.
Figure 13.7. Use of a balanced mains supply to cancel ground currents stemming from interwinding capacitance in the mains
transformer. This is an expensive solution.
Figure 14.1. Audio system of the future based on data technology.
Figure 14.2. In pulse code modulation the analog waveform is measured periodically at the sampling rate. The voltage (represented
here by the height) of each sample is then described by a whole number. The whole numbers are stored or transmitted rather
than the waveform itself.
Figure 14.3. Binary digits (a) can only have two values. At (b) some everyday binary terms are shown, whereas (c) shows some
terms that cannot be expressed by a binary digit.
Figure 14.4. An ideal binary signal (a) has two levels. After transmission it may look like (b), but after slicing the two
levels can be recovered. Noise on a sliced signal can result in jitter (c), but reclocking combined with slicing makes the
final signal identical to the original as shown in (d).
Figure 14.5. A large number of real phenomena can be used to represent binary data.
Figure 14.6. In a binary number, the digits represent increasing powers of two from the LSB. Also defined here are MSB and
wordlength. When the wordlength is eight bits, the word is a byte. Binary numbers are used as memory addresses, and the range
is defined by the address wordlength. Some examples are shown here.
Figure 14.7. The wordlength of a sample controls the resolution as shown in (a). The ability to address memory locations is
also determined in the same way as in (b).
Figure 14.8. In (a) two convertors are joined by a serial link. Although simple, this system is deficient because it has no
means to prevent noise on the clock lines causing jitter at the receiver. In (b) a phase-locked loop is incorporated, which
filters jitter from the clock.
Figure 14.9. In the digital sampler, the recording medium is a RAM. Recording time available is short compared with other
media, but access to the recording is immediate and flexible as it is controlled by addressing the RAM.
Figure 14.10. If the memory address is arranged to come from a counter that overflows, the memory can be made to appear circular.
The write address then rotates endlessly, overwriting previous data once per revolution. The read address can follow the write
address by a variable distance (not exceeding one revolution) and so a variable delay takes place between reading and writing.
Figure 14.11. In nonreal-time transmission, data are transferred slowly to a storage medium, which then outputs real-time
data. Recordings can be downloaded to the home in this way.
Figure 14.12. (a) Time compression is used to shorten the length of track needed by the video. Heavily time-compressed audio
samples can then be recorded on the same track using common circuitry. In MPEG, multiplexing allows data from several TV channels
to share one bit stream (b).
Figure 14.13. In cases where error correction is inadequate, concealment can be used, provided that the samples have been
ordered appropriately in the recording. Odd and even samples are recorded in different places as shown here. As a result,
an uncorrectable error causes incorrect samples to occur singly, between correct samples. In the example shown, sample 8 is
incorrect, but samples 7 and 9 are unaffected and an approximation to the value of sample 8 can be had by taking the average
value of the two. This interpolated value is substituted for the incorrect value.
Figure 14.14(a). Interleaving is essential to make error-correction schemes more efficient. Samples written sequentially in
rows into a memory have redundancy P added to each row. The memory is then read in columns and data are sent to the recording
medium. On replay the nonsequential samples from the medium are deinterleaved to return them to their normal sequence. This
breaks up the burst error (shaded) into one error symbol per row in the memory, which can be corrected by the redundancy P.
Figure 14.14(b). In addition to the redundancy P on rows, inner redundancy Q is also generated on columns. On replay, the
Q code checker will pass on flag F if it finds an error too large to handle itself. Flags pass through the deinterleave process
and are used by the outer error correction to identify which symbol in the row needs correcting with P redundancy. The concept
of crossing two codes in this way is called a product code.
Figure 14.15. The bit stream types of MPEG-2. See the text for details.
Figure 14.16. In a hard disk recorder, a large-capacity memory is used as a buffer or time base corrector between the convertors
and the disk. The memory allows the convertors to run constantly, despite the interruptions in disk transfer caused by the
head moving between tracks.
Figure 14.17. A disk-based audio recorder can capture audio and transmit compressed audio files over the Internet.
Figure 14.18. Block diagram of digital audio tape.
Figure 15.1. The plot of tidal height versus diurnal time for Portsmouth, United Kingdom, time in hours. Mariners will note
the characteristically distorted shape of the tidal curve for the Solent. We could mark the height as a continuous function
of time using the crude arrangement shown.
Figure 15.2. Sending tidal height data to a colleague in two ways: (a) by tracing out the curve shape using a pen attached
to a variable resistor and using a meter driven pen at the far end and (b) by calling out numbers, having agreed what the
scale and resolution of the numbers will be.
Figure 15.3. Symbols and truth tables for the common basic gates. For larger arrays of gates it is more useful to express
the overall logical function as a set of sums (the OR function) and products (the AND function); this is the terminology used
by gate array designers.
Figure 15.4. A simple latch. In this example, the outputs of each of two NAND gates are cross coupled to one of the other
inputs. The unused input is held high by a resistor to the positive supply rail. The state of the gate outputs will be changed
when one of the inputs is grounded and this output state will be steady until the other input is grounded or until the power
is removed. This simple circuit, the R-S flip-flop, has often been used to debounce mechanical contacts and as a simple memory.
Figure 15.5(a). The simplest counter is made up of a chain of edge-triggered D-type FFs. For a long counter, it can take a
sizeable part of a clock cycle for all of the counter FFs to change state in turn. This ripple through can make decoding the
state of the counter difficult and can lead to transitory glitches in the decoder output, indicated in the diagram as points
where the changing edges do not exactly line up. Synchronous counters in which the clock pulse is applied to all of the counting
FFs at the same time are used to reduce the overall propagation delay to that of a single stage.
Figure 15.5(b). This arrangement of FFs produces the shift register. In this circuit, a pattern of Is and 0 s can be loaded
into a register (the load pulses) and then can be shifted out serially one bit at a time at a rate determined by the serial
clock pulse. This is an example of a parallel in serial out (PISO) register. Other varieties include LIFO (last in first out),
SIPO (serial in parallel out), and FILO (first in last out). The diagrams assume that unused inputs are tied to ground or
to the positive supply rail as needed.
Figure 15.6(a). Parallel transmission: a data strobe line (the—sign means active low) would accompany the bit pattern to
clock the logic state of each data line on its falling edge and is timed to occur some time after the data signals have been
set so that any reflections, cross talk, or skew in the timing of the individual data lines will have had time to settle.
After the signal has returned to the high state, the data lines are reset to 0 (usually they would only be changed if data
in the next byte required a change).
Figure 15.6(b). Serial transmission requires the sender and receiver to use and recognize the same signal format or protocol,
such as RS232. For each byte, the composite signal contains a start bit, a parity bit, and a stop bit using inverted logic
(1=−12 V; 0=−12 V). The time interval between each bit of the signal (the start bit, parity bit, stop bit, and data bits)
is fixed and must be kept constant.
Figure 15.7. A practical problem arose where the data signal was intended to be clocked in using the rising edge of a separate
clock line, but excessive ringing on the clock line caused the data line to be sampled twice, causing corruption. In addition,
due to the loading of a large number of audio channels, the actual logic level no longer achieved the 4.5-V target required
for acceptable noise performance, increasing the susceptibility to ringing. The other point to note is that the falling edge
of the logic signals took the data line voltage to a negative value, and there is no guarantee that the receiving logic element
would not produce an incorrect output as a consequence.
Figure 15.8. (a) An apparently simple noise, such as a single string on a guitar, produces a complicated waveform, sensed
in terms of pitch. The important part of this waveform is the basic period of the waveform, its fundamental frequency. The
smaller detail is due to components of higher frequency and lower level. (b) An alternative description is analysis into the
major frequency components. If processing accuracy is adequate, then the description in terms of amplitudes of harmonics (frequency
domain) is identical to the description in terms of amplitude and time (time domain).
Figure 15.9. The relationship between cosine (real) and sine (imaginary) waveforms in the complex exponential eJWT. This assists
in understanding the concept of phase. Note that one property of the spiral form is that its projection onto any plane parallel
to the time axis will produce a sinusoidal waveform.
Figure 15.10. The simple resistor and capacitor attenuator can be analyzed to provide us with an expression for the output
voltage and the output phase with respect to the input signal.
Figure 15.11(a). Composing a square wave from the harmonics is an elementary example of a Fourier series. For the square wave
of unit amplitude the series is of the form.
Figure 15.11(b). In practice, a truly symmetrical shape is rare, as most practical methods of limiting the audio bandwidth
do not exhibit linear phase, but delay progressively the higher frequency components. Band-limiting niters respond to excitation
by a square wave by revealing the effect of the absence of higher harmonics and the so-called “ringing” is thus not necessarily
the result of potentially unstable filters.
Figure 15.11(c). The phase response shows the kind of relative phase shift that might be responsible.
Figure 15.11(d). The corresponding group delay curve shows a system that reaches a peak delay of around 16 μs.
Figure 15.12. (a) A pulse with a period of 2π seconds is repeated every T seconds, producing the spectrum as shown. The spectrum
appears as having negative amplitudes, as alternate “lobes” have the phase of their frequency components inverted, although
it is usual to show the modulus of the amplitude as positive and to reflect the inversion by an accompanying plot of phase
against frequency. The shape of the lobes is described by the simple relationship: (b) A further example of the duality between
time and frequency showing that a widely spread spectrum will be the result of a narrow pulse. The sum of the energy must
be the same for each so that we would expect a narrow pulse to be of large amplitude if it is to carry much energy. If we
were to use such a pulse as a test signal we would discover that the individual amplitude of any individual frequency component
would be quite small. Thus when we do use this signal for just this purpose we will usually arrange to average the results
of a number of tests.
Figure 15.13. A 2-bit full adder needs to be able to handle a carry bit from an adder handling lower order bits and similarly
provide a carry bit. A large adder based on this circuit would suffer from the ripple through of the carry bit as the final
sum would not be stable until this had settled. Faster adding circuitry uses look-ahead carry circuitry.
Figure 15.14(a). The amplitude distribution characteristics of noise can be described in terms of the amplitude probability
distribution characteristic. A square wave of level 0 or +5 V can be described as having a rectangular probability distribution
function (RPDF). In the case of the 5-bit example, which we are using, the RPDF wave form can be considered to have a value
of +0.12 or −0.12 [(meaning +0.5 or −0.5), equal chances of being positive or negative].
Figure 15.14(b). The addition of two uncorrelated RPDF sequences gives rise to one with triangular distribution (TPDF). When
this dither signal is added to a digitized signal it will always mark the output with some noise, as there is a finite possibility
that the noise will have a value greater than 0, so that as a digitized audio signal fades to zero value, the noise background
remains fairly constant. This behavior should be contrasted with that of RPDF for which, when the signal fades to zero, there
will come a point at which the accompanying noise also switches off. This latter effect may be audible in some circumstances
and is better avoided. A wave form associated with this type of distribution will have values ranging from +1.02 through 02
to −1.02.
Figure 15.14(c). Noise in the analogue domain is often assumed to have a Gaussian distribution. This can be understood as
the likelihood of the waveform having a particular amplitude. The probability of an amplitude x occurring can be expressed
as where μ is the mean value, σ is the variance, and X is the sum of the squares of the deviations x from the mean. In practice,
a “random” waveform, which has a ratio between the peak to mean signal levels of 3, can be taken as being sufficiently Gaussian
in character. The spectral balance of such a signal is a further factor that must be taken into account if a full description
of a random signal is to be described.
Figure 15.14(d). The sinusoidal wave form can be described by the simple equation: , where x(t) is the value of the sinusoidal
wave at time t, A is the peak amplitude of the waveform, f is the frequency in Hz, and t is the time in seconds and its probability
density function is as shown here.
Figure 15.14(e). A useful test signal is created when two sinusoidal waveforms of the same amplitude but unrelated in frequency
are added together. The resulting signal can be used to check amplifier and system nonlinearity over a wide range of frequencies.
The test signal will comprise two signals to stimulate the audio system (for testing at the edge of the band, 19 and 20 kHz
can be used) while the output spectrum is analyzed and the amplitude of the sum and difference frequency signals is measured.
This form of test is considerably more useful than a THD test.
Figure 15.15(a). To explain the ideas behind digital filtering, we review the shape of the tidal height curve (Portsmouth,
UK, spring tides) for its underlying detail. The pen Plotter trace would also record every passing wave, boat, and breath
of wind; all are overlaid on the general shape of the curve.
Figures 15.15(b)–15(d). For a small portion of the curve, make measurements at each interval. In the simplest averaging scheme
we take a block of five values, average them, and then repeat the process with a fresh block of five values. This yields a
relatively coarse stepped waveform. (c) The next approach carries out the averaging over a block of five samples but shifts
the start of each block only one sample on at a time, still allowing each of the five sample values to contribute equally
to the average each time. The result is a more finely structured plot that could serve our purpose. (d) The final frame in
this sequence repeats the operations of (c) except that the contribution that each sample value makes to the averaging process
is weighted, using a five-element weighting filter or window for this example whose weighting values are derived by a modified
form of least-squares averaging. The values that it returns are naturally slightly different from those of (c).
Figure 15.15(e). A useful way of showing the process being carried out in (d) is to draw a block diagram in which each time
that a sample value is read it is loaded into a form of memory while the previous value is moved on to the next memory stage.
We take the current value of the input sample and the output of each of these memory stages and multiply them by the weighting
factor before summing them to produce the output average. The operation can also be expressed in an algebraic form in which
the numerical values of the weighting coefficients have been replaced by an algebraic symbol: This is a simple form of a type
of digital filter known as a finite impulse response or transversal filter. In the form shown here it is easy to see that
the delay of the filter is constant and thus the filter will show linear phase characteristics. If the input to the filter
is an impulse, the values you should obtain at the output are identical, in shape, to the profile of the weighting values
used. This useful property can be used in the design of filters, as it illustrates the principle that the characteristics
of a system can be determined by applying an impulse to it and observing the resultant output.
Figure 15.16(a). An impulse is applied to a simple system whose output is a simple exponential decaying response:.
Figure 15.16(b). A digital filter based on an FIR structure would need to be implemented as shown. The accuracy of this filter
depends on just how many stages of delay and multiplication we can afford to use. For the five stages shown, the filter will
cease to emulate an exponential decay after only 24 dB of decay. The response to successive n samples is .
Figure 15.16(c). This simple function can be emulated by using a single multiplier and adder element if some of the output
signal is fed back and subtracted from the input. Use of a multiplier in conjunction with an adder is often referred to as
a multiplier-accumulator or MAC. With the correct choice of coefficient in the feedback path, the exponential decay response
can be exactly emulated:. This form of filter will continue to produce a response forever unless the arithmetic elements are
no longer able to handle the decreasing size of the numbers involved. For this reason, it is known as an infinite impulse
response (IIR) filter or, because of the feedback structure, a recursive filter. Whereas the response characteristics of FIR
filters can be gleaned comparatively easily by inspecting the values of the coefficients used, the same is not true of IIR
filters. A more complex algebra is needed in order to help in the design and analysis, which are not covered here.
Figure 15.17(a). The equivalent of the analogue first-order high- and low-pass filters requires a single delay element. Multipliers
are used to scale the input (or output) values so that they lie within the linear range of the hardware. Digital filter characteristics
are quite sensitive to the values of the coefficients used in the multipliers. The output sequence can be described as . If
0>a2>−1 the structure behaves as a first-order lag. If a2>0 than the structure produces an integrator. The output can usually
be kept in range by ensuring that a1=1−a2.
Figure 15.17(b). The arrangement for achieving high-pass filtering and differentiation again requires a single delay element.
The output sequence is given by The filter has no feedback path so it will always be stable. Note that a1=−1 and with a2=0
and a3=1 the structure behaves as a differentiator. These are simple examples of first-order structures and are not necessarily
the most efficient in terms of their use of multiplier or adder resources. Although a second-order system would result if
two first-order structures were run in tandem, full flexibility of second-order IIR structures requires recursive structures.
Perhaps the most common of these emulates the analogue biquad (or twin integrator loop) filter.
Figure 15.17(c). To achieve the flexibility of signal control, which analogue equalizers exhibit in conventional mixing desks,
an IIR filter can be used. Shown here it requires two single-sample value delay elements and six multiplying operations each
time it is presented with an input sample value. We have symbolized the delay elements by using the z−1 notation, which is
used when digital filter structures are formally analyzed. The output sequence can be expressed as .The use of z21 notation
allows us to express this difference or recurrence equation as . The transfer function of the structure is the ratio of the
output over the input, just as it is in the case of an analogue system. In this case the input and output happen to be sequences
of numbers, and the transfer function is indicated by the notation H(z): . Figure 15.17(c): continued: The value of each of
the coefficients can be determined from knowledge of the rate at which samples are being made available, Fs, and your requirement
for the amount of cut or boost and of the Q required. One of the first operations is that of prewarping the value of the intended
center frequency fc in order to take account of the fact that the intended equalizer center frequency is going to be comparable
to the sampling frequency. The “warped” frequency is given by . And now for the coefficients: The mathematics concerned with
filter design certainly appear more complicated than that which is usually associated with analogue equalizer design. The
complication does not stop here though, as a designer must take into consideration the various compromises brought on by limitations
in cost and hardware performance.
Figure 15.18. (a) Interpolation involves guessing the value of the missing sample. The fastest guess uses the average of the
two adjacent good sample values, but an average based on many more sample values might provide a better answer. The use of
a simple rectangular window for including the values to be sampled will not lead to as accurate a replacement value. The effect
is similar to that caused by examining the spectrum of a continuous signal that has been selected using a simple rectangular
window. The sharp edges of the window function will have frequency components that cannot be separated from the wanted signal.
(b) A more intelligent interpolation uses a shaped window that can be implemented as an FIR, or transversal, filter with a
number of delay stages, each contributing a specific fraction of the sample value of the output sum. This kind of filter is
less likely than the simple linear average process to create audible transitory aliases as it fills in damaged sample values.
Figure 15.19. Correlation is a process in which one sequence of sample values is checked against another to see just how similar
both sequences are. A sinusoidal wave correlated with itself (a process called auto correlation) will produce a similar sinusoidal
wave. By comparison, a sequence of random sample values will have an autocorrelation function that will be zero everywhere
except at the point where the samples are exactly in phase, yielding a band-limited impulse.
Figure 15.20. (a) In the time domain the process of sampling is like one of using a sequence of pulses, whose amplitude is
either 1 or 0, and multiplying it by the value of the sinusoidal waveform. A sample and hold circuit holds the sampled signal
level steady while the amplitude is measured. (b) At a higher frequency, sampling is taking place approximately three times
per sinusoid input cycle. Once more it is possible to see that even by simply joining the sample spikes the frequency information
is still retained. (c) This plot shows the sinusoid being under sample, and on reconstituting the original signal from the
spikes the best-fit sinusoid is the one shown as the dashed line. This new signal will appear as a perfectly proper signal
to any subsequent process and there is no method for abstracting such aliases from properly sampled signals. It is necessary
to ensure that frequencies greater than half of the sampling frequency Fs are filtered out before the input signal is presented
to a sampling circuit. This filter is known as an antialiasing filter.
Figure 15.21. (a) The frequency domain view of the sampling operation requires us to recognize that the spectrum of a perfectly
shaped sampling pulse continues forever. In practice sampling, waveforms do have finite width and practical systems do have
limited bandwidth. We show here the typical spectrum of a musical signal and the repeated spectrum of the sampling pulse using
an extended frequency axis. Note that even modern musical signals do not contain significant energy at high frequencies and,
for example, it is exceedingly rare to find components in the 10-kHz region more than −30 dB below the peak level. (b) The
act of sampling can also be appreciated as a modulation process, as the incoming audio signal is being multiplied by the sampling
waveform. The modulation will develop sidebands, which are reflected on either side of the carrier frequency (the sampling
waveform), with a set of sidebands for each harmonic of the sampling frequency. The example shows the consequence of sampling
an audio bandwidth signal that has frequency components beyond F2/2, causing a small but potentially significant amount of
the first lower sideband of the sampling frequency to be folded or aliased into the intended audio bandwidth. The resulting
distortion is not harmonically related to the originating signal and can sound truly horrid. Use of an antialias filter before
sampling restricts the leakage of the sideband into the audio signal band. The requirement is ideally for a filter with an
impossibly sharp rate of cutoff, and in practice a small guard band is allowed for tolerance and finite cutoff rates. Realizing
that the level of audio signal with a frequency around 20 kHz is typically 60 dB below the peak signal level, it is possible
to perform practical filtering using seventh-order filters. However, even these filters are expensive to manufacture and represent
a significant design problem in their own right.
Figure 15.22. An elementary sample and hold circuit using a fast low distortion semiconductor switch that is closed for a
short time to allow a small-valued storage capacitor to charge up to the input voltage. The buffer amplifier presents the
output to the quantizer.
Figure 15.23. The simplest ADC uses a ramp generator, which is started at the beginning of conversion. At the same time a
counter is reset and the clock pulses are counted. The ramp generator output is compared with the signal from the sample and
hold and when the ramp voltage equals the input signal the counter is stopped. Assuming that the ramp is perfectly linear
(quite difficult to achieve at high repetition frequencies) the count will be a measure of the input signal. The problem for
audio bandwidth conversion is the speed at which the counter must run in order to achieve a conversion within approximately
20 μs. This is around 3.2768 GHz and the comparator would need to be able to change state within 150 μs with, in the worst
case, less than 150 μV of differential voltage. There have been many developments of this conversion technique for instrumentation
purposes.
Figure 15.24. The SAR operates with a DAC and a comparator, initially reset to zero. At the first clock period the MSB is
set and the resulting output of the DAC is compared to the input level. In the example given here the input level is greater
than this and so the MSB value is retained and, at the next clock period, the next MSB is set. In this example the comparator
output indicates that the DAC output is too high, the bit is set to 0, and the next lower bit is set. This is carried out
until all of the DAC bits have been tried. Thus a 16-bit ADC would require only 17 clock periods (one is needed for reset)
in which to carry out a conversion.
Figure 15.25. The basic form of the R–2R digital to analogue (DAG) converter is shown here implemented by ideal current switches.
The reference voltage can be an audio bandwidth signal and the DAC can be used as a true four quadrant multiplying converter
to implement digitally controlled analogue level and equalization changes. Other forms of switching currents are also used
and these may not offer a true multiplication facility.
Figure 15.26. The input sinusoid is shown here prior to sampling as a dotted line superimposed on the staircase shape of the
quantized input signal. The two’s complement value of the level has been shown on the left-hand edge. The error signal is
the difference between the quantized value and the ideal value assuming a much finer resolution. The error signal, or quantizing
noise, lies in the range of ±l q. Consideration of the mean square error leads to the expression for the rms value of the
quantizing noise: where q is the size of a quantizing level. The maximum rms signal amplitude that can be described is .
Together the expression combines to give the expression for SNR(indB): .
Figure 15.27(a). Adding a small amount of random noise to the signal prior to quantizing can help disguise the otherwise highly
correlated quantizing noise. Aided by the binary modulation action of the quantizer, the sidebands of the noise are spread
across the whole audio band width and to a very great degree their correlation with the original distortion signal is broken
up. In this illustration the peak-to-peak amplitude of the noise has been set at ±1.5 q.
Figure 15.27(b). The quantizer maps the noisy signal onto one of a range of unique levels as before.
Figure 15.27(c). The resulting quantizing noise can be compared with the original signal and this time you can see that the
noise waveform has lost the highly structured relationship shown in Figure 15.26.
Figure 15.28. Finally the DAC output is fed to a zero order hold circuit which performs a similar operation to the sample
and hold circuit and then to a reconstruction or output antialiasing filter. The plot of the spectral shape of the zero order
hold shows that there are frequency components, at decreasing levels, at harmonic intervals equal to Fs.
Figure 15.29. A chain of resistors provides a series of reference voltages for a set of comparators whose other input is the
input signal. An 8-bit encoder will need 255 comparators. Their output will drive an encoder that maps the output state of
the 255 comparators onto an 8-bit word. The NMINV control line is used to convert the output word from an offset binary count
to a two’s complement form. A 16-bit converter would require an impracticably large number of comparators (65536) in addition
to posing serious difficulties to setting the 65536 resistor values to the required tolerance value. The technique does have
one virtue in speed and in not needing a sample and hold amplifier to precede it.
Figure 15.30. The relationship between digital input word and analogue output current is not linear. The sign bit is the MSB
and the next three bits are used to set the chord slope. The lower 4 bits set the output steps within each chord. The drawing
shows the equivalent output for a linear 8-bit DAC.
Figure 15.31(a). The oversampling process adds zero valued dummy samples to the straight sampled signal. If oversampling is
being carried out in the DAC direction, then the digital sequence of samples is treated as if these extra dummy samples had
been added in. The sequence is then filtered using an interpolation filter, which creates useful values for the dummy samples.
Figure 15.31(b). At the new sample rate (shown here as 4×Fs). The spectrum of the signal now extends to 4×Fs, although there
is only audio content up to Fs/2. Thus when the signal is passed to the DAC element (an element that will have to be able
to work at the required oversampling speed) the resulting audio spectrum can be filtered simply from the nearest interfering
frequency component, which will be at 4×Fs. Note that the process of interpolation does not add information. If the oversampling
is being carried out in the ADC direction, the analogue audio signal itself will be sampled and quantized at the higher rate.
The next stage requires the reduction of the sequence of data by a factor of four. First data are filtered in order to remove
components in the band between the top of the required audio band and the lower of the 4×Fs sideband and then the data sequence
can be simply subsampled (only one data word out of each four is retained).
Figure 16.1. Digitally encoded/decoded waveform.
Figure 16.2. Quantization error.
Figure 16.3. PCM frequency spectrum (a) when sampled at 44.1 kHz and (b) when four times oversampled.
Figure 16.4. Responses of a low-pass LC filter.
Figure 16.5. Steep-cut LP filter circuit.
Figure 16.6. Basic CD recording system.
Figure 16.7. The EFM process.
Figure 16.8. Single-beam optical readout system.
Figure 16.9. Replay schematic layout.
Figure 16.10. Dynamic matching DAC.
Figure 16.11. Comb filter frequency response.
Figure 16.12. A basic oversampling filter.
Figure 16.13. Impulse response of low-pass FIR filter. Zeros are l/fs apart; cutoff frequency=fs/2.
Figure 16.14. A linear phase LP filter.
Figure 16.15. Effect of four times oversampling and interpolation of intermediate values.
Figure 16.16. Signal noise spectrum after “noise shaping.”
Figure 16.17. Parity bit error correction. Logic: 0+0=0, 0+1=1, 1+1=0.
Figure 16.18. Burst error correction by interleaving.
Figure 17.1. Typical ferrite head windings are placed on alternate sides to save space, but parallel magnetic circuits have
high cross talk.
Figure 17.2. Basic digital recording. At (a) the write current in the head is reversed from time to time, leaving a binary
magnetization pattern shown at (b). When replayed, the waveform at (c) results because an output is only produced when flux
in the head changes. Changes are referred to as transitions.
Figure 17.3. The major mechanisms defining magnetic channel bandwidth.
Figure 17.4. The sensing element in a magneto-resistive head. Transitions are not sensitive to the polarity of the flux, only
the magnitude. At (a) the track magnetization is shown, which causes a bidirectional flux variation in the head as at (b)
resulting in the magnitude output at (c). However, if the flux in the head due to the track is biased by an additional field,
it can be made unipolar as at (d) and the correct output waveform is obtained.
Figure 17.5. (a) Peak shift distortion can be reduced by (b) equalization in replay or (c) precompensation.
Figure 17.6. CD readout principle and dimensions. The presence of a bump causes destructive interference in the reflected
light.
Figure 17.7. The thermomagneto-optical disk uses the heat from a laser to allow a magnetic field to record on the disk.
Figure 17.8. Frequency response of laser pickup. Maximum operating frequency is about half of cutoff frequency Fc.
Figure 17.9. In the digital sampler, the recording medium is a RAM. Recording time available is short compared to other media,
but access to the recording is immediate and flexible as it is controlled by addressing the RAM.
Figure 17.10. Time base corrector (TBC) memory is addressed by a counter that overflows periodically to give a ring structure.
Memory allows read side to be nonsynchronous with write side.
Figure 17.11. In time compression, the unbroken real-time stream of samples from an ADC is broken up into discrete blocks.
This is accomplished by the configuration shown here. Samples are written into one RAM at the sampling rate by the write clock.
When the first RAM is full, the switches change over, and writing continues into the second RAM while the first is read using
a higher frequency clock. The RAM is read faster than it was written and so all data will be output before the other RAM is
full. This opens spaces in the data flow, which are used as described in the text.
Figure 17.12. In a recorder using time compression, the samples can be returned to a continuous stream using RAM as a TBC.
The long-term data rate has to be the same on the input and output of the TBC or it will lose data. This is accomplished by
comparing the read and write addresses and using the difference to control the tape speed. In this way the tape speed will
automatically adjust to provide data as fast as the reference clock takes it from the TBC.
Figure 17.13. In cases where the error correction is inadequate, concealment can be used provided that the samples have been
ordered appropriately in the recording. Odd and even samples are recorded in different places as shown here. As a result an
uncorrectable error causes incorrect samples to occur singly, between correct samples. In the example shown, sample 8 is incorrect,
but samples 7 and 9 are unaffected and an approximation to the value of sample 8 can be had by taking the average value of
the two. This interpolated value is substituted for the incorrect value.
Figure 17.14(a). Interleaving is essential to make error correction schemes more efficient. Samples written sequentially in
rows into a memory have redundancy P added to each row. The memory is then read in columns and data are sent to the recording
medium. On replay, the nonsequential samples from the medium are deinterleaved to return them to their normal sequence. This
breaks up the burst error (shaded) into one error symbol per row in the memory, which can be corrected by the redundancy P.
Figure 17.14(b). In addition to the redundancy P on rows, inner redundancy Q is also generated on columns. On replay, the
Q code checker will pass on flags F if it finds an error too large to handle itself. The flags pass through the deinterleave
process and are used by the outer error correction to identify which symbol in the row needs correcting with P redundancy.
The concept of crossing two codes in this way is called a product code.
Figure 17.14(c). Convolutional interleave is shown. Instead of assembling samples in blocks, the process is continuous and
uses RAM delays. Samples are formed into columns in an endless array. Each row of the array is subject to a different delay
so that after the delays, samples in a column are available simultaneously which were previously on a diagonal. Code words
which cross one another at an angle can be obtained by generating redundancy before and after the delays.
Figure 17.15. A typical phase-locked loop where the VCO is forced to run at a multiple of the input frequency. If the input
ceases, the output will continue at the same frequency until it drifts.
Figure 17.16. At the decision points, the receiver must make binary decisions about the voltage of the signal, whether it
is above or below the slicing level. If the eyes remain open, this will be possible in the presence of noise and jitter.
Figure 17.17. FM channel code, also known as Manchester code or biphase mark, is used in AESEBU interface and for time code
recording. The waveform is encoded as shown here. See text for details.
Figure 17.18. In RDAT an 8/10 code is used for recording. Each 8 data bits are represented by a unique waveform generated
by 10 channel bits. A channel bit one causes a transition to be recorded. The transitions cannot be closer than 0.8 of a data
bit, and this is the jitter resistance. This is rather better than FM, which has a jitter window of only 0.5 bits.
Figure 17.19. During an audio replay sequence, the silo is constantly emptied to provide samples and is refilled in blocks
by the drive.
Figure 17.20. Block diagram of PCM adaptor. Note the dub connection needed for producing a digital copy between two VCRs.
Figure 17.21. Typical line of video from PCM-1610. The control bit conveys the setting of the preemphasis switch or the sampling
rate, depending on the frame. The bits are separated using only the timing information in the sync pulses.
Figure 17.22. Block diagram of one channel of a stationary head digital audio recorder. See text for details of the function
of each block. Note the connection from the TBC to the capstan motor so that the tape is played at such a speed that the TBC
memory neither underflows nor overflows.
Figure 17.23. Rotary head recorder. Helical scan records long diagonal tracks.
Figure 17.24. The use of time compression reduces the wrap angle necessary, at the expense of raising the frequencies in the
channel.
Figure 17.25. Block diagram of RDAT.
Figure 17.26. In azimuth recording (a), the head gap is tilted. If the track is played with the same head, playback is normal,
but the response of the reverse azimuth head is attenuated (b).
Figure 17.27. In azimuth recording, the tracks can be made narrower than the head pole by overwriting the previous track.
Figure 17.28. (a) A correctly tracking head produces pilot-tone bursts of identical amplitude. (b) The head is off-track,
and the first pilot burst becomes larger, whereas the second becomes smaller. This produces the tracking error.
Figure 17.29. In DCC audio and auxiliary data are recorded on nine parallel tracks along each side of the tape as shown at
(a) The replay head shown at (b) carries magnetic poles, which register with one set of nine tracks. At the end of the tape,
the replay head rotates 180° and plays a further nine tracks on the other side of the tape. The replay head also contains
a pair of analogue audio magnetic circuits that will be swung into place if an analogue cassette is to be played.
Figure 17.30. In DCC, PCM data from the convertors are reduced to one-quarter of the original rate prior to distribution over
eight tape tracks (plus an auxiliary data track). This allows a slow linear tape speed that can only be read with an MR head.
The data reduction unit is mirrored by the expansion unit on replay.
Figure 17.31. Editing a convolutionally interleaved recording. (a) The existing recording is decoded and re-encoded. After
some time, record can be enabled at (b) when the existing tape pattern is being rerecorded. The crossfader can then be operated,
resulting (c) in an interleaved edit on the tape.
Figure 18.1. AES/EBU interface.
Figure 18.2. SPDIF interface.
Figure 18.3. Digital audio data format.
Figure 18.4. Practical digital audio interfaces.
Figure 18.5. Optical digital audio interface and adaptation to coaxial SPDIF.
Figure 18.6. Data structure of MADI, multichannel audio interface.
Figure 19.1. Subband quantization and how it relates to the masking profile.
Figure 19.2. Cosine function.
Figure 19.3. Dolby Digital as originally coded on film stock.
Figure 20.1. Atari ST computer.
Figure 20.2. FastEddie digital audio editor.
Figure 20.3. Audio editing with cross-fades for edit points.
Figure 20.4. Multitrack audio recording combined with MIDI sequencing.
Figure 20.5. Creative Labs’ Creative Mixer utility.
Figure 20.6. Chain-code generator.
Figure 21.1. The Philips CDR 770 CD recorder deck.
Figure 21.2. Block diagram for MPEG encoding.
Figure 21.3. A typical software mixer panel as seen on the computer screen.
Figure 21.4. The rear of an APEX AD 600A DVD player that also plays CDs and MP3 files, priced in the United States at about
$150.
Figure 22.1. Measuring microphone sensitivity.
Figure 22.2. Response characteristics of a passive filter set. (Courtesy of United Recording Electronics Industries.)
Figure 22.3. Compliantly mounted diaphragm with both sides exposed to a sound field.
Figure 22.4. Simplified illustration of a single diaphragm that is sensitive to a combination of pressure and pressure gradient.
Figure 22.5. Illustration of the principal axis of a cylindrically symmetric microphone.
Figure 22.6. Position of the principal axis of a classic ribbon microphone.
Figure 22.7A. Standard polar patterns.
Figure 22.7B. Microphone three-dimensional directional response. (Courtesy of Shure Brothers Incorporated)
Figure 22.8. Measured polar response of cardioid microphone at 250 Hz and 2 kHz.
Figure 22.9. Polar response of a cardioid microphone.
Figure 22.10. Multipath and space diversity reception.
Figure 22.11. Typical preemphasis and deemphasis curves.
Figure 22.12. Dynamic range compression at the transmitter and complementary expansion at the receiver.
Figure 22.13. A wireless microphone system. (Photo courtesy of Michael Pettersen of Shure, Inc.)
Figure 22.14. Pin arrangements of XLR-3 connectors.
Figure 22.15. Twisted pair exposed to a time-changing magnetic field.
Figure 22.16. Phantom power arrangement for capacitor microphones.
Figure 22.17. Phantom power circuit when electronically balanced inputs are employed.
Figure 22.18. Illustration of direct and grazing sound incidences.
Figure 22.19. An example of a well-engineered tapered microphone structure. (Photo courtesy of Alex Khenkin of Earthworks,
Inc.)
Figure 23.1. Piston in infinitely plane wall.
Figure 23.2. Directivity of piston as a function of piston diameter and wavelength.
Figure 23.3. Air load on a plane piston; mechanical impedance ref.; driving point.
Figure 23.4. Impedance analogue of Figure 23.3.
Figure 23.5. Acoustical, electrical, and mechanical analogues.
Figure 23.6. Schematic representations of a Helmholz resonator.
Figure 23.7. Power response of an infinitely rigid piston.
Figure 23.8. Peak amplitude of a piston to radiate 1 W.
Figure 23.9. Directional radiation pattern with a circular piston in infinite baffle.
Figure 23.10. (a) Concentric and (b) bell modes.
Figure 23.11. Displacement relative applied force.
Figure 23.12. Voice coil temperature versus input power (300 Hz).
Figure 23.13. Moving coil loudspeaker cone, suspensions, and voice coil assembly.
Figure 23.14. Moving coil motor element.
Figure 23.15. Analogue of lumped mechanical constants.
Figure 23.16. Analogue referred to mechanical side.
Figure 23.17. A low-frequency mechanical analogue.
Figure 23.18. Simplified circuit, valid over restricted frequency ranges: (a) very low frequencies, (b) at principal resonance
frequency ω0, (c) above principal resonance frequency, (d) at second resonance frequency, and (e) at high frequencies.
Figure 23.19. Analogue referred to electrical input.
Figure 23.20. Complex impedance of moving coil loudspeaker.
Figure 23.21. A 25-mm OEM soft-dome tweeter.
Figure 23.22. A 200-mm OEM bass midrange loudspeaker drive unit.
Figure 24.1. A moving coil drive-unit, with key parts identified. (Courtesy Funktion One Research)
Figure 24.2. Two types of hf compression drivers made by Emilar, widely used in PA systems from the mid-1970s.
Figure 24.3. The exploded hf dome above this Tannoy drive-unit has no ohmic connections and cannot be burnt out. It employs
inductive coupling technology, the first completely new type of drive-unit to enter mass production for many years. Each new
drive-unit type has its loading peculiarities, which add a new layer of variables to the considerations of amplifier users
and designers alike. (Courtesy of Tannoy Ltd.)
Figure 24.4. Passively crossed over cabinet.
Figure 24.5. Low-level passive.
Figure 24.6. Classic three-way active crossover.
Figure 24.7. Bi-wiring improves sonic quality by avoiding superimposition voltage drops over the greater length of the output
stage to speaker connection, as otherwise LF signal currents upset the hf’s driver signal’s purity, and even vice versa.
Figure 24.8. The impedance of a 15” drive unit mounted on a nominal baffle. In some cabinet designs, there could be two or
more resonant peaks. Note the labeling of the resistive, capacitative, and inductive impedance zones.
Figure 24.9. The impedance of Figure 24.8 (upper graph), shown alongside the phase map (lower graph), clearly shows the relationship
between pure resistance and inductive and capacitative phase—at least in terms of voltage. In some instances, a plot of current
phase might be more appropriate.
Figure 24.10. Views of the damping surface in 2D. The lower plot shows the very low steady-state output source impedance of
a typical transistor amplifier with high NFB. The middle plot shows how this degrades after passing down a few meters of reasonably
rated cable and a series capacitor (which might be the simplest crossover, or for fault protection). The upper plot repeats
the impedance versus frequency behavior of the 15” bass driver. The effective damping factor is the smaller and highly variable
difference between the upper and the middle plots, not the difference between the highest impedance on the upper plot and
the lowest on the lower plot used by amplifier makers!
Figure 24.11. If speakers were simply resistors, the load on the amplifier might appear as here, with the apparent 11-ohm
load simply halving to 5.5 ohms at the one point where the two drivers are both drawing substantial current, the crossover
point. Note that the crossover dip may as well be a resonance and, as such, adds to the amplifier’s load stress.
Figure 24.12. Here, the resistors are replaced by drive-units having the impedance characteristics shown in the lower graph.
The upper graph shows how the impedance seen by the amplifier has changed—notably two dips where there was one.
Figure 25.1. Block diagram of a headphone cross-blend circuit with delay.
Figure 25.2. Moving-iron headphone. The current flowing in the coil either strengthens or weakens the force on the soft iron
diaphragm. AC audio signals thus vibrate the diaphragm in sympathy.
Figure 25.3. Typical moving-coil headphone transducer. The current through the voice coil creates a force on the diaphragm,
which vibrates it in sympathy with the audio input.
Figure 25.4. Cut-away view of a Sennheiser headphone earpiece showing the diaphragm, magnets, and acoustic damping materials.
Figure 25.5. Electrostatic headphone. The transformer steps up the audio signal for feeding to the outer metal plates. The
central diaphragm is given a high DC charge with a power supply. An audio signal causes the diaphragm to be attracted alternately
to the outer plates.
Figure 25.6. (a) Jecklin Float PS-2 electrostatic headphones and energizer unit, (b) Jecklin Float electrostatic headphone
module, and (c) Jecklin Float energizer units.
Figure 25.7. Supra-aural headphones (RE 2390) from Ross Electronics.
Figure 25.8. Sanyo “turbo” intra-aural earphones with Sanyo’s GP600D personal stereo.
Figure 26.1. Magnetic tape and the head gap.
Figure 26.2. Tape path.
Figure 26.3. BH curve.
Figure 26.4. Linearizing effect of AC bias.
Figure 26.5. FM sidebands as a result of speed instability.
Figure 26.6. Multiple tape tracks across width of the tape.
Figure 26.7. The effects of tape speed on saturation and distortion.
Figure 26.8. Analogue mastering recorder.
Figure 26.9. Cassette-based “notebook” multitrack.
Figure 26.10. Roland digital multitrack.
Figure 27.1. System dynamic range.
Figure 27.2(a). VU meter.
Figure 27.2(b). VU meter circuit.
Figure 27.3. Peak reading meters.
Figure 27.4. BBC style PPM.
Figure 27.5. Audio polar displays.
Figure 27.6. Standard levels compared.
Figure 27.7. Signal flow.
Figure 27.8. Schematic of a live-music console.
Figure 27.9. Input strip of an in-line console.
Figure 27.10. In-line console architecture.
Figure 27.11. Fader “flip” mechanism.
Figure 27.12. Equalizer controls.
Figure 27.13. Microphone preamplifier.
Figure 27.14. Microphone transformer.
Figure 27.15. Transformer-based input stage.
Figure 27.16. Insert points.
Figure 27.17. A simple tone control circuit.
Figure 27.18(a–c). Derivation of midband parametric EQ circuit; see text.
Figure 27.18(d). Older, passive equalizer circuit.
Figure 27.19. Fader and pan pot circuit.
Figure 27.20. Mix amplifier.
Figure 27.21. Line output circuit.
Figure 27.22. Balanced input circuit, and CM rejection.
Figure 27.23. Fader automation system.
Figure 27.24. Simple digital audio mixer.
Figure 27.25. RC low-pass filter.
Figure 27.26. Principle of a digital filter.
Figure F27.1. Infinite impulse response filter.
Figure F27.2. Derivation of sin x/x function.
Figure F27.3. Finite impulse response filter.
Figure F27.4. Digital high-pass filter.
Figure F27.5. Digital band-pass filter.
Figure F27.6. Generation of harmonics due to nonlinearity
Figure F27.7. Aliasing of harmonic structure in digital, nonlinear processing.
Figure 28.1. Television signal (viewed at line rate).
Figure 28.2. Television signal (viewed at field rate).
Figure 28.3. Mechanism of color vision.
Figure 28.4. (a) Studio vectorscope display and (b) Color three space.
Figure 28.5. NTSC color-coding process.
Figure 28.6. NTSC color decoder.
Figure 28.7. Color television signal.
Figure 28.8. The shadowmask in action.
Figure 28.9. Video interconnection.
Figure 28.10. Relationships between timing in digital and analogue TV.
Figure 28.11. Serialization system used in bit-serial TV signals.
Figure 28.12. ECL gate.
Figure 28.13. Gennum Corp. serializer chip. (photos courtesy of Gennum Corporation.)
Figure 28.14. Data format for digital audio packets in SDV bit stream.
Figure 28.15. Each EAS subframe is encoded as three contiguous data packets.
Figure 28.16. Format of LTC and VITC time code.
Figure 29.1. Noise criterion (NC) curves.
Figure 29.2. Nc curves.
Figure 29.3. Sound insulation performance of building materials compared with mass law.
Figure 29.4. Typical construction of a double-skin lightweight compartment.
Figure 29.5. Formation of room modes.
Figure 29.6. Frequency response trace of a monitor loudspeaker in a poorly treated control room.
Figure 29.7. Sound pressure level (loudness) variation of first and second modes measured in a poorly treated control room.
Figure 29.8. Preferred room dimension ratios.
Figure 29.9. Axial mode frequency versus room dimension.
Figure 29.10. Typical absorption characteristics of porous material.
Figure 29.11. Typical panel or membrane absorber construction.
Figure 29.12. Typical absorption characteristics of a resonant absorber.
Figure 29.13. Summary of typical absorber characteristics.
Figure 29.14. Frequency response plot of a monitor loudspeaker mounted adjacent to wall.
Figure 30.1. Basic Wien bridge oscillator and add-on square-wave generator.
Figure 30.2. Improved Wien bridge oscillator.
Figure 30.3. Diode-stabilized oscillator.
Figure 30.4. Amplitude control by FET.
Figure 30.5. Output level control.
Figure 30.6. Oscillator using parallel T.
Figure 30.7. Level stabilizer circuit.
Figure 30.8. Phase-locked loop oscillator.
Figure 30.9. Digital waveform generation.
Figure 30.10. ROM-based waveform synthesis.
Figure 30.11. ICL 8038 application circuit.
Figure 30.12(a). Square-wave input waveform (wide bandwidth).
Figure 30.12(b). Poor amplifier stability.
Figure 30.12(c). Relatively rapid (–12 dB/octave) loss of HF gain.
Figure 30.12(d). Output showing conditional stability.
Figure 30.12(e). Poor LF gain.
Figure 30.12(f). Increased gain at LF.
Figure 30.12(g). Excessive HF gain.
Figure 30.12(h). Loss of HF gain.
