Handbook for Sound Engineers

1060 Chapter 28

28.3.5.1 Track Width

The second factor is the loss in SNR in narrow-track
consumer tape formats due to the dissimilar ways that
random noise sources and coherent signals increase. The
noise due to the tape, heads, and electronics is a random
combination of many small independent noise bursts. If
two equal and independent random noise sources of this
type are added together, the noise power is doubled,
producing an increase of 3 dB on a voltmeter.

Coherent sources, on the other hand, are merely
duplicates of the same waveform. If two identical
sources are added together, the value at each point on
the output waveform is exactly twice the value of either
of the input waveforms. In this case the output voltage
is doubled, or a 6 dB increase.

Consider the case of two tracks of a tape recorder
that have recorded the same signal. If the output signals
of the two tracks are added, the noise will add randomly
and the signals will add coherently. The combined
tracks have 6 dB more signal and 3 dB more noise,
yielding a net SNR improvement of 3 dB. Using a
single track of double the original track width would
produce the same result if the noise sources were statis-
tically independent in nature.

The tape noise will follow the 3 dB per doubling
rate if the reproduce amplifier noise is less than the tape
noise. The reproduce amplifier noise typically remains
nearly constant regardless of track width of the head.
The apparent noise will vary, however, as the gain of the
amplifier is adjusted to compensate for changes in the
head output due to increased or decreased track width.
When tracks are made narrower, the amplifier noise that
functions as a coherent source will eventually dominate
the tape noise, creating a signal-to-noise loss of 6 dB
per halving of tape width.

Fig. 28-26 compares the output voltage and
signal-to-noise variation for various track widths,
assuming that all noise sources are truly random for a
noiseless preamplifier and a typical preamplifier. When
the amplifier noise begins to dominate the other noise
sources, there is a rapid loss of SNR with decreasing
track width.

28.3.5.2 Thermal Noise

Both the core and winding of the reproduce head
contribute random noise to the output signal. For the
winding, the noise source is due to the thermal agitation
of the atoms in the copper wire. The amount of thermal
noise is given by the expression

(28-9)

where,

TN is the thermal noise,

K is the Boltzmann’s constant (1.38 × 10^23 joules/K),

T is the absolute temperature in kelvin,

R is the resistance in ohms,

B is the measurement bandwidth in hertz.

A 100: resistor will produce 0.182μV of noise

voltage. Depending on the core size and number of

turns, a playback head may exhibit a resistance from

10–1000:, yielding thermal noise contributions of

0.06–0.6μV. The increase in noise due to more turns of

finer wire in high-inductance heads is offset by a rise in

head output voltage, producing little net change in SNR.

28.3.5.3 Barkhausen Noise

Another major noise source is Barkhausen noise, a

noise due to jumps in the magnetic boundaries of the

core material. The core metal consists of a collection of

many microscopic magnetic zones or domains. When a

magnetic field is applied to the core, the boundaries or

walls of the domains will change as small domains

merge to form larger domains. This merging occurs in

discrete steps since the small domains act as single units

that must each merge completely in one jump. The

resulting step change in the magnetic field generates a

noise burst in the head winding. Since the core contains

millions of constantly switching domains, a statistically

independent random noise is generated. Reducing the

size of the basic domains will decrease the amplitude of

the Barkhausen noise.

Figure 28-22. Noise changes with track width.

dB

+6

0

6

12

Relative SNR

0.25 0.5 1 2 4

Relative track width

Real preamplifier

Noiseless preamplifier

TN= 4 KTRB

1.82 10

8–

= u R volts for a 20 kHz

bandwidth at room temperature