Handbook for Sound Engineers

434 Chapter 14

This means that low-frequency applications often
have quarter-wavelength distance way beyond common
practical applications. Table 14-30 shows common
signals, with the wavelength of that signal and the
quarter-wavelength. To be accurate, given a specific
cable type, these numbers would be multiplied by the
velocity of propagation.

The question is very simple: will you be going as far
as the quarter-wavelength, or farther? If so, then the
characteristic impedance becomes important. As that
distance gets shorter and shorter, this distance becomes
critical. With smaller distances, patch cords, patch
panels, and eventually the connectors themselves
become just as critical as the cable. The impedance of
these parts, especially when measured over the desired
bandwidth, becomes a serious question. To be truly
accurate, the quarter-wavelength numbers in Table
14-28 need to be multiplied by the velocity of propaga-
tion of each cable. So, in fact, the distances would be
even shorter than what is shown.

It is quite possible that a cable can work fine with
lower-bandwidth applications and fail when used for
higher-frequency applications. The characteristic
impedance will also depend on the parameters of the
pair or coax cable at the applied frequency. The resistive
component of the characteristic impedance is generally
high at the low frequencies as compared to the reactive
component, falling off with an increase of frequency, as

shown in Fig. 14-19. The reactive component is high at

the low frequencies and falls off as the frequency is

increased.

The impedance of a uniform line is the impedance

obtained for a long line (of infinite length). It is

apparent, for a long line, the current in the line is little

affected by the value of the terminating impedance at

the far end of the line. If the line has an attenuation of

20 dB and the far end is short circuited, the character-

istic impedance as measured at the sending end will not

be affected by more than 2%.

14.26 Twisted-Pair Impedance

For shielded and unshielded twisted pairs, the character-

istic impedance is

(14-15)

where,

Z 0 is the average impedance of the line,

C is found with Eqs. 14-16 and 14-17,

VP is the velocity of propagation.

For unshielded pairs

. (14-16)

For shielded pairs

(14-17)

where,

His the dielectric constant,

ODi is the outside diameter of the insulation,

DC is the conductor diameter,

Fs is the conductor stranding factor (solid = 1, 7 strand

= 0.939, 19 strand = 0.97.

The impedance for higher-frequency twisted-pair data

cables is

(14-18)

Table 14-30. Characteristics of Various Signals

Signal Type Bandwidth Wave-

length

Quarter-

Wave-

length

Quarter-

Wave-

length

Analog audio 20 kHz 15 km 3.75 km 12,300 ft

AES 3—44.1 kHz 5.6448 MHz 53.15 m 13.29 m 44 ft

AES 3—48 kHz 6.144 MHz 48.83 m 12.21 m 40 ft

AES 3—96 kHz 12.288 MHz 24.41 m 6.1 m 20 ft

AES 3—192 kHz 24.576 MHz 12.21 m 3.05 m 10 ft

Analog video (U.S.) 4.2 MHz 71.43 m 17.86 m 59 ft

Analog video (PAL) 5 MHz 60 m 15 m 49.2 ft

SD-SDI 135 MHz

clock

2.22 m 55.5 cm 1 ft 10 in

SD-SDI 405 MHz

third harmonic

74 cm 18.5 cm 7.28 in

HD-SDI 750 MHz

clock

40 cm 10 cm 4 in

HD-SDI 2.25 GHz

third harmonic

13 cm 3.25 cm 1.28 in

1080P/50-60 1.5 GHz clock 20 cm 5 cm 1.64 in

1080P/50-60 4.5 GHz third

harmonic

66 mm 16.5 mm 0.65 in

Z 0 101670

CV (^) p
------------------=
C = 3.68H
2 ODi
DC Fs
log --------------------

C =
3.68H
1.06 ODi
DC Fs
log --------------------------

Z 0 276 VP
100
©¹§·---------^2 h
DC Fsu
©¹§·---------------------
1 h
DC+Fb

2

1 h

DC Fb+

----------------------

2

+

----------------------------------

©¹

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= ulog u