Handbook for Sound Engineers

Transmission Techniques: Wire and Cable 433

high frequencies rather than a 75ȍ connector—a flat-

tened cable, or too tight a bend radius, which changes

the spacing between the conductors. Anything that

affects the dimensions of the cable, will affect the

impedance and create reflective losses. It would just be

a question of how much reflection is caused. Reflec-

tions thus caused are termed return loss.

The characteristic impedance of common coaxial

cable can be between 30: and 200:. The most

common values are 50: and 75:The characteristic

Zo is the average impedance of the cable equal to

(14-11)

where,
H is the dielectric constant,
D is the diameter of the inner surface of the outer
coaxial conductor (shield) in inches,
d is the diameter of the center conductor in inches.

The true characteristic impedance, at any frequency,

of a coaxial cable is found with the equation

(14-12)

where,

R is the series resistance of the conductor in ohms per

unit length,

f is the frequency in hertz,

L is the inductance in henrys,

G is the shunt conductance in mhos per unit length,

C is the capacitance in farads.

At low frequencies, generally below 100 kHz, the

equation for coaxial cable simplifies to

(14-13)

At high frequencies, generally above 100 kHz, the

equation for coaxial cable simplifies to

(14-14)

14.25 Characteristic Impedance

The characteristic impedance of a transmission line is

equal to the impedance that must be used to terminate

the line in order to make the input impedance equal to

the terminating impedance. For a line that is longer than

a quarter-wavelength at the frequency of operation, the

input impedance will equal the characteristic impedance

of the line, irrespective of the terminating impedance.

Table 14-29. Coaxial Cable Signal Loss (Attenuation) in dB/100 ft

Frequency RG-174/

8216

RG-58/

8240

RG-8X/

9258

RG-8/

8237

RG-8/

RF-9913F

RG-59/

8241

RG-6/

9248

RG-11/

9292

1 MHz 1.9 0.3 0.3 0.2 0.1 0.6 0.3 0.2

10 MHz 3.3 1.1 1.0 0.6 0.4 1.1 0.7 0.5

50 MHz 5.8 2.5 2.3 1.3 0.9 2.4 1.5 1.0

100 MHz 8.4 3.8 3.3 1.9 1.3 3.4 2.0 1.4

200 MHz 12.5 5.6 4.9 2.8 1.8 4.9 2.8 2.1

400 MHz 19.0 8.4 7.6 4.2 2.7 7.0 4.0 2.9

700 MHz 27.0 11.7 11.1 5.9 3.6 9.7 5.3 3.9

900 MHz 31.0 13.7 13.2 6.9 4.2 11.1 6.1 4.4

1000 MHz 34.0 14.5 14.3 7.4 4.5 12.0 6.5 4.7

Characteristic impedance—: 50.0 50.0 50.0 52.0 50.0 75.0 75.0 75.0

Velocity of propagation—% 66 66% 80% 66% 84% 66% 82% 78%

Capacitance pF/ft, pF/m 30.8/101.0 29.9/98.1 25.3/83. 0 29.2/96.8 24.6/80.7 20.5/67.3 16.2/53.1 17.3/56.7

Figure 14-19. Impedance of coaxial cable from 10 Hz to
100 MHz.

10,000

1000

100

10

1

0.00001 0.0001 0.001 0.01 0.1 1 10 100

Impedance

7

Frequency MHz

Z 0 =

Z 0 =

L

C

R

f2PC

Z 0 =

Low frequency curve

Transition Curve

High Frequency Curve

R + j2PfL

R + j 2 PfC

Low frequency

region Transitionregion

High frequency

region

Zo

138

H

--------- D

d

= log--- -

Zo Rj+^2 SfL

Gj+ 2 UC

= ------------------------

Zo R

j 2 USC

= ----------------

Zo L

C

--- -=