96
TRANSMISSION ASPECTS OF VOICE TELEPHONY
5.4.3.1
Calculating the Resistance Limit
. To calculate the dc loop resistance for
copper conductors, the following formula is applicable:
R
dc
=
0
.1095
d
2
,
(5.1)
where
R
dc
= loop resistance ( /mi) and d = diameter of the conductor (inches).
If we want a 17-mile loop, allowing 100
per mile of loop (for the 1700-
limit),
what diameter of copper wire would we need? Apply Eq. (5.1).
100
= 0.1095/d
2
d
2
= 0.1095/100 = 0.001095
d = 0.0331 inches or 0.84 mm or about 19 gauge
By applying resistance values from Table 5.1, we can calculate the maximum loop length
for 1700-
maximum signaling resistance. As an example, for a 26-gauge loop,
1700
/83.5 = 20.359 kft
or 20,359 feet
.
This, then, is the signaling limit for 26-gauge (copper) subscriber loop. It is not the loss
(attenuation) limit, or what some call the transmission limit.
Another guideline in the design of subscriber loops is the minimum loop current off-
hook for effective subset operation. For example, the North American 500-type subset
requires at least 20 mA for efficient operation.
5.4.3.2
Calculating the Loss Limit
. For our discussion here, the loss at 1000 Hz of a
subscriber loop varies with diameter of the wire and the length of the loop. Table 5.2 gives
values of loss (attenuation) per unit length for typical subscriber low-capacitance wire pair.
Table 5.1
Loop Resistance for Various
Conductor Gauges
AWG
Ohms/1000 ft
of Loop
Ohms/Mile
of Loop
Ohms/km
of Loop
28
132
697
433
26
83.5
440
268
24
51.9
274
168.5
22
32.4
171
106
19
16.1
85
53
Table 5.2
Loss per Unit Length of Subscriber Wire Pairs
AWG
Loss/1000 ft
(dB)
dB/km
dB/mi
28
0.615
2.03
3.25
26
0.51
1.61
2.69
24
0.41
1.27
2.16
22
0.32
1.01
1.69
19
0.21
0.71
1.11
16
0.14
0.46
0.74