2.2 The repeater section length

The attenuation added by the l km line at a certain frequency is determined by multiplication

A_sec = α_t(f_max)·l, where α_t – is the attenuation coefficient of 1 km line corresponding to the temperature t (in order to calculate it use the methodical guide line Проектирование цифровых систем передачи. Брескин В.А. p. 68-70 respectively to yours type of cable. Attention: there is a mistake in the table 2.2 α_α has to be multiplied by 10­ ^{- 3}).

p_rec = p_tr – α_t(f_max)·l = p_tr – A_sec – is the signal’s level at the output of l km line. p_tr – is the level at the input of line (ID). There are noises at each point of line.

T he LD is drawn for the worst case. The worst case is the highest frequency of the group signal (F2 – in the complex assignment). There is next frequency dependence of attenuation for all types of metal cables.

Figure 2.3

The repeater section length is determined from the nonlinear equation:

A_{i expectable} (l) = A_{i acceptable} (l)

A_{i acceptable} – is determined by the noise requirements (for the speech signals it’s 40 dB, ID).

A_{i expectable} (l) is determined by the repeater station self-noises (p_n in ID) and the useful signal’s level at the output of the section (at the input of IS).

A_{i expectable} (l) = p_s – p_n = p_rec – p_n

So the necessary number of IS can be determined by the next ratio:

,

Where l_e – is the effective repeater section length, L – is line path length (ID). The value under [ ] should be rounded up to the nearest integer value.

Let’s define the l_e : if L = 200 km, A_{i acceptable} = 40 dB, p_n = -120 dBp.

1. Let’s assume, that after calculations α_t = 4.319 dB/km.

2. Let’s determine the received signal’s immunity for l_e = 1 km

The number of IS equals to:

3. The noises of LP amplifiers are accumulated. So the noise power level at the input of TS recipient path can be calculated by using the next ratio.

p_n∑ = p_{n 1amp} + 10 lg (N_NRS) = -97.011 dBp

4. The level of the received signal is:

p_rec = p_tr – α_t · l_e = 0.681dBp

5. The expected immunity of the received signal is:

A_{i exp} = p_rec - p_n∑ = 97.693 dB

6. R epeat the calculations until the A_{i expectable} (l) > A_{i acceptable} (l). Than draw the graphics and determine the cross-point of immunities.

Figure 2.4

l_e – is the effective repeater section length. The nominal repeater section length:

l_nom = 0.8 · l_e = 0.8 · 17 ≈ 13.6 km.

There are next types of repeater section length:

• l_e – is the effective repeater section length

• l_nom – is the nominal repeater section length, l_nom ≤ l_max

• l_max – is the maximal repeater section length, l_max < l_e

• l_min – is the minimal repeater section length, 0< l_min < l_nom

l_min in ATS is given in technical data and determined by the correcting possibility of the variable (AGC) and fixed equalizer devises. So let’s take l_min = 0.5 l_nom in complex assignment.

During the placement of ISs the most of sections have the l_nom length, but the sections adjacent to the SRS or TS will be shortened l_min < l_sh < l_n.