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Noise due to unlinearity
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When carrying a traffic channel load the unlinear transfer characteristic of the active devices in the system generate harmonics and more complex intermodulation products that very quickly take on the characteristics of gaussian noise.
This noise source is referred to as intermodulation or cross modulation noise.
The initial problem is to define the power presented to the system by speech traffic.
20.7.4.1 Single channel load
The average power in each channel of a transmission band carrying normal 'busy hour' speech traffic referred to a OdBr point of measurement is Lo (dBmO) as in Equation 20.7 (Bell, 1971), where Pvo is the long term average power in a single talker dBmO, g is the standard deviation of the distribution of talker volumes and t is the traffic activity factor.
Single talker volume (Pyo)
This is the power in dBmO of a continuous individual talker measured using a long term averaging meter (10 seconds) at a OdBr point. This includes power due to signalling frequencies.
The precise value for P has been the subject of much measurement and study over the years. The UK figure used for trunk networks is -12.9dBmO. In the Bell System a figure of-13.9dBmO has been adopted for International use. (Most of the figures have been derived from Holbrook and Dixon, 1939.)
Loud and soft talker factor (0.115g2)
P is the average power in an individual talker. However, analysing a large number of talkers will show that they all have different volumes compared to the standard talker i.e. there are loud and soft talkers.
The distribution of the talker volumes (in dB) has been found to be Normal, with a standard deviation of g. (Figure 20.10(a).)
In order to find the average power per talker from a distribution of talker volumes the average or expected value is derived from the log normal distribution (see Figure 20.10(b)). This derives that the average power per talker over a large number of talkers is 0.115g greater than the average power of a single talker. (Bennett, 1940)
20.7.4.2 Multichannel load
The average traffic power Pn in a multichannel load of N channels is given by Equation 20.8, where N a 240, assuming that a single channel load figure is given by the -15dBmO value in Table 20.6.
For N < 240 the statistics of the activity factor dictate that a slightly higher value for the average load should be used. A best fit curve is given by Equation 20.9 (CCITT, 1985).
20.7.4.3 Unlinearily characterisation
For a sinusoid fundamental signal at the output of a typical amplifier, the output power of the second and third harmonics would appear as in Figure 20.11. In order to calculate the effect of the unlinearity on the transmission it is necessary to be able to quantify the harmonics and associated intermodulation products.
At the overload point, or clipping region, the harmonics increase very rapidly with increasing fundamental level and the characterisation of harmonic performance of the amplifier in this region is not practical.
As the output level is reduced and moves out of the overload region, the shape of the harmonic curve passes the knee and enters a linear portion of the graph where the second harmonic level reduces by 2dB and the third harmonic by 3db for every ldB drop in fundamental signal. The harmonic performance is characterised in this region.
If the amplifier transfer characteristics in the 'linear' region are assumed to be a square law, Equation 20.10 is obtained, where v is the input voltage, given by Equation 20.11, v is the output voltage, and a, a, a are constants of the amplifier.
Activity factor (1 (Nog t)
Not all the channels are fully occupied with continuous talkers. This gives rise to an activity factor t.
Conversation between two parties consist of 50% listening and 50% talking. The activity in any one direction is therefore 0.5.
In addition not all of the channels are in use. Even in the peak period only 70% of the circuits are occupied at any one time. The activity factor t is therefore reduced to 0.35. The figure normally used for t is 0.25.
Values for Lo, Pyo, g and t are given in Table 20.6. (CCITT, 1985; Bell, 1971.)
From this transfer characteristic Equations 20.12 and 20.13 may be obtained.
Thus the second harmonic (cos 2 to /) is proportional to the square of input signal amplitude V. Likewise the third harmonic (cos 3 co () is proportional to the cube of the input signal amplitude.
In dB terms it can be shown (Bell, 1971) that at a transmission level of OdBmO the power in a sinusoidal harmonic or intermodu-lation tone, P (x) in dBmO, at the amplifier output is related to the output level of the fundamental tones A and B by Equations 20.14 to 20.18, where P (x) is the harmonic or intermodulation power in dBmO, P(x) is the fundamental power in dBmO, H and Hv are the second and third harmonic powers in dBmO, characterised for the amplifier with fundamentals at OdBmO. (Figure 20.11.)
Thus, once H and H have been determined by measurement, all the second and third order intermodulation products can be deduced for a specific transmission level.
20.7.4.4 Determination ofunlinearity noise from a multichannel load
The technique used (Bennett, 1940) is to show that, for the purpose of calculating unlinearity or intermodulation noise, a channel loaded with a single sinusoid can be considered equivalent to a channel loaded with gaussian (or speech) noise by the application of a suitable factor k(x) to the noise contribution. A band of n speech channels thus becomes a band of n sinusoids and the problem is reduced to one of counting intermodulation products falling into the channel of interest for each product (A + B, 2A- B, etc.).
The total intermodulation noise in any particular channel is the summated power contribution from each of these products.
Bennett's formula, rearranged to give the weighted noise contribution W(x) within a specified channel is as in Equation 20.19.
The suffix (x) refers to the type of intermodulation under consideration i.e. H(A + B) etc. (Table 20.7) In Equation 20.9 PJx) is the power of the intermodulation product (x) in dBmO at the output of the system for OdBmO fundamentals; k(x) is the speech tone modulation factor (a factor in dB to convert the sinusoid P (x) to the equivalent intermodulation product power for bands of 4kHz gaussian noise); P is the power in a single average talker in dBmO (see Table 20.6); g is the standard deviation of the distribution of all talkers from loud to soft (see Table 20.6); e(x) and d(x) are factors to account for the relationship between the power in the talker (the fundamental signal) and the resulting intermodulation product (e(x) is a factor to modify the talker volume Pvo and d(x) to modify the standard deviation of talker volumes g); t is the transmission activity factor or the probability that a particular channel is active (see Table 20.6); u(x) is the number of channels involved in forming the particular intermodulation product and therefore tu'x' is the probability that the particular intermodulation product from a particular set of channels is present; C is the psophometric weighting correction factor for 4kHz and is 3.6dB. U(x) is the number of intermodulation products for a particular type (i.e. A + B, A + B, etc.) falling in a particular channel of interest.
The factor U(x) is derived from Bennett's formulae but for simplicity are usually shown in graphical form as in Figure 20.12.
These graphs are valid for systems of greater than 500 channels (Bell, 1971).
20.7.4.5 Approximate value for the weighted intermodulation noise contribution
For wide band systems there are three major intermodulation contributors A + B, A- B and A + B - C. Assuming the CC1TT accepted values for channel loading (see Table 20.6) a rule of thumb calculation can be made for unlinearity contributions using Equations 20.20 to 20.22, where W (x) is the approximate noise power in a selected channel, Pm(x) is the power of the (x) product in dBmO for OdBmO fundamentals, U (x) is the factor obtained from Figure 20.13 for a channel at frequency f.
20.7.4.6 Weighted noise power in pWOp
The total weighted intermodulation noise power can be determined from Equation 20.23, where x = all products, (A+B), (A-B), etc.
20.7.4.7 Determination of unlinearity noise using spectral densities
The problem with Bennett's method is the difficulty of dealing with shaped frequency spectra (pre-emphasis at the output of Line repeaters for instance.)
A method using spectral densities (Bell, 1971) overcomes this difficulty and can be extended to include the shape of the H^ and H across the band.
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From Equation 20.10 the ratio of the total second order distortion voltage to the fundamental signal at the output of the amplifier or system is given by Equation 20.24, where v is the system input signal (assumed Gaussian).
The terms in Equation 20.24 can be expressed as a power in volts squared where S (f) and S (f) are the power spectral densities in volts squared per Hertz. S (f) is the figure for the multichannel input signal voltage, v., and S2(f) for the input signal voltage squared, v?. This is shown in Equation 20.25.
If v is assumed Gaussian then Equation 20.26 may be obtained, ignoring d.c. terms and where represents the convolution integral.
The second order noise power NP2 in watts is therefore given by Equation 20.27, where Pch is the traffic load per channel in watts.
Likewise the third order noise power NP in watts is given by Equation 20.28, where the mean square voltage is given by Equation 20.29 and Pch is the traffic load per channel in watts.
The convolution is best performed numerically on a per system basis.
1 Learn the words & word combinations:
| Prophometric weighting | Псофометрическое взвешивание |
| Weighting factor | Весовой коэффициент |
| Gaussian noise | Нормальный шум |
| Boltzmann constant | Постоянная Больцмана |
| Circuit element | Элемент цепи |
| Transmission band | Полоса пропускания |
| Activity factor | Коэффициент активности |
| Traffic volume | Интенсивность движения |
| Trunk network | Сеть магистральных линий связи |
| Transfer characteristic | Переходная характеристика |
| Multichannel load (multiplexed) | Информационная нагрузка многоканальной системы |
| Correction factor | Поправочный коэффициент Коэффициент исправления |
| Convolution integral | Интеграл свертки |
| Traffic load | Информационная нагрузка (трафик) |
| Wire point | Место присоединения, монтажная точка |
2 Read & translation the text (orally) 20.7:
3 Find Russian equivalents:
| ü noise contributions | ü the topical entity |
| ü the virtual outgoing switch point | ü the degree of annoyance ü a channel of interest |
| ü random movement of electrons | ü a traffic load channel |
| ü single channel load figure | ü loud & soft talker factor |
| ü shaped frequency spectra | ü full channel width |
4 Find English equivalents:
| ü шум | ü тепловой |
| ü определить (оценить) с точки зрения передачи | ü подходить ü допускается |
| ü цифра силы шума | ü первоначальный |
| ü точное значение | ü средний |
| ü сопутствует возникновению | ü снижение |
| ü реорганизованный | ü действительны |
| ü весовой коэффициент |
5 Answer the questions:
1 What power levels are in common uses?
2 What is thermal noise?
3 How can you explain intermodulation or cross modulation noise?
4 What does the level of the harmonics depend on?
5 What does the Bennett’s formula explain to calculate?
PART 4 (20.8 – 20.10)
Дата публикования: 2015-03-29; Прочитано: 245 | Нарушение авторского права страницы | Мы поможем в написании вашей работы!
