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Reduction Of Noise In A Eletrical System

Reduction of noise in an electrlcal system.

R.V.K. Charan
Department of Physics, Gaya College, Gaya

Abstract  :- "Spontaneous fluctuation or the noise is ubiquitous in the output signal of a electrical system. Various methods are suggested here to reduce such fluctuations or noise to extract the original signal as far as possible".

1.      Introduction : Spontaneous fluctuations are generated in a electrical  system along with the original signal which can be termed as noise in the signal. Noise in a system affects the sensitivity. These fluctuations or noise are quite ubiquitous and natural in the system. One can never thought of a signal free from such noise. So it can not be completely eliminated. The origin of such noise can be traced according to corpuscular theory of matter (Wolf1, 1978). These noise can, however, be used as measurement tool to determine the response of a system by noise excitation (Beripohl2, 1970).

                   The present study elaborates some important methods by use of the filters, averagers, discriminator, etc. to minimise such fluctuations or noise to get the original signal as far as possible.

2.      Theoretical concept : The quality of a signal can be expressed as the ratio of the signal to such noise as :

          S/N=         .............................................(1)

                   To minimize the noise it is necessary to improve the aforesaid ratio but in case of weak signal such as in impulsed NMR, fluorescence decay, etc. the ratio becomes so poor to be measured. Unless there is any prior information about the signal or the noise , no distinction can be made between them. Hence the technique to improve the S/N ratio entirely depends on the nature of informations . The improvement of S/N ratio can be more clearly expressed in terms of signal - to- noise - improvement-ratio i.e.

          SNIR =         ............................ (2)

          But if the signal is little known beyond its bandwidth, then it is advisable to use filters to attenuate the noise.

          In case of "beat noise” the SNIR of a common-path interferometer based optical coherence tomotography (OCT) system was experimentally found (Xiaolu Li et al3, 2008) to be twice as large as the excess noise term. The result further showed that the source power and reference reflectively can be easily controlled to optimise the SNIR.

3.      Use of Filters : If the noise has a power spectrum N (w), the SNIR obtained after using a filter in a system can be given as,

          SNIR =  ………………………..(3)

          where the  ws, and wf, are the cut of frequencies of the system and the filter respectively.

          In the presence of white noise i.e N (w)= constant, the.

          SNIR  = (ws/wf)o.5                                                                               ………………………….

          From eq. (3) above it is evident that to minimize the noise the SNIR is to be kept maximum for which wf, is to be minimum. A favourable filter can be designed to reduce the wf by reducing the filter bandwidth smaller and smaller. But the bandwidth can not be reduced beyond a limit as the output signal carrying the signal information get destroyed resulting in the increase of the output noise. Therefore, the design of such a best and most favourable filter requires much more informations than merely the signal bandwidth (Blichikoff3, 1976). The output of such a designed optimum filter for no loss of wave energy and no addition of noise can be expressed as.

           …………………………. (4)

          where the hn is the white noise and 't' is the shift of time to assure the physical realisibility. But such a designed optimum filter improves the SNIR ratio by only 1 to 2 db as compared to non-optimum filters. This is because almost all the signal informations are buried or consumed in the output noise.

1. 4.    Averaging of Signal :- Averaging  of signals is a very  powerful method for extracting the already buried or consumed signal information to further improve the SNIR (Heiftje4, 1972 and Anon5, 19761). In it the signal is made repetitive and a reference trigger is required to mark the occurrence of the available signal. Its basis lies in the assumption that the noise, which is being uncorrelated to the signal, should be averaged out in an incoherent fashion where as the signal should be build up coherently after averaging through several repetitions. These conditions are well satisfied in various experiments, such as in pulsed NMR, ultrasonics, flow detection, etc.

4a.    Box-Car Averager - Averaging of signals can be well done through a Box-car averager . In it the noisy signal is amplified and fed to an analog gate which is made to open for a certain time by a gating pulse derived by delaying the trigger by a certain time.'T'. The  output of the analog gate is then fed to a simple RC integrator, and the integrated value of the sampled signal then forms the output signal. It can be shown after computation that the output signal voltage after 'n' sampling can be expressed as (Neelkantan6, 1978)

      ….. (5)

          where = 1/RC

          From the eq. (5) above it is obvious that the samples are exponentially weighted and so it is also called as "Experimental Averager". It is quite inexpensive. The SNIR, here, is proportional to the square root of 'n' (i.e. the no. of averaged sample) The main disadvantage, here, is that the value of SNIR remains limited only to 40-50db (Anon5, 19761)

4b.    Averaging through Lock-in-Amplifier : The value of SNIR can be further improved by using a Lock-in-Amplifier system . It requires a periodic signal of known wave shape together with a reference (Anon7, 19622). As the signal frequency of the wave shape is known here it is easy to narrow the passband of the Band Pass-Filter and consequently the noise bandwidth. This was unknown is the box-car-averager, and so the passband could not be made narrow. This may be termed as a special case of the box-car-averager. The passed signal through the band pass filter in the narrow band is amplified and then multiplied to a phase shifter reference signal. The emerged signal is then processed through a low pass filter to get the original signal. The method provides a means of reducing the measurement time as well as some inherent improvement in the value of SNIR but the value can be improved only up to 60db.

5.      Reduction of spurious pulses : If the signal is not a wave shape but rather in pulses, then the spurious pulses. i.e. the noise or unwanted signals can be minimised by improving the S/N ratio through an amplitude discriminator. This method does not reduce the pulse rate but merely eliminates the spurious pulse to get the original shape of the pulse. It is also called a single channel analyser. It is used to detect  - radiation out of the output pulse which are naturally combined with neutron pulse emerging from neutron detector in a nuclear power reactor. In spectroscopy, where the pulse shapes are in terms of rise and fall, a "Pulse shaped Discriminator" is used in stead of the aforesaid Amplitude Discriminator to minimise the spurious pulses. The pulses shaped discriminator consists of a R- C differentiator followed by a zero crossing comparator where the pulses are accepted only if the time difference (i.e. t2- t1) is within the specified limit. (Bormann8, 1972)

6.      Conclusion : - The unwanted signals or the spontaneous flow of undesirable  pulses i.e. the noise in a physical system can be minimised up to a great  extent through the aforesaid methods. These methods are very useful for extracting the desired original signal/ pulse out of the output signal/pulse of an instrument in a physical system. However noise is not always a nuisance or a disturbance in a system but also a tool of the system parameter to determine the system-response and efficiency, such as measured in a Noise Thermometer (Crovini9, 1975)

          Acknowledgment : The author expresses his sincere gratitude to the libraries of B.H.U. Varanasi, Magadh University, Bodh-Gaya and Gaya College, Gaya. His gratitude further extends to his wife for inspiring all the time and for sparing from domestic problems to facilitate the study.

Reference

1.      Wolf, (ed) Noise in Physical System, Springer - Verlag, Berlin, 1978.

2.      Breiphol, A.M., Probalistic Systems Analysis, Wiley, New York, 1978.

3.      Xiaolu Li et al. signal- to- noise ratio analysis of all -fibre common -path optial coherence tomotography Appl. Opt. 47, 4833- 4840,,

          ( 2008), U.S. Opital Society.

4.      Blnchikoff, H.J. and Zverev, A.I., Filtering in the time and frequency domains, Wiley, New York, 1976.

5.      Heirtje, G.M., Anal, Chem., 1972, 44, 81.

6.      Anon, Signal Averagers, Princeton, Applied Research Corporation. 19761.

7.      NeelKantan, K. and Dattagupta, S., Pramana (J. Phys.) 1978, 11, 295.

8.      Anon, Lock -in-amplifiers , Princeton Applied Research Corporation, 19762.

9.      Bormann, M., Schroder, V., Scobel, W, and Wide., L, Nucl, Instum, Methods, 1972, 98, 613.

10.    Crovini, L. and Actis, A., Temp, Measurement, (eds) B.F. Billing and T.J. Quinn, Institute of Physics, London, 1975.

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