On a worldwide scale, eight million lightning flashes occur daily. This is about 100 lightning flashes per second. The sum of all these lightning flashes results in atmospheric noise.At low frequencies (below approximately 2 MHz or so) radio signals travel as ground waves, which follow the Earth's curvature due to diffractionwith the layers of atmosphere. This enables AM radio signals in low-noise environments to be received well after the transmitting antenna has dropped below the horizon. Additionally, frequencies between approximately 1 and 30 MHz, can be reflected by the F1/F2 Layer, thus giving radio transmissions in this range a potentially global reach (see shortwave radio), again along multiply deflected straight lines. The effects of multiple diffraction or reflection lead to macroscopically "quasi-curved paths".However, at higher frequencies and in lower levels of the atmosphere, neither of these effects are significant. Thus any obstruction between the transmitting antenna and the receiving antenna will block the signal, just like the light that the eye may sense. Therefore, since the ability to visually see a transmitting antenna (disregarding the limitations of the eye's resolution) roughly corresponds to the ability to receive a radio signal from it, the propagation characteristic of high-frequency radio is called "line-of-sight". The farthest possible point of propagation is referred to as the "radio horizon".
Space (or Extraterrestrial noise) is observable at frequencies in the range of about 8Mhz to 1.43 Ghz, the latter frequency corresponding to the 21cm hydrogen line. Apart from man made noise it is the strongest component over the range of about 20 to 120Mhz. Not very much of it below 20Mhz penetrates down through the ionosphere, and it also disappears at frequencies in the excess of 1.5Ghz because of the mechnisms generating it.
The telephone cables of analog telephone system is divided into number of line sections as shown, and each line section has some amount of power loss which is compensated by adding amplifiers known as repeaters. So if the power loss of a line section is L then amplifier of power Gain G is chosen such that LG=1.TheEach amplifier in every section adds its own noise and so the noise accumulates as the signal travels along the system.Input signal to first section of line is Ps and input noise at this point is assumed to be negligible. This signal power remain same at the output of 1st section since the loss l in this section is being compensated by gain G of the amp .The noise at the output of 1st repeater is Pn1 and consists of the noise added by the line section and the amplifier.As the signal progresses along the link, the power output at each repeater remains the same i.e Ps because LG =1 for each link. But the total noise at the output of Mth link will be Pn1 + Pn2 +….If the links are identical and each link contributes to Pn, the total noise power becomes PnM = MPn
Amplifier noise is generated in many components throughout the amplifier , but it proves convenient to imagine it to originate from some Equivalent power source at the input of the amplifier .
Consider first two amplifiers in cascade . The problem is to determine the overall noise factor F in terms of individual noise factors and available power gains .
BY : BhavyaWadhwa, RamanGujral
Noise in electrical terms may be defined as any unwantedintroduction of energy tending to interfere with the properreception and reproduction of transmitted signals. Noise is mainly of concern in receiving system, where it sets alower limit on the size of signal that can be usefully received. Evenwhen precautions are taken to eliminate noise from faultyconnections or that arising from external sources, it is found thatcertain fundamental sources of noise are present within electronicequipment that limit the receivers sensitivity. Classification of noise NOISE NOISE WHOSE SOURCES ARE NOISE CREATED WITHIN EXTERNAL TO THE RECEIVER THE RECEIVER ITSELF
EXTERNAL NOISE Noise created outside the receiver External noise can be further classified as:1. Atmospheric2. Extraterrestrial3. Industrial ATMOSPHERIC NOISE Atmospheric noise or static is caused by lightning discharges inthunderstorms and other natural electrical disturbances occurring inthe atmosphere. Since these processes are random in nature, it is spread over most ofthe RF spectrum normally used for broadcasting.
Atmospheric Noise consists of spurious radio signals withcomponents distributed over a wide range of frequencies. It ispropagated over the earth in the same way as ordinary radiowaves of same frequencies, so that at any point on theground, static will be received from all thunderstorms, local anddistant. Atmospheric Noise becomes less at frequencies above 30 MHzBecause of two factors:-1. Higher frequencies are limited to line of sight propagation i.e. less than 80 km or so.2. Nature of mechanism generating this noise is such that very little of it is created in VHF range and above. EXTRATERRESTRIAL NOISE COSMIC NOISE SOLAR NOISE
Solar Noise Under normal conditions there is a constant noise radiation fromsun, simply because it is a large body at a very high temperature (over 6000°C on the surface, it therefore radiates over a very broadfrequency spectrum which includes frequencies we use forcommunication. Due to constant changing nature of the sun, it undergoes cycles ofpeak activity from which electrical disturbances erupt, such ascorona flares and sunspots. This additional noise produced from alimited portion of the sun, may be of higher magnitude than noisereceived during periods of quite sun.Cosmic Noise Sources of cosmic noise are distant stars ( as they have high
temperatures), they radiate RF noise in a similar manner as ourSun, and their lack in nearness is nearly compensated by their significantnumber.The noise received is called Black Body noise and is distributed fairlyuniformly over the entire sky.Space (or Extraterrestrial noise) is observable at frequencies in therange of about 8MHz to 1.43 GHz. INDUSTRIAL NOISE This noise ranges between 1 to 600 MHz ( in urban, suburban andother industrial areas) and is most prominent. Sources of such Noise : Automobiles and aircraft ignition, electricmotors, switching equipment, leakage from high voltage lines and amultitude of other heavy electrical machines.
INTERNAL NOISE Noise created by any of the active or passive devices found inreceivers. Because the noise is randomly distributed over the entire radiospectrum therefore it is proportional to bandwidth over which it ismeasured. Internal noise can be further classified as:1. Thermal Noise2. Shot Noise3. Low frequency or flicker Noise4. Burst Noise5. Partition Noise
Thermal Noise The noise generated in a resistance or a resistive component is random and is referred to as thermal, agitation or Johnson noise. CAUSE :• The free electrons within an electrical conductor possess kinetic energy as a result of heat exchange between the conductor and its surroundings.• Due to this kinetic energy the electrons are in motion, this motion is randomized through collisions with imperfections in the structure of the conductor. This process occurs in all real conductors and gives rise to conductors resistance.• As a result, the electron density throughout the conductor varies
randomly, giving rise to randomly varying voltage across the ends of conductor. Such voltage can be observed as flickering on a very sensitive voltmeter.• The average or mean noise voltage across the conductor is zero, but the root-mean-square value is finite and can be measured.• The mean square value of the noise voltage is proportional to the resistance of the conductor, to Ideal its absolute temperature, to the frequency Filter H(f) bandwidth of the device measuring the noise.• The mean-square voltage measured on themeter is found to be En2 = 4RkTBn ①
Where En = root-mean-square noise voltage, volts R = resistance of the conductor, ohms T = conductor temperature, kelvins Bn = noise bandwidth, hertz k = Boltzmann’s constant ( )And the rms noise voltage is given by : En = √(4RkTBn )NOTE: Thermal Noise is not a free source of energy. To abstract the noise power, the resistanceR is to be connected to a resistive load, and in thermal equilibrium the load will supply as muchenergy to R as it receives.
R V RL En In analogy with any electrical source, the available average power isdefined as the maximum average power the source can deliver. Considera generator of EMF En volts and internal resistance R . Assuming that RL is noiseless and receiving the maximum noisepower generated by R; under these conditions of maximum powertransfer, RL must be equal to R. Then Pn = V2/RL = V2/ R = (En/2)2 /R = En2 /4RUsing Equation ①, Pn = kTBn
Example:Calculate the thermal noise power available from any resistor at roomtemperature (290 K) for a bandwidth of 1MHz. Calculate also thecorresponding noise voltage, given that R = 50 ΩSolution For a 1MHz bandwidth, the noise power is Pn = 1.38 × 10-23 × 290 × 106 R = 4 × 10-15 W R (G=1/ En2 = 4 × 50 × 1.38 × 10-23 × 290 = 810-13 En2 = 4RkTBn = 0.895 In2 = 4GkTBn The thermal noise properties of a resister R may be a.) Equivalent Current Voltagerepresented be the equivalent voltage generator . Source Source Equivalent current generator is found using the Norton’s Theorem.Using conductance G = (1/R), the rms noise current is given by : In2 = 4GkTBn
Resisters in Series let Rser represent the total resistance of the series chain, where Rser = R1 + R2 + R3 + ….; then the noise voltage of equivalent series resistance is En2 = 4Rser kTBn = 4( R1 + R2 + R3 + …)kTBn = En12 + En22 + En32 + .....Hence the noise voltage of the series chain is given by: En = √ (En12 + En22 + En32 + .....) Resisters in Parallel With resistors in parallel it is best to work in terms of conductance. Let Gpar represent the parallel combination where Gpar = G1 + G2 + G3 +…; then In2 = 4Gpar kTBn = 4( G1 + G2 + G3 + …)kTBn = In12 + In22 + In33 + ….
REACTANCE Reactances do not generate thermal noise. Thisfollows from the fact that reactances cannotDissipate power. Consider an inductive or capacitive reactanceconnected in parallel with a resistor R. In thermal equilibrium, equal amounts of power must be exchanged;that is, P1 = P2 . But since the reactance cannot dissipate power, thepower P2 must be zero, and hence P1 must also be zero.Shot Noise Shot noise is random fluctuation that accompanies any direct currentcrossing potential barrier. The effect occurs because the carriers(electrons and holes in semiconductors) do not cross the barriersimultaneously but rather with random distribution in the timing ofeach carrier, which gives rise to random component of currentsuperimpose on the steady current.
In case of bipolar junction transistors , the bias current crossing theforward biased emitter base junction carries the shot noise. When amplified, this noise sounds as though a shower of lead shotswere falling on a metal sheet. Hence the name shot noise. Although it is always present, shot noise is not normally observedduring measurement of direct current because it is small compared tothe DC value; however it does contribute significantly to the noise inamplifier circuits.The mean square noise component is proportionto the DC flowing, and for most devices the mean- IDCSquare, shot-noise is given by: In2 = 2Idc qe Bn ampere2 TimeWhere Idc is the direct current in ampere’s, qe is the magnitude ofelectronic charge and Bn is the equivalent noise bandwidth in hertz.
ExampleCalculate the shot noise component of the current present on the directcurrent of 1mA flowing across a semiconductor junction, given that theeffective noise bandwidth is 1 MHz.SOLUTION In2 = 2 × 10-3 × 1.6 × 10-19 × 106 = 3.2 × 10-16 A2 = 18 nAFlicker Noise ( or 1/f noise ) This noise is observed below frequencies of few kilohertz and itsspectral density increases with decrease in frequency. For this reason it issometimes referred to as 1/f noise.The cause of flicker noise are not well understood and is recognizableby its frequency dependence. Flicker noise becomes very significant atfrequency lower than about 100 Hz. Flicker noise can be reduced
significantly by using wire-wound or metallic film resistors rather thanthe more common carbon composition type. In semiconductors, flicker noise arises from fluctuations in the carrierdensities (holes and electrons), which in turn give rise to fluctuations inthe conductivity of the material. I.e the noise voltage will be developedwhenever direct current flows through the semiconductor, and themean square voltage will be proportional to the square of the directcurrent.Burst Noise It consists of sudden step-like transitions between two or morediscrete voltage or current levels, as high as severalhundred microvolts, at random and unpredictable times. Each shift inoffset voltage or current often lasts from several milliseconds toseconds, and sounds like popcorn popping if hooked up to an audiospeaker.
The most commonly invoked cause is the random trapping andrelease of charge carriers at thin film interfaces or at defect sites inbulk semiconductor crystal. In cases where these charges have asignificant impact on transistor performance (such as under an MOSgate or in a bipolar base region), the output signal can be substantial.These defects can be caused by manufacturing processes, such asheavy ion-implantation, or by unintentional side-effects such as surfacecontamination.Typical popcorn noise, showing discrete levels of channel current modulation due to the trapping andrelease of a single carrier, for three different bias conditions
Partition Noise Partition noise occurs whenever current has to divide between two ormore electrodes and results from the random fluctuations in thedivision.It is therefore expected that a diode would be less noisy than atransistor if the third electrode draws current. It is for this reason thatthe input stage of microwave receivers is often a diode circuit. In case of common base transistor amplifier , as the emitter current isdivided into base and collector current , the partition noise effect arisesdue to random fluctuation in the division of current between thecollector and the base. Signal to noise ratioIt is defined as ratio of signal power to noise power at the samepoint. I.e S/N = Ps/ Pn= V2s / V2n
S/N Ratio of a Tandem Connection Different sections of a Telephone Cable in analog telephone system. LG=1 LG=1 L G L G G Ps Ps Ps Pn1 Pn1 + Pn2 Pn1 + Pn2 + …. + PnM PsDifferent Parameters: Total Noise at the output of Mth link =L = Power Loss of a line section Pn1 + Pn2 + …. + PnMG = Amplifier gainPs = Input signal Power PnM = MPnPn1 = Noise due to 1st repeaterPnM = Noise due to Mth Output signal to noise ratio :-repeater(S/N)1 = Signal to noise ratio of (S/N)o = 10log (Ps / MPn )nay one link = (S/N)1 dB – (M) dB(M)dB = No of Links expressed aspower ratio in decibels
NOISE FACTOR Noise factor is the ratio of available S/N ratio at the input to the available S/N ratio at the output . Noise signal source at room temperature To = 290K providing an input to an amplifier . The available noise power = Pni = kToBn .Available signal power = Psi Available signal to noise ratio from the source is (S/N)in = Psi /kTo Bn Power gain of the amplifier = G Available output signal power Pso = GPsi Available Output noise power = Pno = GkTo Bn ( if the amplifier was entirely noiseless )Real amplifiers contribute noise and the available output signal to noiseratio will be less than that at the input.
The noise factor F is defined as F = (available S/N power ratio at the input) / (available S/N power ratio at the output) F = ( Psi /kTo Bn ) X (Pno /GPsi ) F = Pno /GkTo Bn It follows from this that the available output noise power is given by Pno =FGkTo Bn F can be interpreted as the factor by which the amplifier increasesthe output noise , for ,if amplifier were noiseles the output noisewould be GkTn Bn . The available output power depends on the actual input powerdelivered to the amplifier .
Noise factor is a measured quantity and will be specified forgiven amplifier or network. It is usually specified in decibels , whenit is referred to as the noise figure. Thus noise figure = (F) dB = 10logF ExampleThe noise figure of an amplifier is 7dB. Calculate the output signalto noise ratio when the input signal to noise ratio is 35 dB. Sol . From the definition of noise factor , (S/N)o = (S/N)in – (F) dB = (35 – 7) dB = 28 db
Amplifier Input Noise in terms of F The total available input noise is Pni = Pno / G ( Pno = Available output noise power) = FkTo Bn The source contributes an availablepower kTo Bn and hence the amplifierPna = FkTo Bn – kTo Bn = (F – 1)kTo Bn Amplifier kTo Bn (F-1)kTo Bn Gain, G Pno = Noise FGkTo Bn Factor F
ExampleAn amplifier has a noise figure of 13dB. Calculateequivalent amplifier input noise for a bandwidth of 1MHz.Sol. 13 dB is a power ratio of approximately 20 : 1. hence Pna = (20 – 1)X 4 X 10-21 X 106 = 1.44pW.Noise figure must be converted to a power ratio F to beused in the calculation.
Noise factor of amplifiers in cascade The available noise power at the output of the amplifier 1 isPno1 = F1 G1 kTo Bn and this available to amplifier 2.Amplifier 2 has noise (F2 – 1)kTo Bn of its own at its input, hence totalavailable noise power at the input of amplifier 2 is Pni2 = F1 G1 kTo Bn + (F2 -1)kTo Bn Now since the noise of amplifier 2 is represented by its equivalentinput source , the amplifier itself can be regarded as being noiseless andof available power gain G2 , so the available noise output of amplifier 2is Pno2 = G2 Pni2 = G2 ( F1 G1 kTo Bn + (F2 –1)kTo Bn ) - (1)
The overall available power of the two amplifiers in cascade is G = G1 G2 and let overall noise factor be F ; then output noise powercan also be expressed as Pno = FGkToBn (2) equating the two equations for output noise (1) and (2) F1 G1 kTo Bn + (F2 -1)kTo Bn = FGkToBn F1 G1 + (F2 -1) = FG F = F1 G1 / G + (F2 – 1)/G where G = G1 G2 F = F1 + ( F2 – 1)/ G1
This equation shows the importance of high gain , lownoise amplifier as the first stage of a cascaded system. Bymaking G1 large, the noise contribution of the secondstage can be made negligible, and F1 must also be small sothat the noise contribution of the first amplifier is low. The argument is easily extended for additional amplifiersto give F = F1 + (F2 -1)/G1 + (F3 -1)/ G1 G2 This is known as FRISS’ FORMULA.