Electrical Noise Electrical noise is defined as any undesirable electrical energy that falls within the passband pf the
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Electrical Noise Electrical noise is defined as any undesirable electrical energy that falls within the passband pf the signal. For example, in audio recording any unwanted elecrical signals that fall within the audio frequency band of 0kHz to 15kHz will interfere with the music and , therefore, are considered noise. Figure below shows the effect that noise has on an electrical signal. Figure show a sinewave with out noise, and the same signal except in the presence of noise. Noise can be divided into two general categories: correlated and uncorrelated. Correlation implies a relationship between the signal and the noise. Therefore, correlated noise exists only whena signal is present. Uncorrelated noise, on other hand is present all the time whether there is a signal or not.
Correlated Noise Correlated Noise is noise that is correlated (mutually related) to the signal and cannot be present in a circuit unless there is an input signal- simply state, no signal, no noise! Correlated noise is produced by nonlinear amplification and includes harmonic and intermodulation distortion, which are both forms of nonlinear distortion. All amplifiers are nonlinear to some extent. Therefore, all signal amplification produces nonlinear distortion. Nonlinear distortion is also produced when signal pass through nonlinear devices such as diodes. Correlated noise is a form of internal noise. Harmonic Distortion Harmonic Distortion is when unwanted harmonics of a signal are produced through non- linear amplification (mixing). Harmonics are integer multiples of the original input signal. The original signal is the first harmonic and is called the fundamental frequency. Two times the original signal frequency is the second harmonic, three times is the third harmonic There are various degrees of harmonic distortion. Second order harmonic distortion is the ratio of rms amplitude of the second harmonic frequency to the rms amplitude of the fundamental frequency. Third order harmonic distortion is the ratio of the rms amplitude of the third harmonic to the rms amplitude of the fundamental frequency and so on.. Total harmonic distortion is the combined rms amplitude of the higher harmonics to the rms amplitude of the fundamental frequency. Mathematically total harmonic distortion (THD) % THD = Vhigher x 100 Vfundamental Where % THD = percent total harmonic distortion Vhigher = quadratic sum of the rms voltages of the harmonics above the fundamental frequency , ( v22 + v32 + vn2)1/2 Vfundamental = rms voltage of the fundamental frequency Problem 1: Determine a) Second, third and twelfth harmonics for a 1 kHz repetitive wave b) % second order, third order and total harmonic distortion for a fundamental frequency with an amplitude of 8 Vrms, a second harmonic amplitude of 0.2 Vrms and third harmonic amplitude of 0.1 Vrms
Intermodulation Distortion Intermodulation distortion is the generation of unwanted sum and difference frequencies when two or more signals are amplified in a nonlinear device, such as a large-signal amplifier. The emphasis here is on the word unwanted, because in communications circuits it is often desirable to mix two or more signals and produce sum and difference frequencies. The sum and difference frequencies are called cross products. Cross products are produced when harmonics as well as fundamental frequencies mix in a nonlinear device. For intermodulation distortion to occur, there must be two or more input signals. Mathematically, the sum and difference frequencies are Cross products = mf1 + nf2 Where f1 and f2 are fundamental frequencies where f1>f2 and m and n are positive integers between one and infinity. Problem 2: For a nonlinear amplifier with two input frequencies, 3kHz and 8kHz, determine a) First three harmonics present in the output for each input frequency b) Cross-product frequencies produced for values of m and n of 1 and 2
Uncorrelated Noise Uncorrelated noise is present regardless of whether there is a signal present or not. Uncorrelated noise can be further subdivided into two general categories; external and internal.
External Noise. External noise is noise that is generated outside the devicee or circuit. The three primary sources of external noise are: atmospheric, extraterrestrial and man-made. Atmospheric Noise. Atmospheric noise is naturally occuring electrical disturbances that originate within Earth’s atmosphere. Atnospheric noise is commonly called static electricity and is the familiar sputtering, crackling, and so on, often heard from a speaker where there is no signal present. The source of most static electricity is naturally occurring electrical conditions, such as lightning. Static electricity is often in the form of impulses that spread energy throughout a wide range of frequencies. The magnitude of this energy, however, is inveresely proportional to its frequency. Consequently, at frequencies above 30 MHz, or so, atmospheric noise is relatively insignficant. Extraterrestrial Noise. Extraterrestrial noise consists of electrical signals that originate from outside Earth’s atmosphere and is, therefore, sometimes called deep-space noise. Extraterrestrial noise is subdivided into two categories: solar and cosmic.
Solar Noise is generated directly from the sun’s heat. There are two parts to solar noise: a quiet condition when a relatively constant radiation intensity exists and high intensity, a sporadic disturbances caused by sun spot activity and solar flare ups. The magnitude of the sporadic noise caused by sun spot activity follows a cyclic pattern that repeats every 11 years. Cosmic noise sources are continuously distributed throughout the galaxies. Because the source of galactic noise are located much farther away than our sun, their noise intensity is relatively small. Cosmic noise is often called black-body noise and is distributed fairly evenly throughout the sky. Man-Made Noise is simply noise that is produced by mankind. The predominant sources of manmade noise are spark-producing mechanisms such as comutators in electric motors, automobile ignition systems, ac power-generting and switching equipment, and fluorescent lights. Man-made noise is impulsive in nature and contain a wide range of frequencies that are propagated through space in the same manner as radio waves. Man made noise is most intense in the more densely populated metropolitan and industrial areas and is sometimes called industrial noise. Impulse Noise Impulse noise is characterized by high-amplitude peaks of short duration in the total noise spectrum. As the name implies, impulse noise consists of sudden bursts of irregularly shaped pulses that generally last between a few microseconds and a fraction of millisecond, depending on their amplitude and origin. The significance of impulse hits on voice communications is often more annoying than inhibitive as impulse hits produce a sharp, popping, or crackling sound. On data circuits, however noise can be devastating. More impulse noise is encountered during transmission through mutual induction and electromagnetic radiation and is, therefore, generally considered a form of external noise. Common source of impulse noise include transients produced from electromechanical switches (such as relays and solenoids); electric motors, appliances, and lights( especially fluorescent lights); power lines; automotive ignition systems; poor-quality solder joints; and lightning. Interference Interference is a form of external noise and, as the name implies, means to disturb or detract from. Electrical interference is when information signals from one source produce frequencies that fall outside their allocated bandwidth and interfere with information signals from another source. Most interference occurs when harmonics or cross product frequencies from one source fall into the passband of neighboring channel. For example, CB radios transmit signals in the 27 MHz to 28 Mhz range. Their second harmonic frequencies (54MHz to 55MHz) fall within the band allocated to VHF television (channel3 in particular). If one person transmits on a CB radio and produces a high-amplitude second harmonic component, it could interfere with other people’s television reception. Most interference occurs in the radio- frequency spectrum
Internal noise is electrical interference generated within a device or circuit. There are three primary kinds of internally generated noise: shot, transit time and thermal. Transit-Time Noise. Any modification to a stream of carrieres as they pass from the inut to the output of a device (such as from the emitter to the collector of a transistor) produces an irregular, random variation categorized as transit-time noise. When the time it takes for a carrier to propaget through a device is an appreciable part of the time of one cycle of the signal, the noise becomes noticeable. Transittime noise in transistors is determined by carrier mobility, bias voltage, and transistor construction. Carriers traveling from emitter to collector suffer from emitter-time delays, base transit-time delays, and collector
recombination-time and propagation-time delays. If transit delays are excessive at high frequencies, the device may add more noise than amplfication to the signal. Excess Noise is also called flicker noise or 1/f noise (because the noise power varies inversely with frequency). Sometimes it is called pink noise because there is proportionately more energy at the lowfrequency end of the spectrum than with white noise, just as pink light has a higher proportion of red (the low frequency end of the visible spectrum) than does white light. Ezcess noise is found in tubess but is a more serious problem in semiconductors and in carbon resistors. It is not fully understood, but it is believed to be caused by variations in carrier density. Excess noise is rarely a problem in communication circuits, because it declines with increasing frequency and is usually insignificant above approximately 1 kHz Partition Noise is similar to shot noise in its spectrum and mechanism of generation, but it occurs only in devices where a single current separates into two or more paths. An exampke of such device is a bipolar junction transistor, where the emitter current is the sum of the collector and base currents. As the charge carriers divide into one stream or the other, a random element in the current is prodeuced. A similar effect can occur in vacuum tubes. The amount of partition noise depends greatly on the characteristics of the particular device, so no equation for calculating it will be given here. The same is true of shot noise in device with three or more terminals. Device manufacturers provide noise figure information on their data sheets when a device is intended for use in circuits where signal levels are low and noise is important Partition noise is not a problem in field effect transistors, where the gate current is negligible Shot Noise is caused by the random arrival of carrieres (holes and electrons) at the output element of an electronic device such as a diode, field-effect transistor or bipolar transistor. Shot noise was first observed in the anode current of a vacuum-tube amplifier and was described mathematically by W. Schottky in 1918. The current carriers (for both AC and DC) are not moving in continuous, steady flow because the distance they travel varies due to their random path of motion Shot noise is randomly varying and is superimposed onto any signal present. When amplified, shot noise sounds similar to metal pellets falling on a tin roof. Shot noise is sometimes called transistor noise an is additive with thermal noise.
Problem 3: A diode noise generator is required to produce 10 uV of noise in a receiver with an input impedance of 75 ohms, resistive and a noise power bandwidth of 200 kHz. What must the current through the diode be?
Thermal Noise is associated with the rapid and random movement of electrons within a conductor due to thermal agitation. This random movements was first noted by english botanist Robert Brown. Brown first observed evidence for the moving particle nature of matter in pollen grains. Random movement of electrons was first recognized in 1927 by JB Johnson of Bell Telephone Laboratories. Electrons within a conductor carry a unit negative charge, and the mean square velocity of an electron is proportional to the absolute temperature. Consequently, each flight of electron between collisions with molecules constitutes
a short pulse of current that develops a small voltage across the resistive component of the conductor. Because this type of electron movement is totally random and in all directions, the average voltage in the substance due to this movement is 0 Vdc. How ever, such random movement does produce an ac component. The ac component produced from thermal agitation has several names including thermal noise because it is temperature dependent, Brownian noise after its discoverer, Johnson noise after the man who related Brownian particle movement, and white noise because the random movement is at all frequencies. Hence, thermal noise is the random motion of free electrons within a conductor caused by thermal agitation. Johnson proved that thermal noise power is proportional to the product of bandwidth and temperature. Mathematically, noise power is N= KTB Where N= noise power (watts) B= bandwidth (hertz) K= Boltzmann’s proportionality constant (1.38x10-23 J/K) T= absolute temperature (kelvin) (17o or 290K)
Problem 4 A receiver has a noise power bandwidth of 10 kHz. A resistor that matches the receiver input impedance is connected across its antenna terminals. What is the noise power contributed by that resistor in the receiver bandwidth, if the resistor has a temperature of 27 C?
Noise Voltage Figure below shows the equivalent circuit for a thermal noise source where the internal resistance of the source (Ri) is in the series with the rms oise voltage (Vn). For the worst-case condition and maximum power transfer of noise power, the load resistance (R) is made equal to (Ri). Thus the noise voltage dropped across R is equal to half of the noise source (VR= VN/2), and from the equation of noise power, the noise developed across the load resistor is equal to KTB. The mathematical expression for VN is derived as VN=(4RKTB)1/2
Problem 5 For an electronic device operating at a temperature of 17oC with a bandwidth of 10kHz, determine 1. Thermal noise power in watts and dBm. 2. RMS noise voltage for a 100 ohms internal resistance and 100 ohms load resistance
Problem A 300 ohms resistor is connected across the 300 ohms antenna input of a television receiver. The Bandwidth of the receiver is 6 MHz and the resistor is at 20 C. Find the noise power and noise voltage
Problem The circuit shows two resistor in series at two different temperatures. Find the total noise voltage and noise power produced at the load over a bandwidth of 100 kHz.
SIGNAL TO NOISE POWER RATIO Signal-to-Noise power ratio (S/N) is the ratio of the signal power level to the noise power level. Mathematically, signal-to-noise power ratio is expressed as S = Ps N Pn Where Ps = signal power (watts) Pn = noise power (watts) The signal-to-noise power ratio is often expressed as a logarithmic function with the decibel unit. S (dB) = 10 log Ps N Pn Problem For an amplifier with an output signal power of 10W and an output noise power of 0.01 W. Determine the signal to noise power ratio.
Problem For an amplifier with an output signal voltage of 4V, an output noise voltage of 0.005V and input output resistance of 50 ohms. Determine the signal to noise power ratio
Noise Factor and Noise Figure Noise Factor and Noise figure are figures of merit used to indicate how much the signal-to-noise ratio deteriorates as a signal passes through a circuit or series of circuits. Noise factor is simply a ratio of input signal-to-noise power ratio to output signal-to noise power ratio. In other words, it is a ratio of ratios. Mathematically, noise factor is F = input signal-to-noise power ratio (unitless ratio) output signal-to noise power ratio Noise figure is simply the noise factor stated in dB and is a parameter commonly used to indicate the quality of a receiver. Mathematically, noise figure is NF(dB) = 10 log F In essence, noise figure indicates how much the signal-to-noise ratio deteriorates as a waveform propagates from the input to the output of a circuit. For example, an amplifier with a noise figure of 6dB means that the signal-to-noise ratio at the output is 6dB less than it was at the input. If a circuit is perfectly noiseless and adds no additional noise to the signal, the signal-to-noise ratio at the output will equal the signal-to-noise ratio at the input. For a perfect, noiseless circuit the noise factor is 1 and the noise figure is 0dB. An electronic circuit amplifies signals and noise within its passband equally well. Therefore, if the amplifier is ideal and noiseless, the input signal and noise are amplified the same, and the signal-to-noise ratio at the output will equal the signal-to-noise ratio at the input. In reality, however, amplifiers are not ideal. Therefore, the amplifier adds internally generated noise to the waveform, reducing the overall signalto-noise ratio. The most predominant noise is thermal noise, which is generated in all electrical components. Therefore, all networks, amplifiers, and system add noise to the signal and, thus, reduce the overall signal-to-noise ratio as the signal passes through them. Figure below show an ideal noiseless amplifier with a power gain (Ap), an input signal power level (Si), and an input noise power level (Ni). The output signal level is simply ApSi, and the output noise level is Ap Ni. Therefore, the input and output S/N ratios are equal and expressed mathematically as Sout = ApSi = Si Nou ApNi Ni Where Ap equals amplifier power gain.
A nonideal amplifier that generates an internal noise (Nd). As with the ideal noiseless amplifier, both the input signal and noise are amplified by the circuit gain. However, the circuit adds the internally generated noise to the waveform. Consequently, the output signal-to-noise ratio is less than the input signal-to-noise ratio by an amount proportional to Nd. Mathematically, the S/N ratio at the output of a non-ideal amplifier is expressed mathematically as Sout = Nout Where
ApSi ApNi + Nd
Si_______ Ni + Nd/Ap
Ap = amplifier power gain Nd = internal noise
Problem A transistor amplifier has a measured S/N power of 10 at its input and 5 at its output. Calculate the noise factor and noise figure
Problem For a non-ideal amplifier and the following parameters, determine a) Input S/N ratio b) Output S/N ratio c) Noise factor and Noise figure Input Signal Power = 2 x 10 -10 W Input Noise Power = 2 x 10 -18 W Power Gain = 1,000,000 Internal Noise (Nd) = 6 x 10 -12 W
Friiss’ Formula When two or more amplifiers are cascaded , the total noise factor is the accumulation of the individual noise factors. Friiss formula is used to calculate the total noise factor of several cascaded amplifiers. Mathematically, friiss’ formula is FT = F1 + F2-1 + F3-1 + Fn-1 A1 A1A2 A1A2… An Problem For three cascaded amplifier stages, each with noise figures of 3 dB and power gains of 120 dB. Determine the total noise figure
Problem Consider a receiver with a noise figure of 10dB. Its output signal to noise ratio is 50 dB. What is the input equivalent signal to noise ratio in decibel?
EQUIVALENT NOISE TEMPERATURE - is a hypothetical value that cannot be directly measured
Problem Determine a. Noise figure for an equivalent noise temperature of 75K b. Equivalent noise temperature for a noise figure of 6 dB
Problem An amplifier operating over the frequency range from 18 to 20 Mhz has a 10kohms input resistor. At ambient temperature of 27oC, determine the a) noise power, b) rms noise voltage, c) rms noise current
Problem In ckt shown, the BW of the amplifier is 2.5 MHz and temperature is 27oC. Determine a) individual rms noise voltage generated by noise resistor b) total noise voltage c) individual noise power, d) total noise power and total noise power using PnT= VnT2/(4RT)
Problem If the noise voltage at 50 ohms resistor is 1.82 uV, determine the noise voltage at a) 75 ohms and b) 300 ohms resistor. Also determine the noise current of each resistor in parallel.
Problem The first stage of a two-stage amplifier has a voltage gain of 10, 600 ohms input resistor, a 1,600 ohms equivalent noise resistance and a 27kohms output resistor. For the 2nd stage, these values are 25, 10 kohms, 81 kohms and 1 Mohms respectively. Also determine the noise voltage when the BW is 4 MHz at 27 oC
Problem There are 20 amplifiers connected in cascade, each having a SNR of 100dB. Determine the overall signal to noise ratio
Problem Consider a receiver with a noise figure of 10dB. Its output signal to noise ratio is 50 dB. What is the input equivalent signal to noise ratio in decibel?
Problem A mixer stage has a noise figure of 25 dB and this is preceded by an amplifier that has a noise figure of 12 dB and an available power gain of 20 dB. Calculate the overall noise factor and noise figure referred to the input
Problem A receiver connected to an antenna whose resistance is 30 ohms has an equivalent noise resistance of 50 ohms. What is the receiver’s noise temperature?