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Electrical Noise Wang C. Ng Nature of electrical noise • Noise is caused by the small current and voltage fluctuations that are generated internally. • Noise is basically due to the discrete nature of electrical charges. • Externally generated noise is not considered here. Why study noise? • It sets the lower limit for the detectable signals. • It sets the upper limit for system gains. • Develop mathematical models to take the effects of noise into account when analyzing electrical circuits/systems. • Find ways to reduce noise. Thermal noise • Due to random motion of electrons. • It is ubiquitous (resistors, speakers, microphones, antennas, …) • It is directly proportional to absolute temperature. • White noise - Frequency independent up to 1013 Hz. Thermal noise modeling • The noise amplitude is represented by the rms value: vn 4kTRf 20 where 4kT 1.66 10 V-C Thermal noise modeling • The rms noise voltage for a 1-KW resistor is about 4 nV/Hz1/2. • The amplitude distribution is Gaussian with m = 0 and s = vn . • A series voltage source (vn) can be added to a resistor to account for the thermal noise. Thermal noise modeling • Examples: – A 1-KW resistor in a system with a bandwidth of 100 MHz generates about 40 mV of noise voltage. – A 1-MW resistor in this system generates about 40 mV of noise voltage. – 10 1-MW resistor in this system generates about 0.4 V of noise voltage. Shot noise • Shot noise is due to the random arrivals of electron packets at the potential barrier of forward biased P/N junctions. • It is always associated the a dc current flow in diodes and BJTs. • It is frequency independent (white noise) well into the GHz region. Shot noise modeling • The noise amplitude is represented by the rms value: in 2qI D f where q 1.6 10 19 C Shot noise modeling • The rms noise current for a diode current of 1 mA is about 20 pA/Hz1/2. • The amplitude distribution is Gaussian with m = ID and s = in . • A parallel current source (in) can be added to a diode to account for the shot noise. Shot noise modeling • Examples: – For a diode current of 1 mA in a bandwidth of 1 MHz shot noise generates about 20 nA of noise current. – For a diode current of 10 mA in a bandwidth of 100 MHz shot noise generates about 2 mA of noise current. – 100 diodes would generate .2 mA of noise current. Flicker noise • Flicker noise is due to contamination and crystal defects. • It is found in all active devices. • It is inversely proportional to frequency (also called 1/f noise) . • DC current in carbon resistors cause flicker noise. • Metal film resistors have no flicker noise. Flicker noise modeling • The noise amplitude is represented by the rms value: a I in K1 b f f where a 0.5 to 2 and b 1 Flicker noise modeling • The constant K1 is device dependent and must be determined experimentally. • The amplitude distribution is non-Gaussian. • It is often the dominating noise factor in the low-frequency region. • It can be described in more details with fractal theory. Other noise types • Burst noise (popcorn noise): System Noise Analysis Wang Ng Introduction • Noise sources can be added to a device models to represent the effect of noise. • We need a means to characterize the noise performance of a system (black box). • Noise figure • Noise temperature Noise figure • Used for resistive source impedance. • Most communication systems have a 50-W source impedance (Thevenin equivalent). • Signal-to-noise (S/N) ratio • Noise figure: F = (S/N)in / (S/N)out • F is a direct measure of the S/N ratio degradation caused by the system. Noise figure calculations • For an ideal (noiseless) amplifier: Sout = G Sin Nout = G Nin • For a real system: F = (Sin/Nin)(Nout/Sout) = Nout/GNin or F = (Total noise)/(Noise due to input) • F in in general frequency dependent. System noise • Internally generated noise can be computed from: Nsys = (F - 1)GNin since Nout = Nsys + GNin Cascade systems • Gain: Gtotal = G1 G2 … GN • Noise figure: Ftotal = F1 + (F2 - 1)/G1 + (F3 - 1)/G1G2 + … + (FN - 1)/G1G2 … GN • What does this tell us? We should pay most attention to the reduce the noise of the first system (Why???) Noise temperature • It is the temperature at which the noise generated from the source resistance equals to the system noise. • The noise temperature of a system is a better measure when F is close to 1 (lownoise system) • Noise temperature: Tn = T(F-1) Radiometer • A modern radiometer can measure noise temperature variation down to 100th or even less in K. • This instrument can be used for remote sensing/imaging. • Possible extra credit presentation. Summary • System noise measure: Noise figure and noise temperature • Internal noise calculation • Cascade system noise • First stage noise