Electrical Noise Wang C Ng Nature of electrical

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:

Thermal noise modeling • The rms noise voltage for a 1 -KW resistor is about 4 n. V/Hz 1/2. • 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 thermal noise.

Thermal noise modeling • Examples: – A 1 -KW resistor in a system with a bandwidth of 100 MHz generates about 40 m. V of noise voltage. – A 1 -MW resistor in this system generates about 40 m. V 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:

Shot noise modeling • The rms noise current for a diode current of 1 m. A is about 20 p. A/Hz 1/2. • 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 m. A in a bandwidth of 1 MHz shot noise generates about 20 n. A of noise current. – For a diode current of 10 m. A in a bandwidth of 100 MHz shot noise generates about 2 m. A of noise current. – 100 diodes would generate. 2 m. A 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:

Flicker noise modeling • The constant K 1 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 = G 1 G 2 … GN • Noise figure: Ftotal = F 1 + (F 2 - 1)/G 1 + (F 3 - 1)/G 1 G 2 + … + (FN - 1)/G 1 G 2 … 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 (low-noise system) • Noise temperature: Tn = T(F-1)

Radiometer • A modern radiometer can measure noise temperature variation down to 100 th 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