EE142 Lecture15

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Amin ArbabianJan M. Rabaey

Lecture 15: Introduction to Noise

EE142 – Fall 2010

Oct. 14th, 2010

University of California, Berkeley

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Announcements

Midterm next Thursday, includes up to end of this lecture.

Last year’s notes in which I went through the derivation of available thermal noise power using thermodynamic/QM arguments will be posted for interested students.– It also discusses the relationship between thermal and shot

noise.

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Noise

All electronic amplifiers generate noise. This noise originates from the random thermal motion of carriers and the discreteness of charge.

Noise signals are random and must be treated by statistical means. Even though we cannot predict the actual noise waveform, we can predict the statistics such as the mean (average) and variance.

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Power Spectral Density (PSD)

We need a way to describe energy or power of a (stationary) stochastic process.

PSD of a stochastic signal is the amount of power per unit of frequency as a function of frequency.

Formally, PSD is defined from the autocorrelation signal:

The autocorrelation is defined as:

We can show that under specific conditions:

Looks familiar

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Signal Power

Taking the inverse:

For a zero mean signal:

So upon integrating the PSD signal over all frequencies we obtain the total signal power (as expected).

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Filtered Random Process

Assuming a stochastic signal going through a linear filter

The PSD is filtered by the square of the transfer function (expected since this is signal power).

H(f)X Y

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Power Spectrum of Noise

The power spectrum of the noise shows the concentration of noise power at any given frequency. Many noise sources are “white” in that the spectrum is flat (up to extremely high frequencies)

In such cases the noise waveform is totally unpredictable as a function of time. In other words, there is absolutely no correlation between the noise waveform at time t1 and some later time t1 + δ, no matter how small we make δ.

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Resistor Noise

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Resistor Noise (2)

Here B is the bandwidth of observation and kT is Boltzmann’s constant times the temperature of observation.

This result comes from thermodynamic considerations, thus explaining the appearance of kT.

Often we speak of the “spot noise”, or the noise in a specific narrowband f:

Since the noise is white, the shape of the noise spectrum is determined by the external elements (L’s and C’s).

(Remember the PSD is filtered by the square of the transfer function)

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Resistor Example

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Combination of Resistors

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Resistive Circuits

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Noise of Passive Circuits

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Noise of Passive Circuits (2)

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Example: Noise of an RC circuit

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Noise from a Receiving Antenna

Assume we construct an antenna with ideal conductors so Rwire = 0:

If we connect the antenna to a spectrum analyzer, though, we will observe noise.

The noise is also “white” but the magnitude depends on where we point our antenna (sky versus ground).

For example:– Sky (toward zenith) 3-5K

– Sky (toward horizon) 50-100K

– Ground 290-300K

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Antenna Equivalent Temperature

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Diode Shot Noise

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Noise in BJT

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BJT Hybrid-Pi Model

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FET Noise

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FET Channel Resistance

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FET Noise Equivalent Circuit