Electronic Noise• Noise phenomena• Device noise models• Representation of noise (2-ports):

– Motivation– Output spectral density– Input equivalent spectral density– Noise figure– Sampling noise (“kT/C noise”)

• SNR versus Bits• Noise versus Power Dissipation

– Dynamic range– Minimum detectable signal

Noise in Devices and Circuits

•Noise is any unwanted excitation of a circuit, any input that is not an information-bearing signal.• External noise: Unintended coupling with other parts of the physical world; in principle, can be virtually eliminated by careful design.• Intrinsic noise: Unpredictable microscopic events inherent in the device/circuit; can be reduced, but never eliminated. •Noise is especially important to consider when designing low-power systems because the signal levels (typically voltages or currents) are small.

Noise vs random process variations

• random process variations– Variations from one device to another– For any device, it is fixed after fabrication

• Noise– Unpredictable variations during operation– Unknown after fabrication– Remains unknown after measurement during

operation– May change with environment

Time domain description of noise

What is signal and what is noise?

)()()( tntstx

srmsT

s PSrmsSdttsT

P )(,)(102

nrmsT

n PNrmsNdttnT

P )(,)(10

2

Signal and noise power:

Physical interpretation

power

If we apply a signal (or noise) as a voltage source across a one Ohm resistor, the power delivered by the source is equal to the signal power.

Signal power can be viewer as a measure of normalized power.

Signal to noise ratio

)(log20)(log10 1010rms

rms

n

s

N

S

P

PSNR

SNR = 0 dB when signal power = noise power

Absolute noise level in dB:w.r.t. 1 mW of signal power

)log(10dB30

mW1log10din

n

nmn

P

PP

B

SNR in bits• A sine wave with magnitude 1 has power

= 1/2.• Quantize it into N=2n equal levels between

-1 and 1 (with step size = 2/2n)• Quantization error uniformly distributed

between +–1/2n

• Noise (quantization error) power=1/3 (1/2n)2

• Signal to noise ratio = 1/2 ÷ 1/3 (1/2n)2 =1.5(1/2n)2 = 1.76 + 6.02n dB or n bits

-1<=C<=+1

C=0: n1 and n2 uncorrelatedC=1: perfectly correlated

Adding uncorrelated noises

Adding correlated noises

For independent noises

Frequency domain description of noise

T

TTn dttntn

TR )()(

2

1lim)(

))(()()( nnn RfSfPSD F

dffPSDP nn )(

dffPSDP nn )(0

Given n(t) stationary, its autocorrelation is:

The power spectral density of n(t) is:

For real signals, PSD is even. can use single sided spectrum: 2x positive side

↑ single sided PSD

)()( fXtx

dffXdttx22)()(

)()( fPSDR xx

dffPSDRdttx xx

T

TT

)()0()(lim

2

Parseval’s Theorem:

If

If x(t) stationary,

Interpretation of PSD

PSDx(f)

Pxf1 = PSDx(f1)

Types of “Noise” • “man made”

– Interference– Supply noise– …– Use shielding, careful layout, isolation, …

• “intrinsic” noise– Associated with current conduction– “fundamental” –thermal noise– “manufacturing process related” – flicker noise

Thermal Noise • Due to thermal excitation of charge carriers in a

conductor. It has a white spectral density and is proportional to absolute temperature, not dependent on bias current.

• Random fluctuations of v(t) or i(t)• Independent of current flow• Characterization:

– Zero mean, Gaussian pdf– Power spectral density constant or “white” up to about

80THz

Thermal noise dominant in resisters

Example:R = 1kΩ, B = 1MHz, 4µV rms or 4nA rms

HW

Equivalently, we can model a real resistor with an ideal resistor in parallel with a current noise source. What rms value should the current source have?

Show that when two resistors are connected in series, we can model them as ideal series resistors in series with a single noise voltage source. What’s the rms value of the voltage source?

Show that two parallel resistors can be modeled as two ideal parallel resistors in parallel with a single noise current source. What’s the rms value of the current source?

Noise in Diodes Shot noise dominant– DC current is not continuous and smooth but

instead is a result of pulses of current caused by the individual flow of carriers.

It depends on bias, can be modeled as awhite noise source and typically larger than

thermal noise. − Zero mean – Gaussian pdf – Power spectral density flat – Proportional to current – Dependent on temperature

Example:ID= 1mA, B = 1MHz, 17nA rms

MOS Noise Model

Flicker noise

–Kf,NMOS 6 times larger than Kf,PMOS

–Strongly process dependent

−when referred to as drain current noise, it is inversely proportional to L2

BJT Noise

Sampling Noise • Commonly called “kT/C” noise

• Applications: ADC, SC circuits, …

von

R

C

Used:

Filtering of noise

H(s)x(t) y(t)

|H(f )|2 = H(s)|s=j2f H(s)|s=-j2f

Noise Calculations 1) Get small-signal model2) Set all inputs = 0 (linear superposition)

3) Pick output vo or io4) For each noise source vx, or ix Calculate Hx(s) = vo(s) / vx(s) (or … io, ix)5) Total noise at output is

6) Input Referred Noise: Fictitious noise source at input: 22

,2, )(/ sAvv Toneffin

Example: CS Amplifier

CL

VDD

RL

Von=(inRL +inMOS)/goT

goT = 1/RL + sCL

LBnR RTki

L

142

mBnMOS gTki3

242

o=1/RLCL

Some integrals

HW

In the previous example, if the transistor is in triode, how would the solution change?

HW

If we include the flicker noise source, how would that affect the computation? What do you suggest we should modify?

HW

In the example, if RL is replaced by a PMOS transistor in saturation, how would the solution change? Assume appropriate bias levels.