365 Noise and Noise Rejection

8/12/2019 365 Noise and Noise Rejection

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Slide 1

Noise Noise Rejection

• Noise Sources

• Characterizing Noise

– Signal-to-Noise Ratio (SNR, S/N)

– Power Spectral Density

• Modes of Interference

• Noise Rejection:– Filtering

– Modulation

– Shielding & Grounding– Differential Amplifier

– Averaging



Slide 2

Noise

• NoiseNoise is any unsteady component of the measurement signalthat causes the instantaneous value of the signal to differ fromits “true value”.

Time

x(t)

x t s t n t( ) ( ) ( ) ActualSignal

Noise



Slide 3

Noise Sources

• Internal– Temperature-induced random noise in conductors

(Johnson noise)

– Random current fluctuations in transistors (Shot noise)

– Flicker noise

• External

– AC Interference

– Communication Interference– Switching Interference

– Mechanical/Structural Vibration



Slide 4

• Average Signal PowerAverage power (in Watts) dissipated when voltage signal is connectedto a 1 W resistor:

– Assume the actual signal s(t) and the noise n(t) are independent of

one another:

– Root Mean Square (RMS) voltage of a signal is:

Ex: For x(t) = A sin(w t + f ), the average power of x(t) is:

Noise Characterization

x tT

x t dtT 2 2

0

1( ) ( )

x t s t n t2 2 2( ) ( ) ( ) SignalPower

NoisePower

x t x t( ) ( )rm s 2



Slide 7

• Random Noise– Observe “random” signal for several observation periods:

• Signal is different from period to period.

• The average power for each observation period is about thesame.




Slide 8


• Random Signal– Can be approximated by a periodic signal, in which the first

observation period portion of the signal is repeated. The

approximation is valid if:• The observation period is long.

• The approximation is only used for calculating the powerdistribution in the random signal.

n t

n tn t n t Periodic

n t A

M k t

P

P

P k O kk

( ):

( ):( ) ( )

( ) cos( )

Random Signal

Periodic Approximation

0

12 w



Slide 11


• Power Spectral Density ((w ))

– Signal power is a stationary quantity that can be used to quantifyrandom signals.

– Power Spectral Density, (w ), is a quantity that is a measure of howthe power of a random signal is distributed among all possiblefrequencies.

The power of a signal due to frequencycomponents between w 1 and w 2 is:

The total power of a signal is the areaunder the (w ) curve:

W dw w w

w w w

1 21

2

, ( )

w

(w )

w 1 w 2 W dTOT

0

( )w w



Slide 12


• Special Random Signals

White Noise :

Uniform power spectral density

Band Limited White Noise :

Band limited uniform power spectraldensity

( )w w Aconstant

0

( )w w w

w w

A C

C

constant

0

0

w

(w )

A

w

(w )

w C

A



Slide 14

• Shot Noise

Quantization of electrons causes fluctuation of current flowing throughtransistor junctions.

– Shot noise is white noise with a uniform power spectral density:

for current measurement:

for voltage measurement:

where

Q: What is the RMS voltage due to Johnson and Shot noise?

Sources of Noise

S nI f I q( ) 2 [amperes / Hz]2

S nV f I qR( ) 2 2 [volts / Hz]2

q C R

I An

1 59 10

19

. [ ] - Electron charge Resistance in the device [ ]

Nominal current flowing in the device [ ]

W



Slide 16

Noise Propagation

• Noise measured at the output:When a device, such as an amplifier, amplifies the input signal,so too does it amplify internal noise:

Device

T ( jw)

Input

x(t)

Output

y(t)

( )W f df out

TOT

0

( ) ( ) ( ) out in f T j f f 2 2



Slide 17

Noise

Example: A voltage amplifier uses transistors in its circuitry, and has a total resistance of 10 kW, withnominal current of 30 mA, at a temperature of 40 oC. Its frequency response function can beapproximated as an ideal low-pass filter with gain of 10 and cutoff frequency of 1000 Hz.

a) Determine total noise power at the amplifier output, considering both Johnson and Shotnoise.



Slide 18

b) Assuming that the measured input signal is a pure sinusoid having amplitude of 0.33 V

and frequency of 10 Hz, calculate the SNR of the output signal (in dB).



Slide 19

Sources of Noise

External

• AC Interference

60/120/180/240 Hz sinusoidal interference due to power lines,fluorescent lights, fans, etc.

• Communication Interference

Radio/TV (1-100 MHz), cordless phone, cellular communicationinterference.

• Switching Interference

Switching interference due to switching power supplies, relays,

lightning, arc welders, auto ignition systems, etc.

• Mechanical/Structural Vibration

Normally under 20 Hz.



Slide 20

Noise Spectrum



Slide 21

Modes of Interference

• Series Mode Interference

Noise or interference voltage V SM “enters” the measurement system inseries with the measurement signal voltage ETH .

ETH

RC / 2

RC / 2

ZL

V SM ZOUT

Source Load

V L

V Z

Z R Z E V E V

E

V

LL

OUT C LTH SM TH SM

dB

TH

SM

( )

log SN 20 10



Slide 22

Modes of Interference

• Common Mode Interference

The potentials on both sides of the signal circuit are raised by acommon voltage V CM relative to a common earth ground .

V E V

V V

V V V E

A TH CM

B CM

L A B TH

Differential Measurement

Source Load

V L = V A V BETH

RC / 2

RC / 2

ZL

ZOUT V A

V B

V CM



Slide 23

• Shielding & Grounding

– Inductive Coupling

AC Power line in close proximity toone of the measurement leads will

generate a series mode interference:

where i is the power line current

M is the mutual inductance.

Solution:

(1) Physical separation

(2) Shorter cable length

(3) Twisted pair

Noise Rejection

V M d

dtiSM

M d 1



Slide 24


– Capacitive Coupling

Induce both common mode andseries mode noise.

Solution:

(1) Physical separation

(2) Shielding

Noise Rejection

V C C C

V V C C C

V

V V

V V V

BE

AC EE

AC

CM E

SM B E

1

1 1

2

2 2

;

V AC

GND

Screen (Shield)

Measurement Circuit



Slide 25


– Ground Loop

Noise Rejection

V

V i Z Z R

Z

V V V

E V V

E V i Z Z i Z

E V i Z Z Z

E i

R

V

V i R

V i Z

E E E SEC

RE

L R S

th P S

th E E E SE

V

E RE

V

th E E E SE RE

th E

C

SM

SM EC

CM E RE

P S

U

0

2

2

2

Forms loop TUPS

( )

( )

( )

( )

( )

Solution:Single Ground for all devices!!

using low-impedance grounding



Slide 26

Noise Rejection

• Filtering



Slide 27

Noise Rejection

• Filtering



Slide 28

Noise Rejection

• Modulation



Slide 29

Noise Rejection

• Averaging

The S/N ratio of a periodic signal can be increased by takingrepeated measurements of the signal.

Periodic signal s(t) = s(t + kT ) k = 1, 2, 3, ...1st Sample:

2nd Sample:

3rd Sample:

th Sample:

Sum:

Average:

s t n t

s t T n t

s t T n t

N s t N T n t

Ns t n t

N

kk

N

( ) ( )

( ) ( )

( ) ( )

( ( ) ) ( )

( ) ( )

1

2

3

1

2

1

Time

Volt

T



Slide 33

Noise Rejection - Common Mode

Noise• Differential Amplifier considering Common Mode Rejection

Source

ETH

ZOUT V A

V B

V CM

V OUT

Ri

Ri

R F

R F

-+

( )V R

RV V

R

R

V OU T

F

iB A

F

i

CM

1

CMRR

Ex: Let V A - V B = 1 mV, RF /Ri = 1000, V CM = 1V and CMRR = 10 4 , find V OUT .



Slide 34

Noise Rejection - Common Mode

Noise• Instrumentation Amplifier

V R

R V V OG

A B

1 2 1 ( )

V OUT

-+

R 2

R 2

R 2

R 2

-

+

-+

R1

R1

V B

V A

• Closed-loop differential-input device

• “Committed gain” amplifier.

• High input impedance, high CMRR, low offset drift, low input bias current.

RG

365 Noise and Noise Rejection

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