365 Noise Mod Main

8/12/2019 365 Noise Mod Main

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oise & oise Rejection

Noise Sources Characterizing Noise

Signal-to-Noise Ratio (SNR, S/N) Power Spectral Density

Modes of Interference

Slide 1

Noise Rejection: Filtering Modulation

Shielding & Grounding Differential Amplifier Averaging

FIG. 1: Whether noise is a nuisance or a signal may depend on whom you ask.(Cartoon by Rand Kruback. Used with permission of Agilent Technologies.)


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oise

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

Slide 2

Time

x(t)

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

ActualSignal

Noise


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oise Sources

Internal Temperature-induced random noise in conductors

(Johnson noise) Random current fluctuations in transistors (Shot noise)

Slide 3

Flicker noise

External AC Interference

Communication Interference Switching Interference Mechanical/Structural Vibration


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

Assume the actual signal s(t) and the noise n(t) are independent ofone another:

oise Characterization

x tT

x t dtT 2 20

1( ) ( )

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

Slide 4

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

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

SignalPower

NoisePower

x t x t( ) ( )rms 2


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Signal-to-Noise Ratio (SNR, S/N)Characterizes the noisiness of a particular signal, x(t) = s(t) + n(t):

SNR is usually expressed in decibels (dB):


SN

Signal PowerNoise Power

s tn t

2

2

( )( )

Slide 5

The uncertainty of a measurement is the inverse of the SNR.

SN

Signal PowerNoise Power

or

S N Signal RMSNoise RMS

dB

dBrms

rms

s tn t

s tn t

10 10

20 20

10 10

2

2

10 10

log log ( )( )

log log ( )( )


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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 the

same.


Slide 7


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

observation period portion of the signal is repeated. Theapproximation is valid if: The observation period is long.

Slide 8

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

n t

n t n t n t Periodic

n t A

M k t

P

P

P k O kk

( ):

( ): ( ) ( )

( ) cos( )

Random Signal

Periodic Approximation

-012


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Average Power Spectrum

If kth harmonic is applied across a 1

resistor, the average power dissipated

n t n t A

M k tP k O kk

( ) ( ) cos( ) -012

W k

Slide 9

Power Spectrum : plot of W k vs k(similar to Line Spectrum).

Cumulative Power for the first N harmonics is:

2 2

0

1cos ( )

OT

k k O k O

k

W M k t dt T

-

W A M N kk

N

14

120

2 2

1

W

W N

W 3

W 1


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Cumulative Power Spectrum In the limiting case when T O ,

O 0 , W N becomes acontinuous function of frequency

:

W ( )

W W T N O

( )lim

Slide 10

Power Spectral Density ( )The derivative of the cumulativepower W ( ) :

( ) ( )

( ) ( )

dd

W

f ddf

W f

[Watt /(rad/sec)]

or

[Watt /Hz]


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Power Spectral Density ( ) Signal power is a stationary quantity that can be used to quantify

random signals. Power Spectral Density, , is a quantity that is a measure of how

the power of a random signal is distributed among all possible

Slide 11

.

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

The total power of a signal is the areaunder the curve:

W d

1 2 1

2

, ( )

1 2 W dTOT 0 ( )


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Special Random Signals White Noise :Uniform power spectral density

( ) Aconstant

0

A

Slide 12

Band Limited White Noise :Band limited uniform power spectraldensity

( )

A C

C

constant 0

0

C

A


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Sources of oise

Internal Thermal (Johnson) Noise

Temperature-induced random motion of the electrons in resistors andsemiconductors causes a corresponding random voltage. Johnson Noise is a type of white noise with uniform power spectral

density: 2

Slide 13

where

Thermal noise amplitude roughly obeys a Gaussian distribution. Can only be reduced by reducing temperature and measurement

bandwidth.

J

o

o

k J/ K R

T K

. -1 38 10 23

vo s z

[ ] - Boltzmann' s constant

Resistance in the device [ ]

Absolute temperature of the device [ ]


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Shot NoiseQuantization of electrons causes fluctuation of current flowing throughtransistor junctions. Shot noise is white noise with a uniform power spectral density:

for current measurement:

Sources of oise

2

Slide 14

for voltage measurement:

where

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

nI

S nV f I qR( ) 22 [volts / Hz]2

q C RI An

-

1 59 1019

. [ ] - Electron charge Resistance in the device [ ] Nominal current flowing in the device [ ]


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Sources of oise

Internal Flicker Noise

Low-frequency noise, including random drift, present in transistors.Many naturally occurring processes, such as ocean currents, alsoexhibit 1/ f type behavior:

C

Slide 15

Flicker noise is usually important at low frequencies, f < 1000 Hz. Avoid DC measurement when very small signals are to be

measured.

vo s zF n f

C f

n f f F

Material dependent constant

Frequency [Hz]

1 1( )


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oise Propagation

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

Slide 16

Device

T ( j )

Input

x(t)

Output

y(t)

W f df outTOT

0

out in f T j f f 2 2


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oise Example:

A voltage amplifier uses transistors in its circuitry, and has a total resistance of 10 k , 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 17


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b) Assuming that the measured input signal is a pure sinusoid having amplitude of 0.33 Vand frequency of 10 Hz, calculate the SNR of the output signal (in dB).

Slide 18


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Sources of oise

External AC Interference

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

Communication Interference

Slide 19

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

Switching InterferenceSwitching interference due to switching power supplies, relays,lightning, arc welders, auto ignition systems, etc.

Mechanical/Structural VibrationNormally under 20 Hz.


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oise Spectrum

Slide 20


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Series Mode InterferenceNoise or interference voltage V SM enters the measurement system inseries with the measurement signal voltage ETH .

RC / 2V SM ZOUT

Slide 21

ETH

RC / 2

ZL

Source Load

V L

V ZZ R Z

E V E V

EV

LL

OUT C LTH SM TH SM

dB

TH

SM

( )

log S N 20 10


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

RC / 2ZOUT V A

Slide 22

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

ZL

V B

V CM


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Shielding & Grounding Inductive Coupling

AC Power line in close proximity toone of the measurement leads willgenerate a series mode interference:

oise Rejection

V M d iSM

Slide 23

where i is the power line current M is the mutual inductance.

Solution:

(1) Physical separation

(2) Shorter cable length(3) Twisted pair

M d1


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Shielding & Grounding Capacitive Coupling

Induce both common mode andseries mode noise.

oise Rejection

V C

C C V V C

C C V B AC E AC 1 2

;

Slide 24

Solution:(1) Physical separation(2) Shielding

V V V V V

CM E

SM B E -

V AC

GND

Screen (Shield) Measurement Circuit


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Shielding & Grounding Ground Loop

oise Rejection

V

V i Z Z R Z

V V V

E E E SEC

RE

L R S

U

-

0

2

Forms loop TUPS

( )

Slide 25

E V V E V i Z Z i Z

E V i Z Z Z

E iR

V

V i R

V i Z

th P S

th E E E SE

V

E RE

V

th E E E SE RE

th EC

SM

SM EC

CM E RE

P S

- - -

-

2

2

( )

( )

( )

( )

Solution:

Single Ground for all devices !!using low-impedance grounding


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oise Rejection

Filtering

Slide 26


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oise Rejection

Filtering

Slide 27


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oise Rejection

Modulation

Slide 28


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oise 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, ...

Slide 29

2nd Sample:3rd Sample:

th Sample:

Sum:

Average:

s t T n ts t T n t

N s t N T n t

Ns t n tN

kk

N

( ) ( )( ) ( )

( ( ) ) ( )

( ) ( )

-

1

2

3

1

2

1

Time

Volt

T


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oise Rejection

Averaging Average after N repeated measurements:

If nk(t) is zero mean,

x t s tN

n t s t n tkk

N

( ) ( ) ( ) ( ) ( ) 11

Slide 30

is zero mean

n t

N N nn

nn

( )

2

2

SN

s t

SN

s t s t

N

N s tS

N N S

N

Orig n

N n n n

N Orig

2

2

2

2

2

2

2

2 avg

avg


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oise Rejection - Common Mode

oise Differential Amplifier (Instrumentation Amplifier)

E

ZOUT V A

-

Ri R F

Slide 31

V E V V V

V RR

V V RR

E

A TH CM

B CM

OUT F

iB A

F

iTH

- - Differential Measurement

Source

V OUT

V B

V CM

Ri

R F


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More realistic Op Amp model:If a common mode voltage V CM exists

Common Mode Rejection Ratio (CMRR)


oise

-+ AOL

V -

V +V O

V A V V A V O OL CM CM - -( )

Slide 32

CMRR Differential GainCommon Mode Gain A

AOL

CM

-+ AOL

V -

V +V O

V CM CMRR

V A V V A V

V A V V V O OL

OL

CM

O OLCM

-

-

-

-

( )

( )

CMRR

CMRR


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oise Instrumentation Amplifier

-+

R 2 R 2 -

+

R1

V A

RG

Slide 34

V RR V V O G A B

-1 2

1

( )

OUT R 2

R 2

-+

R1

V B

Closed-loop differential-input device Committed gain amplifier. High input impedance, high CMRR, low offset drift, low input bias current.

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