INF 5460Electronic noise –Estimates and countermeasures

Lecture 10 (Mot 7)

Modelling system noise

• Modelling of noise must include:– Sensors

– Bias and coupling network

– Amplifiers

• We use our standard method: 1. Determine the total noise at output: Eno2. Determine the system gain: Kt 3. Divide Eno with Kt: Eni²=Eno²/Kt²

2

A general voltage noise model

• Equivalent noise voltage at the input –general expression:

– A, B, C and D are functions of resistors, capacitors, coils etc and not functions of currents or voltages.

2222222222CSnnSni EDZICEBEAE

3

A general current noise model• Equivalent noise

current at the input –general expression:

• Neither J, K, L nor M are functions of voltage or current.

• It is irrelevant whether one calculates the equivalent input noise voltage or current.

2

2222

2

22222

C

Cn

S

nnsni

Z

EMIL

Z

EKIJI

4

Effect of parallel load resistance 1/2• Input (i.e. without Rp):

• Output (i.e. with Rp).

2

2

2

2

S

S

no

so

E

V

E

V

N

S

S

PS

p

so VRR

RV

22

2

P

SP

SS

PS

Pno E

RR

RE

RR

RE

2

2

2

2

2

2

2

2

2

2

2

2

p

p

ss

s

p

sp

ss

ps

p

s

ps

p

no

so

ut

ut

ER

RE

V

ERR

RE

RR

R

VRR

R

E

V

N

S

5

Effect of parallel load resistance 2/2

When Rs=Rp then Es=Ep and we get that (S/N)ut= ½(Vs²/Es²)= ½(S/N)inn. Rp equally reduces Vs and Es but

contribute in addition with its own noise. When Rs≫Rp

decreases (S/N)ut towards zero, while when Rs≪Rp will (S/N)ut increase towards (S/N)inn which is the best that can be achieved.

2

2

2

2

2

2

2

2

2

2

2

2

p

p

ss

s

p

sp

ss

ps

p

s

ps

p

no

so

ut

ut

ER

RE

V

ERR

RE

RR

R

VRR

R

E

V

N

S

6

Calculation with amplifier noise

1. Noise at output

2. System gain

3. Equivalent input noise

We compare with our well-known equation:

• Terms in front of En: If Rp≪Rs

we have that En will contribute a lot. If Rs=Rp the contribution from En will be equal to 4En². If Rp ≫ Rs contributes En with only En²

• Inp²RS² is a new term. This is the thermal noise in Rp.

22222

2

22 |||| SpnpSpnn

pS

p

Sno RRIRRIERR

REE

pS

p

tRR

RK

2222

2

2

2

22

Snpnn

p

pS

S

t

noni RIIE

R

RRE

K

EE

2222

2

22

Snns

t

noni RIEE

K

EE

7

Increased Rp & Vb1)

Rp must be made as high as possible. If a certain voltage is required over RS or a certain current through RS we may change the bias voltage accordingly.

Example: RS=1k, Rp=1.5k and VB=2.5V. If we change to new values Rp=199k and VB=200V the voltage over the sensor and the current through the sensor remains the same but the noise is significantly reduced.

2)

Alternatively, maybe it is possible to use a coil instead of Rp?

222

2

22 1 SSnS

nni ERILj

REE

8

1k sensor requiring 1V and 1mA

Green: 1.5k, 2.5V

Blue: 199k, 200V1.5k, 2.5V 49k, 50V

AC gain -4.4dB -0.2dB

Noise gain 0.60 0.98

Noise out 3.2nV/Hz 4.0nV/Hz

Noise eq. input 5.3nV/Hz 4.1nV/Hz

9

Bias impedance: R and L• 1MHz signal frequency

• Load R or L

• Simulations:

– Transient

– AC

– Noise

• (HP-filter on output to get same DC)

At 1MHz R 4k L 200µH

Gain 0.80 0.78

V(onoise) 3.6nV/Hz 3.2nV/Hz

V(inoise) 4.6nV/Hz 4.1nV/Hz

10

Effect of shunt capacitances

Here we have replaced the resistance Rp with a capacitor Cp

1)

2)

11

1

1

1

1

1

222

222

222

2

2

22

2

22

pS

Snn

ps

S

p

S

p

S

nn

p

S

p

Sno

CR

RIE

CRE

CjR

CjR

IE

CjR

CjEE

1

1

1

1

222

2

pS

p

S

p

tCR

CjR

CjK

11

3)

We compare with our well-known expression:

En² is multiplied by (RS²Cp²²+1). Note ! RS²Cp²² will often be substantially less than 1.

Only the En² contribution increases. NB! Cp is no noise source! Cp is not the input capacitance of the amplifier. This is included in En, In and Kt.

2222222

2

22 1 SnpSnS

t

noni RICREE

K

EE

2222

2

22

Snns

t

noni RIEE

K

EE

12

Noise in a resonant circuit1) Noise at output

Calculation of parts:

222

2

22 ||||||

||

pp

pP

pP

CLSnn

CLS

CL

Sno XXRIEXXR

XXEE

Sppsp

p

p

pp

S

p

pS

CLS

CL

RCLRLj

Lj

Lj

LCR

LjCjR

XXR

XX

pp

pp

22

11

1

11

1

||

||

ppSSp

pS

p

pS

CLSLCRRLj

LRj

CjLjR

XXRpp 211

1||||

2

22

2

22

11

1

11

1

p

pS

nn

p

pS

Sno

CjLjR

IE

LjCjR

EE

13

2) Signal gain

3) Equivalent input noise

•

The In-coefficient is independent of frequency

The En-coefficient will have a weight larger than 1 except at resonance. At the resonance (²CpLp=1) is the reactance element 0 and the coefficient equal to 1. We will then end up with our well-known expression (without Cpand Lp).

Lp and Cp does not contribute itself but affects others.

2

2

2

11

1

||

||

p

pS

CLS

CL

t

jLjCR

XXR

XXK

pp

pp

2

2

22

22

2

22

11

11

11

p

pS

p

pS

n

p

ppS

nS

t

noni

CjLjR

LjCjR

ILj

LCREE

K

EE

22

22

221

1 Sn

p

ppS

nS RILj

LCREE

14

The gain (top figure) is largest at resonance frequency. That is also the case for the noise output (in the middle). However, the equivalent noise at the input (bottom) is lowest at the resonance. This means that the signal is amplified more than the increase in noise at resonance.

15

Summary• Resistance in parallel:

• Capacitor in parallel:

• Coil in parallel:

• Xs in the series and Xp in parallel:

Xs and Xp are combinations of capacitances and coils in series and/or parallel (No resistances!)

• XLC is a coil and a capacitor in parallel:

2222

2

22 1 Snpnn

P

SSni RIIE

R

REE

22222222 1 SnnpSSni RIECREE

222

22

222 1 Snn

SSni RIE

L

REE

222

2

22 1 nSSn

p

SSSni IXRE

X

XREE

LC

Lj

CjLj

CjLj

X LC 211

1

16

When we can not reduce the noise…• Large SNR and DR is achieved either by

reducing the noise or increasing the signal. Is it any potential for increasing the maximum signal range?

• Make the signal range approach the supply voltage range– The signal range in traditional amplifiers is

only a limited region of the voltage supply region a)

– Rail-to-rail amplifiers approach the full supply voltage range. However these amplifiers are much more complex. b)

• Use differential amplifiers– Differential amplifiers has twice the signal

range (and better CMRR) but the component noise increases (from 2 and upwards).

Rail-to-rail diff in/out amplifier

18

Rail-to-rail test bench

19

Rail-to-rail amplifier

• Vout_cm=1.65, Vin_cm=0-3.3V

• Vin_cm=1.65, Vout_cm=0-3.3V

• AC (Vout_cm=Vin_cm=1.65V)

• Noise (Vout_cm=Vin_cm=1.65V)

20

NCM-eye• Goal: Measure resistance in

rock

• Two ASICs designed for 200°C operation temperature

• Measurement setup:– 100-200V AC is set up over the

rock region to be inspected

– Sensor front ends width very high input impedance (10-100G) measure the local voltage level

– Voltage differences between neighbour pairs are found

– Resulting values are converted into a digital format and feed into common buses

Very high input impedance preamp• GBW=10MHz

• Zin = 1-100G

22