Equipment Noise Characterization

Ps(W)

NTH(W) = kTB

B

Desired Signal

Thermal Noise

G1 GN

kTB

PSNR S 1

1

kTBG

GPSNR S

kTB

P

kTBG

GP

GGGkTB

GGGPSNR S

T

TS

N

NS

21

21

Ideal Components

Contained within

bandwidth “B”

Noise Ratio

G1

N1(mW)

PS1(mW) + NTH(mW) G1(PS1(mW) + NTH(mW) + N1(mW))

mWN

mWPSNR

TH

Sin

1 mWNmWN

mWPSNR

TH

Sout

1

1

BkT

N

SNR

SNRNR

out

in

0

11

T0 is ALWAYS 290 K for Noise Ratio Computations

mWNmWN

SNRSNRTH

inout11

1

mWNmWNmWN

mWP

THTH

S

1

1

1

1

mWNmWNmWN

mWP

THTH

S

1

1

1

101 NRBkTN

If NR is given, then we can compute

Definition:

A measure of how much a system degrades SNR.

Ratio of noise added to thermal noise (KT0B)

+ +

Equipment Noise Characterization

PS0(dBm)NTH(dBm) = 10 log10(kT0B) + 30 dB

B

Desired Signal

Thermal Noise

G1

dBmNdBmPdBSNR THS 00

1

1

0 1 ( )

S TH

SNR dB

P dBm L dB N dBm

SNR dB L dB

Practical Components

L1(dB)

dBLdBmPdBmP SS 101

Noise spectral density out of any device can never be less than kT.

N1(dBm)Shot noise contribution of first amp.We model the noise contribution as being added at the amp input, and amplified by the amp’s gain.

Since noise power is being added, we must use mW, NOT dBm.

Because kTB is in Watts!

+ +

Cascade Noise Ratio

G1 , NR1

N1

G2 , NR2

N2BkT

PSNR

BkTP

Sin

S

0

1

01

G1(PS1 + kT0B+ N1) G2(G1(PS1 + kT0B + N1)+N2)

11 2010012121 NRBkTNRBkTBkTGGPGG S

121102121 NRNRGBkTGPGG S

11

1

211

1

21102

121

NRNRG

GSNR

NRNRGBkTG

PGGSNR in

Sout

1

212,1

1

G

NRNR

SNR

SNRNR

out

in

12121

3

1

21,1

111

N

NN GGG

NR

GG

NR

G

NRNRNR

Which can be Generalized to N Stages: Friis’ Formula

+ +

+ +

Noise Ratio with Preceding Insertion Loss

B G1 , NR1L1(dB)

N1(dBm)BkT

PSNR

BkTP

Sin

S

0

1

01

1PS1 + kT0B

101

101

L

G1(1 PS1 + kT0B + N1)

1100

11

101

111

NRBkTBkT

P

NBkTG

PGSNR SS

out

1

1

1

1

0

1

NRSNR

NRBkT

Pin

S

1

1

NR

SNR

SNRNR

out

inT

11GGT

Since the effects of preceding loss are multiplicative w.r.t. both noise ratio and gain, it makes sense to deal with losses using dB units . . .

+ +

Noise Figure (dB)

Noise Figure, NF(dB), is Noise Ratio expressed in dB: )(log10)( 10 NRdBNF

Noise characteristics for devices are usually published/specified by Noise Figure (dB).

When a device with specified Gain and Noise Figure (GI , NFI ; both in dB) is preceded by one or more passive devices with specified total insertion loss (LI in dB), they can be combined into a single stage having

GC(dB) = GI(dB) – LI(dB) and NFC(dB) = NFI(dB) + LI(dB)

GI , NFILIGC , NFC

System Noise FigureThe overall noise figure for a system containing both active gain stages and passive loss stages is computed as follows:

1. Combine all passive losses with their succeeding gain stages using

GC,I (dB) = GI(dB) – LI (dB) and NFC,I(dB) = NFI(dB) + LI (dB)

2. The sum of the resulting combined gains (in dB) is total system gain, GSYS(dB)

2. Convert all combined gains and noise figures to their ratio metric (non-dB) values

3. Apply Friis’ formula using the resulting combined Gains and Noise Ratios to obtain overall Noise Ratio for the system.

4. Convert overall Noise Ratio back into dB’s : NFSYS(dB)

System Noise TemperatureConcepts of Noise Figure and Noise Ratio were developed when virtually all communications system were terrestrially based, hence the implicit use of T0 = 290 K (the mean blackbody temperature of the earth). No one ever aimed an antenna up at the sky and expected to receive anything meaningful.

With the advent of space communication and radio astronomy, an equivalent concept of noise temperature was developed which seemed to make more sense in that context:

10 NRTTeq

If we subtract one from each side of Friis’ formula and then multiply both sides by T0, we have:

121

0

21

30

1

20100

11111

N

NSYS GGG

NRT

GG

NRT

G

NRTNRTNRT

Substituting the definition of equivalent noise temperature from above,

12121

3

1

21

N

NSYS GGG

T

GG

T

G

TTT

DiscussionConsider Friis’ Formula: 12121

3

1

21,1

111

N

NN GGG

NR

GG

NR

G

NRNRNR

The Noise Ratio contributions of all but the first stage are reduced by the gains of preceding stages.

1.The gain of the first stage should be high, to reduce the contributions of succeeding stages.

2.The Noise Ratio of the first stage should be as low as possible, since it contributes directly to the system noise ratio.

3.Any passive losses prior to the first gain stage should be minimized, as it detracts from 1 and 2 above.

ExampleG1 = 15 dB

NF1 = 6 dB L1 = 2 dB

G3 = 25 dB

NF3 = 16 dB L2 = 5 dB

G2 = 10 dB

NF2 = 12 dB G4 = 18 dB

NF4 = 12 dB

Step 1: Combine all passive losses with succeeding gain stages.

G2 = 10 dB

NF2 = 12 dB G4 = 18 dB

NF4 = 12 dB G3 = 20 dB

NF3 = 21 dB G1 = 13 dB

NF1 = 8 dB

Step 2: Convert Gains and Noise Figures ratio-metric Forms

G2 = 10

NR2 = 16G4 = 64

NR4 = 16G3 = 100

NR3 = 128G1 = 20

NR1 = 6.4

Step 3: Combine Gains and Noise Ratios Using Friis’ Formula

32 41

1 1 2 1 2 3

11 1

16 1 128 1 16 16.4 6.4 0.75 0.64 .00075

20 20 10 20 10 1007.79

SYS

NRNR NRNR NR

G G G G G G

Step 4: Convert overall Gain and Noise Ratio Back to dB

9 61SYS SYSNF dB G dB