Transcript G 1

Equipment Noise Characterization
Desired
Signal
Thermal
Noise
Contained within
bandwidth
“B”
Ideal Components
NTH(W) = kTB
Ps(W)
B
SNR 
PS
kTB
G1
GN
PS G1
SNR 
kTBG1
PS G1G2 GN 
PS GT
PS
SNR 


kTBG1G2 GN  kTBGT kTB
Noise Ratio
PS1(mW) + NTH(mW)
SNRin 
PS1 mW 
NTH mW 
G1
+
+
N1(mW)
G1(PS1(mW) + NTH(mW) + N1(mW))
SNRout 

Definition:

SNRin
N
NR 
 1 1
SNRout
kT0 B
A measure of how much a
system degrades SNR.
PS1 mW 
NTH mW   N1 mW 
PS1 mW 
NTH mW 1 N1 mW  NTH mW 

PS1 mW  
1


NTH mW   1  N1 mW  NTH mW  


1

SNRout  SNRin 
 1  N1 mW  NTH mW  
If NR is given, then we can compute
N1  kT0 BNR 1
Ratio of noise added to thermal noise (KT0B)
T0 is ALWAYS 290 K for Noise Ratio Computations
Equipment Noise Characterization
Desired
Signal
Thermal
Noise
Practical Components
Noise spectral
density out of any
device can never
be less than kT.
NTH(dBm) = 10 log10(kT0B) + 30 dB
PS0(dBm)
B
L1(dB)
SNR0 dB  PS 0 dBm  NTH dBm
PS1 dBm  PS 0 dBm  L1 dB
SNR1  dB 
 PS  dBm  L1  dB   NTH  dBm
 SNR0 (dB)  L1  dB 
Because kTB is in Watts!
G1
+
+
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.
Cascade Noise Ratio
PS1  kT0 B
+
PS1
+
SNRin 
kT0 B
G1 , NR1
G2 , NR2
+
+
N1
N2
G1(PS1 + kT0B+ N1)
G2(G1(PS1 + kT0B + N1)+N2)
 G1G2 PS1  G2 G1 kT0 B  kT0 BNR1 1  kT0 BNR2 1
 G1G2 PS1  G2kT0 BG1NR1  NR2 1
GG P
1
G1
SNRout  1 2 S1
 SNRin
G2kT0 B G1NR1  NR2 1
G1NR1  NR2 1
SNRin
NR 1
NR1,2 
 NR1  2
SNRout
G1
Which can be Generalized to N Stages: Friis’ Formula
NR1, N  NR1 
NRN 1
NR2 1 NR3 1

 
G1
G1G2
G1G2 GN 1
Noise Ratio with
Preceding Insertion Loss
a1 10
PS1  kT0 B
P
SNRin  S1
kT0 B
B
 L1 10
L1(dB)
G1 , NR1
+
+
N1(dBm)
a1PS1 + kT0B
SNRout 

NRT 
G1(a1 PS1 + kT0B + N1)
G1a1PS1
a1PS1

G1 kT0 B  N1  kT0 B  kT0 BNR1 1
PS1 a1
a
 SNRin 1
kT0 B NR1
NR1
SNRin NR1

SNRout a1
GT  a1G1
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:
NF(dB)  10log10( NR)
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)
LI
GI , NFI
and
NFC(dB) = NFI(dB) + LI(dB)
GC , NFC
System Noise Figure
The 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 Temperature
Concepts 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:
Teq  T0 NR 1
If we subtract one from each side of Friis’ formula and then multiply
both sides by T0, we have:
T0 NRSYS 1  T0 NR1 1 
T0 NR2 1 T0 NR3 1
T NRN 1

  0
G1
G1G2
G1G2 GN 1
Substituting the definition of equivalent noise temperature from above,
TSYS  T1 
T
TN
T2
 3  
G1 G1G2
G1G2 GN 1
Discussion
NRN 1
NR 1 NR 1
Consider Friis’
NR1, N  NR1  2  3  
Formula:
G1
G1G2
G1G2 GN 1
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.
Example
G1 = 15 dB
NF1 = 6 dB
G2 = 10 dB
NF2 = 12 dB
L1 = 2 dB
G1 = 13 dB
NF1 = 8 dB
G3 = 25 dB G4 = 18 dB
NF3 = 16 dB NF4 = 12 dB
L2 = 5 dB
G2 = 10 dB
NF2 = 12 dB
G3 = 20 dB
NF3 = 21 dB
G4 = 18 dB
NF4 = 12 dB
NR2 1 NR3 1 NR4 1
NRSYS  NR1 


G1
G1G2 G1G2G3
16 1 128 1
16 1
 6.4 


 6.4  0.75  0.64  .00075
20
20 10
20 10 100 G = 100
G2 = 10
G4 = 64
3
G1 = 20
 7.79
NR2 = 16
NR3 = 128
NR4 = 16
NR1 = 6.4
NFSYS  9dB
GSYS  61dB
Step
Step
Step4:
2:1:Convert
3:
Combine
Combine
Gains
overall
Gains
all passive
and
Gain
andNoise
Noise
losses
and Figures
Noise
Ratios
withRatio
succeeding
Using
ratio-metric
Back
Friis’
togain
Formula
Forms
dB stages.