ece 4710: lecture #39 1 summary thus far we have: developed link formula to predict p rx for...
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ECE 4710: Lecture #39 1
Summary
Thus far we have: Developed link formula to predict PRX for system and link
parameters (PT , GAT , d, etc.) Si = PRX
Described basic properties of thermal noise Characterized noise performance of individual devices
» F and Te
» Active and passive/lossy
Characterized effective antenna temperature Ta
» Allows us to estimate input noise power : Ni = k Ta B
One more step to complete link budget analysis» What is S/N ratio at receiver output (S/N )o = ???
ECE 4710: Lecture #39 2
S / N @ Rx Output
Output S / N normally specified at input to detector Baseband BER vs. Eb / No results rely upon S / N at input to
detector/demodulator Output S / N sometimes called Carrier to Noise (C/N) ratio
» Carrier implies RF/IF prior to demodulation to baseband
Must perform noise analysis for entire RF / IF system Develop system noise characteristics
» Tes and Fs
Sole purpose is to accurately estimate No
So is simply Si + device gains device losses
ECE 4710: Lecture #39 3
S / N @ Rx Output
IFFilter
˜
Antenna
Low NoiseRF Amp
LPF
BasebandAmplifier
LocalOscillator
Mixer
IFAMP
Demod /Detector
DSP
Si = PRX
Ni = k Ta B
G1 F1 L2 L3 G2 F2 So
No
OutputData
ECE 4710: Lecture #39 4
Cascaded Linear Devices
iNiS
1F 2F
1oN
1oS2oN2oS
2o
is NS
NSF
)/(
)/(
1G 2G
sF
System Noise Figure
1DN 2DN
1Di1o NNGN 1
2D1Di2D1Di2D1o2o NNGNGGNNNGGNNGN 221122
i2o SGGS 21
ECE 4710: Lecture #39 5
System Noise Figure
System Noise Figure
We want to solve for Fs in terms of F1 and F2
Must determine relationship between device noise terms (ND1 and ND2) and device noise figures (F1 and F2)
i
2D1Di
i
2o
2oi
ii
2o2o
ii
2o
is NGG
NNGNGG
NGG
N
NSGG
NS
NS
NS
NS
NSF
21
221
2121 /
/
/
/
)/(
)/(
i
2D
i
1Ds NGG
N
NG
NF
211
1
ECE 4710: Lecture #39 6
Device Noise Model #1
iN Dio NGNN
DN
Thermal Noise
Source
i
D
i
Di
i
o
oi
ii
oo
ii
o
i
NG
N
NG
NGN
NG
N
NGS
NS
NS
NS
NS
NSF
1
io GSS iS
ECE 4710: Lecture #39 7
System Noise Figure
Using &
then
Extending this for many cascaded devices
System Noise Figure
i
2D
i
1Ds NGG
N
NG
NF
211
1 )1(or1 FNGNNG
NF iD
i
D
)1( 11 FNGN i1D)1( 22 FNGN i2D
1
21
21
22
1
11 1)1()1(1
G
FF
NGG
FNG
NG
FNGF
i
i
i
is
321
4
21
3
1
21
111
GGG
F
GG
F
G
FFFs
ECE 4710: Lecture #39 8
Key Observation: if first stage in cascaded system has high gain then F1 will dominate overall system noise figure
Low Noise Amplifiers (LNAs) Special class of RF amplifiers with high gain and low
noise figure Used to ensure that system noise figure will be small so
that overall S / N performance in Rx is very good
System Noise Figure
321
4
21
3
1
21
111
GGG
F
GG
F
G
FFFs
ECE 4710: Lecture #39 9
Noise Figure Example
IFFilter
Antenna
Low NoiseRF Amp
IFAMP
G2 = 15 dB L3 = 1 dB
Cable
90 ft.loss = 1 dB / 30 ft F2 = 2 dB
L4 = 2 dB G5 = 40 dB
F5 = 10 dB
321
4
21
3
1
21
111
GGG
F
GG
F
G
FFFs
210dB3)ft30/dB1(90 3/1011 LF
6.311058.110 15/102
2/102 GF
211
11 LG
dB 6.4or 35.4 )63.0(8.0)6.31(5.0
110
8.0)6.31(5.0
158.1
)6.31(5.0
126.1
5.0
158.12
sF
8.026.1126.110 3
1/103 GF
ECE 4710: Lecture #39 10
Noise Figure Example
IFFilter
Antenna
Low NoiseRF Amp
IFAMP
G1 = 15 dB L3 = 1 dB
F1 = 2 dB
L4 = 2 dB G5 = 40 dB
F5 = 10 dB
dB 4.5or .802 )63.0(8.0)5.0(6.31
110
8.0)5.0(6.31
158.1
)5.0(6.31
126.1
6.31
1258.1
sF
Cable
90 ft.loss = 1 dB / 30 ft
L2 = 3 dB
For low noise performance amplification is required at or near antenna before the signal is passed via
transmission line to rest of system
ECE 4710: Lecture #39 11
System Temperature
For cascaded linear devices the effective system temperature can be shown to be
Same observation as Fs low noise (small Te1) and high gain first stage mean overall system noise performance is very good
Relationship between Fs and Tes
321
4
21
3
1
21 GGG
T
GG
T
G
TTT eee
ees
29011 es
o
ess
T
T
TF
ECE 4710: Lecture #39 12
System Parameters
Device #1
G1 F1 Te1
Device #2
G2 F2 Te2
Device #3
G3 F3 Te3
Device #4
G4 F4 Te4
Antenna
iNiS
BTkN ai
GS FS Tes
oN
oS
321
4
21
3
1
21
111
GGG
F
GG
F
G
FFFs
321
4
21
3
1
21 GGG
T
GG
T
G
TTT eee
ees
iSoS SGSGGGGG 4321
a
oS
io
TTF
NSNS
)1(1
aT
Sesao GTTBkN )(
2
2
4
d
GGPPS ARATTx
Rxi
ECE 4710: Lecture #39 13
System Output Noise
System output noise formula :
Ideal case is Tes = 0 output noise is only from amplified input noise
For Tes >> Ta system noise dominates Rx
» Any improvement in Fs or Tes has significant impact on overall
system noise performance
For Ta Tes input noise & system noise ~ same
» Largest possible improvement in S / N is only factor of 2 3 dB!!
For Ta >> Tes input noise dominates Rx» LNA should NOT be used no benefit
esSiSSesao TBkGNGGTTBkN )(
ECE 4710: Lecture #39 14
Link Budget Equation
All communication systems designed for certain baseband S / N performance
Analog TV S / N = 40-45 dB Landline Voice Telephony S / N = 30-45 dB Analog Cellular S / N = 15-20 dB Digital Cellular S / N = 7-10 dB for BER < 10-3
Satellite Digital TV S / N = 13-16 dB for BER < 10-9
In digital communications desired BER determines required Eb / No
ECE 4710: Lecture #39 15
Link Budget Equation
In communication system design System analysis works backward from required (S / N)o
Link analysis works forward from transmitter and PTx
Two meet at Rx front end PRx
What is the minimum detectable signal, Smin, at Rx front end (antenna output) that is needed to produce required output signal to noise ratio?
ECE 4710: Lecture #39 16
Link Budget Equation
Two key formulas :
Rewriting S / N formula and solve for Si = Smin
a
oS
io
TTF
NSNS
)1(1
2
2
4
d
GGPPS ARATTx
Rxi
a
os
REQo
oamin T
TF
N
SBTkS
11
REQo
o
N
S
S/N required prior to detector / demodulator for desired baseband performance
ECE 4710: Lecture #39 17
Link Budget Equation
In link formula let
Complete end to end description of most important parameters affecting communication system End-to-end Tx + Channel + Rx Example: What is Tx power required to achieve desired
performance?
a
os
REQo
oa
ARATTxRxmini T
TF
N
SBTk
d
GGPPSS
11
4 2
2
2
241
1
ARAT
a
os
REQo
oa
Tx GG
dT
TF
N
SBTk
P