Post on 02-Jan-2017
RFIC Design and Testing for Wireless Communications
A PragaTI (TI India Technical University) CourseJuly 18, 21, 22, 2008
Lecture 6: Basic Concepts – Linearity, noise figure, dynamic range
By
Vishwani D AgrawalVishwani D. AgrawalFa Foster Dai
200 Broun Hall, Auburn UniversityAuburn, AL 36849-5201, USA
1
RFIC Design and Testing for Wireless Communications
TopicsMonday, July 21, 2008
9:00 – 10:30 Introduction – Semiconductor history, RF characteristics
11:00 – 12:30 Basic Concepts – Linearity, noise figure, dynamic range2:00 – 3:30 RF front-end design – LNA, mixer4:00 – 5:30 Frequency synthesizer design I (PLL)
T d J l 22 2008Tuesday, July 22, 2008
9:00 – 10:30 Frequency synthesizer design II (VCO)
11:00 – 12:30 RFIC design for wireless communications2:00 – 3:30 Analog and mixed signal testing
Basic Concepts – Linearity, noise figure, dynamic range, FDAI, 2008 2
Units for Microwave and RFIC DesignPeak-to peak voltage: VppRoot-mean-square voltage:
22pp
rms
VV =
Power in Watt :VVPwatt pprms
22
==
22
Power in dBm : RR
Pwatt8
==
⎟⎠⎞
⎜⎝⎛=
mWmWPwattPdBm 1
][ log10 10
On a 50Ohm load, 0dBm=1mW=224mVrms=632mVpp
⎠⎝ mW1
Basic Concepts – Linearity, noise figure, dynamic range, FDAI, 2008 Page 3
Noise Figure
• In RF design, most of the front-end receiver blocks are characterized in terms of “noise figure” rather than input referred noisereferred noise.
• Noise factor F is defined as
NNNNNNSSNR addedoaddedosourceototalooiiin 1F )()()()( ++
F
NNNGNNSSNR sourceosourceosourceoi
o
oo
ii
out
in
10log10NF Figure, Noise
1F)(
)(
)(
)()(
)(
)(
=
+======
• Noise figure measures how much the SNR degrades as the signal passes through a system.
• For a noiseless system, SNRin = SNRout, namely, F=1, y , , y, ,NF=0dB, regardless of the gain. This is because both the input signal and the input noise are amplified (or attenuated) by the same factor and no additional noise is introduced.
Basic Concepts – Linearity, noise figure, dynamic range, FDAI, 2008 Page 4
Thermal NoiseTh l i (J h i ) d t d th l ti f• Thermal noise (Johnson noise) – due to random thermal motion of electrons and is generated by resistors, base and emitter resistance rb,rE,and rc. of bipolar devices, and channel resistance of MOSFETs. Thermal noise is a white noise with Gaussian amplitude distribution.
• Thermal noise floor: KHzdBm
mWkT 0290at /174
1log10 −=⎟
⎠⎞
⎜⎝⎛
2nbV
Qrb
M 2IR2
nV+
_ +
re
Q MnI
n _
2neV
+_
fkTRVn Δ= 42fgkTI mn Δ⎟
⎠⎞
⎜⎝⎛=
3242
>2/3 for submirocn MOS
Basic Concepts – Linearity, noise figure, dynamic range, FDAI, 2008 Page 5
>2/3 for submirocn MOS
Shot Noise• Shot noise (Schottky noise) – due to the particle-like nature of
charge carriers. Only the time-average flow of electrons and holes appears as constant current. Any fluctuation in the number of charge carriers produces a random noise current at that instant.Shot noise is a Gaussian white process associated with the transferShot noise is a Gaussian white process associated with the transfer of charge across an energy barrier (e.g., a p-n junction). This random process is called shot noise and is expressed in amperes per root hertz.
2,bnI
Q 2,cnIfqII n Δ= 22
Bbn qIi 2= Ccn qIi 2=
Basic Concepts – Linearity, noise figure, dynamic range, FDAI, 2008 Page 6
Flicker noise• Flicker noise (1/f noise) – found in all active devices. In bipolar
transistors, it is caused by traps associated with contamination and crystal defects in the emitter-base depletion layer. These traps capture and release carriers in a random fashion with noise energyand release carriers in a random fashion with noise energy concentrated in low frequency. K depends on processing and may vary by order of magnitude.
250 ,2 ~.aff
IKI
aC
n ≈Δ=
• In MOSFETs, 1/f noise arises from random trapping of charge at the oxide-silicon interfaces. Represented as a voltage source in series with the gate, the noise spectral density is given by
fWLCoxKVn
12 =
Basic Concepts – Linearity, noise figure, dynamic range, FDAI, 2008 Page 7
Noise Power Spectral Density
z)
-135
e Po
wer
(dB
m/H
z10dB/Dec
Total Noise
-150
-145
-140N
oise
Thermal and Shot Noise
Flicker Noise
-160
-155
0.1 1 10 100 1000Frequency (kHz)
The 1/f corner frequencyThe 1/f corner frequency can be significantly higher for MOSFET
Basic Concepts – Linearity, noise figure, dynamic range, FDAI, 2008 Page 8
BJT Model with Noise Sourcesrb cb’
vbb
4kT
Cμ
Cπ gmvb’erπicnibn
ibf
2qIB
4kTrb
ro
2qIC
ee1/f noise Base
Shot Noise
CollectorShot Noise
ca) cb)rbb
vrb
4kTrb
b’ icn
2qICibn
a)rbb b’ icn
c
2qIi
b)
4kTrb
baseshot noise
collectorshot noise
e2qIB2qIB
q Cbn
4kTr
e2qIB2qIB
2qICibn
Basic Concepts – Linearity, noise figure, dynamic range, FDAI, 2008 Page 9
shot noise rb
CMOS Model with Noise Sources
Input-referred noise
vgs CGS
CGD
gmvgs r
vo
IndkTV 82
=ro
kT2 8
mgV
3n =
⎟⎠⎞
⎜⎝⎛= mgkTI
324
2
nd mgZkTI 2
in
2
n 38
=
• Gate resistance can be added to the noise model with gate resistivity ρ
LWRGATE ρ
31
=
Basic Concepts – Linearity, noise figure, dynamic range, FDAI, 2008 Page 10
Linear vs. Nonlinear Systems
• A system is linear if for any inputs x1(t) and x2(t), x1(t) y2(t), x2(t) y2(t) and for all values of constants a and b, it satisfies
a x1(t)+bx2(t) ay1(t)+by2(t)a x1(t)+bx2(t) ay1(t)+by2(t)
A t i li if it d t ti f• A system is nonlinear if it does not satisfy the superposition law.
Basic Concepts – Linearity, noise figure, dynamic range, FDAI, 2008 Page 11
Effects of Nonlinearity
• Harmonic DistortionHarmonic Distortion• Gain Compression• DesensitizationDesensitization• Intermodulation
• For simplicity, we limit our analysis to memoryless time invariant system Thusmemoryless, time invariant system. Thus,
...)()()()( 33
221 +++= txtxtxty ααα (3.1)
Basic Concepts – Linearity, noise figure, dynamic range, FDAI, 2008 Page 12
Effects of Nonlinearity -- HarmonicsIf a single tone signal is applied to a nonlinear system, the output generally exhibits fundamental and harmonic frequencies with respect to the input frequency. In Eq. (3.1), if
tAtAtAty ωαωαωα coscoscos)( 3322 ++
frequencies with respect to the input frequency. In Eq. (3.1), if x(t) = Acosωt, then
ttA
tAtA
tAtAtAty
ωωα
ωαωα
ωαωαωα
)3coscos3(4
)2cos1(2
cos
coscoscos)(3
32
21
321
++++=
++=
tA
tAtA
AAω
αω
αω
αα
α 3cos4
2cos2
cos)4
3(
2
33
22
33
1
22 ++++=
Observations:1. even order harmonics result from αj with even j and vanish if the system has odd symmetry, i.e., differential circuits.
Basic Concepts – Linearity, noise figure, dynamic range, FDAI, 2008 Page 13
2. For large A, the nth harmonic grows approximately in proportion to An.
Effects of Nonlinearity -- Gain Compression
tA
tAtA
AAty ωα
ωα
ωα
αα 3cos
42cos
2cos)
43
(2
)(3
32
23
31
22 ++++= (3.2)
• Under small-signal assumption, the system is
4242
g ynormally linear and harmonics are negligible. Thus, α1A dominates small-signal gain = α1.
• For large signal nonlinearity becomes evident• For large signal, nonlinearity becomes evident. large-signal gain = . The gain varies when input level changes.
4/3 331 Aαα +
• If α3 < 0, the output is a “compressive” or “saturating” function of the input the gain is compressed when A increases
Basic Concepts – Linearity, noise figure, dynamic range, FDAI, 2008 Page 14
compressed when A increases.
Output of Bipolar Differential Pair
⎟⎟⎠
⎞⎜⎜⎝
⎛ −=
T
idCEEF
id
od
VV
RIVV
2tanhα( ) K+−+−= 753
3157
152
31tanh xxxxx
Basic Concepts – Linearity, noise figure, dynamic range, FDAI, 2008 Page 15
Effects of Nonlinearity – 1dB Compression Point (d
BV)
11 13
log20α
=−dB dBA
ut V
olta
ge
1dB11
1
31311
380801450
43
αα
αα
==
+ −−
dB
dBdB
A
AA
dBA1
Out
pu
20logAin
331 3808.0145.0
αα−dBA
VdB pp 8/
l102
dBA −1 20logAin
• 1-dB compression point is defined as the input signal level that causes small-signal gain to drop 1 dB It’s a measure of the maximum input
mWdBm pp
150log10
×Ω=
small signal gain to drop 1 dB. It s a measure of the maximum input range.
•1-dB compression point occurs around -20 to -25 dBm (63.2 to 35 6 V i 50 Ω t ) i t i l f d d RF lifi
Basic Concepts – Linearity, noise figure, dynamic range, FDAI, 2008 Page 16
35.6mVpp in a 50-Ω system) in typical frond-end RF amplifiers.
Effects of Nonlinearity – Desensitization (Blocking)• Desensitization -- small signal experiences a vanishingly small gain when co-exists with a large signal, even if the small signal itself does not drive the system into nonlinear range.A l i t t i t x(t) = A cosω t+ A cosω t t E (3 1) h
,cos23
43)( 1
2213
31311 L+⎟
⎠⎞
⎜⎝⎛ ++= tAAAAty ωααα
Applying two-tone inputs x(t) = A1cosω1t+ A2cosω2t to Eq.(3.1), we have
gain of desired 24 ⎠⎝
,cos23)( 11
2231 L+⎟⎠⎞
⎜⎝⎛ += tAAty ωααFor A1<< A2, it reduces to
signal
2 ⎠⎝
Observations:• Weak signal’s gain decreases as a function of A2 if α3 < 0. For sufficiently largeWeak signal s gain decreases as a function of A2 if α3 < 0. For sufficiently large A2, the gain drops to zero the weak signal is “blocked” by the strong signal. (Why cannot we see stars during day?)• Many RF receivers must be able to withstand blocking signals 60 to 70 dB
t th th t d i l
Basic Concepts – Linearity, noise figure, dynamic range, FDAI, 2008 Page 17
greater than the wanted signals.
Effects of Nonlinearity – Intermodulation
• Harmonic distortion is due to self-mixing of a single-t i l It b d b l filt itone signal. It can be suppressed by low-pass filtering the higher order harmonics.
• However there is another type of nonlinearity• However, there is another type of nonlinearity --intermodulation (IM) distortion, which is normally determined by a “two tone test”.
• When two signals with different frequencies applied to a nonlinear system, the output in general exhibits some components that are not harmonics of the input frequencies. This phenomenon arises from cross-mixing (multiplication) of the two signals
Basic Concepts – Linearity, noise figure, dynamic range, FDAI, 2008 Page 18
mixing (multiplication) of the two signals.
Effects of Nonlinearity – IntermodulationAA)(
DC Term++=
+=
AAty
AtAtx
)(21)(
coscos)(2
22
12
2211
α
ωω
1st Order Terms
⎥⎤
⎢⎡
+⎥⎦⎤
⎢⎣⎡ ++
tAAAA
tAAAA
)2(3
cos)2(43
22
122
211311 ωαα
2nd Order [ ]++
+⎥⎦⎤
⎢⎣⎡ ++
tAtA
tAAAA
2cos2cos21
cos)2(4
22
212
12
222
212321
ωωα
ωαα
Terms[ ][ ]++
+−++
tAtA
ttAA
3cos3cos41
)cos()cos(2
23
213
13
2121212
ωωα
ωωωωα
3rd Order terms
[ ][ ][ ] ⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧
−++
+−++
ttAA
ttAA
)2cos()2cos(
)2cos()2cos(43
4
12122
21
212122
13
ωωωω
ωωωωα
Basic Concepts – Linearity, noise figure, dynamic range, FDAI, 2008 Page 19
[ ] ⎭⎩ 121221
Intermodulation – Why do we care about IM3 mostly?
In wireless communication system such as cellular handsets with narrow-band operating frequencies (i.e., a few tens of MHz), only the IM3 spurious signals (2w1 - w2) and (2w2 - w1) fall within the filter passband.
Basic Concepts – Linearity, noise figure, dynamic range, FDAI, 2008 Page 20
Intermodulation -- Third Order Intercept Point (IP3)
• Two-tone test: A1=A2=A and A is sufficiently small so that higher-order nonlinear terms are negligible and the gain is relatively constant and equal to α1.constant and equal to α1.
• As A increases, the fundamentals increases in proportion to A, whereas IM3 products increases in proportion to A³.
⎤⎡⎤⎡
+=
+=
Aty
AtAtx
)(
coscos)(2
2
21
α
ωω 3133
13
231 and
34
49 IIPOIPIIPA α
αα
αα ==→>>
dBA dB 69145.01
[ ] [ ]+++++
+⎥⎦⎤
⎢⎣⎡ ++⎥⎦
⎤⎢⎣⎡ +
ttAttA
tAAtAA
)cos()cos(2cos2cos1
cos49cos
49
22
22
3112
31
ωωωωαωωα
ωααωααdB
AIP
dB 6.93/43
1 −≈=
[ ] [ ]
[ ] [ ][ ] ⎭
⎬⎫
⎩⎨⎧
−+++−++
++
+−++++
tttt
AttA
ttAttA
)2cos()2cos()2cos()2cos(
433cos3cos
41
)cos()cos(2cos2cos2
2121
21213321
33
21212212
ωωωωωωωω
αωωα
ωωωωαωωα
Basic Concepts – Linearity, noise figure, dynamic range, FDAI, 2008 Page 21
[ ] ⎭⎩ ++ tt )2cos()2cos(44 2121 ωωωω
Intermodulation – IP2 vs. IP3
20
40 IP2
FundamentalA1α A1α
A1=A2=A2ND Order IM Product:
2
12 α
α=IPA
20
0
20 Fundamental
22 Aα
1
22 Aα
-60
-40
-20IP3
1
1
121 ωω − 1ω 2ω 21 ωω +
Freq
3RD Order IM Product 4 α
-80 3
-100
3rd Order IM Product
2nd Order IM Product
1
3 Order IM Product3
13 3
4αα
=IPA
PΔ
A1α A1α
3
-60
-120 IIP3
-40 -20 0 20 40
IM Product2
Freq
334
3 Aα 334
3 Aα
Basic Concepts – Linearity, noise figure, dynamic range, FDAI, 2008 Page 22
0212 ωω − 1ω 2ω
Freq122 ωω −
Calculate IIP3 without Extrapolation
1 AA A 1
PΔ
A1α A1α
33 A 3
20logAi
33 A
P
Freq
334Aα 3
343 Aα
20logAin
P/2
212 ωω − 1ω 2ωFreq
122 ωω −
][2
][][3 dBmPdBPdBmIIP in+Δ
=
Basic Concepts – Linearity, noise figure, dynamic range, FDAI, 2008 Page 23
Relationship Between 1-dB Compression and IP3
1-dB compression point with single tone applied:
3
13 3
4αα
=IPA3
11 145.0
αα
=−dBA dBAA
dB
IP 66.904.31
3 ==
1-dB compression point with two tones applied:
dBAIP 4142553
23
1
3 αα
dBA dB
IP 4.1425.522.0
3
11
3 ===
αα
Basic Concepts – Linearity, noise figure, dynamic range, FDAI, 2008 Page 24
Determine IIP3 and 1-dB Compression Point from Measurement
• An amplifier operates at 2 GHz with a gain of 10dB. Two-tone test with equal power applied at the input, one is at 2.01 GHz. At the output, four tones are observed at 1.99, 2.0, 2.01, and 2.02GHz. The power levels of the tones are -70,-20,-20, and -70dBm. Determine the IIP3 and 1-dB compression point for this amplifier.
• Solution: 1.99 and 2.02 GHz are the IP3 tones.
( ) [ ] [ ]dBP
dBmPPGPIIP
66146695
57020211020
213 311 −=+−+−−=−+−=
OIP3)log(20 1 A
dBmPdB 66.1466.951 −=−−=
334
3log20 AP
][2
][][3 dBmPdBPdBmIIP in+Δ
=
IIP320logAin
4
P/2
Basic Concepts – Linearity, noise figure, dynamic range, FDAI, 2008 Page 25
2
Intermodulation of Cascade Nonlinear Stages
...)()()()(
...)()()()(3
132
12112
33
2211
+++=
+++=
tytytyty
txtxtxty
βββ
ααα
L
)(t)(t)(t )(2 ty)(1 ty)(tx
A A A1,3IPA 2,3IPA 3,3IPA
Linearity is more important for back-end stages.
K+++≈ 23,3
21
21
22,3
21
21,3
23
11
IPIPIPIP AAAAβαα
Basic Concepts – Linearity, noise figure, dynamic range, FDAI, 2008 Page 26
,,,
Noise Figure of Cascade Stages
( ) NFNFNF 111 −−−( )GGG
NFGG
NFG
NFNFNFmppp
m
ppptot
)1(.....2111
3
1
21
1.....
1111
−
++++−+=
NFtot – total equivalent Noise FigureNFm – Noise Figure of mth stage
G A il bl i f th tGpm – Available power gain of mth stage
Noise figure is more important for front-end stages.
Basic Concepts – Linearity, noise figure, dynamic range, FDAI, 2008 Page 27
Sensitivity
• Sensitivity -- defined as the minimum signal level that the system can detect with acceptable SNR.
OUT
RSsig
OUT
in
SNRPP
SNRSNRNF
/==
• The overall signal power is distributed across the channel bandwidth, B, integrating over the bandwidth to obtain total mean square power
BSNRNFPP OUTRStotsig •••=,
here P is the so rce resistance noise po er
BSNRNFPPdBdBHzdBmRSdBmin log10min/min, +++=
Basic Concepts – Linearity, noise figure, dynamic range, FDAI, 2008 Page 28
where PRS is the source resistance noise power.
Maximum Input Power
OIP3)log(20 1 A
2,
3outIMout
inIIP
PPPP
−+=
20logA
334
3log20 AP
23
2,, inIMininIMin
in
PPPPP
−=
−+=
2 PP +IIP320logAin
P/2 32 ,3 inIMIIP
in
PPP
+=
where PIM,out denotes output-referred power of IM3 products, Pout=Pin+G, PIM,OUT= PIM,in+G. The input level for which the IM products become equal to the noise floor F is thus given by
3log101742
32 33 BNFdBmPFPP IIPIIP
in++−
=+
=
Basic Concepts – Linearity, noise figure, dynamic range, FDAI, 2008 Page 29
Dynamic Range• Dynamic Range (DR) -- defined as the ratio of the maximum to
minimum input levels that the circuit provides a reasonable signal quality.
• Spurious Free Dynamic Range (SFDR) determine the upper• Spurious-Free Dynamic Range (SFDR) -- determine the upper end of dynamic range on the intermodulation behavior and the lower end on sensitivity.
• The upper end of the dynamic range is defined as the e uppe e d o t e dy a c a ge s de ed as t emaximum input power in a two tone test for which the 3rd IM products do not exceed the noise floor F=-174dBm+NF+10logB.
• The SFDR is thus given by
min3
min3
,max, 3)(2
)(3
2SNR
FPSNRF
FPPPSFDR IIPIIP
miminin −−
=+−⎟⎠
⎞⎜⎝
⎛ +=−=
• Example: NF=9dB, PIIP3=-15dBm, B=100kHz, SNRmin=12dB SFDR=(-15-(-174+9+50))/1.5-12=54.7dB.
Basic Concepts – Linearity, noise figure, dynamic range, FDAI, 2008 Page 30