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VGAVGA
충북대학교 전자정보대학 김영석
2 1 92010.9
1
Outline1. AGC System
I t d ti– Introduction– System Analysis
2. VGA – Control Block– Gain Cell
3. RSSI– Limiting Amplifier– Rectifier
2전자정보대학 김영석
AGC in GPS ReceiverRF Freq = 1.575GHzIF F 4 092MHIF Freq = 4.092MHzIF Bandwidth = 2MHzBPF selects GPS signal, but rejects the Image
3Torrre07,GloNav
3전자정보대학 김영석
AGC in GPS Receiver• AGC Input: Below Thermal Noise • AGC Output: ADC Full ScaleAGC Output: ADC Full Scale• AGC 40dB Variable Gain Range• MOSFET M1,2 in Triode ,
=> Variable Gain• Removes DC Offset • AGC Loop
4 4전자정보대학 김영석
AGC TheoryAGC(Automatic Gain Control): Automatically Controlling Gain, High Enough to Operate ADC
y
Originally Used to Remove Radio FadingAmplifying Vin => Peak Detection => Low pass Filtering Compare with VREF => Loop Filter => VGA Gain ControlCompare with VREF => Loop Filter => VGA Gain Control
V O U T
PeakD etector
VG AV IN
LPF
V C
LoopFilter V R EF
+-
5 5전자정보대학 김영석
AGC with Several VGA StagesLarge Gain in the 1st Stage Reduce the Noise FigureBut When Signal Large Enough
g
g g gNoise Figure Not CriticalGain of 1st Stage May Be Low
LPF LPFVG A VG A LPF Buffer
R F Front-End
X1
BasebandD em odulator
R SSI
Analog Baseband AG C
6 6전자정보대학 김영석
AGC Transfer CharacteristicsVi < V1 (Low Input)
AGC InoperativeLinear
V1< Vi <V2AGC OperativeAGC OperativeOutput Constant
Vi > V2 (High Input)AGC InoperativeLinearPrevent System InstabilityPrevent System Instability Problems
7
Modern Communication Circuits, Smith
7전자정보대학 김영석
AGC: Linear in Decibels
Linear in DecibelsGain in decibels (dB) vary linearly with VCGain in decibels (dB) vary linearly with VCIf Input has Step Increase in 3dB, Output has Step Increase of 3dB and Decay Exponentially after Settling Time
, : 1 PVVeKPAmpGainVariable ioaVc ==
))((:)ln(:
:
2
122
1
VVsFVVoltageControlVKVAmpcLogarithmi
VVDetectorEnvelope o
−==≈
)log(20 ),log(20 )(ln)](1[ln ,
))((: 2
VeVeletVsaFVsaFVSolving
VVsFVVoltageControl
iioo
rio
rc
==+=+
)(1)(7.8
)(1 saFVsaF
saFe
e rio +
++
=∴
8Modern Communication Circuits, Smith
8전자정보대학 김영석
AGC: Linear in Decibels
F(s) usually LPF Loop Bandwidth < Modulating Frequency(AM)Loop Bandwidth < Modulating Frequency(AM)
Steady State Output Change = SmallL G i LLoop Gain = Large
Fe
ChangeStateSteady o 0)0(1
1: ≈+
=ΔΔ
S t DC O t t i D ib l P ti l t V
FilterofGainDCFwhereaFei
)0( )0(1
=+Δ
System DC Output in Decibels Proportional to Vr
)( =KsFlet
)1( 655.81655.8
1:
/1)(
>>≈+
++
=
+=
aKVaKaKV
aKe
eOutputDC
BssFlet
rri
o
9 9전자정보대학 김영석
AGC: Linear in Decibels
Closed-Loop Transfer FunctionaK > 0 => LHP Pole => /1
)( Bs
KsFlet+
=aK 0 LHP Pole Inherently StableAGC = High Pass Filter
1
1
1
/1
sBs
aKe
e
Bs
io
+
+
+Δ
=Δ
+
Low Freq: Output Change = Small (AGC Operation)High Freq: Output Pass =>
)1(1
aKB ++
High Freq: Output Pass AGC NonOperation (Ex: Pass AM Signal)wL =B(1+aK) < wM(AmplitudewL =B(1+aK) < wM(Amplitude Modulation Freq)
10 10전자정보대학 김영석
AGC: Linear in Decibels
Filter = Integrator (Infinite DC Gain)C
ri aCVssese
sCsF
655.8)()(
)(
+=
=
rot
o
VteOutputStateSteadyaCsaCs
se
655.8)(lim:
)(
0=
++
+
→
Ex: Time Response to a Step Change in InputTime Constant of Exponential Decay = AGC Bandwidth = aC
i
i
sesse
DecibelChangeStepUnits
se
Δ=Δ
=Δ
)()(
), (1)(
aCtoo
o
eteaCs
se
aCsse
−=Δ+
=Δ∴
+Δ
)( ,1)(
)(
11 11전자정보대학 김영석
AGC: Pseudo-Linear• No Logarithmic Amp => NonLinear System
V
oo
orc
ioaV
PVdVS l i
VVsFVVoltageControlPVVeKPAmpGainVariable c
/))((:
,: 1
−===
• Loop Transmission ci
ii
oo
dVdPVsFVdV
Solving)(1/
,+
=
– Nonlinear, Function of Input Signal– BW = Pole = 1/Speed =Input Signal Dependent
12 12전자정보대학 김영석
AGC: Psuedo-Linear
Ex: No Log Amp, P=Vc(linear), F(s)=K/sVdV /
ci
ci
ii
oo
sKV
P
dVdPVsF
PVdVVdV
+=
+=
1)(1//
i
i
i
cc
sΔ
sVΔV
InputinChangeStepSmall =)( :
tKVi
o
o
i
i
o
o ieΔtVΔV
KVsΔ
sVΔV −=
+=∴ )( ,)(
Time Constant (Speed) of AGC is Dependent on Input Signal Amplitude Vi
13 13전자정보대학 김영석
AGC System Componentsy pExponential Amp (VGA)
LT
cLm
o RVI
RgVV
V
21 −=−=
−
cTc
aVL
T
VVs eKRVeI
1
/ =−=
Logarithmic Amp
/C
VVs
s
i
V
eIRV
I To==
)ln(ss
iTo IR
VVV =
14 14전자정보대학 김영석
AGC Settling TimePreamble Duration > Settling (Acquisition) Time of AGC Loop
g
Nonlinear AGC System => Settling Time is Input Signal Dependent. Long Preamble 2
1)( VkGC ekVG CG= ⋅Long Preamble
Addition of Logarithmic Function => Linear in Decibels
212
2)(
vGM
GC
kkGC
ekVG
=
=
τ
Analysis:VGA Must Have Exponential Function
21)( Vk
GC
CekVG CG= ⋅
Constant AGC Time ConstantWithout Log Amp, AGC Operates OK But Nonlinear AGC Time
212 vGM kkGC
=τ
OK. But Nonlinear AGC Time Constant. Inversely Proportional to VREF=VIN
REFGM VkGC
12=τ
15
Khoury98
15전자정보대학 김영석
AGC Settling TimeAGC ABM(Analog Behavioral Model) SimulationAGC1: VGA with Exponential Gain Control
g
AGC2: VGA with Linear Gain Control=> Input Decrease => Longer Time Constant
ss
VGeG CVC
μτμτ
503TimeSettling 163.0
331, 2535.1
1
≈≈=>=
+==
sμτ 5.03TimeSettling ≈≈=>
16Khoury98
16전자정보대학 김영석
VGA Theory• VGA(Variable Gain Amplifier: 자동 이득 조절기): Voltage Gain (dB) is Linear to
Control Signal
y
• Voltage Gain is dB => VGA Gain has dB-Linear Char.• VGA = Exp Amp (cf: RSSI = Log Amp)
G i C t l b Di it l Si l 2NR• Gain Control by Digital Signal 2 R
2R
R
• Gain Control by Analog Signal
V IN
V O UT
-
+
VIN +
2II Δ
+2II Δ
−II Δ+
VIN -
TriodeTransistor
17 17전자정보대학 김영석
VGA Exponential Function ApproximationVGA Has Exponential Function of Control Signal
p pp
Control SignalExponetial Function Approximations
Pseudo Exponential (Harjani95)p ( j )
Taylor Series (Chang01)
Pseudo Exp + Taylor (Dong05)Pseudo Exp + Taylor (Dong05)
18 18전자정보대학 김영석
VGA Exponential Function ApproximationPseudo Exponential Appro.[Harjani95]-0.7<x<0.7, 30dB Gain Variability=>
p pp
Require 2 Stages for 60dBDifferential Pairs Q1,Q2 + Load Q3,Q4 Voff: Current Mirror in SaturationVoff: Current Mirror in Saturation Region3rd Stage: Large Diff Gain, CMFB
11)( 2
ax
axax
axax
eeexf
−+
≈==−
)/1()/1(
Required Stages 2/1/1
1
111
1
1
3
1
3
1
bbb
bbbD
b
b
m
m
IIIIIIIIIIIIIIII
gg
Gain
axe
−=−=+=+=
=>−+
==ββ
)/1( 113 bbbD IIIIII ==
19 19전자정보대학 김영석
VGA Exponential Function ApproximationPseudo-exponential[Motamed98]Exp(Control Current IC) => I1/I2
p pp
cnxn Ixwheree
xx
IIxf α==
−+
== )11()( )2(
2
1
I1/I2 => Vds
2
113
2453
33
1
II*IRV
*IRV
)-V*(VKI
-triodeNds
/NPG
THG∝==
=
Vds => Multiplier
2
p
20 20전자정보대학 김영석
VGA Exponential Function Approximation
Pseudo-exponential[Huang98] 5.0)
11(
)()(
/ xKIIII
II
ggGain controlbiasiiiloadminputm
+=
+===
ββ
ββ
p pp
exponential[Huang98]Diff Pairs M1/M2, Diode Connected
,, )1
()( xIII
ggcontrolbiaslll
loadminputm −−ββ
Diode Connected Loads M3/M4
Cascading Two Cells => Exp(x)=> Exp(x)
21 21전자정보대학 김영석
VGA Control Block• Control Block : x=Vc
22
Duong06
22전자정보대학 김영석
VGA Gain CellGain Cell + CMFB
23
Duong06
23전자정보대학 김영석
VGA2 VGA StagesTechnology: 0.18umVDD=0.18V, I=3.6mABandwidth: 40MHz – 1GHzGain Variation: 48dB 26dBGain Variation: -48dB – 26dB
24
Duong06
24전자정보대학 김영석
DC Offset CancellationDC Output Feedback to Input Through LPF. HF Signal Does not Pass.Adding this DC Output (-) to DC Input => Remove DC Offset DC Offset is Removed in First Stage before It Becomes Too LargeResidual Offset is removed in Last Stage
25
Ta05
25전자정보대학 김영석
VGA ExampleVGA Control Block
p
0674
)1()1()(
25
262
22
=
=−+++
≈==−
aSimulationFromVx
II
axkaxk
eeexf
C
D
Dax
axax
067.4, =aSimulationFrom
26 26전자정보대학 김영석
VGA ExampleGain Block with CMFB
p
27 27전자정보대학 김영석
VGA ExampleVGA Output: AC, Transient
p
28 28전자정보대학 김영석
VGA ExampleCMFB
p
29 29전자정보대학 김영석
AGC ExampleAGC Block Diagram2 VGAs
30 30전자정보대학 김영석
AGC Example
3 VGAs
31 31전자정보대학 김영석
AGC Example
Error Amp + Full Wave Rectifier(FWR)
32 32전자정보대학 김영석
RSSIRSSI(Received Signal Strength Indicator): Represent the Received Signal Strength Used to Adjust Gains of Baseband Processor. Power Off when No SignalMagnitude of Received Signal [dBm], RSSI Transfer Char. V vs dBm. g g [ ]RSSI is Log Amplifier. (cf. VGA is Exponential Amp)Ref: Huang00
33 33전자정보대학 김영석
Log Amplifier
)log( xy =
• Char.
g p
)log( xy =
• Input Sine Wave modulated by• Input Sine Wave modulated by Triangular Signal => Log Output of Triangular Signal
• ASK Amplitude => Log of Amplitude Pulse
34 34전자정보대학 김영석
Log AmplifierLog Amp
Limiting Amp + FWR(Full Wave Rectifier)
g p
Summation + LPFGain and Bandwidth of Unit Limiting Amp
(N # f St At T t l V lt G i )(N = # of Stages, At=Total Voltage Gain)
35 35전자정보대학 김영석
Log Amplifier• Clipping by 1st Stage:
g p
• Clipping by 2nd Stage:
V IN
4V L
5V L
V]
T rue Logarithm ic R esponse
L ith i E
A vV IN
∑
V IN
V 1
V 2
V 3
V n
V O UT
A v A v A v V log
LPF
3V L
2V L
V
V OU
T [VLogarithm ic Error
Logarithm ic O utput
V L
5V
L
AV
4V
L
AV
3V
L
AV
2V
L
AV
V
L
AV
0-100
6V
Lt A
VV ≈
10-5 1
36
V IN [dB m , V]
36전자정보대학 김영석
Limiting AmplifierConventional NMOS Load: Low Voltage Operation is Difficult due to Body Effect =>
g p
Operation is Difficult due to Body Effect => Folded Load
M 3 M 4
V (+) V ( )
V out(-) V out(+)
M 1 M 2 V (+) V ( )
V out(-) V out(+)
M 1 M 2
M 3 M 4
V B2
ID 3 ID 1
V in(+) V in(-)
V B
M 1 M 2 V in(+) V in(-)
V B1
M 1 M 2
37 37전자정보대학 김영석
Limiting Amplifier(1) An NMOS differential pair with NMOS loads [Khorram95]
g p
3
1m
gg
Gain =3mg
(a) (b)
38 38전자정보대학 김영석
Limiting Amplifier(2) Source-coupled pair with Folded diode load [Huang00] =>Low Voltage operation
g p
load [Huang00] =>Low Voltage operation1m
gg
Gain =3mg
39 39전자정보대학 김영석
Limiting Amplifier(3) Current mirror type [Kim01]:
Khorram95: Load has Body Effect
g py
Eliminate Body Effect. Low Voltage Operation. But High Current Consumption
3
1
m
m
gg
Gain =
40 40전자정보대학 김영석
RectifierFWR(Full Wave Rectifier)Tie 2 Current Mirrors =>Tie 2 Current Mirrors => FWR-out ResistorVin(+) > Vin(-): ID1 > IBVin(+) > Vin(-): ID1 > IB, Current Mirror 1 On => Current to FWR-out Vin(+) < Vin(-): ID2 < IB, Current Mirror 2 On =>Current to FWR-out => Full Wave Rectification
41 41전자정보대학 김영석
Rectifier(1) Unbalanced Source-Coupled Pairs [Kimura93]Linearity Improvements by Unbalanced Source-Coupled Pair(M1-M4)y p y p ( )Vin+ > Vin- : ID3, ID6, ID8 Increase => Output HighVin+ < Vin- : ID2, ID6, ID8 Increase => Output High => FWR
42 42전자정보대학 김영석
Rectifier(2) Source degenerated differential pairs and two current mirrors [Kim01]Source degenerated differential pairs => Improve LinearityVin+ > Vin- : ID1, ID3, ID5 Increase => Output HighVin+ < Vin : ID2 ID4 ID6 Increase => Output High => FWRVin+ < Vin- : ID2, ID4, ID6 Increase => Output High => FWR
43 43전자정보대학 김영석
Rectifier(3) Multiplier based on Gilbert cells [Khorram95]Four-Quadrant MOS MultiplierQ p
44 44전자정보대학 김영석
Rectifier(4) Open-loop Current-mode rectification [Huang00]Depending on Iin Direction =>Mrn/MrpON/OFF (Half Wave Rec.)Two Parallel Circuits => Full Wave RecTwo Parallel Circuits => Full Wave Rec.Instead of Mrp, NMOS Didoe Mr1 is usedMg1-Mg4: Convert V => Ig g
45 45전자정보대학 김영석
DC Offset CancellationDC offset cancellations(1) feedback type [Huang00]( ) yp [ g ]
46 46전자정보대학 김영석
RSSI ExampleLimiting AmplifierGain =gm21/gm23= 10dB
pg g
47 47전자정보대학 김영석
RSSI ExampleFull Wave Rectifier
p
48 48전자정보대학 김영석
RSSI ExampleFWR DC Transfer Curve/Transient Char.
p
49 49전자정보대학 김영석
RSSI ExampleRSSI
p
50 50전자정보대학 김영석
RSSI ExampleRSSI Output
1.0V
p
0.5V
0V
Time
50us 100us 150us 200usV(vi+) V(fwr1:fwr_out)
51 51전자정보대학 김영석
ConclusionAGC System
Linear in Decibels AGCLinear in Decibels AGC Pseudo-Linear AGC
VGAControl BlockGain BlockExample
RSSILimiting AmplifierRectifierE lExample
52 52전자정보대학 김영석
평가 문제1. Linear in Decibels AGC System의 블록 다이어그램을 그려라.2. Linear in Decibels AGC System과 비교하여 Pseudo-Linear AGC
평가 문제
System의 문제점은 무엇인가?3. Linear in Decibels AGC System에서 사용되는 VGA는 출력 전압이 제어전
압에 대해서 어떤 특성(함수)을 가지나?압에 대해서 어떤 특성(함수)을 가지나?4. RSSI의 출력은 입력 전압에 대해서 어떤 함수를 가지나?
53 53전자정보대학 김영석
참고 문헌[Chang01] C.-C. Chang et al., “CMOS Current-Mode Exponential-Control Variable-Gain Amplifier”, Electronics Circuits, vol. 37, pp. 868-869, 2001.[Duong05] Q-H. Duong et al., “An All CMOS 84dB-Linear Low-Poer Variable Gain Amplifier”, Symposium on VLSI
참고 문헌
Circuits, pp. 114-117, 2005.[Harjani95] R. Harjani, “A Low-Poer CMOS VGA for 50 Mb/s Disk Drive Read Channels”, IEEE Trans. Circuits Syst. II, vol. 42, pp. 370-376, 1995.[Huang98] P.-C. Huang et al., “A 3.3-V CMOS Wideband Exponential Control Variable-Gain-Amplifier”, ISCAS, pp. 285 288 1998285-288, 1998.[Huang00] P-C. Huang, “A 2-V 10.7-MHz CMOS Limiting Amplifier/RS냐”, IEEE J. of Solid-State Circuits, vol. 35, pp. 1474-1480, 2000.[Kim01] H.-S. Kim et al., “CMOS Limiters with RSSI for Bluetooth Receivers”, MWSCAS, pp. 812-815, 2001.[Kimura93] K Kimura “A CMOS Logarithmic IF Amplifier with Unbalanced Source Coupled Pairs” IEEE J of[Kimura93] K. Kimura, A CMOS Logarithmic IF Amplifier with Unbalanced Source-Coupled Pairs , IEEE J. of Solid-State Circuits, vol. 28. pp. 78-83, 1993.[Khorram95] S. Khorram et al., “A CMOS Limiting Amplifier and Signal-Strength Indicator”, Symp. on VLSI Circuits, pp. 95-96, 1995.[Khoury98] J. M. Khoury, “On the Design of Constant Settling Time AGC Circuits”, IEEE Trans. Circuits Syst. II, [ y ] y, g g , y ,vol. 45, pp. 283-294, 1998.[Motamed98] A. Motamed et al., “A Low-Voltage Low-Power Wide-Range CMOS Variable Gain Amplifier”, IEEE Trans. Circuits Syst. II, vol. 45, pp. 800-811, 1998.[Smith98] Modern Communication Circuits, 2nd Edition, J. R. Smith[Ta05] C. M. Ta et al., “A 2.7mW, 0.064mm2 Linear-in-dB VGA with 60dB Tuning Range, 100MHz Bandwidth, and two DC Offset Cancellation Loops”, RFIT2005, pp. 74-77, 2005.[Torre07] V. D. Torre, “A 20 mW 3.24 mm2 Fully Integrated GPS Radio for Location Based Services”, IEEE J. of Solid-State Circuits, vol. 42, pp. 602-612, 2007.
54 54전자정보대학 김영석
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