1_system characterization

– Most active devices are nonlinear. The nonlinearity shall be taken into account in wireless system design.
•
How large can the system handle (with “acceptable” distortions)?
Assume equal signal level A1 = A2 = A
ω1 , ω2 → a1 A + a3 A2ω2 →
•
9 4
ω1 ± ω2 → a2 A2
3 a3 A3 4 3 2ω2 ± ω1 → a3 A3 4 2ω1 ± ω2 →
C-N Kuo, Fall 2005
1-12
RF Integrated Circuit Design
Characterization
Cascaded Nonlinear Stages
y1(t) = a1 * x(t) + a2 * x2(t) + a3 * x3(t) +K
y2(t) = b1 * y1(t) + b2 * y1 (t) + b3 * y1 (t) +K
Non-Linear System2
2
3
x (t )
•
Non-Linear System1
y1 (t )
y2 (t )
Cascaded IIP3
1
2 AIIP 3, t
=
1
2 AIIP 3,1
+
a12 a12b12 + +K 2 2 AIIP A IIP 3, 3 3, 2 a1 AIIP 2, 2
Pout ( dBm )
OIP3
ω1 , ω2 → a1 A + a3 A3
9 4
Pout ( dBm )
OIP2
ω1 , ω2 → a1 A + a3 A3
9 4
∆
2ω1 − ω2 →
3 a3 A3 4
Pin ( dBm )
ω1 + ω2 → a2 A2
Pin ( dBm )
IIP2
AIIP 2 = a1 a2
•
Cascade IIP2
1 AIIP 2,t
=
1 AIIP 2,1
+
C-N Kuo, Fall 2005
1-13
RF Integrated Circuit Design
3dB
Pin 2 ( dBm)
Pin 2, −3dB
•
Cross modulation
A2 (1 + m cos ωmt ) cos ω2t
A1 cos ω1t
Desired signal Large blocker Desired signal Large blocker
NLS
C-N Kuo, Fall 2005
C-N Kuo, Fall 2005
1-4
RF Integrated Circuit Design
Characterization
Linearity Analysis
• For memoryless nonlinear system (or frequency independent nonlinear), power series approach can be employed. For most weakly nonlinear system, third-order polynomial is good enough to analyze most nonlinear effects. e.g. amplifier circuit
x(t ) = A cos ω1t x(t ) = A cos ω1t + A cos(ω2t + θ 2 )
•
Æ 0dB Æ 3dB
PAR is a stochastic process in digital communication. This demands higher linearity requirement in circuit and system design.
2ω2 − ω1
ω1 + ω2
ωs ω1 ω2
C-N Kuo, Fall 2005
ωs ω1 ω2
2ω1 2ω2
3ω1 3ω2
1-8
RF Integrated Circuit Design
Characterization
Intermodulation (cont’)
• Third-order intermodulation (IMD3) • Second-order intermodulation (IMD2)
•
x (t )
Non-Linear System
y(t) = a1 * x(t) + a2 * x2 (t) + a3 * x3(t) +K
VIN VBQ +VS VT
VIN = VBQ + VS
I C = I CO e VT = I CO e
Q1
VBQ VS = I CO e VT . eVT
C-N Kuo, Fall 2005
1-3
RF Integrated Circuit Design
Characterization
Analysis Method
Available in various CAD tools • • • • Time domain numerical integration method Frequency domain harmonic balance method Circuit envelope method … Handy formulation • • Power series analysis Volterra series analysis
2rd-order IMD
3rd-order IMD
Practical consideration. When ω1 – ωs = ω2 - ω1, third-order IMD falls into frequency band of interest.
Desired signal
2ω1 − ω2
Pin ,−1dB
C-N Kuo, Fall 2005 1-6
RF Integrated Circuit Design
Characterization
Distortion in Nonlinear System (cont’)
• Desensitization & blocking G
Desired signal Large blocker Nonlinear System Desired signal Large blocker
ω1 ± ω2 ± ω3 → a3 A3
C-N Kuo, Fall 2005 1-10
3 2
RF Integrated Circuit Design
Characterization
Broadband Signal
• In wide-bandwidth systems
– Adjacent channel power ratio (ACPR)
RF Integrated Circuit Design
Characterization
System Characterization
Linearity analysis Noise figure Dynamic range Types of noise sources Calculation with noise quantities
A
nonlinear system
a1 A
1 a2 A 2 2
ω
• Gain compression
Gain (dB)
3 a3 A3 4
1 a2 A 2 2
1 a3 A3 4
DC
ω
2ω
(2-H)
3ω
(3-H)
1dB
Pin ( dBm )
⇒ A−1dB = 0.145
a1 a = 0.381 1 a3 a3
BW
C-N Kuo, Fall 2005
1-11
RF Integrated Circuit Design
Characterization
Peak-to-Average Ratio
• In multi-carrier system, peak amplitude is much higher than the average.
AIIP 3 =
4 a1 3 a3
IIP3
⇒ IIP 3( dBm ) = 9.6dB + Pin , −1dB ( dBm )
C-N Kuo, Fall 2005
1-9
RF Integrated Circuit Design
Characterization
Broadband Characterization
frequency
Harmonics Intermodulation Triple Beat
2 2 2 2 + 3 x12 x2 + 3 x12 x3 + 3 x2 x1 + 3 x2 x3 + 3 x3 x1 + 3 x3 x2
+ 6 x1 x2 x3
Twice as large as the IM3 products
x (t )
•
Linear System