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01/04/2011 - 1 ATLCE - B2 - © 2011 DDC
Politecnico di Torino - ICT School
Analog and Telecommunication Electronics
B2 - Amplifiers nonlinearity
» Reference circuit» Nonlinear models » Effects of nonlinearity» Applications of nonlinearity
01/04/2011 - 2 ATLCE - B2 - © 2011 DDC
Lesson B2: Nonlinearity & distortion
• Large signal amplifiers– Reference circuit– Nonlinear device model
• Effects of nonlinearity – Distortion and Harmonics, – Gain changes
• Output spectrum– Intermodulation– Intercept Point
• Lab 2: Large signal behaviour (nonlinear)
• Text reference: Tuned amplifiers: sect 1.2.3
01/04/2011 - 3 ATLCE - B2 - © 2011 DDC
Amplifiers in radio structure
PA (power amplifier)
TX output amplifiers
- High efficiency, low distorsion
IF channel
LNA (low noise amplifier)
RX input amplifiers
- Low noise, wide dynamic
01/04/2011 - 4 ATLCE - B2 - © 2011 DDC
Reference circuit
• Basic transistor amplifier in passband– Get rid of bias network and coupling capacitors
Vcc
Vi
C1 Q1
Vo
C4
Ie
Z’e
Zc
Vcc
Vi
Q1
VoIe
Zc
Ie(DC)
Ie(DC)
Ze
01/04/2011 - 5 ATLCE - B2 - © 2011 DDC
Other configurations
• Same model can be used for other configurations– Differential– CB– CC
• First step:– Zc Rc– Ze Ce CC (in passband)
01/04/2011 - 6 ATLCE - B2 - © 2011 DDC
• Linear model IC = gm VBE or hfe iB approximation• Actual IC(VBE) log curve
– vi(t) = Vi cos t– x = Vi / VT– VBE = Vi + VE
BJT: nonlinear model
01/04/2011 - 7 ATLCE - B2 - © 2011 DDC
Analysis with nonlinear BJT model
• ex cos t can be expanded in Fourier series
– In(x): modified Bessel functions, I kind, order n
• Collector current IC with nonlinear model
01/04/2011 - 8 ATLCE - B2 - © 2011 DDC
Collector current
• DC term (= I)
• Amplitude-dependent gain
• n = 1: fundamental
• n = 2, 3, … harmonics
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In/Io vs input signal amplitude
01/04/2011 - 10 ATLCE - B2 - © 2011 DDC
In(x)
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DC component of Ic
• The DC component of the collector current IC is I
• Same current I of the emitter bias generator
• The DC voltage at the emitter (VE) changes with signal amplitude
– VE = VE(x) = VT lge I/(IS I0(x))
– A 0-DC signal (Vi) causes a DC shift in the circuit » nonlinearity !
– IE constant (DC); VE(x) variable DC (compensates I0(x)
01/04/2011 - 12 ATLCE - B2 - © 2011 DDC
Collector current and output voltage
• Output voltage VO = - iC ZC(ω):
– Load impedance
– Collector current: fundamental + harmonics
• Combined effects of– nonlinearity (iC)– Load impedance vs frequency (ZC(ω))
VO(ω)= -ZC(ω)I
01/04/2011 - 13 ATLCE - B2 - © 2011 DDC
Lesson A3: amplifiers nonlinearity
• Large signal amplifiers– Reference circuit– Nonlinear device model
• Effects of nonlinearity – Harmonics, – Gain changes
• Output spectrum– Intermodulation– Intercept Point
• Lab 2: Large signal behaviour (nonlinear)
01/04/2011 - 14 ATLCE - B2 - © 2011 DDC
Effects of nonlinearity
• Signal distorsion– Sine Vi not-sine Vo– Harmonic content– Intermodulation
• Gain compression– Gain depends on signal level – Compression:
» Increasing the input signal the gain decreases
• These effects can be visualized with the “distortion” simulator, available on the website (set for “exponential nonlinearity”)
01/04/2011 - 15 ATLCE - B2 - © 2011 DDC
Example of output spectrum
• Output harmonics for Vi = 13 mVp and 52 mVp
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Output distortion: x = 1
• Mediul level signal– Vi = 26 mV, x = 1
– Barely visible distorsion
01/04/2011 - 17 ATLCE - B2 - © 2011 DDC
Output harmonics: x = 5
• High level signal– Vi = 130 mV, x = 5
– high distorsion
– Harmonics– Class B circuit
01/04/2011 - 18 ATLCE - B2 - © 2011 DDC
Output harmonics: x = 10
• Very high level signal– Vi = 260 mV, x = 10
– very high distorsion
– High harmonics– Class C circuit
01/04/2011 - 19 ATLCE - B2 - © 2011 DDC
MOS transistor
• Circuit and bias point– Quadratic model (JFET) ID = IDSS (1 - VGS/VP)2
– Exp-quad-lin model (MOS)
• Small signal (linear model)– Same model as BJT VO = - gm RD Vi
• Large signal– Complex math model: lin + square + exp– Heuristic models– Same effects:
» Harmonics» Variable gain
01/04/2011 - 20 ATLCE - B2 - © 2011 DDC
Large signal for MOS amplifier
• Nonlinear model
– ID(VGS) characteristic with various parts:
– Quadratic, exponential, linear, …
– Heuristic models
• Effects similar to BJT:
– Arising of harmonics at the output, distorsion
– Gain compression
01/04/2011 - 21 ATLCE - B2 - © 2011 DDC
Nonlinearity: fight or exploit ?
• We get: – Distortion & Harmonics, – Variable gain
• Remove distortion & harmonics: tuned circuits– No effect on gain compression
• Keep harmonics: frequency multipliers
• Stabilize the gain: negative feedback– Reduces signal on nonlinear element
• Use gain variation: compressor, mixers, VGA
01/04/2011 - 22 ATLCE - B2 - © 2011 DDC
Limit the effects of nonlinearity
• Negative feedback– OpAmp or OpAmp-like with feedback– Add feedback to transistor amplifiers
(Emitter resistance)
• Suitable for wideband amplifiers
01/04/2011 - 23 ATLCE - B2 - © 2011 DDC
Reduce harmonics and distorsion
• Tuned circuit at the output (ZC)– Gain: |AV| ZC/ZE
• Suitable for narrowband amplifiers– Can attenuate the harmonics
– TX output stage (PA)» Remove unwanted components
– RX front end amplifiers (LNA)» Remove unwanted signals» Remove noise
01/04/2011 - 24 ATLCE - B2 - © 2011 DDC
Lesson A3: amplifiers nonlinearity
• Large signal amplifiers– Reference circuit– Nonlinear device model
• Effects of nonlinearity – Harmonics, – Gain changes
• Output spectrum– Intermodulation– Intercept Point
• Lab 2: Large signal behaviour (nonlinear)
01/04/2011 - 25 ATLCE - B2 - © 2011 DDC
Nonlinearity parameters
• How to characterize nonlinearity for an amplifier– 1 dB compression level
• Intercept Point (IP)– (IP2)– IP3
• How to compensate the effects of nonlinearity– Predistorsion
» Analog» Digital
01/04/2011 - 26 ATLCE - B2 - © 2011 DDC
1 dB compression level
• Signal amplitude with gain (linear) - 1 dB
01/04/2011 - 27 ATLCE - B2 - © 2011 DDC
Effects of compression
• Quadrature Amplitude Modulations (QAM)– Shift of high energy constellation points– Narrow noise margin
01/04/2011 - 28 ATLCE - B2 - © 2011 DDC
Compensation of nonlinearity
• Compression modifies signal constellation– Need for knowing/ limiting/ correct– Predistorsion to compensate nonlinearity
• Analog predistortion– Gain expander– Known nonlinearity type
• Signal synthesized from numeric samples by DAC– Predistorsion of numeric values– Parameters from amplifier characterization
» Measurement of output power for test signals » Build look-up table, algorithm ..
– Generic, can correct any nonlinearity and drifts
01/04/2011 - 29 ATLCE - B2 - © 2011 DDC
Compensation of nonlinearity
• Dynamic expander– Introduces a distortion which compensates compression– Reduces harmonic content
01/04/2011 - 30 ATLCE - B2 - © 2011 DDC
Compensating predistorter
01/04/2011 - 31 ATLCE - B2 - © 2011 DDC
Harmonics with two-tone input signals
• Nonlinear output expressed as power series• Vo = A Vi + B Vi2 + C Vi3 + …
– Single-tone input Fa: harmonics 2Fa, 3Fa, 4Fa, ….– Dual-tone input: Vi = Va + Vb; Fa and Fb
• Vi2 = (Va + Vb)2 = Va2 + 2 Va Vb + Vb2
– Order 2 products: 2Fa, Fa-Fb, Fa+Fb, 2Fb (+DC)– outband, can be filtered out
• Vi3 = (Va + Vb)3 = Va3 + 3 Va2Vb + 3 Va Vb2 + Vb3
– Order 3 terms: 3Fa, 2Fa-Fb, 2Fa, 2Fb-Fa, 2Fb, 3Fb (+DC)– inband; cannot be filtered
01/04/2011 - 32 ATLCE - B2 - © 2011 DDC
Output spectrum with nonlinearity
• Input signals: – two sinewave
f1 and f2
• Output signal:– Inputs: f1, f2– harmonics
2f1, 2f2, 3f1, ...– Beats
f2-f1, f1+f2– Harmonic
beats2f1-f2, 2f2-f1, ..
intermodorder 2(sum&diff)
intermodorder 3
harmonics
Order 2 Order 3
useful signal band
01/04/2011 - 33 ATLCE - B2 - © 2011 DDC
Intermodulation
• Input signal: sine waves f1 and f2
• Output spectrum:
Intermodulation terms (order 3):2f2-f1, 2f1-f2
Fundamental (input signals)f1, f2
Difference and sum:f2-f1, f2+f1
II harmonic: 2f1, 2f2
01/04/2011 - 34 ATLCE - B2 - © 2011 DDC
Intermodulation Simulator
• Java applet in the course website– Learning material simulators intermodulation– Input signal with two sine components F1 e F2– Output spectrum for various cases:
• Linear transfer function– The output includes only F1 and F2
• Nonlinear transfer function; the output includes:– Harmonics:
2f1, 2f2, 3f1, ...– Beats between input signals:
f2-f1, f1+f1– Beats among harmonics on input signals:
2f1-f2, 2f2-f1, ..
01/04/2011 - 35 ATLCE - B2 - © 2011 DDC
Intermodulation Simulator: example
Linear transfer function
Exponentialtransfer function
01/04/2011 - 36 ATLCE - B2 - © 2011 DDC
Numerical example
• Amplifier band: 900 MHz – 1,1 GHz– Vi = Va + Vb: Fa = 1 GHz , Fb = 1,01 GHz
• Order 2: 2Fa, 2Fb, Fa-Fb, Fa+Fb– 2 GHz, 2,02 GHz, 2,01 GHz, 10 MHz– All components outband, can be filtered
• Order 3: 3Fa, 3Fb, 2Fa-Fb, 2Fb-Fa– 3 GHz, 3,03 GHz, 1,02 GHz, 0,99 GHz– Some components inband, cannot be filtered
• Order 3 terms more dangerous (inband!)
• Higher order components have lower amplitude
01/04/2011 - 37 ATLCE - B2 - © 2011 DDC
Intermodulation in amplifiers
• Ideal amplifier:– no harmonics, – no distortion, – no intermodulation
• Effects of intermodulation in LNA (RX chain)– Spurious signals in the IF chain
» feedthrough from other channels
• Effects in PA (TX chain)– Emission of unwanted signals
» Wasted power» Interference towards other channels
• Quantitative parameter: Intercept Point (IP)
01/04/2011 - 38 ATLCE - B2 - © 2011 DDC
Amplitude of high order terms
• Output signal– Vu = K1 Vi + K2 Vi2 + K3 Vi3 + ….– Vu = K1(AVa+BVb) + K2(AVa+BVb)2 + K3 (AVa+BVb)3
• Critical term: K3– (…)3 = A3Va3+3A2BVa2Vb+3AB2VaVb2+B3Vb3
– Difference beats inband
• Doubling the input levels: – A 2A, B 2B– K1(AVa+BVb) x 2– K3(3A2BVa2Vb) x 23 = x 8
• Harmonic raises faster than fundamental
01/04/2011 - 39 ATLCE - B2 - © 2011 DDC
Intermodulation vs input levels
• Raising the input level, intermodulation terms go up faster than fundamental
– Reduced distance fundamental III-order terms
01/04/2011 - 40 ATLCE - B2 - © 2011 DDC
Intercept Point
• Order 3 signals – For increasing
input level, order-3 terms raise faster than fundamental
• Order 3 Intercept Point (IP3)
– Same (extrapolated) amplitude for Fiand 3Fi terms
IP3
Pout
Pin
Fi
3 Fi
IP3
01/04/2011 - 41 ATLCE - B2 - © 2011 DDC
Other IPs
• IP can be defined for any order
• Low order– Slow raise
• High order– Fast raise– Low K
• Most dangerous:– Order 3
01/04/2011 - 42 ATLCE - B2 - © 2011 DDC
Usable dynamic range
• The usable dynamic range of an amplifier is limited
IP3oPout
PinNoisefloor
Usable input range
Compressionintercept point
01/04/2011 - 43 ATLCE - B2 - © 2011 DDC
Lab 2: BJT nonlinear amplifier
• Specs: same basic circuit as Lab 1
• Large signal behavior– Gain (versus input level)– Output harmonics contents– Output voltage range
• References in the text– Design procedure: sect 1, 1.P1– Lab measurements: sect 1, 1.L1 (part 2)
• Experiment guide in the website– Learning material Instructions for lab experiments A2
01/04/2011 - 44 ATLCE - B2 - © 2011 DDC
Lesson B2: final questions
• Which different types of amplifiers can be found in a radio system?
• Why RF amplifiers do not use Op Amps?
• Draw the frequency spectrum at the output of an amplifier with sine input, with linear and nonlinear behavior.
• Describe some effects of nonlinearity in the amplifiers of the reference radio system.
• Describe some techniques to avoid or counteract the effects of nonlinearity in amplifiers.
• Where does intermodulation come from?
• Which parameter(s) describe the nonlinear behavior of an amplifier?
01/04/2011 - 45 ATLCE - B2 - © 2011 DDC
Lesson B2: tests
• Harmonics content for various input signal levels (dBc, referred to carrier).
– Draw output spectrum for: » Vi = 52 mV» Vi = 130 mV
• In the circuit designed for the lab experiment– Evaluate small signal gain with linear model (gm o hie)– Evaluate gain for large input signal with nonlinear model