analog and telecommunication electronics€¦ · • amplifier band: 900 mhz – 1,1 ghz – vi =...
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Politecnico di Torino - ICT School
Analog and Telecommunication Electronics
B2 - Amplifiers nonlinearity
» Reference circuit» Nonlinear models » Effects of nonlinearity» Applications of nonlinearity
AY 2015-16
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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
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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
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Various types of amplifiers
• Operating point (DC bias)– Class A– Class B– Class C– Other classes (D, E, … mixed)
• Frequency response– Wideband– Narrowband– DC
• This section focused on – class A/B/C narrowband– BJT circuits (easy math model)
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Reference circuit
• Basic BJT class A amplifier in passband ( class B, C)– 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
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Other configurations
• Same model can be used for other configurations– Differential– Common Base (CB)– Common Collector (CC)
• First step:– Zc Rc– Ze Ce Short Circuit (in passband)
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• 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
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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
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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
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Nonlinearity effects
• Saturation turns sinewaves into squarewaves
Small signal:no distortion (I2, I3 ≈ 0)
Linear model (no distortion)
Large signal:saturation, high harmonic content becomes a squarewave
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In(x)
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DC component of Ic
• The DC component I of the collector current IC is:
• Same current I of the emitter bias generator (fixed)
• Io(x), therefore 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 !
– I (IE) constant (DC); VE(x) variable DC
compensates I0(x)
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Collector current and output voltage
• Output voltage VO = - iC ZC(ω):
– Load impedance DC
– Collector current fundamental + harmonics
• Combined effects of– nonlinearity (iC)– Load impedance vs frequency (ZC(ω))
VO(ω,t)= -ZC(ω) I
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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)
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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”)
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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
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Output harmonics: x = 5
• High level signal– Vi = 130 mV, x = 5
– high distorsion
– Harmonics– Class B circuit
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Output harmonics: x = 10
• Very high level signal– Vi = 260 mV, x = 10
– very high distorsion
– High harmonics– Class C circuit
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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» Gain compression
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Nonlinearity: fight or exploit ?
• We get: – Distortion & Harmonics, – Variable gain
• Remove distortion & harmonics: tuned circuits– No effect on gain compression
• Use harmonics – frequency multipliers
• Stabilize the gain: negative feedback– Reduces signal on nonlinear element
• Use gain variation– Compressor, mixers, variable gain (VGA), oscillators, …
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Limit the effects of nonlinearity
• Remove (reduce) nonlinearity Negative Feedback
• OpAmp or OpAmp-like (high open-loop gain – “external” feedback)
– Good (mandatory) for DC– Not for High Frequency (k 10 MHz )– For HF Differential IN / differential OUT OpAmp
(OpAmpl with +/- IN and OUT)
• Add feedback to transistor amplifiers(Emitter/Source resistance)
– Acceptable for DC – Suitable for wideband amplifiers– Analyzed in this lesson
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Reduce harmonics and distortion
• Keep nonlinearity, but reduce the effects
• Tuned circuit at the output (ZC)– Gain: |AV| ZC/ZE
• Suitable for narrowband amplifiers– Can attenuate the harmonics
– TX output stage (PA)» Remove unwanted signal components
– RX front end amplifiers (LNA)» Remove unwanted signals» Remove noise
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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)
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Nonlinearity parameters
• How to characterize nonlinearity for an amplifier– 1 dB compression level
• Intercept Point (IP)– (IP2)– IP3
• Reduce nonlinearity– Feedback
• Compensate the effects of nonlinearity– Predistortion
» Analog» Digital
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1 dB compression level
• Signal amplitude with gain (linear) - 1 dB
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Effects of compression
• Quadrature Amplitude Modulations (QAM)– Shift of high energy constellation points– Reduced noise margins Possible
detection error
Reduced noise margin
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Compensation of nonlinearity
• Compression modifies signal constellation– Need for knowing/ limiting/ correcting– Predistortion to compensate nonlinearity
• Analog predistortion– Gain expander– Known nonlinearity type
• Signal synthesized from numeric samples by DAC– Predistortion 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
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Compensation of nonlinearity
• Dynamic expander– Introduces a distortion which compensates compression– Reduces harmonic content
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Compensating predistorter
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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
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Output spectrum with nonlinearity
• Input signals: – two sinewaves
f1 and f2
• Output signal:– Inputs: f1, f2– harmonics
2f1, 2f2, 3f1, ...– Beats
f2-f1, f1+f2– Harmonic
beats: intermodulation2f1-f2, 2f2-f1, ..
intermodorder 2(sum&diff)
intermodorder 3
harmonics
Order 2 Order 3
useful signal band
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Intermodulation experiment (Lab 2)
• 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
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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 TF; the output includes:– Harmonics:
2f1, 2f2, 3f1, ...– Beats between input signals:
f2-f1, f1+f1– Beats among harmonics on input:
2f1-f2, 2f2-f1, ..
F1 F2
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Intermodulation Simulator: example
Linear transfer function
Exponentialtransfer function
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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
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Intermodulation in amplifiers
• Ideal amplifier:– no harmonics, – no distortion, – no intermodulation
• Effects of intermodulation in LNA (RX chain input)– Spurious signals in the IF chain
» feedthrough from other channels
• Effects in PA (TX chain output)– Emission of unwanted signals
» Wasted power» Interference towards other channels (or other systems)
• Quantitative parameter: Intercept Point (IP)
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Amplitude of high order terms
• Output signal– Vu = K1 Vi + K2 Vi2 + K3 Vi3 + ….– Vu = K1(A Va+B Vb) + K2(A Va+B Vb)2 + K3 (A Va + B Vb)3
• Critical term: K3– (…)3 = A3 Va3+3 A2 B Va2 Vb+3 A B2 Va Vb2+B3 Vb3
– 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
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Intermodulation vs input levels
• Raising the input level, intermodulation terms go up faster than fundamental
– Reduced distance fundamental
III-order terms
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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
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Other IPs
• IP can be defined for any order
• Low order– Slow raise
• High order– Fast raise– Low K
• Most dangerous:– Order 3
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Usable dynamic range
• The usable dynamic range of an amplifier is limited
IP3oPout
PinNoisefloor
Fundamental power
Usable range
III harmonicpower
CompressionIntercept Point 3: IP3
Usable input range
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Lab 2: BJT nonlinear amplifier
• Specs: same basic circuit as Lab 1 (small signal)
• Large signal behavior without/with Re– 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
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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?
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Lesson B2: tests
• Harmonics content for various input signal levels (dBc, referred to carrier).
– Draw output spectrum for: » Vi = 52 mV» Vi = 130 mV
• For the circuit designed for the lab experiment– Evaluate small signal gain with linear model (gm o hfe)– Evaluate gain for large input signal with nonlinear model
(e.g. for Vi = 50, 100, 200, 500, … mV)