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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)