Politecnico di Torino ICT School Telecommunication Electronics A3 Amplifiers nonlinearity» Reference circuit» Nonlinear models» Effects of nonlinearity» Applications of nonlinearity Large signal amplifiers Reference circuit Nonlinear device model Effects of nonlinearity Harmonics, Gain changes Output spectrum Intermodulation Intercept Point Lesson A3: amplifiers nonlinearity Lab 2: Large signal behaviour (nonlinear) Text reference: Tuned amplifiers: sect 1.2.3 08/09/2008-1 TLCE - A3-2007 DDC 08/09/2008-2 TLCE - A3-2007 DDC Amplifiers in radio structure Reference circuit Basic transistor amplifier in passband Get rid of bias network and coupling capacitors LNA (low noise amplifier) IF channel Zc Vcc C4 Vcc Zc RX input amplifiers C1 Q1 Q1 - Low noise, wide dynamic Ie Vo Ie Vo PA (power amplifier) Vi Ie (DC) Z e Vi Ie (DC) Ze TX output amplifiers - High efficiency, low distorsion 08/09/2008-3 TLCE - A3-2007 DDC 08/09/2008-4 TLCE - A3-2007 DDC Other configurations Same model can be used for other configurations Differential CB CC First step: Zc Rc Ze Ce CC (in passband) Linear model I C = g m V BE or h fe i B approximation Actual I C (V BE ) log curve v i (t) = V i cos ωt x = V i /V T V BE = V i + V E BJT: nonlinear model 08/09/2008-5 TLCE - A3-2007 DDC 08/09/2008-6 TLCE - A3-2007 DDC Page 1 2007 DDC 1
Analysis with nonlinear BJT model Collector current e x cos ωt can be expanded in Fourier series I n (x): modified Bessel functions, I kind, order n Collector current I C with nonlinear model DC term Amplitude-dependent gain n = 1: fundamental n = 2, 3, harmonics 08/09/2008-7 TLCE - A3-2007 DDC 08/09/2008-8 TLCE - A3-2007 DDC In/Io vs input signal amplitude In(x) 08/09/2008-9 TLCE - A3-2007 DDC 08/09/2008-10 TLCE - A3-2007 DDC DC component of Ic The DC component of the collector current I C is I Output voltage V O = - i C Z C (ω): Collector current and output voltage Same current I of the emitter bias generator The DC voltage at the emitter (V E ) changes with signal amplitude V E = V E (x) = V T lg e I/(I S I 0 (x)) A 0-DC signal (Vi) causes a DC shift in the circuit» nonlinearity! V O = - Z C (ω) Load impedance Collector current: fundamental + harmonics Combined effects of nonlinearity (i C ) Load impedance vs frequency (Z C (ω)) 08/09/2008-11 TLCE - A3-2007 DDC 08/09/2008-12 TLCE - A3-2007 DDC Page 2 2007 DDC 2
Large signal amplifiers Reference circuit Nonlinear device model Effects of nonlinearity Harmonics, Gain changes Output spectrum Intermodulation Intercept Point Lesson A3: amplifiers nonlinearity Lab 2: Large signal behaviour (nonlinear) 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 Effects of nonlinearity These effects can be visualized with the distortion simulator, available on the website (set for exponential nonlinearity ) 08/09/2008-13 TLCE - A3-2007 DDC 08/09/2008-14 TLCE - A3-2007 DDC Example of output spectrum Output distortion: x = 1 Output harmonics for Vi = 13 mvp and 52 mvp Mediul level signal Vi = 26 mv, x = 1 Barely visible distorsion 08/09/2008-15 TLCE - A3-2007 DDC 08/09/2008-16 TLCE - A3-2007 DDC High level signal Vi = 130 mv, x = 5 Output harmonics: x = 5 Very high level signal Vi = 260 mv, x = 10 Output harmonics: x = 10 high distorsion very high distorsion Harmonics Class B circuit High harmonics Class C circuit 08/09/2008-17 TLCE - A3-2007 DDC 08/09/2008-18 TLCE - A3-2007 DDC Page 3 2007 DDC 3
MOS transistor Circuit and bias point Quadratic model (JFET) I D = I DSS (1 - V GS /V P ) 2 Exp-quad-lin model (MOS) Small signal (linear model) Same model as BJT V O = - g m R D V i Large signal Complex math model: lin + square + exp Heuristic models Same effects:» Harmonics» Variable gain Large signal for MOS amplifier Nonlinear model I D (V GS ) characteristic with various parts: Quadratic, exponential, linear, Heuristic models Effects similar to BJT: Arising of harmonics at the output, distorsion Gaincompression 08/09/2008-19 TLCE - A3-2007 DDC 08/09/2008-20 TLCE - A3-2007 DDC We get: Distortion & Harmonics, Variable gain Nonlinearity: fight or exploit? Remove distortion & harmonics: tuned circuits No effect on gain compression Keep harmonics: frequency multipliers Negative feedback OpAmp or OpAmp-like with feedback Add feedback to transistor amplifiers (Emitter resistance) Suitable for wideband amplifiers Limit the effects of nonlinearity Stabilize the gain: negative feedback Reduces signal on nonlinear element Use gain variation: compressor, mixers, VGA 08/09/2008-21 TLCE - A3-2007 DDC 08/09/2008-22 TLCE - A3-2007 DDC Tuned circuit at the output (Z C ) Gain: A V Z C /Z E 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 Reduce harmonics and distorsion Large signal amplifiers Reference circuit Nonlinear device model Effects of nonlinearity Harmonics, Gain changes Output spectrum Intermodulation Intercept Point Lesson A3: amplifiers nonlinearity Lab 2: Large signal behaviour (nonlinear) 08/09/2008-23 TLCE - A3-2007 DDC 08/09/2008-24 TLCE - A3-2007 DDC Page 4 2007 DDC 4
Nonlinearity parameters How to characterize nonlinearity for an amplifier 1 db compression level Signal amplitude with gain (linear) - 1 db 1 db compression level Intercept Point (IP) (IP2) IP3 How to compensate the effects of nonlinearity Predistorsion» Analog» Digital 08/09/2008-25 TLCE - A3-2007 DDC 08/09/2008-26 TLCE - A3-2007 DDC Effects of compression Quadrature Amplitude Modulations (QAM) Shift of high energy constellation points Narrow noise margin 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 08/09/2008-27 TLCE - A3-2007 DDC 08/09/2008-28 TLCE - A3-2007 DDC Compensation of nonlinearity Compensating predistorter Dynamic expander Introduces a distortion which compensates compression Reduces harmonic content 08/09/2008-29 TLCE - A3-2007 DDC 08/09/2008-30 TLCE - A3-2007 DDC Page 5 2007 DDC 5
Harmonics with two-tone input signals Output spectrum with nonlinearity Nonlinear output expressed as power series Vo = A Vi + B Vi 2 + C Vi 3 + Single-tone input Fa: harmonics 2Fa, 3Fa, 4Fa,. Dual-tone input: Vi = Va + Vb; Fa and Fb Vi 2 = (Va + Vb) 2 = Va 2 + 2 Va Vb + Vb 2 Order 2 products: 2Fa, Fa-Fb, Fa+Fb, 2Fb (+DC) outband, can be filtered out Vi 3 = (Va + Vb) 3 = Va 3 + 3 Va 2 Vb + 3 Va Vb 2 + Vb 3 Order 3 terms: 3Fa, 2Fa-Fb, 2Fa, 2Fb-Fa, 2Fb, 3Fb (+DC) inband; cannot be filtered Input signals: two sinewave f1 and f2 Output signal: Inputs: f1, f2 harmonics 2f1, 2f2, 3f1,... Beats f2-f1, f1+f1 Harmonic beats 2f1-f2, 2f2-f1,.. intermod order 2 (sum&diff) intermod order 3 useful signal band harmonics Order 2 Order 3 08/09/2008-31 TLCE - A3-2007 DDC 08/09/2008-32 TLCE - A3-2007 DDC Intermodulation Intermodulation Simulator Input signal: sine waves f1 and f2 Output spectrum: Intermodulation terms (order 3): 2f2-f1, 2f1-f2 Difference and sum: f2-f1, f2+f1 Fundamental (input signals) f1, f2 II harmonic: 2f1, 2f2 Java apples 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,.. 08/09/2008-33 TLCE - A3-2007 DDC 08/09/2008-34 TLCE - A3-2007 DDC Intermodulation Simulator: example Inband interferences Exponential transfer function Vu = A Vi + B Vi 2 + C Vi 3 + If Vi = Va + Vb (Va + Vb) 2 (Va + Vb) 3 B and C cause high-order product Order 2: 2Fa, 2Fb, Fa-Fb, Fa+Fb» outband, can be filtered out Linear transfer function Order 3: 3Fa, 3Fb, 2Fa-Fb, 2Fb-Fa» inband; cannot be filtered 08/09/2008-35 TLCE - A3-2007 DDC 08/09/2008-36 TLCE - A3-2007 DDC Page 6 2007 DDC 6
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 Numerical example Order 3 terms more dangerous (inband!) Higher order components have lower amplitude Ideal amplifier: no harmonics, no distortion, no intermodulation Intermodulation in amplifiers 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) 08/09/2008-37 TLCE - A3-2007 DDC 08/09/2008-38 TLCE - A3-2007 DDC Amplitude of high order terms Output signal Vu = K1 Vi + K2 Vi 2 + K3 Vi 3 +. Vu = K1(AVa+BVb) + K2(AVa+BVb) 2 + K3 (AVa+BVb) 3 Critical term: K3 ( ) 3 = A 3 Va 3 +3A 2 BVa 2 Vb+3AB 2 VaVb 2 +B 3 Vb 3 Difference beats inband Doubling the input levels: A 2A, B 2B K1(AVa+BVb) x 2 K3(3A 2 BVa 2 Vb) x 2 3 = x 8 Harmonic raises faster than fundamental Raising the input level, intermodulation terms go up faster than fundamental Reduced distance fundamental III-order terms Intermodulation vs input levels 08/09/2008-39 TLCE - A3-2007 DDC 08/09/2008-40 TLCE - A3-2007 DDC Intercept Point Other IPs Order 3 signals For increasing input level, order-3 terms raise faster than fundamental Order 3 Intercept Point (IP3) Same (extrapolated) amplitude for Fi and 3Fi terms IP3 Pout Fi IP3 3 Fi Pin IP can be defined for any order Low order Slow raise High order Fast raise Low K Most dangerous: Order 3 08/09/2008-41 TLCE - A3-2007 DDC 08/09/2008-42 TLCE - A3-2007 DDC Page 7 2007 DDC 7
Usable dynamic range The usable dynamic range of an amplifier is limited Pout IP3o Specs: same basic circuit as Lab 1 Large signal behavior Gain (versus input level) Output harmonics contents Output voltage range Lab 2: BJT nonlinear amplifier Noise floor Usable input range Pin Compression intercept point 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 08/09/2008-43 TLCE - A3-2007 DDC 08/09/2008-44 TLCE - A3-2007 DDC Lesson A3: final questions Lesson A3: tests Which different types of amplifiers can be found in a radio system? 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 nonlinearity in amplifiers 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 (g m o h ie ) Evaluate gain for large input signal with nonlinear model Where does intermodulation come from? Which parameter(s) describe the nonlinear behavior of an amplifier? 08/09/2008-45 TLCE - A3-2007 DDC 08/09/2008-46 TLCE - A3-2007 DDC Page 8 2007 DDC 8