Analog and Telecommunication Electronics

Transcription

1 Politecnico di Torino - ICT School Analog and Telecommunication Electronics B3 - Using nonlinearity» Tuned amplifier» Frequency multiplier» Gain compressor» Adding feedback AY /03/ ATLCE - B DDC 2016 DDC 1

2 Lesson B3: using nonlinearity Reducing the effects of nonlinearity Tuned amplifiers Large signal gain Gm(x) Re feedback Gain stabilization Exploiting nonlinearity Dynamic compressors Frequency multipliers Text reference: Elettronica per Telecom.: sect. 1.2 Transistori fuori linearità 15/03/ ATLCE - B DDC 2016 DDC 2

3 Nonlinearity: fight or exploit? We get: Distortion Harmonics Variable gain Remove harmonics: tuned circuits Keep harmonics: frequency multipliers Stabilize the gain: negative feedback Use gain variation: compressor, VGA, mixers Sine oscillators: Use gain change to get Aβ = 1 15/03/ ATLCE - B DDC 2016 DDC 3

4 Limit the effects of nonlinearity Negative feedback OpAmp or OpAmp-like with feedback Add feedback to transistor amplifiers (Emitter resistance)» Reduce actual signal amplitude on the nonlinear element (pn junction) Same effect for any frequency Suitable for wideband amplifiers No problem for fully integrated circuits 15/03/ ATLCE - B DDC 2016 DDC 4

5 Reduce harmonics and distorsion Tuned circuit at the output: Z C (ω) Gain: A V Z C (ω)/z E (ω) Suitable for narrowband amplifiers Can attenuate the harmonics (and other unwanted signals) TX output stage (PA)» Remove unwanted components RX front end amplifiers (LNA)» Remove unwanted (outband) signals» Remove noise Fully integrated amplifiers low L C values Tuned circuis feasible for F > K x 100 MHz 15/03/ ATLCE - B DDC 2016 DDC 5

6 Tuned amplifiers LNA (low noise amplifier) IF amplif. (tuned amplifiers) PA (power amplifier) 15/03/ ATLCE - B DDC 2016 DDC 6

7 Dual-conversion heterodyne receiver Va X X DEM. Wideband LNA + filter O1 IF1 filter +Amplif. O2 IF2 filter +Amplif. f i1 =f a f O1 f a f O1 f f Input RF filter First IF: High easy image removal Second IF (IF2) Low Simple channel filter f i2 = f i1 f O2 f i1 f O2 f i1b Tuning by shifting O1 (or O2) 15/03/ ATLCE - B DDC 2016 DDC 7

8 LRC tuned circuits z( ) Q X Resonance: o Damping: k logω Quality factor: Q = 1/2 O k O Attenuation: X Q k 1 k 15/03/ ATLCE - B DDC 2016 DDC 8

9 Tuned amplifiers I C depends only on V BE I C 15/03/ ATLCE - B DDC 2016 DDC 9

10 Tuned amplifiers V O depends on I C (V BE ) and Z C ( ) I C V O In this example O = I 15/03/ ATLCE - B DDC 2016 DDC 10

11 Output spectrum Harmonic contents of collector current Ic I C current spectrum depends only on Vi amplitude I Effects of LC on Vu Vu spectrum depends also from Zc, that is the resonator Q add (in db) the level caused by nonlinearity with resonant circuit attenuation X X depends from frequency offset Z i and quality factor Q 1 X Q k Z k k i 15/03/ ATLCE - B DDC 2016 DDC 11

12 Examples: fixed Q, variable Vi Harmonic content of Ic depends only on input signal level The tuned circuit Q factor modifies the harmonic content of Vu Zc, Q = 200 (fixed) Ic(ω) For Vi mvp Vi = 5mV Vi = 20mV Vi = 200mV Vu(ω) 15/03/ ATLCE - B DDC 2016 DDC 12

13 Examples: variable Q, fixed Vi Harmonic content of Ic depends only on input signal level The tuned circuit Q factor modifies the harmonic content of Vu Zc, Q = 50, 200, 500 Q = 50 Q = 200 Q = 500 Ic(ω) for Vi = 200 mvp (fixed) Vu(ω) 15/03/ ATLCE - B DDC 2016 DDC 13

14 Example: tuned amplifier design Functional parameters: Input signal level Gain Spectral purity Power and efficiency Circuit parameters Collector current I C (= I E = I) Resonant circuit Q Exercise B3-a From signal level and Q, compute output spectrum Compute the Q required to get a given spectral purity 15/03/ ATLCE - B DDC 2016 DDC 14

15 Lesson A4: how to use nonlinearity Reducing the effects of nonlinearity Tuned amplifiers Gain stabilization Exploiting nonlinearity Dynamic compressors Frequency multipliers Sine oscillators Positive feedback amplifiers Negative transconductance 15/03/ ATLCE - B DDC 2016 DDC 15

16 Large-signal gain Input signal Small signal (linear model) Large signal (slide B2-12) (only fundamental component) v(t) xv cos t i T v o(t) RC gmv i(t) I I(x) v (t) R 2 v (t) 1 o C i xvt I 0(x) Introducing large signal transconductance: G m (x) (gain for the fundamental) v (t) R G (x)v (t) o C m i I G m(x) 2 xv T 0 I(x) 1 I (x) 15/03/ ATLCE - B DDC 2016 DDC 16

17 Small signal Gm(x) Very low-level input signal (x 0) G m (x)/g m = 1 (small signal, linear) As input level increases, G m (x)/g m decreases (less gain) Compression Steep slope for x = 3 6 compression 15/03/ ATLCE - B DDC 2016 DDC 17

18 Verification for small signal Low level input signal: x 0 Fundamental component v (t) R G (x)v (t) I 0 (x) = 1 o C m i Same results as from small signal (linear) analysis I I(x) G 1 m(x) 2 xv I (x) T 0-15/03/ ATLCE - B DDC 2016 DDC 18

19 Gain change Small signal As signal amplitude increases, the gain decreases: compression High compression Output saturation: squarewave output high distortion: 15/03/ ATLCE - B DDC 2016 DDC 19

20 Signal level for 1 db compression From G m (x) curve: G m (x) = g m - 1 db = 0,89 g m x 1; Vi 26 mv 15/03/ ATLCE - B DDC 2016 DDC 20

21 Compressing amplifiers: where? RF signal have variable, unknown amplitude In FM receivers, AM is noise compression OK In AM receivers, AM is the useful signal NO compression FM IF amplifiers: remove AM (fast): Compressing amplifiers AM IF amplifiers: keep AM, but Received signal amplitude changes (fading, slow) Need for AGC» Compensate slow changes» Ignore fast changes (modulation!) 15/03/ ATLCE - B DDC 2016 DDC 21

22 Gain compression: example Functional parameters: Input level Compression coefficient Circuit parameter Resonant circuit Q Test B.3-a Analysis of a compressing amplifier» From input levels, compute AM index at the output m V max V max V min V min 15/03/ ATLCE - B DDC 2016 DDC 22

23 Gain stabilization: emitter feedback Input signal V I partitioned among V BE and R E Voltage drop on R E : R E i C V BE = V i i C R E V BE = V i G m (x ) V BE R E x = V BE /V T ; x = V i /V T x is defined by an equation without closed form solution: Can be solved only with successive approximation - 15/03/ ATLCE - B DDC 2016 DDC 23

24 Gain with emitter feedback V x i ; x' VT V BE V V V i R ; i G (x')v BE i C E C m BE T V V G (x')v R V BE i m BE E BE 1 Vi G (x')r m E G (x')r V G (x')r V V m C O m C BE i 1 G m(x')re x' 1 x G (x')r m E - Can be solved only with successive approximation 15/03/ ATLCE - B DDC 2016 DDC 24

25 Frequency multipliers Input signal: sinewave at ω i Vi harmonics in the collectro current I C 15/03/ ATLCE - B DDC 2016 DDC 25

26 Frequency multipliers Input signal at ω i Nonlinearity brings Vi harmonics in the I C (b) A tuned circuit isolates the planned harmonic (c) Different attenuation for 2 ω i and 4 ω i 15/03/ ATLCE - B DDC 2016 DDC 26

27 Frequency multiplier: example Functional parameters (specs): Multiplication factor N Output spectral purity Circuit parameter (design) Input amplitude Tuned circuit Q Design problems Design a frequency multiplier x N, from the input level and spectral purity specifications Compute the minimum Q required for the tuned circuit 15/03/ ATLCE - B DDC 2016 DDC 27

28 Frequency multiplier: test B.3-c Test B.3-c An AM signal with Vmax = 260 mv; Vmin = 26 mv goes through a BJT amplifier (without emitter feedback). Find the modulation index Mo at the output Solution x = 10 1 G m /g m = 0,190 0,893 (slide B3-17) Vo = -RcG m (x) Vi M = (V max V min )/(V max + V min );» Input signal: Mi = 0,8» Output signal: Mo = (10 G m (10) G m (1))/(10 G m (10) + G m (1)) = 0,36 15/03/ ATLCE - B DDC 2016 DDC 28

29 Lesson B3: final test Which are the techniques usable to reduce harmonic content and distortion in amplifiers? Is there any difference between the spectral content of collector current and of collector voltage in a tuned amplifier? Define large signal transconductance. Which parameters describe a RLC tuned circuit? Where can be useful a compressing amplifier? Describe how the Emitter DC voltage depends on input signal level. Define the 1-dB compression point. List the parameters which define the spectral purity of a frequency multiplier. 15/03/ ATLCE - B DDC 2016 DDC 29