Analog and Telecommunication Electronics

Transcription

1 Politecnico di Torino - ICT School Analog and Telecommunication Electronics B5 - Multipliers/mixer circuits» Error taxonomy» Basic multiplier circuits» Gilbert cell» Bridge MOS and diode circuits» Balanced mixers AY /03/ ATLCE - B DDC 2016 DDC 1

2 Lesson B5: multipliers and mixers Analog multipliers Parameters and errors Transconductance multipliers, 1/2/4 quadrant Gilbert cell Diode bridge Mixer parameters Balanced and I/Q mixers Noise, gain References: Elettronica per Telecom.: Moltiplicatori Analogici Design with Op Amp : 13.2 Analog multipliers 07/03/ ATLCE - B DDC 2016 DDC 2

3 Frequency translation basics (beats) Werner s relations sina x sinb = 0,5 [cos(a-b) - cos(a+b)] sina x cosb = 0,5 [sin(a-b) + sin(a+b)] cosa x cosb = 0,5 [cos(a-b) + cos(a+b)] Telecom applications Frequency translation: Heterodyne RX and TX» I, II, conversion, Image rejection mixers Mo-Demodulation» Standard AM mo-demod» Suppressed carrier (DSB), Single Side Band (SSB)» Digital AM (ASK. PAM)» Phase Detector». 07/03/ ATLCE - B DDC 2016 DDC 3

4 Mixers and Multipliers Mixers: Frequency translation» Frequency conversion in heterodyne receivers and transmitters Phase detectors» PLL and demodulators Multipliers: Mo-demodulators» AM and PAM modulation and demodulation Variable gain amplifiers (analog computation) digital 07/03/ ATLCE - B DDC 2016 DDC 4

5 Mixers in the handset RF Mixers (first conversion) I/Q Mixers (second conversion) 07/03/ ATLCE - B DDC 2016 DDC 5

6 Mixers in a GPS receiver Image reject mixer Mixer II 07/03/ ATLCE - B DDC 2016 DDC 6

7 Many uses of multipliers: GP2015 Mixers Variable gain amplifier Phase detectors 07/03/ ATLCE - B DDC 2016 DDC 7

8 Multiplier as mixer Mixing is achieved by multiplication sena x senb = 0,5 [cos(a-b) cos(a+b)] With sine inputs, the output of a multiplier includes Difference component Sum component Other terms, caused by nonlinearity and errors Only one term is used (sum or difference beat) Filters Cancellation 07/03/ ATLCE - B DDC 2016 DDC 8

9 Ideal multipliers Ideal multiplier: Vo = Km Vx Vy Sine input signals, frequency Fx and Fy Vo spectrum includes only Fx - Fy and Fx + Fy f fx fy fx fx f fy-fx fy+fx 07/03/ ATLCE - B DDC 2016 DDC 9

10 Errors in multipliers: real circuits Ideal multiplier: Vo = Km Vx Vy Sine input signals, frequency Fx and Fy Vo spectrum includes only Fx - Fy and Fx + Fy Actual multiplier Offset Vo = Km (Vx + ΔVx) (Vy + ΔVy) + ΔVo Vo = Km Vx Vy + ΔVy Vx + ΔVx Vy + Eo + other terms order >2 Vo = Km Vx Vy + Ex Vx + Ey Vy + Eo +.. Sine input signals, frequency Fx and Fy Feedthrough Vo spectrum includes Fx-Fy, Fx+Fy, Fx, Fy, DC + other higher order terms: 2Fx, 2Fx-Fy, 3Fx-2Fy,... Harmonics: M Fx ± N Fy Distortion 07/03/ ATLCE - B DDC 2016 DDC 10

11 Spectrum with real mixer Vo = Km Vx Vy + Ex Vx + Ey Vy + Eo +. f fx fy fo fx fa fb fy-fx fy fy+fx fd f 07/03/ ATLCE - B DDC 2016 DDC 11

12 Spurious outputs: feedthrough Input signals reach the output Mainly due to mixer unbalance or signal DC: Vo = Km Vx (Vy + ΔVy) = Km Vx Vy + Km Vx ΔVy DC error on Vy (offset) ΔVy causes Vx feedthrough f fo fx fy-fx fy fy+fx 07/03/ ATLCE - B DDC 2016 DDC 12

13 Nonlinearity Nonlinearity causes higher order terms 2fx, 2fy, 2fx+fy, 2fx-fy, 2fx+2fy, 3fx, 3fy, 3fx+fy,.. Can be removed with tuned circuits fo fa fb fy-fx fc fy+fx fd f 07/03/ ATLCE - B DDC 2016 DDC 13

14 Lesson B5: multipliers and mixers Analog multipliers Parameters and errors Transconductance multipliers, 1/2/4 quadrant Balanced mixer, Gilbert cell Diode bridge Mixer parameters Noise, gain, intermodulation, IP 07/03/ ATLCE - B DDC 2016 DDC 14

15 Example of mixer with nonlinear circuit BJT amplifier with input Vx on B and Vy on E Effective input voltage: V BE = Vx Vy (or V BE = Vx + Vy) Nonlinearity makes Vx Vy appear in Ic Tuned circuit isolates desired component Constraints on Vx and Vy: V BE > 0, that is Vx > Vy Need DC component high feedthrough errors Merged with input amplifier and local oscillator in (old) low-cost receivers 07/03/ ATLCE - B DDC 2016 DDC 15

16 Mixers with nonlinear networks Vi = Vx + Vy (frequency Fx and Fy) Vo = Fnonlin(Vi) With power series expansion»vo = A 0 + A 1 (Vx + Vy) + A 2 (Vx+Vy) Vo components» Vx, Vy frequency Fx e Fy»Vx Vy frequency Fx - Fy and Fx + Fy»Vx 2, Vy 2 frequency 2Fx, 2Fy» Other terms frequency M Fx + N Fy» Order III intermodulation (2Fx - Fy) Useful component (diff or sum beat) isolated by a tuned circuit 07/03/ ATLCE - B DDC 2016 DDC 16

17 Transconductance multiplier For small-signal amplifier: Vo = - Vx g m Rc Gain proportional to transconductance g m g m depends from Ic (Id) Id is controlled by Vy: g m = K Vy Vo = K Rc Vx Vy Single transistor: Vx, Vy > 0: 1 quadrant DC components high feedthrough Differential circuits: 2/4-quadrants No DC, less feedthrough Limited to low-level signals 07/03/ ATLCE - B DDC 2016 DDC 17

18 Transconductance circuit - 1 quadrant V O = V X g m1 R C g m1 = I C /V T R C I C g m2 V Y V O V X (g m2 V Y /V T )g m1 R C g m1 V O K V X V Y I C (polarity!) g m2 07/03/ ATLCE - B DDC 2016 DDC 18

19 Transconductance circuit tuned load Z C (ω) to isolate desired component (sum or diff beat) Z C V O = K Z C (ω) V X V Y V X and V Y > 0 1 quadrant Feedtrough on X and Y! I C Can be extended to 2/4-quadrant 07/03/ ATLCE - B DDC 2016 DDC 19

20 Transconductance circuit - 2 quadrant 2-quadrant: differential V X Balanced mixer No feedthrough from V Y If V X = 0, V O = 0 for any V Y (V Y seen as common mode) DC required on V Y Feedthrough from V X 07/03/ ATLCE - B DDC 2016 DDC 20

21 Transconductance circuit - 4 quadrant Differential V X and V Y : double balanced mixer No feedthrough on V X and V Y Exploit g m Can use MOS or BJT 07/03/ ATLCE - B DDC 2016 DDC 21

22 MOS Gilbert cell Output voltage V Z depends on Drain current unbalance; Drain currents depend on input voltage V X and Source current I 1, I 2 Source current unbalance must depend on input voltage V Y V DD G D V Z V X S I 1 I 2 07/03/ ATLCE - B DDC 2016 DDC 22

23 Multipliers with Gilbert cell V I Conversion The differential V(I) is linear only for low V Limited dynamic range for both inputs» To limit spurious outputs, only small signals Corrective actions Linearize by negative feedback» Re pair in the differential amplifier Wide range V I converter Compensation of exponential nonlinearity» I = exp(log Vi) I = K Vi 07/03/ ATLCE - B DDC 2016 DDC 23

24 Linearized differential stage Emitter feedback Lower gain Wider input dynamic range I 1 -I 2 = ΔI V X /(2R E ) Needs matched R E (hard for ICs!) R E R E 07/03/ ATLCE - B DDC 2016 DDC 24

25 Wide dynamic V I converter Differential V I converter I 1 -I 2 = ΔI V X /R X Needs matched current sources (OK for ICs!) Used also for instrumentation amplifiers Errors from ΔV BE (I E ) 07/03/ ATLCE - B DDC 2016 DDC 25

26 V I dynamic range limits Actual voltage drop on R is not Vx V BE change with current unbalance Io matching Beta matching. V BE1 V BE2 07/03/ ATLCE - B DDC 2016 DDC 26

27 Wide range multiplier: block diagram I V log ΔV = K log Vx Gilbert cell Vz ΔIx = K Vx ΔIy = K Vy Vx V I wide dynamic Vy V I wide dynamic 07/03/ ATLCE - B DDC 2016 DDC 27

28 2016 DDC 28 07/03/ ATLCE - B DDC Complete wide range circuit I 1 I 2 I 3 I 4 I A I B Vo V X Y X Y X A C O A X X X X C O V V R R I R 2 V 2I 1 R V 2 R V 2 R V X X 1 2 R V 2 I I Y Y 4 3 R V 2 I I V V' V V V 6 5 I I I I e e I I T X T BE6 BE5

29 Diode Mixer: single-balanced Single diode Single diode used as switch from Vx to GND Input Vi = Vx + Vy Small Vx, sign defined by Vy» Diode acts as switch controlled by Vy» Output Vx/0» Multiplication by 0/1 Diode half-bridge Couple of diodes as switch from Vx to GND» Diodes act as switches controlled by Vy» Output Vx/0» Multiplication by 0/1 07/03/ ATLCE - B DDC 2016 DDC 29

30 Diode Mixer: double-balanced Couple of diodes Switches Vout between two opposite polarity Vx Output +Vx/-Vx Diode bridge 1 inverts Vx towards the output Diode bridge 2 Sine on Vx, low level signal Squarewave on Vy, large signal Vx + Vy applied to a diagonal Each diode is a switch controlled by Vy Vx direct/inverter on the other diagonal 07/03/ ATLCE - B DDC 2016 DDC 30

31 Switch bridge Mixer Switch bridge (switches V X /-V X at output) Command: V Y Same as multiply by ±1 Strong nonlinearity Diode or MOS switches Double-balanced mixer Used for high frequencies V X V Y V z 07/03/ ATLCE - B DDC 2016 DDC 31

32 Switch Mixer V X analog V Y digital Switches on linked side receive complementary commands The sign of the transfer function is controlled by V Y V Y = H V Z = + V X V X V Y = H V X V z = V x V z = -V x V Y = L V Z = - V X V Y = L 07/03/ ATLCE - B DDC 2016 DDC 32

33 Diode bridge circuits Vx comes from a transformer with center tap V X V Z V Y >> V X (V X has no effect on diode bias) V Y + + V X V Z V X V Z + V Y + V Y 07/03/ ATLCE - B DDC 2016 DDC 33

34 MOS/BJT bridge circuits Same structure as diode bridge Input X on diagonal H Input Y as command (on B or G) Output from diagonal V 07/03/ ATLCE - B DDC 2016 DDC 34

35 Lesson B5: multipliers and mixers Analog multipliers Parameters and errors Transconductance multipliers, 1/2/4 quadrant Balanced mixer, Gilbert cell Diode bridges Mixer parameters Noise, gain, intermodulation, IP 07/03/ ATLCE - B DDC 2016 DDC 35

36 Mixers and amplifiers Mixer seen as amplifier with variable gain (VGA) Constant input = fixed gain for other input Constant Vy amplifier for Vx Constant Vx amplifier for Vy Same requirements as amplifiers No harmonics, no distortion Low noise, wide dynamic Parameters as amplifier + additional 1 db compression, IP2, IP3 Insulation, reflection, Mixer-specific parameters 07/03/ ATLCE - B DDC 2016 DDC 36

37 Mixer parameters Conversion gain IFrms/RFrms Isolation Leakage in unwanted paths Noise figure Nonlinearity Input dynamic range Intermodulation Compression level Intercept Point (order 2, 3, ) 07/03/ ATLCE - B DDC 2016 DDC 37

38 Ideal multiplier linear mixer Only sum and difference spectral lines at output V X (f X ), V Y (f Y ) f X V Z (f X -f Y, f X + f Y ) V X V Y X V Z f Y f X -f Y, f X + f Y fx-fy fy fx fy+fx f 07/03/ ATLCE - B DDC 2016 DDC 38

39 Ideal Mixer output spectrum Sine V Y (f Y ), Wideband V X (F A F B ) Output includes sum and difference beats V X spectrum translated around 0 and 2 f Y 0 Difference fy beat Fa Fb f Sum beat Fb-fy fy 2fy fy+fb f 07/03/ ATLCE - B DDC 2016 DDC 39

40 Mixer and nonlinearity Input nonlinearity generates harmonics Inputs to ideal mixer with order 2, 3 terms With multicomponent input signals Vx = Vxa(Fa) + Vxb(Fb), V X V Y f Y f X ±f Y, 2f Y ± f X, 3f Y ± f X,... X f Y, 2f Y, 3f Y,... V Z possible intermodulation Same problems as amplifiers 07/03/ ATLCE - B DDC 2016 DDC 40

41 Effects of mixer nonlinearity Input nonlinearity Products among Vx, Vy signals and their harmonics V X X V Z Fx±Fy, 2Fx±Fy, 2Fy±Fx, 2Fy±2Fx V Y Output nonlinearity Products among Vx, Vy signals V X Harmonics of the product X V Z Fx±Fy, 2(Fx±Fy), 3(Fy±Fx), V Y Inband terms more dangerous (intermodulation) 07/03/ ATLCE - B DDC 2016 DDC 41

42 Actual mixer real multiplier nonlinearity harmonics V X f X f X, 2f X, 3f X,... V Y X f X -f Y, 2f X -f Y, f X -2f Y, 3f X,... V Z Harmonics beat and intermodulation 07/03/ ATLCE - B DDC 2016 DDC 42

43 Spectrum with nonlinearities Nonlinearity on Vy: components f Y, 2f Y, 3f Y,... Multiple spectral translations: Vx to f Y, 2f Y, 3f Y, f 0 fy Fb 2fy 3fy 4fy-Fb fy-fb 2fy-Fb fy 3fy-Fb fy+fb 2fy+Fb 07/03/ ATLCE - B DDC 2016 DDC 43

44 Mixer vs. amplifiers Input signal: Two sine signal, frequency f1 and f2 Amplifier output: Same frequency Mixer output: Difference/ sum frequency From both: Harmonics: 2f1, 2f2, 3f1,... III ord. beats (intermodulation): 2f1-f2, 2f2-f1,... 07/03/ ATLCE - B DDC 2016 DDC 44

45 Mixer vs. amplifiers Good for an amplifier Good for a mixer 07/03/ ATLCE - B DDC 2016 DDC 45

46 Lesson B5: final test Which are the techniques usable to build units with predefined nonlinearity? Which is the difference among 1/2/4 quadrant multipliers? Define feedthrough in a multiplier How can the Vx feedthrough error be compensated? Which is the main limit of transconductance multipliers? Draw the output spectrum for linear and nonlinear mixers with input signals: Vx: 2,3 + 2,5 MHz (2 components), Vy: 10 MHz An analog multiplier mixer receives on Vx a MHz signal, and a pulse sequence (δ) a 25 MHz rate on Vy. Draw the complete output spectrum from 0 to 400 MHz at the output Vz (assume a fully linear multiplier). 07/03/ ATLCE - B DDC 2016 DDC 46