ATLCE - B5 07/03/2016. Analog and Telecommunication Electronics 2016 DDC 1. Politecnico di Torino - ICT School. Lesson B5: multipliers and mixers

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1 Politecnico di Torino - ICT School Lesson B5: multipliers and mixers Analog and Telecommunication Electronics B5 - Multipliers/mixer circuits» Error taxonomy» Basic multiplier circuits» Gilbert cell» Bridge MOS and diode circuits» Balanced mixers AY Analog multipliers Parameters and errors Transconductance multipliers, 1/2/4 quadrant Gilbert cell Diode bridge Mixer parameters Balanced and I/Q mixers Noise, gain Reerences: Elettronica per Telecom.: Moltiplicatori Analogici Design with Op Amp : 13.2 Analog multipliers 07/03/ ATLCE - B DDC 07/03/ ATLCE - B DDC 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 R and T» 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». 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 ampliiers (analog computation) digital 07/03/ ATLCE - B DDC 07/03/ ATLCE - B DDC Mixers in the handset Mixers in a GPS receiver Image reject mixer Mixer II RF Mixers (irst conversion) I/Q Mixers (second conversion) 07/03/ ATLCE - B DDC 07/03/ ATLCE - B DDC 2016 DDC 1

2 Many uses o multipliers: GP2015 Multiplier as mixer Mixers Phase detectors Variable gain ampliier Mixing is achieved by multiplication sena x senb = 0,5 [cos(a-b) cos(a+b)] With sine inputs, the output o a multiplier includes Dierence component Sum component Other terms, caused by nonlinearity and errors Only one term is used (sum or dierence beat) Filters Cancellation 07/03/ ATLCE - B DDC 07/03/ ATLCE - B DDC Ideal multipliers Errors in multipliers: real circuits Ideal multiplier: Vo = Km Vx Vy Sine input signals, requency Fx and Fy Vo spectrum includes only Fx - Fy and Fx + Fy x y-x x y x y+x Ideal multiplier: Vo = Km Vx Vy Sine input signals, requency Fx and Fy Vo spectrum includes only Fx - Fy and Fx + Fy Actual multiplier Oset 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, requency 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 07/03/ ATLCE - B DDC Spectrum with real mixer Vo = Km Vx Vy + Ex Vx + Ey Vy + Eo +. Spurious outputs: eedthrough Input signals reach the output Mainly due to mixer unbalance or signal DC: Vo = Km Vx (Vy + ΔVy) = Km Vx Vy + Km Vx ΔVy x y DC error on Vy (oset) ΔVy causes Vx eedthrough o x a b y-x y y+x d o x y-x y y+x 07/03/ ATLCE - B DDC 07/03/ ATLCE - B DDC 2016 DDC 2

3 Nonlinearity Lesson B5: multipliers and mixers Nonlinearity causes higher order terms 2x, 2y, 2x+y, 2x-y, 2x+2y, 3x, 3y, 3x+y,.. Can be removed with tuned circuits o a b y-x c y+x d 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 07/03/ ATLCE - B DDC Example o mixer with nonlinear circuit BJT ampliier with input Vx on B and Vy on E Eective 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 eedthrough errors Merged with input ampliier and local oscillator in (old) low-cost receivers Mixers with nonlinear networks Vi = Vx + Vy (requency 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 requency Fx e Fy»Vx Vy requency Fx - Fy and Fx + Fy»Vx 2, Vy 2 requency 2Fx, 2Fy» Other terms requency M Fx + N Fy» Order III intermodulation (2Fx - Fy) Useul component (di or sum beat) isolated by a tuned circuit 07/03/ ATLCE - B DDC 07/03/ ATLCE - B DDC Transconductance multiplier Transconductance circuit - 1 quadrant For small-signal ampliier: Vo = - Vx g m Rc Gain proportional to transconductance g m g m depends rom Ic (Id) Id is controlled by Vy: g m = K Vy V O = g m1 R C g m1 = I C /V T I C g m2 R C Vo = K Rc Vx Vy Single transistor: Vx, Vy > 0: 1 quadrant DC components high eedthrough Dierential circuits: 2/4-quadrants No DC, less eedthrough V O (g m2 /V T )g m1 R C V O K (polarity!) I C g m1 g m2 Limited to low-level signals 07/03/ ATLCE - B DDC 07/03/ ATLCE - B DDC 2016 DDC 3

4 Transconductance circuit tuned load Transconductance circuit - 2 quadrant Z C (ω) to isolate desired component (sum or di beat) Z C 2-quadrant: dierential Balanced mixer V O = K Z C (ω) and > 0 1 quadrant Feedtrough on and Y! Can be extended to 2/4-quadrant I C No eedthrough rom I = 0, V O = 0 or any ( seen as common mode) DC required on Feedthrough rom 07/03/ ATLCE - B DDC 07/03/ ATLCE - B DDC Dierential and : double balanced mixer No eedthrough on and Exploit g m Can use MOS or BJT Transconductance circuit - 4 quadrant V DD MOS Gilbert cell Output voltage depends on Drain current unbalance; Drain currents depend on input voltage and Source current I 1, I 2 Source current unbalance must depend on input voltage G D S I 1 I 2 07/03/ ATLCE - B DDC 07/03/ ATLCE - B DDC Multipliers with Gilbert cell Linearized dierential stage V I Conversion The dierential V(I) is linear only or low V Limited dynamic range or both inputs» To limit spurious outputs, only small signals Corrective actions Linearize by negative eedback» Re pair in the dierential ampliier Wide range V I converter Compensation o exponential nonlinearity» I = exp(log Vi) I = K Vi Emitter eedback Lower gain Wider input dynamic range I 1 -I 2 = ΔI /(2R E ) Needs matched R E (hard or ICs!) R E R E 07/03/ ATLCE - B DDC 07/03/ ATLCE - B DDC 2016 DDC 4

5 Wide dynamic V I converter V I dynamic range limits Dierential V I converter I 1 -I 2 = ΔI /R Needs matched current sources (OK or ICs!) Used also or instrumentation ampliiers Errors rom ΔV BE (I E ) 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 07/03/ ATLCE - B DDC Wide range multiplier: block diagram Complete wide range circuit I V log ΔV = K log Vx Gilbert cell Vz V I2 I1 2 R VY I3 I4 2 R Y Vo ΔIx = K Vx Vx V I wide dynamic Vy V I wide dynamic ΔIy = K Vy VBE5 VBE6 I5 VT e I6 V' V I8 I T 2 e I7 I1 V V 1 VO RC2 2 R R 2IA V I 1 I 2 I 3 I 4 RC VO 2 V VY IA R RY I A I B 07/03/ ATLCE - B DDC 07/03/ ATLCE - B DDC Diode Mixer: single-balanced Single diode Single diode used as switch rom Vx to GND Input Vi = Vx + Vy Small Vx, sign deined by Vy» Diode acts as switch controlled by Vy» Output Vx/0» Multiplication by 0/1 Diode hal-bridge Couple o diodes as switch rom Vx to GND» Diodes act as switches controlled by Vy» Output Vx/0» Multiplication by 0/1 Diode Mixer: double-balanced Couple o 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 07/03/ ATLCE - B DDC 2016 DDC 5

6 Switch bridge Mixer Switch Mixer Switch bridge (switches /- at output) Command: Same as multiply by ±1 Strong nonlinearity Diode or MOS switches Double-balanced mixer V z analog digital Switches on linked side receive complementary commands The sign o the transer unction is controlled by = H V z = V x Used or high requencies = H = + = L = - = L V z = -V x 07/03/ ATLCE - B DDC 07/03/ ATLCE - B DDC Diode bridge circuits MOS/BJT bridge circuits Vx comes rom a transormer with center tap >> ( has no eect on diode bias) Same structure as diode bridge Input on diagonal H Input Y as command (on B or G) Output rom diagonal V /03/ ATLCE - B DDC 07/03/ ATLCE - B DDC Analog multipliers Parameters and errors Transconductance multipliers, 1/2/4 quadrant Balanced mixer, Gilbert cell Diode bridges Mixer parameters Noise, gain, intermodulation, IP Lesson B5: multipliers and mixers Mixers and ampliiers Mixer seen as ampliier with variable gain (VGA) Constant input = ixed gain or other input Constant Vy ampliier or Vx Constant Vx ampliier or Vy Same requirements as ampliiers No harmonics, no distortion Low noise, wide dynamic Parameters as ampliier + additional 1 db compression, IP2, IP3 Insulation, relection, Mixer-speciic parameters 07/03/ ATLCE - B DDC 07/03/ ATLCE - B DDC 2016 DDC 6

7 Mixer parameters Ideal multiplier linear mixer Conversion gain IFrms/RFrms Isolation Leakage in unwanted paths Noise igure Nonlinearity Input dynamic range Intermodulation Compression level Intercept Point (order 2, 3, ) Only sum and dierence spectral lines at output ( ), ( Y ) ( - Y, + Y ) Y - Y, + Y x-y y x y+x 07/03/ ATLCE - B DDC 07/03/ ATLCE - B DDC Sine ( Y ), Wideband (F A F B ) Output includes sum and dierence beats spectrum translated around 0 and 2 Y 0 Dierence y Fa Fb beat Ideal Mixer output spectrum Fb-y y 2y y+fb Sum beat Input nonlinearity generates harmonics Inputs to ideal mixer with order 2, 3 terms With multicomponent input signals Vx = Vxa(Fa) + Vxb(Fb), possible intermodulation Same problems as ampliiers Y Mixer and nonlinearity ± Y, 2 Y ±, 3 Y ±,... Y, 2 Y, 3 Y,... 07/03/ ATLCE - B DDC 07/03/ ATLCE - B DDC Eects o mixer nonlinearity Actual mixer real multiplier Input nonlinearity Products among Vx, Vy signals and their harmonics Fx±Fy, 2Fx±Fy, 2Fy±Fx, 2Fy±2Fx nonlinearity harmonics, 2, 3,... Output nonlinearity Products among Vx, Vy signals Harmonics o the product Fx±Fy, 2(Fx±Fy), 3(Fy±Fx), - Y, 2 - Y, -2 Y, 3,... Harmonics beat and intermodulation Inband terms more dangerous (intermodulation) 07/03/ ATLCE - B DDC 07/03/ ATLCE - B DDC 2016 DDC 7

8 Spectrum with nonlinearities Mixer vs. ampliiers Nonlinearity on Vy: components Y, 2 Y, 3 Y,... Multiple spectral translations: Vx to Y, 2 Y, 3 Y, 0 y y-fb 2y-Fb y Fb 3y-Fb 2y y+fb 4y-Fb 3y 2y+Fb Input signal: Two sine signal, requency 1 and 2 Ampliier output: Same requency Mixer output: Dierence/ sum requency From both: Harmonics: 21, 22, 31,... III ord. beats (intermodulation): 21-2, 22-1,... 07/03/ ATLCE - B DDC 07/03/ ATLCE - B DDC Mixer vs. ampliiers Lesson B5: inal test Good or an ampliier Good or a mixer Which are the techniques usable to build units with predeined nonlinearity? Which is the dierence among 1/2/4 quadrant multipliers? Deine eedthrough in a multiplier How can the Vx eedthrough error be compensated? Which is the main limit o transconductance multipliers? Draw the output spectrum or 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 rom 0 to 400 MHz at the output Vz (assume a ully linear multiplier). 07/03/ ATLCE - B DDC 07/03/ ATLCE - B DDC 2016 DDC 8