Prof. C. Patrick Yue Slide 1

Mixer Design Overview

q Noise Figure – impacts receiver sensitivityq Linearity (IIP3) – impacts receiver blocking performanceq Conversion gain – lowers noise impact of following stagesq Power match – want maximize voltage gain rather than power match for

integrated designsq Power – want low power dissipationq Isolation – want to minimize interaction between the RF, IF, and LO portsq Sensitivity to process/temp variations – need to make it manufacturable

in high volume

Prof. C. Patrick Yue Slide 2

Types of Mixer

q Multiplication through device non-linearityq Multiplication through switching

� Active mixers� Passive mixers

Prof. C. Patrick Yue Slide 3

Ideal Mixer Behavior

Prof. C. Patrick Yue Slide 4

Non-Ideality in Mixers

q Image problemq LO feedthroughq Self mixing due to reverse LO feedthrough

Prof. C. Patrick Yue Slide 5

Mixer Based on Non-Linearity

q Drain current of an MOSFET exhibits a square dependence on gate overdrive

q Collector current of an BJT exhibits a exponential dependence on base-emitter voltage drive

Prof. C. Patrick Yue Slide 6

Single-Device Mixer Using MOSFET (Square-Law Mixer)

Prof. C. Patrick Yue Slide 7

Practical Configuration for Single-Device Mixer

Prof. C. Patrick Yue Slide 8

Single-Device Mixer Using BJT

Prof. C. Patrick Yue Slide 9

Design Considerations for Mixer Based on Device Non-Linearity

q Design simplicityq Noise Figure

� The square law MOSFET mixer can be designed to have very low noise figure

q Linearity� By operating the square law MOSFET mixer in the square law region the

linearity of the mixer can be improved considerably� BJT mixer is less linear as it produces a host of non-linear components due

to the exponential nature of the BJT mixer

q Power Dissipation� Very low power dissipation due to single device operation

q Power Gain� Reasonable power gain can be achieved

q Isolation� Poor isolation from LO to RF port – by far the biggest short coming

Prof. C. Patrick Yue Slide 10

Mixing Through Switching

Prof. C. Patrick Yue Slide 11

Spectral Components Due to Mixing

Prof. C. Patrick Yue Slide 12

Simple Switching Mixer (Single-Balanced Mixer)

q M1 acts as a transconductance to convert the RF voltage signal to a current q M2 and M3 commute the current between the two output branches.

Prof. C. Patrick Yue Slide 13

The Issue of Balance in Mixers

bias

Prof. C. Patrick Yue Slide 14

Achieving Balanced LO Signal with DC Baising

)()()()(])()([)( tLOtRFtLOtRFtLOtLOtRF ×−×=−×

Prof. C. Patrick Yue Slide 15

Single-Balanced Mixer

Prof. C. Patrick Yue Slide 16

LO Feedthrough in Single-Balanced Mixers

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Ideal Double-Balanced Mixer

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Achieving Balanced RF Signal with Biasing

)()()()(])()([)(

)()()()(])()([)(

])()([])()([

tLOtRFtLOtRFtLOtLOtRF

tLOtRFtLOtRFtLOtLOtRF

tLOtLOtRFtRF

×−×=−×⇒

×−×=−×⇒

−×−

Prof. C. Patrick Yue Slide 19

Double-Balanced Mixer ImplementationI1+I4 I2+I3

Prof. C. Patrick Yue Slide 20

Gilbert Cell (Four Quadrant) Mixer

Prof. C. Patrick Yue Slide 21

Mixer Voltage Conversion Gain

q Voltage conversion gain of a mixer depends on several factors� Input transconductance� Multiplication factor� Load resistance

Prof. C. Patrick Yue Slide 22

Common-Source Transconductance Stage in Mixer

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CS Transconductance Stage with Degeneration

Prof. C. Patrick Yue Slide 24

Transconductor Stage in Mixer

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Prof. C. Patrick Yue Slide 25

Common-Gate Transconductance Stage in Mixer

Prof. C. Patrick Yue Slide 26

Mixer Multiplication Factor

Prof. C. Patrick Yue Slide 27

Mixer Voltage Conversion Gain

q If the sinusoidal LO swing is sufficiently large to completely switch the current, we can approximate the LO by a square wave

q Consider only the fundamental term in LO

]})cos[(4

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q After the low-pass filter,

outeffmoutout RgRiGain _2π

==⇒

Prof. C. Patrick Yue Slide 28

Mixer Noise Analysis

q Three contributors to mixer noise� Transconductance stage� Switching pairs� Load resistance

Prof. C. Patrick Yue Slide 29

Design Consideration for Minimizing Mixer NF

q Design the transducer for minimum noise figureq Noise from M2 and M3 can be minimized through fast switching of M2 &

M3 by� making LO amplitude large to ensure complete (> 90%) current commuting � making M2 and M3 as small as possible (i.e. increasing fTof M2 and M3)

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NF Expression for Double-Balanced Mixer [1]

where

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Mixer NF for Single-Sideband Systems

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Mixer NF Double Sideband Systems

Prof. C. Patrick Yue Slide 33

Design Consideration for Mixer Linearity

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Design Consideration for Mixer Linearity

Prof. C. Patrick Yue Slide 35

Measured IIP3 for a 0.8-µm SB Mixer [2]

q At high bias current, the switching pair nonlinearity dominatesq At low bias current, the transconductance stage nonlinearity dominates

� For short channel devices, the transconductance stage nonlinearity dominates� IIP3 is proportional to (VRF_DC – Vth)

Prof. C. Patrick Yue Slide 36

Measured IIP3 for a 0.8-µm SB Mixer [2]

q At high frequencies, excessively large LO amplitude degrades IIP3 due to parasitic capacitive coupling which is nonlinear

q For low-voltage design (< 2V), this is usually not a big concern

Prof. C. Patrick Yue Slide 37

Passive Mixers

q Very high linearity (assuming the current are completely commuted)� 20–30 dBm of IIP3 achievable

q High noise figure (noise due to the the switching devices)� 20–30 dB of NF

q Voltage conversion loss

(Biasing not shown)

Prof. C. Patrick Yue Slide 38

Passive Mixers with Biasing Shown

Prof. C. Patrick Yue Slide 39

References

1. M. T. Terrovitis and R. G. Meyer, “Noise in Current-Commuting CMOS Mixers” IEEE Journal of Solid-State Circuits, Vol. 34, No. 6, June 1999.

2. M. T. Terrovitis and R. G. Meyer, “Intermodulation Distortion in Current-Commutating CMOS Mixers,” IEEE Journal of Solid-State Circuits, Vol. 35, No. 10, October 2000.

3. Prof. M. Perrott, MIThttp://ocw.mit.edu/OcwWeb/Electrical-Engineering-and-Computer-Science/6-776Spring-2005/CourseHome/index.htm

4. Prof. L. Larson, UC San DiegoECE 265A and 265B lecture notes