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1 Mixer Design • Introduction to mixers • Mixer metrics • Mixer topologies • Mixer performance analysis • Mixer design issues

1 Mixer Design Introduction to mixers Mixer metrics Mixer topologies Mixer performance analysis Mixer design issues

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Page 1: 1 Mixer Design Introduction to mixers Mixer metrics Mixer topologies Mixer performance analysis Mixer design issues

1

Mixer Design

• Introduction to mixers

• Mixer metrics

• Mixer topologies

• Mixer performance analysis

• Mixer design issues

Page 2: 1 Mixer Design Introduction to mixers Mixer metrics Mixer topologies Mixer performance analysis Mixer design issues

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What is a mixer

• Frequency translation device– Convert RF frequency to a lower IF or base band for

easy signal processing in receivers– Convert base band signal or IF frequency to a higher

IF or RF frequency for efficient transmission in transmitters

• Creative use of nonlinearity or time-variance– These are usually harmful and unwanted– They generates frequencies not present at input

• Used together with appropriate filtering– Remove unwanted frequencies

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Two operation mechanisms

• Nonlinear transfer function– Use device nonlinearities creatively!– Intermodulation creates the desired

frequency and unwanted frequencies

• Switching or sampling– A time-varying process – Preferred; fewer spurs– Active mixers– Passive mixers

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An ideal nonlinearity mixer

x(t)

y(t)

x(t)y(t)If

tBty

tAtx

2

1

cos)(

cos)(

Then the output is

tAB

tAB

tBtA )cos(2

)cos(2

coscos 212121

down convert up convert

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Commutating switch mixer

)(tVRF

)(tVLO)(tVLO

)(tVIF

ttA

tsqtA

tVtV

LORFLORFRF

LORFRF

LORF

)(3cos31

)cos(2

sin

)()(

ωωωωπ

ωω

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A non-ideal mixer

x

y'

output+ +

+

aixi +

y

noise

Distortion+ gain

RF-LO

LO-RF LO-IF

RF-IF

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• Conversion gain – lowers noise impact of following stages

• Noise Figure – impacts receiver sensitivity• Port isolation – want to minimize interaction

between the RF, IF, and LO ports• Linearity (IIP3) – impacts receiver blocking

performance• Spurious response• Power match – want max voltage gain rather

than power match for integrated designs• Power – want low power dissipation• Sensitivity to process/temp variations – need to

make it manufacturable in high volume

Mixer Metrics

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Conversion Gain• Conversion gain or loss is the ratio of the

desired IF output (voltage or power) to the RF input signal value ( voltage or power).

signal RF theof voltager.m.s.

signal IF theof voltager.m.s.Gain Conversion Voltage

source thefrompower Available

load the todeliveredpower IF Gain ConversionPower

If the input impedance and the load impedance of the mixer are both equal to the source impedance, then the voltage conversion gain and the power conversion gain of the mixer will be the same in dB’s.

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Noise Figures: SSB vs DSB

Imageband

Signalband

Thermal noise

LO

IF

Signalband

Thermal noise

LO

0

Single side band Double side band

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SSB Noise Figure

• Broadband noise from mixer or front end filter will be located in both image and desired bands

• Noise from both image and desired bands will combine in desired channel at IF output– Channel filter cannot remove this

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• For zero IF, there is no image band– Noise from positive and negative frequencies combine, but the

signals combine as well

• DSB noise figure is 3 dB lower than SSB noise figure – DSB noise figure often quoted since it sounds better

DSB Noise Figure

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Port-to-Port Isolations

RF IF

LO

• Isolation– Isolation between RF, LO and IF ports– LO/RF and LO/IF isolations are the most

important features.– Reducing LO leakage to other ports can be

solved by filtering.

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LO Feed through

• Feed through from the LO port to IF output port due to parasitic capacitance, power supply coupling, etc.

• Often significant due to strong LO output signal – If large, can potentially desensitize the receiver due to the extra

dynamic range consumed at the IF output– If small, can generally be removed by filter at IF output

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Reverse LO Feed through

• Reverse feed through from the LO port to RF input port due to parasitic capacitance, etc.– If large, and LNA doesn’t provide adequate isolation,

then LO energy can leak out of antenna and violate emission standards for radio

– Must insure that isolation to antenna is adequate

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Self-Mixing of Reverse LO Feedthrough

• LO component in the RF input can pass back through the mixer and be modulated by the LO signal– DC and 2fo component created at IF output – Of no consequence for a heterodyne system, but can

cause problems for homodyne systems (i.e., zero IF)

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Nonlinearity in Mixers

• Ignoring dynamic effects, three nonlinearities around an ideal mixer

• Nonlinearity A: same impact as LNA nonlinearity• Nonlinearity B: change the spectrum of LO signal

– Cause additional mixing that must be analyzed– Change conversion gain somewhat

• Nonlinearity C: cause self mixing of IF output

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Focus on Nonlinearity in RF Input Path

• Nonlinearity B not detrimental in most cases– LO signal often a square wave anyway

• Nonlinearity C avoidable with linear loads• Nonlinearity A can hamper rejection of interferers

– Characterize with IIP3 as with LNA designs– Use two-tone test to measure (similar to LNA)

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Spurious ResponseLOnRFmIF

10 , RF

LO

RF

IFm

RF

LOn

RF

IF

RFIFy

RFLOx

10 xymxny

IF Band

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Mixer topologies

• Discrete implementations:– Single-diode and diode-ring mixers

• IC implementations:– MOSFET passive mixer– Active mixers– Gilbert-cell based mixer– Square law mixer– Sub-sampling mixer– Harmonic mixer

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Single-diode passive mixer

• Simplest and oldest passive mixer • The output RLC tank tuned to match IF• Input = sum of RF, LO and DC bias• No port isolation and no conversion gain.• Extremely useful at very high frequency (millimeter wave band)

LR

VRF

VLOCL

DI

DV

IFV

LOV

t

IFV

t

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• Poor gain• Good LO-IF isolation• Good LO-RF isolation• Poor RF-IF isolation• Attractive for very high frequency applications where

transistors are slow.

LR

VLOCL

VRF

LOV

t

IFV

t

IFV

Single-balanced diode mixer

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• Poor gain (typically -6dB)• Good LO-IF LO-RF RF-IF isolation• Good linearity and dynamic range• Attractive for very high frequency applications where

transistors are slow.

VLO VRF

LOV

t

IFV

t

IFV

Double-balanced diode mixer

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CMOS Passive Mixer

• M1 through M4 act as switches

VLO VLOM1 M2

VLO M4 VLOM3

RS

VIF

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CMOS Passive Mixer

• Use switches to perform the mixing operation• No bias current required • Allows low power operation to be achieved

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CMOS Passive Mixer

RF+

RF-

LO+LO-

IF

[*] T. Lee

Same idea, redrawnRC filter not shownIF amplifier can be frequency selective

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IM1

VLO

t

t

VOUT

t

4 4 4. 3 5 ...

3 5out RF RF LO LO LOV V Cos t Cos t Cos t Cos t

LO

RF

4out IFC

RF RF

VG

V

CMOS Passive Mixer

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• Non-50% duty cycle of LO results in no DC offsets!!

IM1

VLO

t

t

VOUT

t

4 4 4. 3 5 ...

3 5out RF RF LO LO LOV V Cos t DC Cos t Cos t Cos t

LO

RF

DC-term of LO

CMOS Passive Mixer

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CMOS Passive Mixer with Biasing

VLO1M 2M

VLO

'1M

'2M

200SR

LC

1biasC nF

1biasC nF

ggR

ggR

1biasC nFggV

sdR

sdR

sdV

SV

2LR k

200

LOV

LOV

LOV

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A Highly Linear CMOS Mixer

• Transistors are alternated between the off and triode regions by the LO signal

• RF signal varies resistance of channel when in triode• Large bias required on RF inputs to achieve triode operation

– High linearity achieved, but very poor noise figure

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Simple Switching Mixer (Single Balanced Mixer)

• The transistor M1 converts the RF voltage signal to the current signal.

• Transistors M2 and M3 commute the current between the two branches.

VLO

RL RL

VLO

VRF

Vout

I IDC RF

M1

M2 M3

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Single balanced active mixer, BJT

• Single-ended input

• Differential LO

• Differential output

• QB provides gain for vin

• Q1 and Q2 steer the current back and forth at LO

LO+ LO-

vin + DC

RL RL

+ out -

VCC

Q1 Q2

QB

vout = ±gmvinRL

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Double Balanced Mixer

• Strong LO-IF feed suppressed by double balanced mixer.• All the even harmonics cancelled.• All the odd harmonics doubled (including the signal).

VLO

RL RL

VLOM2 M3

VRF

VLOM2 M3

VRF

VOUT

I IDC RF I IDC RF

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Gilbert Mixer

• Use a differential pair to achieve the transconductor implementation

• This is the preferred mixer implementation for most radio systems!

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Double balanced mixer, BJT

• Basically two SB mixers– One gets +vin/2, the other gets –vin/2

LO+

+ vin -

RL

+ out -

VCC

Q1 Q2

QB1

LO-

RL

Q3 Q4

QB2

LO+

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Mixers based on MOS square law

VRF

Rb

VBB1

Cl earg

VLO

2

0.ds SQ GSQ TI K V V

2

0

2 2

0 0

.

. 2 .

ds SQ bias RF LO T

SQ bias T RF LO bias T RF LO

I K V V V V

K V V V V V V V V

tt

VV

LORFLORF

LORF

)cos( and )cos(

torise gives )( 2

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Practical Square Law Mixers

VRF

Rb

VBB1

Cl earg 2

0.ds SQ GSQ TI K V V

VLO

Cl earg

IBIAS

LOox

LOsq VL

WCVK

2

be shown to becan gain conversion The

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Practical Bipolar Mixer

VRF

Rb

VBB1

Cl earg I I eC CO

V

VBE

T .

VLO

Cl earg

IBIAS

LOT

CQ Vv

I2

be shown to becan gain conversion The

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MOSFET Mixer (with impedance matching)

VRF

Rb

VBB1

Cl earg

2

0.ds SQ GSQ TI K V V

VLO

Cl earg

Le

LgRS

RLO

VBB2

VDDCmatch

RL

IF Filter

Matching Network

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Sub-sampling Mixer

• Properly designed track-and-hold circuit works as sub-sampling mixer.

• The sampling clock’s jitter must be very small• Noise folding leads to large mixer noise figure.• High linearity

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Harmonic Mixer

• Harmonic mixer has low self-mixing DC offset, very attractive for direct conversion application.

• The RF signal will mix with the second harmonic of the LO. So the LO can run at half rate, which makes VCO design easier.

• Because of the harmonic mixing, conversion gain is usually small

•Emitter-coupled BJTs work as two limiters.•Odd symmetry suppress even order distortion eg LO selfmixing.•Small RF signal modulates zero crossing of large LO signal. •Output rectangular wave in PWM•LPF demodulate the PWM

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Features of Square Law Mixers• Noise Figure: The square law MOSFET mixer can be

designed to have very low noise figure.• Linearity: true square law MOSFET mixer produces only

DC, original tones, difference, and sum tones• The corresponding BJT mixer produces a host of non-

linear components due to the exponential function• Power Dissipation: The square law mixer can be designed

with very low power dissipation.• Power Gain: Reasonable power gain can be achieved

through the use of square law mixers.• Isolation: Square law mixers offer poor isolation from LO

to RF port. This is by far the biggest short coming of the square law mixers.

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Mixer performance analysis

• Analyze major metrics– Conversion gain– Port isolation– Noise figure/factor– Linearity, IIP3

• Gain insights into design constraints and compromise

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Common Emitter Mixer

• Single-ended input

• Differential LO

• Differential output

• QB provides gain for vin

• Q1 and Q2 steer the current left and right at LO

LO+ LO-

vin + DC

RL RL

+ out -

VCC

Q1 Q2

QB

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Common Emitter Mixer

• Conversion gain

LO+ LO-

vin + DC

RL RL

+ out -

VCC

Q1 Q2

QB

vout1 = ±gmvinRL

Two output component:

vout2 = ±IQBDCRL

So gain = ?

IF signal is the RF – LO

component in vout1

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Common Emitter Mixer

• Port isolation

LO+ LO-

vin + DC

RL RL

+ out -

VCC

Q1 Q2

QB

At what frequency is Vout2 switching?

vout2 = ±IQBDCRL

vout2 = SW(LO)IQBDCRL

This is feed through from LO to output

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Common Emitter Mixer

• Port isolation

LO+ LO-

vin + DC

RL RL

+ out -

VCC

Q1 Q2

QB

How about LO to RF?

This feed through is much smaller than LO to output

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Common Emitter Mixer

• Port isolation

LO+ LO-

vin + DC

RL RL

+ out -

VCC

Q1 Q2

QB

How about RF to LO?

If LO is generating a square wave signal, its output impedance is very small, resulting in small feed through from RF to LO to output.

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Common Emitter Mixer

• Port isolation

LO+ LO-

vin + DC

RL RL

+ out -

VCC

Q1 Q2

QB

What about RF to output?

Ideally, contribution to output is:

SW(LO)*gmvinRL

What can go wrong and cause an RF component at the output?

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Common Emitter Mixer

• Noise Components:1. Noise due to loads

2. Noise due to the input transistor (QB)

3. Noise due to switches (Q1 and Q2)

LO+ LO-

RL RL

+ out -

Q1 Q2

QB

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Common Emitter Mixer

1. Noise due to loads:– Each RL contributes

vRL2 = 4kTRLf

– Since they are uncorrelated with each other, their noise power’s add

– Total contribution of RL’s: voRL

2 = 8kTRLf

LO+ LO-

RL RL

+ out -

Q1 Q2

QB

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Common Emitter Mixer

2. Noise due input transistor (the transducer):

– From BJT device model, equivalent input noise voltage of a CE amplifier is:

LO+ LO-

RL RL

+ out -

Q1 Q2

QB fg

rkTvm

bCEin

2

142

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Common Emitter Mixer

2. Noise due to input transistor:

– If this is a differential amplifier, QB noise would be common mode

– But Q1 and Q2 just switching, the noise just appears at either terminal of out:

LO+ LO-

RL RL

+ out -

Q1 Q2

QB

222

, CEinQout vgainvB

vin(CE)2

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Common Emitter Mixer

2. Noise due to input transistor:

– Noise at the two terminals dependent?

– Accounted for by incorporating a factor “n”.

LO+ LO-

RL RL

+ out -

Q1 Q2

QB

vin(CE)2

fg

rnkTRgv

vgainnv

mbLmQout

CEinQout

B

B

2

1422

,

222,

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Common Emitter Mixer

• Total Noise due to RL and QB:

– If we assume rb is very small:

When:rb << 1/(2gm) and

n=1

LO+ LO-

RL RL

+ out -

Q1 Q2

QB

418

2Lm

LT Rg

kTRf

v

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Common Emitter Mixer

3. What about the noise due to switches?

– When Q2 is off and Q1 is on, acting like a cascode or more like a resister if LO is strong

– Can show that Q1’s noise has little effect on vout

– VE1~VC1, VBE1 has similar noise as VC1, which cause jitter in the time for Q1 to turn off if the edges of LO are not infinitely steep

LO+ LO-

RL RL

+ out -

Q1 Q2

QB

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Common Emitter Mixer

3. What about the noise due to switches:

– Transition time “jitter” in the switching signal:

LO+ LO-

RL RL

+ out -

Q1 Q2

QB

no noise

noise

Effect is quite complex, quantitative analysis later

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Common Emitter Mixer

• How to improve Noise Figure of mixer:

– Reduce RL– Increase gm and

reduce rb of QB

– Faster switches– Steeper rise or fall

edge in LO– Less jitter in LO

LO+ LO-

RL RL

+ out -

Q1 Q2

QB

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Common Emitter Mixer

• IP3:– The CE input transistor

(QB) converts vin to Iin

• BJTs cause 3rd-order harmonics

– Multiplying by RL is linear operation

– Q1 & Q2 only modulate the frequency

IP3mixer = IP3CE’s Vbe->I

LO+ LO-

RL RL

+ out -

Q1 Q2

QB

...)6

1

2

111( 3

32

2/)(

ininint

DCvvV

sQ vv

vv

vv

IeIItt

tinBB

B

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Double Balanced Mixer

• Basically two CE mixers– One gets +vin/2, the other gets –vin/2

LO+

+ vin -

RL

+ out -

VCC

Q1 Q2

QB1

LO-

RL

Q3 Q4

QB2

LO+

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+1

-1Local Oscillator

Double Balanced Mixer

vout = – gmvinRL

vout = gmvinRL

LO+

+ vin -

RL

+ out -

VC

C

Q1 Q2

QB1

LO-

RL

Q3 Q4

QB2

LO+

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Double Balanced Mixer

• Benefits:– Fully Differential

– No output signal at LO

• Three stages:– CE input stages– Switches– Output load

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Double Balanced Mixer• Noise:

– Suppose QB1 & QB2 give similar total gm

– Similar to CE Mixer

• IP3:– Similar Taylor series

expansion of transducer transistors

– Vin split between two Q’s, it can double before reaching the same level of nonlinearity

– IIP3 improved by 3 dB

LO+

+ vin -

RL

+ out -

VCC

Q1 Q2

QB1

LO-

RL

Q3 Q4

QB2

LO+

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Common Base Mixers

• Similar operation to CE mixers

• Different input stage– QB is CB

• Slightly different output noise– Different CB input noise

• Better linearity

LO+ LO-

VBias

RL RL

+ out -

VC C

Q1 Q2

QB

IDC

vin

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Mixer Improvements

• Debiasing switches from input transistors:– To lower NF we want

high gm, but low Q1 and Q2 current

• Conflicting!

– We can set low ISwitches and high IQb using a current source

LO+ LO-

vin + DC

RL RL

+ out -

VCC

Q1 Q2

QB

ISwitches

IQb

Idifference

41

21

2Lm

SLm

Rg

RRg

cNF

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MOS Single Balanced Mixer

• The transistor M1 converts the RF voltage signal to the current signal.

• Transistors M2 and M3 commute the current between the two branches.

VLO

RL RL

VLO

VRF

Vout

I IDC RF

M1

M2 M3

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IM1

VLO

t

t

VOUT

t

MOS Single Balanced Mixer

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IF Filter

VOUT t

VOUT

t

MOS Single Balanced Mixer

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LO

RF IF

LO RF

IF Filter

LO RF

LO RF LO RF

MOS Single Balanced Mixer

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LO RF 2 LO

SMIX

3 LO

RF

SLO LO

LO RF

MOS Single Balanced Mixer

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Single Balanced Mixer (Incl. RF input Impd. Match)

This architecture, without impedance matching for the LO port, is very commonly used in many designs.

VLO

RL RL

VLO

Vout

M2 M3

RS

VS Rb

GGVLs

LgCl earg G VM RF

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Single Balanced Mixer (Incl. RF & LO Impd. Match)

• This architecture, with impedance matching for the LO port, maximizes LO power utilization without wasting it.

VLO

RL RLVout

M2 M3

RS

VS Rb

1GGVLs

LgCl earg G VM RF

Lm2 Lm3

2GGV

Lg

2GGV

LgLOV

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Single Balanced Mixer Analysis: Linearity

• Linearity of the Mixer primarily depends on the linearity of the transducer (I_tail=Gm*V_rf). Inductor Ls helps improve linearity of the transducer.

• The transducer transistor M1 can be biased in the linear law region to improve the linearity of the Mixer. Unfortunately this results in increasing the noise figure of the mixer (as discussed in LNA design).

VLO

RL RL

VLO

Vout

M2 M3

RS

VS RbGGV

Ls

LgCl earg G VM RF

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• Using the common gate stage as the transducer improves the linearity of the mixer. Unfortunately the approach reduces the gain and increases the noise figure of the mixer.

VLO

RL RL

VLO

VoutM2 M3

RS

VSIbias Cc

GGV

Single Balanced Mixer Analysis: Linearity

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Single Balanced Mixer Analysis: Isolation

• The strong LO easily feeds through and ends up at the RF port in the above architecture especially if the LO does not have a 50% duty cycle. Why?

VLO

RL RL

VLO

Vout

M2 M3

RS

VS Rb

GGV

Ls

LgCl earg G VM RF

LO-RF Feed through

0.5 LOT

0.5 LOT

0.5 LOT

0.5 LOT

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Single Balanced Mixer Analysis: Isolation

• The amplified RF signal from the transducer is passed to the commuting switches through use of a common gate stage ensuring that the mixer operation is unaffected. Adding the common gate stage suppresses the LO-RF feed through.

VLO VLOM2 M3

RS

VS RbVBB1

Ls

LgCl earg

Weak LO-RF Feed through

G VM RF

VBB2

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Single Balanced Mixer Analysis: Isolation

• The strong LO-IF feed-through may cause the mixer or the amplifier following the mixer to saturate. It is therefore important to minimize the LO-IF feed-through.

VLO

RL RL

VLO

VoutM2 M3

RS

VS RbVBB1

Ls

LgCl earg G VM RF

LO-IF Feed through

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Double Balanced Mixer

• Strong LO-IF feed suppressed by double balanced mixer.• All the even harmonics cancelled.• All the odd harmonics doubled (including the signal).

VLO

RL RL

VLOM2 M3

VRF

VLOM2 M3

VRF

VOUT

I IDC RF I IDC RF

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Double Balanced Mixer

• The LO feed through cancels.

• The output voltage due to RF signal doubles.

VLO

RL RL

VLOVoutM2 M3

VRF

VLOVoutM2 M3

VRF

VOUT

I IDC RF I IDC RF

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Double Balanced Mixer: Linearity

• Show that:1/ 2 3/ 2

312 * . ...

2 2 2SQ SQ

IF DC L RF RFDC DC

K KV I R V V

I I

VLO

RL RL

VLOM2 M3

VRF

VLOM2 M3

VRF

VOUT

I IDC RF I IDC RF1M1M

IIP in voltsI

KDC

SQ3

8

3

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Mixer Input Match

VLO

RL RL

VLO

VoutM2 M3

RS

VS RbVBB1

Ls

LgCl earg

S g T SR R L 1g s

gs

L LC

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Mixer Gain

VLO

RL RL

VLO

VRF

Vout

M1

M2 M3

0 : . .2

: . .2

LOout cc DC sig L cc DC sig L

LOLO out cc cc DC sig L DC sig L

TV V I I R V I I R

TT V V V I I R I I R

1

2T

MS

GR

ttttRISWRIV LOLOLOLOLsigLsigsigout

7cos

7

15cos

5

13cos

3

1cos

4*

tAGVGI RFRFMRFMsig cos

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Mixer Output Match

• Heterodyne Mixer: – If IF frequency is low (100-200MHz) and signal

bandwidth is high (many MHz), output impedance matching is difficult due to:

– The signal bandwidth is comparable to the IF frequency therefore the impedance matching would create gain and phase distortions

– Need large inductors and capacitors to impedance match at 200MHz

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Mixer Output Match (IF)

VLO

400LR

VLO

VRF

Vout

M1

M2 M3

3.0CCV V

400

2parL nH

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Mixer Output Match (direct conversion)

VLO

RL RL

VLOVoutM2 M3

RS

VS RbVBB1

Ls

LgCl earg

LC

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85

Mixer Noise Analysis

VLO

RL RL

VLO

VRF

Vout

,DC mix RF NoiseI I I

M1

M2 M3

LO RF

VOUT

t

Instantaneous Switching

LO RF LO RF

Noise in RF signal band and in image band both mixed into IF signal band

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Mixer Noise Analysis

• If the switching is not instantaneous, additional noise from the switching pair will be added to the mixer output.

• Let us examine this in more detail.

VLO

RL RL

VLO

VRF

Vout

,DC mix RF NoiseI I I

M1

M2 M3 VOUT

t

Finite Switching Time

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Mixer Noise Analysis• Noise analysis of a single balanced mixer cont...:

• When M2 is on and M3 is off:

– M2 does not contribute any additional noise (M2 acts as cascode)

– M3 does not contribute any additional noise (M3 is off)

VLO

RL RL

VLO

VRF

Vout

M1

M on2 M off3 VOUT

t

Finite Switching Time

,DC mix RF NoiseI I I

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Mixer Noise Analysis

• Noise analysis of a single balanced mixer cont...:

• When M2 is off and M3 is on:

– M2 does not contribute any additional noise (M2 is off)

– M3 does not contribute any additional noise (M3 acts as cascode)

VLO

RL RL

VLO

VRF

Vout

M1

M off2 M on3 VOUT

t

Finite Switching Time

,DC mix RF NoiseI I I

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Mixer Noise Analysis• Noise analysis of a single balanced mixer cont...:

• When VLO+ = VLO- (i.e. the LO is passing through zero), the noise contribution from the transducer (M1) is zero. Why?

• However, the noise contributed from M2 and M3 is not zero because both transistors are conducting and the noise in M2 and M3 are uncorrelated.

VLO

RL RL

VLO

VRF

Vout

M1

M on2 M on3 VOUT

t

Finite Switching Time

,DC mix RF NoiseI I I

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Mixer Noise Analysis• Optimizing the mixer (for noise figure):

• Design the transducer for minimum noise figure.• Noise from M2, M3 minimized by fast switching :

– making LO amplitude large– making M2 and M3 short (i.e. increasing fT of M2 and M3)

• Noise from M2, M3 can be minimized by using wide M2/M3 switches.

VLO

RL RL

VLO

VRF

Vout

M1

M on2 M on3

VOUT

t

Trise

...m DCg W fixed I 1

...T DCfixed IW

,DC mix RF NoiseI I I

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Mixer Noise Analysis• Noise Figure Calculation:

• Let us calculate the noise figure including the contribution of M2/M3 during the switching process.

VLO

RL RL

VLO

VRF

Vout

M1

M on2 M on3 VOUT

t

Trise

,DC mix RF NoiseI I I

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Mixer Noise Analysis: RL Noise• Noise Analysis of Heterodyne Mixer (RL noise):

VLO

RL RL

VLO

VRF

Vout

M1

M2 M3

IF RF LO

,DC mix RF NoiseI I I

2 4 2noise RL Lv kT R

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Mixer Noise Analysis: Transducer Noise

• Noise Analysis of Heterodyne Mixer (Transducer noise):

VLO

RL RL

VLO

VRF

Vout

M1

M2 M3

1 1

1

.

4 4 4. 3 5 ...

3 5

noise M switch noise M

noise M LO LO LO

i i t SW t

i t Cos t Cos t Cos t

VLO

t,DC mix RF NoiseI I I

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• Noise Analysis of Heterodyne Mixer (Trans-conductor noise):

IF LO

21 1

4. .4noise M m

ch

kTi f kTg

R

1 1

1

.

4 4 4. 3 5 ...

3 5

noise M switch noise M

noise M LO LO LO

i i t SW t

i t Cos t Cos t Cos t

3 LO

4 43 ...

3LO LOSW f

2

21 12 2

4 1 12. . 1 .. . 4

3 5noise M IF mi kTg

5 LO

21 14. 4noise M IF mi kTg

Mixer Noise Analysis: Transducer Noise

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95

Mixer Noise Analysis: Switch Noise

• Noise Analysis of Heterodyne Mixer (switch noise):

VLO VLOM on2 M on3 id3id2

ikT

RkTgd

chm 4

4

idg vm gs g vm gs

4.gn

m

kTv

g

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• Noise Analysis of Heterodyne Mixer (switch noise):

• Show that:

VLO

RL RL

VLO

VRF

Vout

M1

M2 M3

out outi i

VLO

Gm

VLO

,2 3 2,3

2. DC mixm m m m

IG g g g

V

,DC mix RF NoiseI I I

0mG

Mixer Noise Analysis: Switch Noise

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• Noise Analysis of Heterodyne Mixer (switch noise) cont...:

Gm

VLO2,3n mv

iout

2,3.out m n mi t G t v t

2LOT

T

Mixer Noise Analysis: Switch Noise

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• Noise Analysis of Heterodyne Mixer (switch noise) cont...:

0 01

.21

. . . .2/ 2

.2 2

p

m m m pkLO pLO

TSin k

TG t G T G Cos k t

T TTk

p 2 p 3 p

2,3n mv f

p 2 p 3 p

2,32,3

42. .n m

m

kTv

g

2

/ 2pLOT

2

LOT

T

2 22,3 2 3n m n m n mv v v

G tm

G fm

Mixer Noise Analysis: Switch Noise

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• Noise Analysis of Heterodyne Mixer (switch noise) cont...:

p 2 p 3 p

2,3n mv f

p 2 p 3 p

2,3n mv f

2 2 22,3 0 2,3

1. . .

2

noise M IF m n mLO

i G T vT

G fm

G fm

Mixer Noise Analysis: Switch Noise

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• Noise Analysis of Heterodyne Mixer (switch noise) cont...:

2 2 22,3 0 2,3

1. . .

2

noise M IF m n mLO

i G T vT

,

0

2 DC mixm

IG

V

V Slope T . LO LO LOV t A Cos t

90

90LO

LO

LOLO LOt

t

dV tSlope A

dt

2 2 2 22,3 0 2,3 0

2,3

,0

, ,

,

1 1 4. . . . . . 2. .

/ 2 / 2

2.1 1. . . 2. .4 . . . 2. .4

/ 2 / 2

2 2 1. 2. .4 . . 2. .4 .

/ 2 / 2

4. 4

noise M IF m n m mLO LO m

DC mixm

LO LO

DC mix DC mix

LO LO LO LO

DC mix

kTi G T v G T

T T g

IG T kT T kT

T T V

I ITkT kT

T V T A

IkT

A

LO

Total Noise Contribution due to switches M2 and M3

2,32,3

42. .n m

m

kTv

g

,2 3 2,3

2. DC mixm m m m

IG g g g

V

Mixer Noise Analysis: Switch Noise

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Mixer Noise Analysis: Total Noise• Noise Analysis of Heterodyne Mixer (total noise):

,2

1 1

0

4. 4 4. 4 . DC mixnoise M IF m

GSQ T

Ii kTg kT

V V

,22,3 4. 4 DC mix

noise M IFLO

Ii kT

A

2 4 2noise RL Lv kT R

, ,2

0

4 1 4. . . 4. . .DC mix DC mixnoise MIX IF L L L

LOGSQ T

I Iv kTR R R

AV V

0

1

2DS short DS short

m short ox satGS GSQ T

dI Ig WC v

dV V V

2 2 2 2 2 21 2,3noise MIX IF noise RL L noise M L noise Mv v R i R i

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• Noise Analysis of Heterodyne Mixer (total noise):

2noise MIX IFv

1.6GSQV V0.8GSQV V

VLO

, ,2

0

4 1 4. . . 4. . .DC mix DC mixnoise MIX IF L L L

LOGSQ T

I Iv kTR R R

AV V

Mixer Noise Analysis: Total Noise

(VGSQ-VT0) ↑ M1 linearity ↑ and noise↓

ALO ↑ noise contribution from M2/M3 ↓

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Homodyne Mixer Noise Analysis: Transducer Noise

• Noise Analysis of Homodyne Mixer (noise from transducer M1):

LO

RF

VLO

RL RL

VLO

VRF

Vout

M1

M2 M3

,DC mix RF NoiseI I I

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Homodyne Mixer Noise Analysis: RL Noise

• Noise Analysis of Homodyne Mixer (noise from RL):

LO

RF

VLO

RL RL

VLO

VRF

Vout

M1

M2 M3

Noise from RL

,DC mix RF NoiseI I I

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Homodyne Mixer Noise Analysis: non-50% duty LO

• Noise Analysis of Homodyne Mixer (M2,M3 mismatched or non-50% duty cycle of LO)}:

VLO

RL RL

VLO

VRF

Vout

M1

M2 M3

1

4 43 ...

3M LO LOI DC Cos t Cos t

VLO

t

2LOT T

2LOT T

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Homodyne Mixer Noise Analysis: non-50% duty LO

• Noise Analysis of Homodyne Mixer (M2,M3 mismatched or non-50% duty cycle of LO)--{Noise from M1}:

VLO

RL RL

VLO

VRF

Vout

M1

M2 M3 INoise M 1INoise thermal

INoise f 1/

, 1/DC mix RF Noise thermal Noise fI I I I

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Homodyne Mixer Noise Analysis: non-50% duty LO

• Noise Analysis of Homodyne Mixer (M2,M3 mismatched or non-50% duty cycle of LO)--{Noise from M1}:

VLO

RL RL

VLO

VRF

Vout

M1

M2 M3

, 1/

4 4. 3 ...

3DC mix RF Noise thermal Noise f LO LOI I I I DC Cos t Cos t

LO

RF

3 LO

DC-term of LO

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Homodyne Mixer Noise Analysis: non-50% duty LO

• Noise Analysis of Homodyne Mixer (M2,M3 mismatched or non-50% duty cycle of LO)--{Noise from M2/M3}:

VLO VLOM on2 M on3 id3id2

i i id d thermal d f 1/

21/

1. .f

d f mox

Ki g

C WL f

g vm gs g vm gs

1/

1.f

gn fox

Kv

C WL f

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Homodyne Mixer Noise Analysis: non-50% duty LO

• Noise Analysis of Homodyne Mixer (M2,M3 mismatched or non-50% duty cycle of LO)--{Noise from M2/M3}:

VLO

RL RL

VLO

VoutM2 M3

1/gn fv

, 1/DC mix RF Noise thermal Noise fI I I I

VLO1/gn fv

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Homodyne Mixer Noise Analysis: non-50% duty LO

• Noise Analysis of Homodyne Mixer (M2,M3 mismatched or non-50% duty cycle of LO)--{Noise from M2/M3}:

VLO1/gn fv

iout

i i iout out no noise noise f 1/

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Homodyne Mixer Noise Analysis: non-50% duty LO

• Noise Analysis of Homodyne Mixer (M2,M3 mismatched or non-50% duty cycle of LO)--{Noise from M2/M3}:

1/gn fv tT t

Slope Slope ALO LO2

VLO1/gn fv

iout

i i iout out no noise noise f 1/

T

iout

1/

2gn f

LO LO

v tT t

A

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Homodyne Mixer Noise Analysis: non-50% duty LO

• Noise Analysis of Homodyne Mixer (M2,M3 mismatched or non-50% duty cycle of LO)--{Noise from M2/M3}:

1/,max ,max

0 0

. . . .2 2 2

gn fLO LODC DC

k kLO LO

v tT TNoise Energy T t I t k I t k

A

iout

,DC mixI

,DC mixI

1/gn fv t

iout

0.5 LOT

1/gn fv f

t

t

t

f

f

f

1

0.5 LOT

1

0.5 LOT

1/1/ ,max.

2gn f

noise f DCLO

v fi I

A

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Increasing Headroom in DBM (Option 1)

eL

2parL nH

eL

1Q

2 1Q '2 1Q

'1Q

inV

comgdV

2 2Q '2 2Q bR

bV

LOV LOV

cC cCinV

bR

ccV

gndV

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Increasing Headroom in DBM (Option 2)

200SR

eL

Lb

2parL nH

eL

Lb

BQIBQI

200LR

10C nF 10C nF

1Q

2 1Q '2 1Q

'1QSV

SV

inV

inV

comgdV

2 2Q '2 2Q

bR bR bRbRbV

bV bV

LOV LOV

3.0CCV V

cC cC

LR LRggV

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Increasing Headroom in DBM (Option 3)

200SR

eL

Lb

2parL nH

eL

Lb

BQIBQI

200LR

10C nF 10C nF

1Q

2 1Q '2 1Q

'1QSV

SV

inV

inV

comgdV

2 2Q '2 2Q

bR bR bRbRbV

bV bV

LOV LOV

3.0CCV V

cC cC

LR LRggV