lec10 mixers

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6.976 High Speed Communication Circuits and Systems

Lecture 10 Mixers

Michael Perrott

Massachusetts Institute of Technology

Copyright 2003 by Michael H. Perrott


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M.H. Perrott MIT OCW

Mixer Design for Wireless Systems

Design Issues- Noise Figure impacts receiver sensitivity- Linearity (IIP3) impacts receiver blocking performance- Conversion gain lowers noise impact of following stages- Power match want max voltage gain rather than power

match for integrated designs

- Power want low power dissipation- Isolation want to minimize interaction between the RF, IF,and LO ports

- Sensitivity to process/temp variations need to make itmanufacturable in high volume

Zin

Zo LNA To Filter

From Antennaand Bandpass

Filter

PC boardtrace

PackageInterface

Local Oscillator Output

Mixer RF in IF out


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4/45M.H. Perrott MIT OCW

The Issue of Aliasing

When the IF frequency is nonzero, there is an imageband for a given desired channel band- Frequency content in image band will combine with that

of the desired channel at the IF output

- The impact of the image interference cannot be removedthrough filtering at the IF output!

f -f o f o

= 2cos(2 f ot)

RF inRF in(f) Desired

channelImage

Interferer

0

f -f o f o0

1 1


IF out

LO out(f)

f -f o f o

IF out(f)

0

f -f

f -f



LO Feedthrough

LO feedthrough will occur from the LO port to IF output portdue to parasitic capacitance, power supply coupling, etc.- Often significant since LO output much higher than RF signal

If large, can potentially desensitize the receiver due to the extradynamic range consumed at the IF outputIf small, can generally be removed by filter at IF output

f -f o f o

= 2cos(2 f ot)


channelImage

Interferer

0

f -f o f o0

1 1


IF out

LO out(f)

f -f o f o

IF out(f)

0

f -f

f -f

LOfeedthrough

LOfeedthrough



Reverse LO Feedthrough

Reverse LO feedthrough will occur from the LO portto RF input port due to parasitic capacitance, etc.- If large, and LNA doesnt provide adequate isolation,

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

- Must insure that isolate to antenna is adequate

f -f o f o

= 2cos(2 f ot)


channelImage

Interferer

0

f -f o f o0

1 1


IF out

LO out(f)

f -f o f o

IF out(f)

0

f -f

f -f

LOfeedthrough

Reverse LOfeedthrough

LOfeedthrough




Self-Mixing of Reverse LO Feedthrough

LO component in the RF input can pass back throughthe mixer and be modulated by the LO signal- DC and 2f o component created at IF output- Of no consequence for a heterodyne system, but cancause problems for homodyne systems (i.e., zero IF)

f -f o f o

= 2cos(2 f ot)


channelImage

Interferer

0

f -f o f o0

1 1


IF out

LO out(f)

f -f o f o

IF out(f)

0

f -f

f -f

LOfeedthrough


LOfeedthrough


Self-mixingof reverse

LO feedthrough



Removal of Image Interference Solution 1

An image reject filter can be used before the mixer toprevent the image content from aliasing into the desiredchannel at the IF outputIssue must have a high IF frequency

- Filter bandwidth must be large enough to pass all channels- Filter Q cannot be arbitrarily large (low IF requires high Q)

f -f o f o

= 2cos(2 f ot)


channelImage

Interferer

0

f -f o f o0

1 1


IF out

LO out(f)

f -f o f o

IF out(f)

0

f -f

f -f

LOfeedthrough



LO feedthrough

ImageRejectionFilter




Mix directly down to baseband (i.e., homodyne approach)

- With an IF frequency of zero, there is no image bandIssues many!- DC term of LO feedthrough can corrupt signal if time-varying- DC offsets can swamp out dynamic range at IF output- 1/f noise, back radiation through antenna

f -f o f o

= 2cos(2 f ot)


channel

0

f -f o f o0

1 1


IF out

LO out(f)

f -f o f o

IF out(f)

0

f=0

LOfeedthrough


LOfeedthrough



LO feedthrough




Rather than filtering out the image, we can cancel it out

using an image rejection mixer - Advantages Allows a low IF frequency to be used without requiring ahigh Q filter Very amenable to integration

- DisadvantageLevel of image rejection is determined by mismatch in gain

and phase of the top and bottom pathsPractical architectures limited to 40-50 dB image rejection

f

-f 1 f 1

2cos(2 f 1t)

2sin(2 f 1t)

a(t)

b(t)

e(t)

g(t)

RF in IF out2cos(2 f 2t)

2sin(2 f 2t)

Lowpass

RF in(f) Desired

channelImage

Interferer

0

c(t)

d(t)

Lowpass



Image Reject Mixer Principles Step 1

f

-f 1 f 1

2cos(2 f 1t)

2sin(2 f 1t)

a(t)

b(t)

e(t)

g(t)


2sin(2 f 2t)

Lowpass

RF in(f) Desired

channelImage

Interferer

0

f -f 1 f 10

f -f 1

f 10

f -f 1 f 1

A(f)

0

f -f 1 f 1

B(f)

0

c(t)

d(t)

j

-j

1 1 1

j

-j

Lowpass

Lowpass

Lowpass

Note: we are assuming RF in(f)is purely real right now



f

-f 1 f 1

2cos(2 f 1t)

2sin(2 f 1t)

a(t)

b(t)

e(t)

g(t)


2sin(2 f 2t)

Lowpass

RF in(f) Desired

channelImage

Interferer

0

f -f 1 f 10

f -f 1

f 10

f -f 1 f 1

C(f)

0

f -f 1 f 1

D(f)

0

c(t)

d(t)

j

-j

1 1 1

j

-j

Lowpass



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e(t)

g(t)

IF out

-f 2 f 2

E(f)

0

-f 2 f 2

G(f) 1

2

12

1

-1

1

-1-2

f

f

-f 2 f 20

2

f

IF out(f)Baseband

Filter


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What if RF in(f) is Purely Imaginary?

Both desired and image signals disappear!- Architecture is sensitive to the phase of the RF input

Can we modify the architecture to fix this issue?

0 f

IF out(f)(after baseband filtering)

f

-f 1 f 1

2cos(2 f 1t)

2sin(2 f 1t)

a(t)

b(t)

e(t)

g(t)


2sin(2 f 2t)

Lowpass

RF in(f)Desiredchannel

ImageInterferer

0

c(t)

d(t)

Lowpass

-j

j


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Modification of Mixer Architecture for Imaginary RF in(f)

Desired channel now appears given two changes- Sine and cosine demodulators are switched in secondhalf of image rejection mixer

- The two paths are now added rather than subtractedIssue architecture now zeros out desired channelwhen RF in(f) is purely real

0 f

IF out(f)(after baseband filtering)

f

-f 1 f

1

2cos(2 f 1t)

2sin(2 f 1t)

a(t)

b(t)

e(t)

g(t)

RF in IF out

2cos(2 f 2t)

2sin(2 f 2t)

Lowpass


ImageInterferer

0

c(t)

d(t)

Lowpass

-j

j

2


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Overall Mixer Architecture Use I/Q Demodulation

Both real and imag. parts of RF input now pass through

0 f

IF out(f) (I component)(after baseband filtering)

f -f 1 f 1

2cos(2 f 1t)2sin(2 f 1t)

a(t)

b(t)

RF in

IF outI

2cos(2 f 2t)

2sin(2 f 2t)

Lowpass

Desiredchannel

ImageInterferer

0

Lowpass

1

2

f -f 1 f 1

real part of RF in(f)

0

-j

j

1

imag. part of RF in(f)2cos(2 f 2t)

2sin(2 f 2t)

IF outQ

0 f

2

IF out(f) (Q component)(after baseband filtering)


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Mixer Single-Sideband (SSB) Noise Figure

Issue broadband noise from mixer or front end filterwill 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- Mixers are inherently noisy!

f -f o f o

= 2cos(2 f ot)


Imageband

0

f -f o f o0

1 1

LO out

IF out

LO out(f)

f

IF out(f)

0

f -f

f -f


Noise

RF in

Noise from Desiredand Image bands add

Noise

No

2N o

S RF

S RF

ChannelFilter


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Mixer Double-Sideband (DSB) Noise Figure

For zero IF, there is no image band

- Noise from positive and negative frequencies combine, butthe signals do as wellDSB noise figure is 3 dB lower than SSB noise figure

- DSB noise figure often quoted since it sounds better For either case, Noise Figure computed through simulation

f -f o f o

= 2cos(2 f ot)


0

f -f o f o0

1

LO out

LO out(f)

f

IF out(f)

0 f -f


Noise

RF in

Noise frompositive and negativefrequency bands add

Noise

No

2N o

S RF

2S RF

IF out

ChannelFilter


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A Practical Issue Square Wave LO Oscillator Signals

Square waves are easier to generate than sine waves- How do they impact the mixing operation when used asthe LO signal?

-We will briefly review Fourier transforms (series) tounderstand this issue

= 2sgn(cos(2 f ot))

RF in


IF out

1t

TT

W

LO out(t)


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Two Important Transform Pairs

Transform of an impulse train in time is an impulsetrain in frequency

T2

T2

1

x(t)

t

X(f)

f

T1

T

s(t)

t

S(f)

f

T1

T1

T1

T

1

T

Transform of a rectangle pulse in time is a sinc functionin frequency


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Decomposition of Square Wave to Simplify Analysis

Decomposition in time

1

y(t)

tTT

W

s(t)

tT

1

T

*1x(t)

t

W

Consider now a square wave with duty cycle W/T


24/45


Associated Frequency Transforms

Decomposition in frequency

1

y(t)

tTT

W

X(f)

fW1

W S(f)

f

T1

T1

T1

Consider now a square wave with duty cycle W/T


25/45


Overall Frequency Transform of a Square Wave

Fundamental at frequency 1/T- Higher harmonics have lower magnitude

If W = T/2 (i.e., 50% duty cycle)- No even harmonics!

If amplitude varies between 1 and -1 (rather than 1 and 0)

- No DC component

1

y(t)

tTT

W

Y(f)

f

T1

1

TW

W

Resulting transform relationship


26/45


Analysis of Using Square-Wave for LO Signal

Each frequency component of LO signal will now mixwith the RF input- If RF input spectrum sufficiently narrowband with respect

to f o , then no aliasing will occur

Desired output (mixed by the fundamental component)can be extracted using a filter at the IF output

f -f o f o

= 2sgn(cos(2 f ot))

RF inRF in(f)

0

f -f o f o0


IF out

LO out(f)

f -f o f o

IF out(f)

03f o-3f o -3f o 3f o2f o2f o2f o-2f o

DesiredOutput

Even order harmonicdue to not having anexact 50% duty cycle

DC componentof LO waveform


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Voltage Conversion Gain

Defined as voltage ratio of desired IF value to RF inputExample: for an ideal mixer with RF input = Asin(2 (f o +

f)t) and sine wave LO signal = Bcos(2 f o t)

For practical mixers, value depends on mixer topologyand LO signal (i.e., sine or square wave)

f -f o f o

Bcos(2 f ot)

RF in = Acos(2 ( f o+f)t)

RF in(f)

0

f -f o f o0

LO ouput =

IF out

LO out(f)

f -f o f o

IF out(f)

0

f

f -f

A2

B2

AB4


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Impact of High Voltage Conversion Gain

Benefit of high voltage gain- The noise of later stages will have less of an impact

Issues with high voltage gain- May be accompanied by higher noise figure than could beachieved with lower voltage gain

- May be accompanied by nonlinearities that limitinterference rejection (i.e., passive mixers can generallybe made more linear than active ones)

f -f o f o

Bcos(2 f ot)

RF in = Acos(2 ( f o+f)t)

RF in(f)

0

f -f o f o0

LO ouput =

IF out

LO out(f)

f -f o f o

IF out(f)

0

f

f -f

A2

B2

AB4


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Impact of Nonlinearity in Mixers

Ignoring dynamic effects, we can model mixer asnonlinearities around an ideal mixer

-Nonlinearity A will have the same impact as LNAnonlinearity (measured with IIP3)

- Nonlinearity B will change the spectrum of the LO signalCauses additional mixing that must be analyzed

Changes conversion gain somewhat- Nonlinearity C will cause self mixing of IF output

MemorylessNonlinearity A

y

w10 w2W

RF in(w) DesiredNarrowbandSignal

Interferers

IdealMixer

RF in IF out

LO signal

MemorylessNonlinearity B

MemorylessNonlinearity C


30/45


Primary Focus is Typically Nonlinearity in RF Input Path

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

Nonlinearity C can be avoided by using a linear load(such as a resistor)Nonlinearity A can hamper rejection of interferers

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

MemorylessNonlinearity A

y

w10 w2W

RF in(w) DesiredNarrowbandSignal

Interferers

0 w12w 2+w1

w2 2w 22w 1-w2 2w 1+w22w 2-w1 w1+w2

w2-w1 2w 1 3w 23w 1W

Y(w) Corruption of desired signal

IdealMixer

RF in IF out

LO signal

MemorylessNonlinearity B

MemorylessNonlinearity C

x

z


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The Issue of Balance in Mixers

A balanced signal is defined to have a zero DCcomponent

Mixers have two signals of concern with respect tothis issue LO and RF signals- Unbalanced RF input causes LO feedthrough- Unbalanced LO signal causes RF feedthrough

Issue transistors require a DC offset

f -f o f o

RF in

RF in(f)

0

f -f o f o0

LO sig

IF out

LO sig(f)

f -f o f o

IF out(f)

0

f

f -f

LOfeedthrough

RFfeedthrough

DC component

DC component


32/45


Achieving a Balanced LO Signal with DC Biasing

Combine two mixer paths with LO signal 180 degreesout of phase between the paths

- DC component is cancelled

RF in

LO sig

IF out

1

-1

RF in

LO sig

IF out1

0

LO sig

1

0

0


33/45


Single-Balanced Mixer

Works by converting RF input voltage to a current, thenswitching current between each side of differential pair Achieves LO balance using technique on previous slide

- Subtraction between paths is inherent to differential outputLO swing should be no larger than needed to fully turn onand off differential pair - Square wave is best to minimize noise from M 1 and M 2

Transconductor designed for high linearity

M1

I1

Io = G mVRFTransconductor VRF

Io

I2

M2VLO VLO

DC

VRF (t)


34/45


Transconductor Implementation 1

Apply RF signal to input of common source amp- Transistor assumed to be in saturation- Transconductance value is the same as that of thetransistor

High V bias places device in velocity saturation

- Allows high linearity to be achieved

M1R s

VRF

Vbias

Cbig

Io

Rbig


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Apply RF signal to a common gate amplifier Transconductance value set by inverse of seriescombination of R

sand 1/g

mof transistor

- Amplifier is effectively degenerated to achieve higherlinearity

Ibias can be set for large current density throughdevice to achieve higher linearity (velocity saturation)

M1R s

VRF Ibias

Cbig

Io

Vbias


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Add degeneration to common source amplifier - Inductor better than resistor

No DC voltage dropIncreased impedance at high frequencies helps filter outundesired high frequency components

- Dont generally resonate inductor with C gsPower match usually not required for IC implementationdue to proximity of LNA and mixer

M1R s

VRF

Vbias

Cbig

Ldeg

Io

Rbig


37/45


LO Feedthrough in Single-Balanced Mixers

DC component of RF input causes very large LOfeedthrough

-Can be removed by filtering, but can also be removed byachieving a zero DC value for RF input

M1

I1

Io = G mVinTransconductor VRF

Io

I2

M2VLO VLO

DC

0-f 1 f 1

VRF (t)

VRF (f)

0-f o f o

VLO(f)-VLO(f)

f

f

0 f o-f 1

I1(f)-I2(f)

f f o f o+f 1-f o-f o-f 1 -f o+f 1

Higher order harmonics




D bl B l d Mi


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Double-Balanced Mixer

DC values of LO and RF signals are zero (balanced)LO feedthrough dramatically reduced!

But, practical transconductor needs bias current

M1

I1

Io = G mVinTransconductor VRF

Io

I2

M2VLO VLO

DC0-f 1 f 1

VRF (t)

VRF (f)

0-f o f o

VLO(f)-VLO(f)

f

f

0 f o-f 1

I1(f)-I2(f)

f f o f o+f 1-f o-f o-f 1 -f o+f 1





A hi i B l d RF Si l i h Bi i


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Achieving a Balanced RF Signal with Biasing

Use the same trick as with LO balancing

RF in

LO sig

IF out1

0

LO sig

1

0DC

VRF (t) RF in

LO sig

IF out1

0

LO sig

1

0

RF in

LO sig

IF out

10

LO sig

1

0

DC

VRF (t)

DC

VRF (t)

signal

signal

DC componentcancels

signal componentadds

D bl B l d Mi I l t ti


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Double-Balanced Mixer Implementation

Applies technique from previous slide- Subtraction at the output achieved by cross-couplingthe output current of each stage

M1

I1


Io

I2

M2

VLO VLO

DC

VRF (t)

M1

I3


Io

I4

M2

VLO VLO

DC

VRF (t)


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A Highly Linear CMOS Mixer


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A Highly Linear CMOS Mixer

Transistors are alternated between the off and trioderegions by the LO signal- RF signal varies resistance of channel when in triode

- Large bias required on RF inputs to achieve triode operationHigh linearity achieved, but very poor noise figure

VLO

VLO

R f1

Cf1

Cb1

R f2

C f2

Cb2

VRF VRF

M1M2

M3M4

VIF

VIF

Passive Mixers


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Passive Mixers

We can avoid the transconductor and simply useswitches to perform the mixing operation- No bias current required allows low power operation to

be achieved

You can learn more about it in Homework 4!

VRF

CL

RL/2 R L/2

RS

/2 Cbig

RS /2 C big

VIF VIF2A in

VLO VLO

VLO VLO

Square Law Mixer


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Square-Law Mixer

Achieves mixing through nonlinearity of MOS device- Ideally square law, which leads to a multiplication term

- Undesired components must be filtered outNeed a long channel device to get square law behavior Issue no isolation between LO and RF ports

M1

VRF

Vbias

LL R L C L

VIFVLO

Alternative Implementation of Square Law Mixer


45/45


Alternative Implementation of Square Law Mixer

Drives LO and RF inputs on separate parts of the

transistor - Allows some isolation between LO and RF signalsIssue - poorer performance compared to multiplication-based mixers

- Lots of undesired spectral components- Poorer isolation between LO and RF ports

Ibias

M1

Vbias

LL R L C L

VIF

Rbig

Cbig

VRF

Cbig2

VLO

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