6.976 high speed communication circuits and …...m.h. perrott mit ocw mixer design for wireless...

6.976High Speed Communication Circuits and Systems

Lecture 10Mixers

Michael PerrottMassachusetts Institute of Technology

Copyright © 2003 by Michael H. Perrott

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 it

manufacturable in high volume

Zin

Zo LNA To Filter

From Antennaand Bandpass

Filter

PC boardtrace

PackageInterface

Local OscillatorOutput

MixerRF in IF out


Ideal Mixer Behavior

RF spectrum converted to a lower IF center frequency- IF stands for intermediate frequency

If IF frequency is nonzero – heterodyne or low IF receiverIf IF frequency is zero – homodyne receiver

Use a filter at the IF output to remove undesired high frequency components

f-fo fo

= 2cos(2πfot)

RF inRF in(f) Desiredchannel

0

f-fo fo0

1 1


IF out

LO out(f)

f-fo fo

IF out(f)

0

∆f

∆f-∆f

Undesiredcomponent

Undesiredcomponent

ChannelFilter


The Issue of Aliasing

When the IF frequency is nonzero, there is an image band 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 removed

through filtering at the IF output!

f-fo fo

= 2cos(2πfot)


ImageInterferer

0

f-fo fo0

1 1


IF out

LO out(f)

f-fo fo

IF out(f)

0

∆f-∆f

∆f-∆f


LO Feedthrough

LO feedthrough will occur from the LO port to IF output port due 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 extra dynamic range consumed at the IF outputIf small, can generally be removed by filter at IF output

f-fo fo

= 2cos(2πfot)


ImageInterferer

0

f-fo fo0

1 1


IF out

LO out(f)

f-fo fo

IF out(f)

0

∆f-∆f

∆f-∆f

LOfeedthrough

LOfeedthrough


Reverse LO Feedthrough

Reverse LO feedthrough will occur 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 isolate to antenna is adequate

f-fo fo

= 2cos(2πfot)


ImageInterferer

0

f-fo fo0

1 1


IF out

LO out(f)

f-fo fo

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 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)

f-fo fo

= 2cos(2πfot)


ImageInterferer

0

f-fo fo0

1 1


IF out

LO out(f)

f-fo fo

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 to prevent the image content from aliasing into the desired channel 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-fo fo

= 2cos(2πfot)


ImageInterferer

0

f-fo fo0

1 1


IF out

LO out(f)

f-fo fo

IF out(f)

0

∆f-∆f

∆f-∆f

LOfeedthrough



LO feedthrough

ImageRejection

Filter



Mix directly down to baseband (i.e., homodyne approach)- With an IF frequency of zero, there is no image band

Issues – 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-fo fo

= 2cos(2πfot)


0

f-fo fo0

1 1


IF out

LO out(f)

f-fo fo

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 a high Q filterVery 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-f1 f1

2cos(2πf1t)

2sin(2πf1t)

a(t)

b(t)

e(t)

g(t)

RF in IF out2cos(2πf2t)

2sin(2πf2t)

Lowpass

RF in(f) Desiredchannel

ImageInterferer

0

c(t)

d(t)

Lowpass


Image Reject Mixer Principles – Step 1

f-f1 f1

2cos(2πf1t)

2sin(2πf1t)

a(t)

b(t)

e(t)

g(t)


2sin(2πf2t)

Lowpass


ImageInterferer

0

f-f1 f10

f-f1

f10

f-f1 f1

A(f)

0

f-f1 f1

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-f1 f1

2cos(2πf1t)

2sin(2πf1t)

a(t)

b(t)

e(t)

g(t)


2sin(2πf2t)

Lowpass


ImageInterferer

0

f-f1 f10

f-f1

f10

f-f1 f1

C(f)

0

f-f1 f1

D(f)

0

c(t)

d(t)

j

-j

1 1 1

j

-j

Lowpass



e(t)

g(t)

IF out2cos(2πf2t)

2sin(2πf2t)

f-f2 f20

f-f2

f20

-f2 f2

C(f)

0

D(f)

0

c(t)

d(t)

j

-j

1 1

1

j

-j

-f2 f2

E(f)

0

-f2 f2

G(f)

12

12

1

-1

1

-1-2

f

f

f

f




e(t)

g(t)

IF out

-f2 f2

E(f)

0

-f2 f2

G(f) 12

12

1

-1

1

-1-2

f

f

-f2 f20

2

f

IF out(f)

BasebandFilter


Image Reject Mixer Principles – Implementation Issues

For all analog architecture, going to zero IF introduces sensitivity to 1/f noise at IF output- Can fix this problem by digitizing c(t) and d(t), and then

performing final mixing in the digital domainCan generate accurate quadrature sine wave signals by using a frequency divider

0

2

f

IF out(f) (after baseband filtering)

f-f1 f1

2cos(2πf1t)

2sin(2πf1t)

a(t)

b(t)

e(t)

g(t)


2sin(2πf2t)

Lowpass


ImageInterferer

0

c(t)

d(t)

Lowpass


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


f-f1 f1

2cos(2πf1t)

2sin(2πf1t)

a(t)

b(t)

e(t)

g(t)


2sin(2πf2t)

Lowpass

RF in(f)Desiredchannel

ImageInterferer

0

c(t)

d(t)

Lowpass

-j

j


Modification of Mixer Architecture for Imaginary RF in(f)

Desired channel now appears given two changes- Sine and cosine demodulators are switched in second half of image rejection mixer- The two paths are now added rather than subtracted

Issue – architecture now zeros out desired channel when RF in(f) is purely real

0 f


f-f1 f1

2cos(2πf1t)

2sin(2πf1t)

a(t)

b(t)

e(t)

g(t)

RF in IF out

2cos(2πf2t)

2sin(2πf2t)

Lowpass


ImageInterferer

0

c(t)

d(t)

Lowpass

-j

j

2


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-f1 f1

2cos(2πf1t)

2sin(2πf1t)

a(t)

b(t)

RF in

IF outI

2cos(2πf2t)

2sin(2πf2t)

Lowpass

Desiredchannel

ImageInterferer

0

Lowpass

1

2

f-f1 f1

real part of RF in(f)

0-j

j

1

imag. part of RF in(f)2cos(2πf2t)

2sin(2πf2t)

IF outQ

0 f

2

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


Mixer Single-Sideband (SSB) Noise Figure

Issue – 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 outputChannel filter cannot remove this

- Mixers are inherently noisy!

f-fo fo

= 2cos(2πfot)


Imageband

0

f-fo fo0

1 1

LO out

IF out

LO out(f)

f

IF out(f)

0

∆f-∆f

∆f-∆f

ImageRejection

FilterNoise

RF in

Noise from Desiredand Image bands add

Noise

No

2No

SRF

SRF

ChannelFilter


Mixer Double-Sideband (DSB) Noise Figure

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

the 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-fo fo

= 2cos(2πfot)


0

f-fo fo0

1

LO out

LO out(f)

f

IF out(f)

0 ∆f-∆f

ImageRejection

FilterNoise

RF in

Noise frompositive and negativefrequency bands add

Noise

No

2No

SRF

2SRF

IF out

ChannelFilter


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 as

the LO signal?- We will briefly review Fourier transforms (series) to

understand this issue

= 2sgn(cos(2πfot))

RF in


IF out

1

tTT

W

LO out(t)


Two Important Transform Pairs

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


Decomposition of Square Wave to Simplify Analysis

Decomposition in time

1

y(t)

tTT

W

s(t)

tT

1

T

*1

x(t)

t

W

Consider now a square wave with duty cycle W/T


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


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


Analysis of Using Square-Wave for LO Signal

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

to fo, then no aliasing will occurDesired output (mixed by the fundamental component) can be extracted using a filter at the IF output

f-fo fo

= 2sgn(cos(2πfot))

RF inRF in(f)

0

f-fo fo0


IF out

LO out(f)

f-fo fo

IF out(f)

03fo-3fo -3fo 3fo2fo2fo2fo-2fo

DesiredOutput

Even order harmonicdue to not having anexact 50% duty cycle

DC componentof LO waveform


Voltage Conversion Gain

Defined as voltage ratio of desired IF value to RF inputExample: for an ideal mixer with RF input = Asin(2π(fo + ∆ f)t) and sine wave LO signal = Bcos(2πfot)

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

f-fo fo

Bcos(2πfot)

RF in = Acos(2π(fo+∆f)t)

RF in(f)

0

f-fo fo0

LO ouput =

IF out

LO out(f)

f-fo fo

IF out(f)

0

∆f

∆f-∆f

A2

B2

AB4


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 be

achieved with lower voltage gain- May be accompanied by nonlinearities that limit

interference rejection (i.e., passive mixers can generally be made more linear than active ones)

f-fo fo

Bcos(2πfot)

RF in = Acos(2π(fo+∆f)t)

RF in(f)

0

f-fo fo0

LO ouput =

IF out

LO out(f)

f-fo fo

IF out(f)

0

∆f

∆f-∆f

A2

B2

AB4


Impact of Nonlinearity in Mixers

Ignoring dynamic effects, we can model mixer as nonlinearities around an ideal mixer- Nonlinearity A will have the same impact as LNA

nonlinearity (measured with IIP3)- Nonlinearity B will change the spectrum of the LO signal

Causes additional mixing that must be analyzedChanges conversion gain somewhat

- Nonlinearity C will cause self mixing of IF output

MemorylessNonlinearity A

y

w10 w2W

RF in(w) DesiredNarrowband

Signal

Interferers

IdealMixer

RF in IF out

LO signal

MemorylessNonlinearity B

MemorylessNonlinearity C


Primary Focus is Typically Nonlinearity in RF Input Path

Nonlinearity B not detrimental in most cases- LO signal often a square wave anywayNonlinearity 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) DesiredNarrowband

Signal

Interferers

0 w12w2+w1

w2 2w22w1-w2 2w1+w22w2-w1 w1+w2

w2-w1 2w1 3w23w1W

Y(w) Corruption of desired signal

IdealMixer

RF in IF out

LO signal

MemorylessNonlinearity B

MemorylessNonlinearity C

x

z


The Issue of Balance in Mixers

A balanced signal is defined to have a zero DC componentMixers have two signals of concern with respect to this issue – LO and RF signals- Unbalanced RF input causes LO feedthrough- Unbalanced LO signal causes RF feedthrough

Issue – transistors require a DC offset

f-fo fo

RF in

RF in(f)

0

f-fo fo0

LO sig

IF out

LO sig(f)

f-fo fo

IF out(f)

0

∆f

∆f-∆f

LOfeedthrough

RFfeedthrough

DC component

DC component


Achieving a Balanced LO Signal with DC Biasing

Combine two mixer paths with LO signal 180 degrees out 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


Single-Balanced Mixer

Works by converting RF input voltage to a current, then switching current between each side of differential pairAchieves 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 on and off differential pair- Square wave is best to minimize noise from M1 and M2

Transconductor designed for high linearity

M1

I1

Io = GmVRF

TransconductorVRF

Io

I2

M2VLO VLO

DC

VRF(t)


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 the

transistorHigh Vbias places device in velocity saturation- Allows high linearity to be achieved

M1

Rs

VRF

Vbias

Cbig

Io

Rbig



Apply RF signal to a common gate amplifierTransconductance value set by inverse of series combination of Rs and 1/gm of transistor- Amplifier is effectively degenerated to achieve higher

linearityIbias can be set for large current density through device to achieve higher linearity (velocity saturation)

M1Rs

VRF Ibias

Cbig

Io

Vbias



Add degeneration to common source amplifier- Inductor better than resistor

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

- Don’t generally resonate inductor with Cgs

Power match usually not required for IC implementation due to proximity of LNA and mixer

M1

Rs

VRF

Vbias

Cbig

Ldeg

Io

Rbig


LO Feedthrough in Single-Balanced Mixers

DC component of RF input causes very large LO feedthrough- Can be removed by filtering, but can also be removed by

achieving a zero DC value for RF input

M1

I1

Io = GmVin

TransconductorVRF

Io

I2

M2VLO VLO

DC

0-f1 f1

VRF(t)

VRF(f)

0-fo fo

VLO(f)-VLO(f)

f

f

0 fo-f1

I1(f)-I2(f)

ffo fo+f1-fo-fo-f1 -fo+f1

Higher orderharmonics





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 = GmVin

TransconductorVRF

Io

I2

M2VLO VLO

DC0-f1 f1

VRF(t)

VRF(f)

0-fo fo

VLO(f)-VLO(f)

f

f

0 fo-f1

I1(f)-I2(f)

ffo fo+f1-fo-fo-f1 -fo+f1






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

1

0

LO sig

1

0

DC

VRF(t)

DC

VRF(t)

signal

signal

DC componentcancels

signal componentadds


Double-Balanced Mixer Implementation

Applies technique from previous slide- Subtraction at the output achieved by cross-coupling

the output current of each stage

M1

I1

Io = GmVRF

TransconductorVRF

Io

I2

M2VLO VLO

DC

VRF(t)

M1

I3

Io = GmVRF

TransconductorVRF

Io

I4

M2VLO VLO

DC

VRF(t)


Gilbert Mixer

Use a differential pair to achieve the transconductorimplementationThis is the preferred mixer implementation for most radio systems!

RF DC VRF(t)

M5 M6VLOM3

I1 I2

M4VLO

VLO

M1 M2

Ibias

VRF(t)RF DC

LO DC

LO DC


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

VLO

VLO

Rf1

Cf1

Cb1

Rf2

Cf2

Cb2

VRF VRF

M1M2

M3M4

VIF

VIF


Passive Mixers

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

be achievedYou can learn more about it in Homework 4!

VRF

CL

RL/2 RL/2

RS/2 Cbig

RS/2 Cbig

VIF VIF2Ain

VLO VLO

VLO VLO


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 behaviorIssue – no isolation between LO and RF ports

M1

VRF

Vbias

LL RL CL

VIFVLO


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 RL CL

VIF

Rbig

Cbig

VRF

Cbig2

VLO

6.976 high speed communication circuits and …...m.h. perrott mit ocw mixer design for wireless...

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