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8/11/2019 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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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
Local Oscillator Output
IF out
LO out(f)
f -f o f o
IF out(f)
0
f -f
f -f
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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)
RF inRF in(f) Desired
channelImage
Interferer
0
f -f o f o0
1 1
Local Oscillator Output
IF out
LO out(f)
f -f o f o
IF out(f)
0
f -f
f -f
LOfeedthrough
LOfeedthrough
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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)
RF inRF in(f) Desired
channelImage
Interferer
0
f -f o f o0
1 1
Local Oscillator Output
IF out
LO out(f)
f -f o f o
IF out(f)
0
f -f
f -f
LOfeedthrough
Reverse LOfeedthrough
LOfeedthrough
Reverse LOfeedthrough
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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)
RF inRF in(f) Desired
channelImage
Interferer
0
f -f o f o0
1 1
Local Oscillator Output
IF out
LO out(f)
f -f o f o
IF out(f)
0
f -f
f -f
LOfeedthrough
Reverse LOfeedthrough
LOfeedthrough
Reverse LOfeedthrough
Self-mixingof reverse
LO feedthrough
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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)
RF inRF in(f) Desired
channelImage
Interferer
0
f -f o f o0
1 1
Local Oscillator Output
IF out
LO out(f)
f -f o f o
IF out(f)
0
f -f
f -f
LOfeedthrough
Reverse LOfeedthrough
Self-mixingof reverse
LO feedthrough
ImageRejectionFilter
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Removal of Image Interference Solution 2
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)
RF inRF in(f) Desired
channel
0
f -f o f o0
1 1
Local Oscillator Output
IF out
LO out(f)
f -f o f o
IF out(f)
0
f=0
LOfeedthrough
Reverse LOfeedthrough
LOfeedthrough
Reverse LOfeedthrough
Self-mixingof reverse
LO feedthrough
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Removal of Image Interference Solution 3
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
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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)
RF in IF out2cos(2 f 2t)
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
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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
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
Image Reject Mixer Principles Step 2
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Image Reject Mixer Principles Step 4
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)
RF in IF out2cos(2 f 2t)
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
RF in(f)Desiredchannel
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)
RF in(f)Desiredchannel
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
ImageRejectionFilter
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)
RF in(f)Desiredchannel
0
f -f o f o0
1
LO out
LO out(f)
f
IF out(f)
0 f -f
ImageRejectionFilter
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
Local Oscillator Output
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
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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
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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
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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
Local Oscillator Output
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
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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
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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
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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)
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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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Transconductor Implementation 2
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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Transconductor Implementation 3
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
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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
Higher order harmonics
Higher order harmonics
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
Higher order harmonics
Higher order harmonics
Higher order harmonics
Higher order harmonics
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 = G mVRFTransconductor VRF
Io
I2
M2
VLO VLO
DC
VRF (t)
M1
I3
Io = G mVRFTransconductor VRF
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
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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