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Mixer Design
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Introduction to mixers
Mixer metrics
Mixer topologies
Mixer performance analysis
Mixer design issues
1
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
2
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
3
An ideal nonlinearity mixer
If
x(t )  A cos 1t
y (t )  B cos 2t
x(t)y(t)
x(t)
y(t)
Then the output is
AB
AB
A cos 1t  B cos 2t 
cos(1  2 )t 
cos(1  2 )t
2
2
down convert
up convert
4
Commutating switch mixer
VRF (t )
VLO (t )
VLO (t )
VIF (t)
VRF (t )  VLO (t )
 ARF sin ω RF t   sqω LO t 
2
1


 ARF cos(ω RF  ω LO )t  cos3(ω RF  ω LO )t   
π
3


5
A non-ideal mixer
RF-IF
x
aixi
+
+
+
output
Distortion
+ gain
+
RF-LO
noise
y'
LO-RF
LO-IF
y
6
Mixer Metrics
• 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
7
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).
r.m.s. voltage of the IF signal
Voltage Conversion Gain 
r.m.s. voltage of the RF signal
IF power delivered to the load
Power Conversion Gain 
Available power from the source
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.
8
Noise Figures: SSB vs DSB
Signal
band
Signal
band
Image
band
Thermal
noise
Thermal
noise
LO
LO
IF
0
Single side band
Double side band
9
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
10
DSB Noise Figure
• 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
11
Port-to-Port Isolations
• 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.
IF
RF
LO
12
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
13
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
14
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)
15
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
16
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)
17
Spurious Response
IF  m  RF  n  LO
IF
LO
IF LO
 n 
m, 0

1
RF
RF
RF RF
y  n  x  m 0  y  x  1
y  IF RF
IF Band
x  LO RF
18
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
19
Single-diode passive mixer
VLO
VLO
L
C
RL

VIF

t
VRF
ID
VIF
VD
•
•
•
•
•
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)
t
20
Single-balanced diode mixer
VLO
VIF
VLO
L
C
RL
t
VRF
VIF
•
•
•
•
•
Poor gain
Good LO-IF isolation
Good LO-RF isolation
Poor RF-IF isolation
Attractive for very high frequency applications where
transistors are slow.
t
21
Double-balanced diode mixer
VLO
VLO
VIF
VRF
t
VIF
•
•
•
•
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.
t
22
CMOS Passive Mixer
RS
VLO
M1
M2
VLO
M4
VLO
VIF
VLO
M3
• M1 through M4 act as switches
23
CMOS Passive Mixer
• Use switches to perform the mixing operation
• No bias current required
• Allows low power operation to be achieved
24
CMOS Passive Mixer
RFLO+
LO-
IF
RF+
Same idea, redrawn
RC filter not shown
IF amplifier can be frequency selective
[*] T. Lee
25
CMOS Passive Mixer
IM1
t


VLO
 LO
 RF
t
VOUT
GC 
Vout  IF  4

VRF  RF  
t
4
4
4

Vout  VRF .Cos  RF t    Cos  LOt  
Cos  3 LOt  
Cos  5 LOt   ...
3
5


26
CMOS Passive Mixer
• Non-50% duty cycle of LO results in no DC offsets!!
IM1
t
DC-term of LO

VLO
t

 LO
 RF
VOUT
t
4
4
4


Vout  VRF .Cos  RF t    DC  Cos  LOt  
Cos  3 LOt  
Cos  5 LOt   ...

3
5


27
CMOS Passive Mixer with Biasing
VLO
200
VLO 
VLO 
Cbias  1nF
RS  200
VS
Vgg
Rsd
Rgg
VLO
M1
VLOCbias  1nF
M2
Vsd
CL
M 2'
Rgg
RL  2k 
M 1'
Rsd
Cbias  1nF
28
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
29
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.
RL
RL
VLO
M2
Vout
M3
VLO
I DC  I RF
VRF
M1
30
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
VCC
RL
RL
+ out -
LO+
vin + DC
Q1
Q2
LO-
QB
vout = ±gmvinRL
31
Double Balanced Mixer
RL
VLO
M2
VRF
RL
VOUT
M3
I DC  I RF
VLO
M2
VRF
M3
VLO
I DC  I RF
• Strong LO-IF feed suppressed by double balanced mixer.
• All the even harmonics cancelled.
• All the odd harmonics doubled (including the signal).
32
Gilbert Mixer
• Use a differential pair to achieve the transconductor
implementation
• This is the preferred mixer implementation for most radio
systems!
33
Double balanced mixer, BJT
• Basically two SB mixers
– One gets +vin/2, the other gets –vin/2
VCC
RL
RL
+ out -
LO+
Q1
Q2
Q3
Q4
LO+
LOQB1
+ vin -
QB2
34
Mixers based on MOS square law
Cl arg e
I ds  K SQ . VGSQ  VT 0 
2
Rb
VLO
VBB1
VRF
I ds  K SQ . Vbias  VRF  VLO  VT 0 

2

 K SQ . Vbias  VT 0   VRF  VLO   2 Vbias  VT 0  . VRF  VLO 
2
2
(VRF  VLO ) 2 gives rise to
cos(RF  LO )t and cos(RF  LO )t
35
Practical Square Law Mixers
I ds  K SQ . VGSQ  VT 0 
Cl arg e
2
Cl arg e
Rb
VRF
VBB1
I BIAS
VLO
The conversion gain can be shown to be
CoxW
K sqVLO 
VLO
2L
36
Practical Bipolar Mixer
IC  ICO . e
Cl arg e
VBE
VT
Cl arg e
Rb
VRF
VBB1
I BIAS
VLO
The conversion gain can be shown to be
I CQ
2
T
v
VLO
37
MOSFET Mixer (with impedance matching)
VDD
Cmatch
IF Filter
RL
VBB2
RS
Cl arg e
Lg
I ds  K SQ . VGSQ  VT 0 
2
RLO
Rb
VRF
VBB1
Cl arg e
Le
Matching
Network
VLO
38
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
39
Harmonic Mixer
•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
• 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
40
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 nonlinear 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.
41
Mixer performance analysis
• Analyze major metrics
– Conversion gain
– Port isolation
– Noise figure/factor
– Linearity, IIP3
• Gain insights into design constraints and
compromise
42
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
VCC
RL
RL
+ out -
LO+
vin + DC
Q1
Q2
LO-
QB
43
Common Emitter Mixer
• Conversion gain
VCC
Two output component:
RL
RL
vout1 = ±gmvinRL
vout2 = ±IQBDCRL
IF signal is the RF – LO
component in vout1
+ out -
LO+
vin + DC
Q1
Q2
LO-
QB
So gain = ?
44
Common Emitter Mixer
• Port isolation
VCC
At what frequency is
Vout2 switching?
RL
RL
+ out -
vout2 = ±IQBDCRL
LO+
Q1
Q2
LO-
vout2 = SW(LO)IQBDCRL
This is feed through from
LO to output
vin + DC
QB
45
Common Emitter Mixer
• Port isolation
VCC
How about LO to RF?
RL
RL
+ out -
This feed through is
much smaller than LO
to output
LO+
vin + DC
Q1
Q2
LO-
QB
46
Common Emitter Mixer
• Port isolation
VCC
How about RF to LO?
RL
RL
+ out -
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.
LO+
vin + DC
Q1
Q2
LO-
QB
47
Common Emitter Mixer
• Port isolation
VCC
What about RF to output?
RL
RL
Ideally, contribution to
output is:
+ out -
SW(LO)*gmvinRL
LO+
What can go wrong and
cause an RF component
at the output?
vin + DC
Q1
Q2
LO-
QB
48
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)
RL
RL
+ out -
LO+
LOQ1
Q2
QB
49
Common Emitter Mixer
1. Noise due to loads:
– Each RL contributes
vRL2 = 4kTRLf
– Since they are
uncorrelated with
each other, their noise
power’s add
– Total contribution of
RL’s: voRL2 = 8kTRLf
RL
RL
+ out -
LO+
LOQ1
Q2
QB
50
Common Emitter Mixer
2. Noise due input
transistor (the
transducer):
– From BJT device
model, equivalent
input noise voltage
of a CE amplifier is:
2
inCE 
v

1 
f
 4kT rb 
2gm 

RL
RL
+ out -
LO+
LOQ1
Q2
QB
51
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
v
terminal of out:
RL
RL
+ out -
LO+
LOQ1
Q2
QB
2
in(CE)
2
out,QB
v
 gain   v
2
2
inCE 
52
Common Emitter Mixer
2. Noise due to input
transistor:
– Noise at the two
terminals dependent?
– Accounted for by
incorporating a factor
“n”.
2
out,QB
 n  gain   v
2
out,QB
 g m RL 
v
v
2
2
2
inCE 
RL
RL
+ out -
LO+
LOQ1
Q2
QB
vin(CE) 2

1 
f
 4nkT  rb 
2gm 

53
Common Emitter Mixer
•
Total Noise due to RL
and QB:
RL
– If we assume rb is very
small:
RL
+ out -
LO+
vT2
 g m RL 
 8kTRL 1 

f
4 

When:
LOQ1
Q2
QB
rb << 1/(2gm) and
n=1
54
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
LO+
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
RL
RL
+ out LOQ1
Q2
QB
55
Common Emitter Mixer
3. What about the noise
due to switches:
RL
– Transition time “jitter”
in the switching signal:
RL
+ out -
LO+
LOQ1
Q2
QB
no noise
noise
Effect is quite complex, quantitative analysis later
56
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
RL
RL
+ out -
LO+
LOQ1
Q2
QB
57
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
I QB  I s e
(VBB  vin ) / vt
RL
RL
+ out -
LO+
LOQ1
Q2
QB
1
1 2
1 3
 I DC (1  vin  2 vin  3 vin  ...)
vt
2v t
6v t
58
Double Balanced Mixer
• Basically two CE mixers
– One gets +vin/2, the other gets –vin/2
VCC
RL
RL
+ out -
LO+
Q1
Q2
Q3
Q4
LO+
LOQB1
+ vin -
QB2
59
Double Balanced Mixer
VC
+1
C
R
R
L
L
+ out -
-1
Local Oscillator
LO+
Q1
Q2
vout = gmvinRL
vout = – gmvinRL
Q3
Q4
LO+
LOQB1
+ vin -
QB2
60
Double Balanced Mixer
• Benefits:
– Fully Differential
– No output signal at LO
• Three stages:
– CE input stages
– Switches
– Output load
61
Double Balanced Mixer
• Noise:
– Suppose QB1 & QB2
give similar total gm
– Similar to CE Mixer
VCC
RL
RL
• IP3:
– Similar Taylor series
LO+
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
+ out -
Q1
Q2
Q3
Q4
LO+
LOQB1
+ vin -
QB2
62
Common Base Mixers
• Similar operation to CE
mixers
• Different input stage
– QB is CB
• Slightly different output
noise
VC C
RL
+ out -
LO+
V Bias
– Different CB input noise
• Better linearity
RL
Q1
Q2
LO-
QB
vin
IDC
63
Mixer Improvements
• Debiasing switches
from input transistors:
– To lower NF we want
high gm, but low Q1
and Q2 current
VCC
RL
RL
+ out
-
LO+
Q1
Q2
LO-
• Conflicting!
– We can set low ISwitches
and high IQb using a
current source
I difference
I Qb
vin + DC
2c  g m RL 
NF  1  2
1 

g m RL RS 
4 
I Switches
QB
64
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.
RL
RL
VLO
M2
Vout
M3
VLO
I DC  I RF
VRF
M1
65
MOS Single Balanced Mixer
IM1
t

VLO
t
VOUT
t
66
MOS Single Balanced Mixer
VOUT
t
IF Filter
VOUT
t
67
MOS Single Balanced Mixer
IF Filter
 RF
 IF
 LO

 LO   RF
 RF  LO
 LO   RF
 LO   RF
68
MOS Single Balanced Mixer
 RF
SMIX
SLO LO

 LO   RF
 RF  LO


2 LO
3 LO
69
Single Balanced Mixer
(Incl. RF input Impd. Match)
RL
VLO
RS
VS
RL
Vout
M3
M2
Cl arg e
Lg
VLO
GMVRF
Rb
VGG
Ls
This architecture, without impedance matching for the LO
port, is very commonly used in many designs.
70
Single Balanced Mixer
(Incl. RF & LO Impd. Match)
VGG 2
VGG 2
RL
RL
VLO
Lg
Lg
Vout
M3
M2
Lm2
RS
VS
Cl arg e
Lg
VLO
Lm3
GMVRF
Rb
VGG1
Ls
• This architecture, with impedance matching for the LO
port, maximizes LO power utilization without wasting it.
71
Single Balanced Mixer Analysis: Linearity
RL
VLO
RS
Lg
Rb
VGG
Vout
M3
M2
Cl arg e
VS
RL
VLO
GMVRF
Ls
• 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).
72
Single Balanced Mixer Analysis: Linearity
RL
VLO
M2
RL
Vout
VLO
M3
VGG
RS
Ibias
Cc
VS
• 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.
73
Single Balanced Mixer Analysis: Isolation
RL
VLO
RL
Vout
M3
M2
VLO
LO-RF Feed through
RS
VS
Cl arg e
0.5TLO
Lg
Rb
VGG
GMVRF
0.5TLO
0.5TLO  
Ls
0.5TLO  
• 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?
74
Single Balanced Mixer Analysis: Isolation
VLO
M3
M2
VLO
GMVRF
VBB2
RS
Cl arg e
VS
Lg
Rb
VBB1
Weak LO-RF Feed through
Ls
• 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.
75
Single Balanced Mixer Analysis: Isolation
RL
LO-IF Feed through
VLO
RS
Lg
Rb
VBB1
Vout
M3
M2
Cl arg e
VS
RL
VLO
GMVRF
Ls
• 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.
76
Double Balanced Mixer
RL
VLO
M2
VRF
RL
VOUT
M3
I DC  I RF
VLO
M2
VRF
M3
VLO
I DC  I RF
• Strong LO-IF feed suppressed by double balanced mixer.
• All the even harmonics cancelled.
• All the odd harmonics doubled (including the signal).
77
Double Balanced Mixer
RL
VLO
M2
VRF
RL
VOUT
Vout
M3
I DC  I RF
VLO
M2
Vout
VRF
M3
VLO
I DC  I RF
• The LO feed through cancels.
• The output voltage due to RF signal doubles.
78
Double Balanced Mixer: Linearity
RL
VLO
M3
M2
VRF
RL
VOUT
I DC  I RF
M1
VLO
M3
M2
I DC  I RF
M1
VLO
VRF
• Show that:
1/ 2
3/ 2


K
K




1


SQ
SQ
3
VIF  2 I DC RL 
*
V

.
V

...




RF
RF
2
I
2
2
I
 DC 
 DC 



IIP3 in  volts 
8 I DC
3K SQ
79
Mixer Input Match
RS  Rg  T LS
RL
VLO
RS
Cl arg e
VS
RL
Vout
M3
M2
VLO
Lg
Rb
VBB1
1
  Lg  Ls  
Cgs
Ls
80
Mixer Gain
RL
RL
Vout
VLO
M3
M2
VLO
I sig  GM VRF  GM ARF cos  RF t
VRF
M1
GM 
1
2 RS
 T 


 
TLO
0
: Vout  Vcc   I DC  I sig  .RL   Vcc     I DC  I sig  .RL
2
TLO
 TLO : Vout  Vcc   Vcc   I DC  I sig  .RL    I DC  I sig  .RL
2
Vout sig  I sig RL * SW  I sig RL
4
1
1
1

cos

t

cos
3

t

cos
5

t

cos 7 LO t  

LO
LO
LO

3
5
7

81
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
82
Mixer Output Match (IF)
400
L par  2nH
VCC  3.0V
RL  400
VLO
M2
VRF
Vout
M3
VLO
M1
83
Mixer Output Match (direct conversion)
RL CL
VLO
RS
Cl arg e
VS
M3
Vout
VLO
Lg
Rb
VBB1
M2
RL
Ls
84
Mixer Noise Analysis
RL
VLO
Instantaneous Switching
RL
Vout
M3
M2
VLO
VOUT
t
I DC ,mix  I RF  I Noise
VRF
M1
Noise in RF signal band and
in image band both mixed
into IF signal band
 
 LO   RF
 RF  LO
 LO   RF
85
Mixer Noise Analysis
RL
VLO
Finite Switching Time
RL
Vout
M3
M2
VLO
VOUT
t
I DC ,mix  I RF  I Noise
VRF
M1
• 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.
86
Mixer Noise Analysis
• Noise analysis of a single balanced mixer cont...:
RL
VLO
Finite Switching Time
RL
Vout
M2  on
M3  off
VLO
VOUT
t
I DC ,mix  I RF  I Noise
VRF
M1
• 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)
87
Mixer Noise Analysis
• Noise analysis of a single balanced mixer cont...:
RL
VLO
Finite Switching Time
RL
Vout
M2  off
M3  on
VLO
VOUT
t
I DC ,mix  I RF  I Noise
VRF
M1
• 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)
88
Mixer Noise Analysis
• Noise analysis of a single balanced mixer cont...:
RL
VLO
RL
Finite Switching Time
Vout
M2  on
M3  on
VLO
VOUT
t
I DC ,mix  I RF  I Noise
VRF
M1
• 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.
89
Mixer Noise Analysis
• Optimizing the mixer (for noise figure):
RL
VLO
RL
VOUT
Vout
M2  on
M3  on
M1
t
VLO
I DC ,mix  I RF  I Noise
VRF
Trise
gm  W ... fixed  I DC
1
T 
... fixed  I DC
W
• 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.
90
Mixer Noise Analysis
• Noise Figure Calculation:
Trise
RL
VLO
RL
Vout
M2  on
M3  on
VOUT
VLO
t
I DC ,mix  I RF  I Noise
VRF
M1
• Let us calculate the noise figure including the contribution
of M2/M3 during the switching process.
91
Mixer Noise Analysis: RL Noise
• Noise Analysis of Heterodyne Mixer (RL noise):
RL
VLO
RL
Vout
M2
M3
VLO
2
vnoise
 RL  4kT  2 RL 
I DC ,mix  I RF  I Noise
VRF
M1
 IF
 RF  LO
92
Mixer Noise Analysis: Transducer Noise
• Noise Analysis of Heterodyne Mixer (Transducer noise):
RL
VLO
RL
Vout
M2
M3
VLO
I DC ,mix  I RF  I Noise
VRF
VLO
t
M1
inoise  M 1 switch  inoise  M 1  t  .SW  t 
4
4
4

 inoise  M 1  t  .  Cos  LOt 
Cos 3 LOt 
Cos 5 LOt  ... 
3
5


93
Mixer Noise Analysis: Transducer Noise
• Noise Analysis of Heterodyne Mixer (Trans-conductor noise):
inoise  M 1 switch  inoise  M 1  t  .SW  t 
4
4
4

 inoise  M 1  t  .  Cos  LOt 
Cos 3 LOt 
Cos 5 LOt  ... 
3
5


 
 IF
2
noise  M 1
i
4

  LO  
 
3 LO
 LO
4kT
  .4kTg m1
 f  .
Rch
SW  f  
 
4
2
inoise


2.
 M 1  IF 
 
 
4
  3 LO   ...
3
5 LO
2
1 1


. 1  2  2  .. . 4kTg m1
 3 5

2
inoise
 M 1  IF   4. 4kTg m1
94
Mixer Noise Analysis: Switch Noise
• Noise Analysis of Heterodyne Mixer (switch noise):
id  
VLO
M2  on
M3  on
id 2 id 3
4kT
  4kTgm
Rch
VLO
vgn   .
4kT
gm

gm vgs
id
gm vgs
95
Mixer Noise Analysis: Switch Noise
• Noise Analysis of Heterodyne Mixer (switch noise):
iout   iout 
RL
VLO
RL
Vout
M2
M3
VLO
VLO
I DC ,mix  I RF  I Noise
VRF
Gm
M1
Gm 0
VLO
• Show that:
Gm  gm 2  gm3  gm 2,3 
2.I DC ,mix
V
96
Mixer Noise Analysis: Switch Noise
• Noise Analysis of Heterodyne Mixer (switch noise) cont...:
VLO
vn  m 2,3
TLO
2
Gm
T
iout  t   Gm t  .vnm2,3 t 
iout
97
Mixer Noise Analysis: Switch Noise
•
Noise Analysis of Heterodyne Mixer (switch noise) cont...:
Gm t
TLO
2
 2 
p  

T
/
2
 LO 
Gm f
T
 p 2 p
3 p
 T  p 
Sin
k.



 T 
2 
1

Gm  t   Gm 0 . 
T .Gm 0 .
.2Cos  k pt 
 T


T


p 
 TLO / 2   LO  k 1
k
.




 2 
2


vn  m 2,3  vn2 m 2  vn2 m3
vnm 2,3  f 
vn m 2,3  2. .
p
2 p
4kT
g m 2,3
3 p
98
Mixer Noise Analysis: Switch Noise
•
Noise Analysis of Heterodyne Mixer (switch noise) cont...:
Gm f
 p 2 p
Gm f
vnm 2,3  f 
3 p
vnm 2,3  f 
 p 2 p
3 p
1
2
inoise


.Gm2 0 .T .vn2 m 2,3
 M 2,3  IF 
 TLO 


 2 
99
Mixer Noise Analysis: Switch Noise
•
Noise Analysis of Heterodyne Mixer (switch noise) cont...:
1
2.I DC ,mix
.Gm2 0 .T .vn2 m 2,3 G  g  g  g
m
m2
m3
m 2,3 
 TLO 
V


2I DC ,mix
 2 
Gm0 
V  Slope. T
VLO  t   ALOCos LOt 
V
 dVLO  t  
4kT
Slope  t 90  

A

vn m 2,3  2. .

LO LO
LO
dt
g m 2,3

 LOt 90

1
1
4kT 
2
2
2
2
inoise  M 2,3  IF  
.Gm 0 .T .vn m 2,3 
.Gm 0 .T .  2. .


TLO / 2
TLO / 2
g
m 2,3 

2
inoise
 M 2,3  IF  


1
TLO / 2
.Gm 0 .T .  2. .4kT  
2 I DC ,mix
TLO / 2
.  2. .4kT  .
I

 4. 4kT  DC ,mix 
  ALO 
1
TLO / 2
.
2.I DC ,mix
V
.T .  2. .4kT 
T 2 I DC ,mix
1

.  2. .4kT  .
V
TLO / 2
ALO LO
Total Noise Contribution due to switches M2 and M3
100
Mixer Noise Analysis: Total Noise
•
Noise Analysis of Heterodyne Mixer (total noise):
2
noise  RL
v
2
noise  M 1
i
 4kT  2 RL 
g m  short 
dI DS  short 1
I DS  short
 WCox vsat 
dVGS
2
VGSQ  VT 0 
IF   4. 4kTgm1  4. 4kT .
V
I DC ,mix
GSQ
 VT 0 
 I DC ,mix 
2
inoise


4.

4
kT


 M 2,3  IF 

A
LO 

2
2
2 2
2 2
vnoise
 MIX  IF   vnoise  RL  RL inoise  M 1  RL inoise  M 2,3
2
noise  MIX
v


I DC ,mix
I DC ,mix




4
kTR
1

4.

.
.
R

4.

.
.
R
 IF 
L 
L
L

A
V

V
 GSQ T 0 
LO




101
Mixer Noise Analysis: Total Noise
•
Noise Analysis of Heterodyne Mixer (total noise):
2
noise  MIX
v


I DC ,mix
I DC ,mix


.RL  4. .
.RL 
IF   4kTRL 1  4. .
 ALO
VGSQ  VT 0 




(VGSQ-VT0) ↑  M1 linearity ↑ and noise↓
ALO ↑  noise contribution from M2/M3 ↓
2
vnoise
 MIX  IF 
VGSQ  0.8V
VGSQ  1.6V
VLO
102
Homodyne Mixer Noise Analysis: Transducer Noise
•
Noise Analysis of Homodyne Mixer (noise from transducer M1):
RL
VLO
RL
Vout
M2
M3
VLO
I DC ,mix  I RF  I Noise
VRF
M1

 LO
 RF
103
Homodyne Mixer Noise Analysis: RL Noise
•
Noise Analysis of Homodyne Mixer (noise from RL):
RL
VLO
RL
Noise from RL
Vout
M2
M3
VLO
I DC ,mix  I RF  I Noise
VRF
M1

 LO
 RF
104
Homodyne Mixer Noise Analysis: non-50% duty LO
•
Noise Analysis of Homodyne Mixer (M2,M3 mismatched or non-50% duty
cycle of LO)}:
TLO
TLO
2
RL
VLO
RL
VRF
2
 T
VLO
Vout
M2
 T
M3
t
VLO
M1
 I M 1    DC 

4

Cos  LOt  
4

Cos  3 LOt   ... 
3

105
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}:
RL
VLO
RL
Vout
M2
VRF
M3
VLO
I Noise M1
I Noise 1/ f
I Noise thermal
M1
I
DC , mix
 I RF  I Noise thermal  I Noise 1/ f

106
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}:
RL
VLO
DC-term of LO
RL
Vout
M2
M3
VLO

VRF
M1
 LO
 RF
3 LO
4
4


I

I

I

I
.
DC

Cos

t

Cos
3

t

...




 DC ,mix RF Noisethermal Noise1/ f  
LO
LO


3

107
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}:
id  id thermal  id 1/ f
VLO
M2  on
id 1/ f
M3  on
id 2 id 3
Kf
1

.g .
CoxWL
f
VLO
vgn 1/ f 
2
m
Kf
1
CoxWL f
.

gm vgs
gm vgs
108
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}:
RL
vgn 1/ f
VLO

M2
I
DC , mix
RL
Vout
M3
VLO
 I RF  I Noise thermal  I Noise 1/ f
vgn 1/ f

VLO
109
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}:
vgn 1/ f
VLO
iout
iout  iout  no  noise  inoise 1/ f
110
Homodyne Mixer Noise Analysis: non-50% duty LO
•
Noise Analysis of Homodyne Mixer (M2,M3 mismatched or non-50% duty
VLO
cycle of LO)--{Noise from M2/M3}: vgn 1/ f
iout
T
iout  iout  no  noise  inoise 1/ f
v
 t  Slope  2 A 
T  t   gn 1/ f
LO LO
Slope
iout
T  t  
vgn 1/ f  t 
2 ALO LO
111
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}:



 TLO   vgn 1/ f  t 
 TLO  
Noise  Energy  T  t  .I DC ,max .   t  k 

.
I
.

t

k
DC ,max  



2
2
A

2




k 0
k

0



LO LO
vgn 1/ f  f 
 inoise 1/ f 
.I DC ,max
2 ALO
vgn1/ f  f 
vgn1/ f  t 

t
I DC , mix
1
0.5TLO
f
iout
0.5TLO
t
 I DC , mix
1
0.5TLO
f
iout
t
f
112
Increasing Headroom in DBM (Option 1)
Vb
Q21 Q2  2 Rb
Rb
Vin
Q2'  2 Q2' 1
Vin
Cc
VLO 
Cc
VLO 
Vgnd
Vcc
Q1
Le
Q1'
Vgdcom
Le
L par  2nH
113
Increasing Headroom in DBM (Option 2)
VCC  3.0V
Vgg
RL
RL
RL  200
Vb
VS
RS  200
Vin
C  10nF
Rb
Q21 Q2  2
I BQ
Rb
Rb Rb '
'
Q2  2 Q21
Vb
Vb
Cc Q '
1
Cc
Q1
VLO  VLO 
Lb
Le
I BQ
Vgdcom
Lb
Vin
C  10nF
VS
Le
L par  2nH
114
Increasing Headroom in DBM (Option 3)
VCC  3.0V
Vgg
RL
RL
RL  200
Vb
VS
RS  200
Vin
C  10nF
Rb
Q21 Q2  2
I BQ
Rb
Rb Rb '
'
Q2  2 Q21
Vb
Vb
Cc Q '
1
Cc
Q1
VLO  VLO 
Lb
Le
I BQ
Vgdcom
Lb
Vin
C  10nF
VS
Le
L par  2nH
115