Post on 24-Dec-2015
transcript
1
Mixer Design
• Introduction to mixers
• Mixer metrics
• Mixer topologies
• Mixer performance analysis
• Mixer design issues
2
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
3
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
4
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
5
Commutating switch mixer
)(tVRF
)(tVLO)(tVLO
)(tVIF
ttA
tsqtA
tVtV
LORFLORFRF
LORFRF
LORF
)(3cos31
)cos(2
sin
)()(
ωωωωπ
ωω
6
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
8
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.
9
Noise Figures: SSB vs DSB
Imageband
Signalband
Thermal noise
LO
IF
Signalband
Thermal noise
LO
0
Single side band Double side band
10
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
12
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.
13
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
14
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
15
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)
16
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
19
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
20
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
36
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
39
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
40
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.
42
Mixer performance analysis
• Analyze major metrics– Conversion gain– Port isolation– Noise figure/factor– Linearity, IIP3
• Gain insights into design constraints and compromise
43
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?
49
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
52
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
55
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
56
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
57
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
58
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
59
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+
60
+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+
61
Double Balanced Mixer
• Benefits:– Fully Differential
– No output signal at LO
• Three stages:– CE input stages– Switches– Output load
62
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+
63
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
64
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
65
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
66
IM1
VLO
t
t
VOUT
t
MOS Single Balanced Mixer
67
IF Filter
VOUT t
VOUT
t
MOS Single Balanced Mixer
68
LO
RF IF
LO RF
IF Filter
LO RF
LO RF LO RF
MOS Single Balanced Mixer
69
LO RF 2 LO
SMIX
3 LO
RF
SLO LO
LO RF
MOS Single Balanced Mixer
70
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
71
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
72
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
73
• 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
74
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
75
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
76
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
77
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
78
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
79
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
80
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
81
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
82
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
83
Mixer Output Match (IF)
VLO
400LR
VLO
VRF
Vout
M1
M2 M3
3.0CCV V
400
2parL nH
84
Mixer Output Match (direct conversion)
VLO
RL RL
VLOVoutM2 M3
RS
VS RbVBB1
Ls
LgCl earg
LC
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
86
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
87
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
88
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
89
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
90
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
91
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
92
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
93
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
94
• 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
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
96
• 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
97
• 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
98
• 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
99
• 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
100
• 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
101
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
102
• 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 ↓
103
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
104
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
105
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
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}:
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
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 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
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}:
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
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}:
VLO
RL RL
VLO
VoutM2 M3
1/gn fv
, 1/DC mix RF Noise thermal Noise fI I I I
VLO1/gn fv
110
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/
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}:
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
112
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
113
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
114
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
115
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