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```RFIC Design and Testing for Wireless Communications
A PragaTI (TI India Technical University) Course
July 18, 21, 22, 2008
Lecture 7: RF front-end design – LNA, mixer
By
Vishwani D. Agrawal
Fa Foster Dai
200 Broun Hall, Auburn University
Auburn, AL 36849-5201, USA
1
RFIC Design and Testing for Wireless Communications
Topics
Monday, July 21, 2008
9:00 – 10:30
Introduction – Semiconductor history, RF characteristics
11:00 – 12:30
Basic Concepts – Linearity, noise figure, dynamic range
2:00 – 3:30
RF front-end design – LNA, mixer
4:00 – 5:30
Frequency synthesizer design I (PLL)
T
Tuesday,
d
July
J l 22,
22 2008
9:00 – 10:30
11:00 – 12:30
2:00 – 3:30
Frequency synthesizer design II
(VCO)
RFIC design for wireless communications
Analog and mixed signal testing
RF front-end design – LNA, mixer, FDAI, 2008
2
LNA Design Challenges
(1) Amplify extremely low signals without adding much
noise.
(2) Amplify large signals without distortions.
(3) Variable gain to compensate large input signal
variation.
(4) Input matching and flat gain over wide bandwidth for
muti-mode transceivers.
(5) Input dynamic range of a WLAN LAN from -80dBm to
-20dBm
Parameters for Microwave and RFIC Design
Peak-to peak voltage: Vpp
Vrms =
Root-mean-square voltage:
V pp
2 2
2
V 2 rms V pp
Pwatt =
=
R
8R
Power in Watt :
PdBm
Power in dBm :
Refection coefficient :
P tt [mW
W]⎞
⎛ Pwatt
= 10 log 10 ⎜
⎟
1mW
⎝
⎠
Z in − RS
Γ = S11 =
Z in + RS
Return loss = −20 log Γ
Voltage standing wave ratio (VSWR):
V max 1 + Γ
=
VSWR =
Vmin 1 − Γ
RF front-end design – LNA, mixer, FDAI, 2008
4
Basic Amplifiers
•
•
•
The common emitter amplifier is often used as a drive for an LNA.
The common-collector, with high input impedance and low output
impedance,
p
, makes an excellent buffer between stages
g or before the
output driver.
The common-base is often used as a cascode in combination with
the common-emitter to form a LNA stage
g with g
gain to high
g frequency.
q
y
VCC
VCC
VCC
vout
vout
vin
vout
vin
vin
VEE
VEE
Common-Emitter
(LNA Driver)
VEE
Common-Collector
(Buffer)
Common-Base
(Cascode)
RF front-end design – LNA, mixer, FDAI, 2008
5
Common-Emitter Amplifier
vi
rb
Cμ
vπ
Cπ
rπ
gmvπ
vo
ro
ZL
•
Voltage gain
•
Note that rπ=βre and gm=1/re. for low frequencies, the parasitic
capacitances have been ignored and rb << rπ.
•
Input impedance at low frequencies
Avo =
vo
r
Z
= − π gmZ L ≈ L
vi
rb + rπ
re
Z in = rb + rπ
RF front-end design – LNA, mixer, FDAI, 2008
6
Miller Capacitance in Common-Emitter Amplifier
Cμ is replaced with two equivalent capacitors CA and CB
Cμ
vπ
vo
⇓
vπ
CA
CB
vo
⎛ vo
C A = Cμ ⎜⎜1 −
⎝ vπ
⎛ v
C B = Cμ ⎜⎜1 − π
⎝ vo
•
⎞
⎟⎟ = Cμ (1 + g m Z L ) ≈ Cμ g m Z L
⎠
⎞
⎛
1 ⎞
⎟⎟ ≈ Cμ
⎟⎟ = Cμ ⎜⎜1 +
⎠
⎝ gmZ L ⎠
Two RC time constants or two poles:
one consisting
g of CA+ Cπ, and the
other consisting CB.
RF front-end design – LNA, mixer, FDAI, 2008
7
Miller Capacitance in Common-Emitter Amplifier
•
The dominant pole is one formed by CA and Cπ:
f P1 =
•
1
2π ⋅ [rπ (rb + Rs )]⋅ [Cπ + C A ]
Recall Ft calculation, the output is loaded with a short circuit Æ removes
Miller multiplication, 3db current gain bandwidth:
fβ =
1
2π ⋅ rπ (Cπ + Cμ )
The unity current gain frequency:
gm
fT =
2π ⋅ (Cπ + Cμ )
RF front-end design – LNA, mixer, FDAI, 2008
8
Common-Base Amplifier
Cμ
rb
vπ
Cπ
rπ
iout
gmvπ
ZL
iin
Current gain (ignoring Cu and ro)
Av ≈
α 0 RL
RS
⋅
1
1 + jωreCπ
⋅
iout
1
1
≈
≈
iin 1 + jωCπ re 1 + j ω
1
1 + jωRL (Cμ + CCS )
At low
l
frequencies,
f
i
th
the currentt gain
i =1
1.
The pole in this equation is usually at much higher
frequency than the one in the common-emitter amplifier
ωT
re < rb + RS
VCC
Cascode LNA
vo / vi ≈ − g m RC
RC
vout
Cascode Q2
VCbias
vc1
Common emitter dominant pole
1
f P1 =
2π ⋅ [rπ 1 (rb1 + Rs )]⋅ [Cπ + 2Cu ]
•
•
•
•
vi
Driver Q1
VEE
re ≈ 1 / g m 2
Current ic1 through Q1 is about the same as the current ic2 through Q2 Å
current gain ~1 Æ Gain is the same as for the common-emitter amplifier.
The cascode transistor reduces the feedback of Cu1 (why?) Æ increased
high frequency gain.
Cascode has good isolation with reduced S12.
linearity; add another pole to the amp Æ -12dB/oct roll-off; add little extra
pp
, cascode NF = common emitter NF);
);
noise ((to the 1st order approximation,
common base may cause noise and oscillation.
RF front-end design – LNA, mixer, FDAI, 2008
10
Bipolar Transistor Noise Model
b
vb
rb
Cμ
b’
4kTrb
ibn
ibf
Cπ
rπ
c
gmvb’e
ro
2qIC
2qIB
e
1/f noise
icn
Collector
C
Base
e
Shot Noise
Shot Noise
2
vbn
= 4kTrb
Base
vbn
rb
Collector
Zπ
i = 2qI B
2
bn
ibn
rπ
Cπ
gmVπ1
ro
icn
icn2 = 2qI c
Emitter
RF front-end design – LNA, mixer, FDAI, 2008
11
Min
nimum Noisee Figure (dB))
Noise Figure versus Bias Current
Output signal
vso ≈ vsi ⋅ g m RL
Base thermal noise
vno ,rb ≈ 4kTrb ⋅ g m RL
Collector shot noise
vno , I c ≈ 2qI C RL
2 40
2.40
2.20
Base shot noise
2.00
base
th
thermal
l
noise
1.80
1.60
0
1.0 2.0 3.0 4.0
vno , I B ≈
2qI C
base
shot
noise
β
Rs g m RL
collector
shot noise
(correlated)
5.0 6.0
Collector Current (mA)
Req
rb
g m RS g m RS
1
NF = 1 +
= 1+
+
+
+
2
RS
RS 2 g m RS
2β 0
2β
RF front-end design – LNA, mixer, FDAI, 2008
12
Noise Figure of A Two Stage LNA
f t = 5GHz
rb = 11Ω
f in = 1GHz
β 0 = 80
β =5
g m = 0.1Ω −1
rb
1
g m RS g m RS
+
+
+
NF dominatedNF = 1 +
2
R
2
g
R
2
β
2β
by base
S
m S
0
resistance
NF increases at
high frequency
11 1
5
5
= 1+
+ +
+
= 1.62dB
50 10 160 50
RF front-end design – LNA, mixer, FDAI, 2008
13
Minimum Noise Figure of Common Emitter LNA
rb
g m RS g m RS
1
1
NF = 1 +
+
+
+
=
1
+
a
+ b ⋅ RS
2
RS 2 g m RS
2β 0
RS
2β
dNF
1
= −a 2 + b = 0
dRS
RS
RS ,opt =
NFmin
a
1
=
b gm
1 + 2 g m rb
f
≈ T
1
1
f
+ 2
β0
2rb
gm
β
RS=50 Ohm Æ
choose bias (gm)
and emitter length to
achieve
hi
noise
i
matching
⎛ 1
⎞
1
= 1 + 2 ab = 1 + (1 + 2 g m rb )⎜
+ 2⎟
⎜ β0 β ⎟
⎝
⎠
RF front-end design – LNA, mixer, FDAI, 2008
14
More on LNA Noise Figure
NF = NFmin
(
b
+
RS − RS ,opt
RS
High frequency, RS ,opt
fT
≈
f
Low frequency, RS ,opt ≈
•
•
•
•
)
2
≈ NFmin
(
f 2 gm
+
RS − RS ,opt
2
2 f T RS
)
2
2rb
2rb
NFmin ≈ 1 + Cπ ω
gm
gm
2rb β 0
gm
NFmin ≈ 1 +
2 g m rb
β0
For a given technology, NFmin is a strong function of bias current.
For low operation frequency, NFmin can be reduced by increasing emitter
length.
For high operation frequency, NFmin is a weak function of emitter length.
Increase device size does reduce rb, yet capacitance also increase.
For high operation frequency, NFmin degrades as frequency increases.
RF front-end design – LNA, mixer, FDAI, 2008
15
Input Matching of LNA Noise
Power matching:
RFin
•
Lb
Input impedance (assuming Cu
and rπ is not significant):
Le
g m Le
j
+ jωLe +
Z in = jωLb + rb −
ωCπ
Cπ
•
( RS − rb )Cπ
RS
≈
Le =
gm
ωT
Power matching: g m Le
+ rb = RS
Real part=Rs
C
π
1
Imaginary
Le + Lb = 2
part=0
ω Cπ
•
Lb =
Q1
1
Cπ ω 2
−
(RS − rb )Cπ
gm
≈
RS − rb
ωT
−
g mω 2
ωT
If Cu is considered, Cπreplaced by Cπ + CA, and therefore a larger
inductor is required for matching.
C A = C μ (1 + g m Z L ) ≈ C μ g m Z L
RF front-end design – LNA, mixer, FDAI, 2008
16
LNA Design Steps
(1) Noise matching: sizing the transistor (emitter length)
and adjusting bias current to achieve minimum NF
RS ,opt
1
=
gm
RFin
Lb
Q1
1 + 2 g m rb
= 50Ω
⎛ 1
⎞
1
1
1
⎜
+ 2
NFmin = 1 + (1 + 2 g m rb )
+ 2⎟
β0
⎜ β0
⎝
β
(2) Power matching: adjusting Le such that the real part
of the LNA input impedance equals to 50 Ohm. For
5AM, Le is about 0.2nH Æ Use multiple downbonds
to reduce the package effect
effect.
Le =
(3) Power matching: adding Lb such that the imaginary part
of the LNA input impedance equals to zero
(4) Gain/bandwidth:
G i /b d idth Choosing
Ch
d ttank
k tto meett gain
i and
d
bandwidth requirements.
RS
ωT
Le
β ⎟⎠
=
50
ωT
ωT
Lb ≈
g mω 2
(5) Using SPICE sim to fine tune the component values,
it ti
iterations
to
t d off
ff the
th various
i
parameters
t
are expected.
t d
RF front-end design – LNA, mixer, FDAI, 2008
17
Mixing with Nonlinearity
•
•
•
Mixer is to convert a signal from one frequency to another Æ
intrinsically needs a nonlinear transfer function. A diode or a transistor
can be used as a nonlinear
ca
o
ea de
device.
ce
Two inputs at ω1 and ω2 , which are passed through a nonlinearity
multiplier will produce mixing terms at ω1±ω2 Æwith other terms
(harmonics, feed-through, intermodulation) that need to be filtered out.
Mixers (multiplier) can be made from an amplifier with a controlled
switch.
VCC
Rc
VCC
Rc
vout -
vout +
v2
switch
v1
i(v1)
RF front-end design – LNA, mixer, FDAI, 2008
18
Controlled Transconductance Mixer
•
The currentt is
Th
i related
l t d to
t the
th input
i
t voltage
lt
v2 by
b th
the ttransconductance
d t
of the input transistors Q1 and Q2. The transconductance is controlled
by the current I0, which in turn is controlled by the input voltage v1.
io
i1
v2
+
Q1
i2
2Io
Q2
-
v1
i0=i1-i2
v2
2Io
-2Io
RF front-end design – LNA, mixer, FDAI, 2008
IO
i1 =
1+ e − v2 / vT
IO
i2 =
1+ e v2 / vT
19
Controlled Transconductance Mixer
IO
⎛
io = i1 − i2 = I o ⎜
−v
⎝1+ e
•
•
If v2<<vT
io ≈ I o
2
/ vT
−
IO
1 + ev
2
/ vT
v
⎞
⎟ = I o tanh 2
2vT
⎠
v2
2vT
Current source is modulated by small v1 Æ Io is replaced with Io+gmcv1,
where gmc is transconductance of the current source:
v2
v2
v2
= I o tanh
+ g mc v1 tanh
io = ( I o + g mc v1 ) tanh
2vT
2vT
2vT
14243
144244
3
V2
feedthrough
multiplication
( mixing )
not appear in differential output
voltage Æ double balanced mixer
RF front-end design – LNA, mixer, FDAI, 2008
20
Double-balanced Mixer
VCC
RC1
vo1
eliminate the v2 feedthrough
vo2
i3
Q3
v2
v1
•
•
•
RC2
pair current:
i6
Q6
Q5
Q4
2Io
2nd
i5
i4
-v1
2Io
v2
v2
i = i6 − i5 = I o tanh
− g mc v1 tanh
2vT
2vT
'
o
Total differential current:
v2
iob = io − i = 2 g mc v1 tanh
2vT
'
o
RF front-end design – LNA, mixer, FDAI, 2008
21
Double-balanced Mixer
⎛ v2
(i3 + i5 ) − (i4 + i6 ) = tanh⎜⎜
⎝ 2vT
⎞
⎛ v2
⎟⎟(i1 − i2 ) = tanh⎜⎜
⎠
⎝ 2vT
A
Assuming
i
⎞ v1
⎟⎟
small signal
⎠ re + RE for V1
VCC
RC1
vo1
RC2
i3
i4
Q4
Q3
vo2
i5
i6
Q6
Q5
v2
i2
i1
Q1
RE
RE
v1
Q2
i1
1 + e −v2 / vT
i2
i5 =
1 + e v2 / vT
i3 =
i1 ≈ I o +
i1
1 + e v2 / vT
i2
i6 =
1 + e −v2 / vT
i4 =
v1 1
2 re + RE
and
2Io
i2 = I o −
v1 1
2 re + RE
VEE
RF front-end design – LNA, mixer, FDAI, 2008
22
Double-balanced Mixer
•
•
•
Output differential voltage
Conversion gain relative to v1
⎛ v2
vo = − tanh⎜⎜
⎝ 2vT
⎞ v1
⎟⎟
RC
⎠ re + RE
⎛ v2
vo
= − tanh⎜⎜
v1
⎝ 2vT
⎞ RC
⎟⎟
⎠ re + RE
With RE=0, a general large-signal expression for the output:
⎛ v1
vo = −2 RC I o tanh⎜⎜
⎝ 2vT
⎞
⎛ v2
⎟⎟ tanh⎜⎜
⎠
⎝ 2vT
⎞
⎟⎟
⎠
RF front-end design – LNA, mixer, FDAI, 2008
23
LO Level at Upper Quad Transistors
•
•
•
•
•
Th diff
The
differential
i l pair
i needs
d an iinput voltage
l
swing
b
4 to 5 vT for
f the
h transistors
i
to be hard-switched one way or the other.
LO input to the mixer should be at least 100mV peak for complete switching. At 50Ω,
100mV peak is -10 dBm.
w1
-10 to 0 dBm (100~300
(100 300 mVpp = 200~600mVpp
200 600mVpp diff) is a reasonable compromise
between noise figure, gain and required LO power. This is also the reasonable level for
all switching circuits
If the LO voltage is too large, large current has to be moved into and out of the bases
of the transistors during transition Æ lead to spikes in the signals and reduce the
switching speed Æ cause an increase in LO feed
feed-through.
through
Large LO also pushes switching transistor into saturation Æ loose switching speed and
inject mixer noise into substrate.
a)
Vc
b)
Rcc
VLO+
Rc
Vin-
Vin+
VLO-
Q3 V Q4
d
Vd
Ibias
RF front-end design – LNA, mixer, FDAI, 2008
24
Slide 24
w1
weishen, 7/16/2003
Mixer Noise
Noise Contributions
N 0tot
NF = 10 log
N 0( source)
11
= 10 log
= 8.65dB
1.5
Output N
Noise Power
(Relativve values)
total
10
top
transistors
8
6
bottom
t
transistors
it
4
2
0
-0.1
0
0.1
source
resistance
VLO (instantaneous)
•
•
•
•
•
•
•
Top transistor contributes significant noise during transition and contributes ignorable noise
when fully switched, either in cutoff or saturation (without gain).
Gain from RF input is maximum when top transistors are fully switched (cascode)
(cascode).
Æ need sharp transition buffer for LO Æ large LO such that minimal time is spent around 0V.
Mixer noise figure can be approximately analyzed using a lowly swept dc voltage at the LO
input or with an actual LO signal.
With a slowly swept dc voltage, the mixer becomes equivalent to a cascode amplifier and the
LO input served as a gain-controlling signal.
For mixer, any noise (or signal) is mixed to two output frequencies, thus reducing the output
level Æ mixer having less gain than the equivalent differential pair.
However, both RF and image is mixed to IF Æ doubling noise power at output.
RF front-end design – LNA, mixer, FDAI, 2008
25
Mixer with Simultaneous Noise and Power Match
•
Use inductor degeneration and inductor input achieving simultaneous noise and
power matching similar to that of a typical LNA.
VCC
RL
RL
LO reject
j t
IF-
IF+
Z0
LE =
2πfT
LO
Q1
RF
VBB
Q2
LE
LE
VBB
Filter
harmonics
•
•
ωg m Z 0
IIP3 ≈
2πfT
Single-to-differential
Noise matching: sizing LE, and RF transistor, and operating the RF transistors at
the current required for minimum NF.
g transistors are sized for maximum fT, (typically
( yp
The q
ten times smaller than the RF transistors.)
RF front-end design – LNA, mixer, FDAI, 2008
26
Mixer Design Issues
Sizing Transistors
•
•
The RF differential pair is basically an LNA stage, and the transistors and
associated passives can be optimized using the LNA design techniques.
The switching
gq
quad transistors are sized so that they
y operate
p
close to their
peak fT at the bias current that is optimal for the differential pair transistors are
biased at their minimum noise current, then the switching transistors end up
Increasing Gain
•
Voltage gain without matching and assuming full switching of the upper quad:
RC
vo =
vin
π re + RE
2
•
•
To increase the gain Æ increase the load resistance RC, to reduce degeneration
resistance RE, or to increase the bias current IB.
Make sure that increasing output voltage swing will not cause the switching
transistors to become saturated.Æ Enough
RF front-end design – LNA, mixer, FDAI, 2008
27
Mixer Design Issues
Increasing IP3
•
Identify which part of the circuit is compressing. Compression can be due to
overdriving of the lower differential pair, clipping at the output, or the LO
bias voltage being too low, causing clipping at the collectors of the bottom
j
the bias and voltage
g swing
g to avoid clipping.
pp g
differential p
1. If the compression is due to the bottom differential pair (RF input), then
linearity can be improved by increasing RE or by increasing bias current.
2. Compression caused by clipping at the output is typically due to the quad
going
g into saturation. Saturation can be avoided by
y reducing
g the
transistors g
cause saturation.
3. If compression is caused by clipping at the collector of the RF input
differential pair, then increasing the LO bias voltage will improve linearity;
h
however,
this
hi may result
l iin clipping
li i at the
h output.
•
•
•
Improving Noise Figure
•
•
•
•
NF will be largely determined by the choice of topology.
topology
Use the simultaneous matched design technique.
To minimize noise, the emitter degeneration resistor should be kept as small
as possible. Use inductor as degeneration to achieve low noise.
Make top transistors switching fast.
RF front-end design – LNA, mixer, FDAI, 2008
28
Mixer Design Issues
M t hi
Matching,
Bias
Bi Resistors,
R i t
and
d Gain
G i
•
•
Use resistive matching to achieve broad band. For a resistively degenerated
mixer, the RF input impedance will be fairly high; for example, with RE=100 Ω,
Zin can be
b off the
th order
d off a Kilo
Kil Oh
Ohm Æ easier
i ffor LNA output
t t stage
t
to
t drive
d i the
th
mixer.
At the output, if matched, the load resistor Ro is equal to the collector resistor
Rc. Furthermore, to convert from voltage gain Av to power gain Po/Pi, one must
consider the output resistance Ri and load resistance Ro=Rc as follows:
vo2
2
⎛
⎞
/
2
R
R
R
Po Ro vo2 Ri
2
C
⎟⎟ i
= 2 = 2
= Av2 i ≈ ⎜⎜
Ro ⎝ π RE ⎠ RC
Pi
v i Ro
vi
Ri
RF front-end design – LNA, mixer, FDAI, 2008
29
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