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RF Microelectronic
LNA and Mixer
Oscillator
KAVOSHCOM
Contents
1.
2.
3.
4.
5.
6.
7.
8.
9.
Introduction
Basic concepts
Digital modulation, Spectral control, Detection
Multiple access standards, TDM, CDM, OFDM
TRx architecture
LNA and Mixer
Oscillator
Frequency Synthesizer
Power Amplifier
April 30, 2017
2
Section 6
6.
LNA and Mixers
a) LNA
i. Input matching vs. NF
ii. BJT vs. CMOS
iii. BW enhancement
b) Mixer
i. BJT Mixers
ii. CMOS Mixers
iii. Noise in Mixers
c) Cascaded stages
April 30, 2017
3
LNA Figures of Merit








Frequency
Noise Figure
Linearity (P-1dB, IIP3)
Bandwidth and Q
Gain S21
Power Consumption
Supply Voltage
S-Parameters






Gain S21
Input Matching S11
Output Matching S22
Reverse Isolation S12
Stability
Image Rejection Capability
April 30, 2017
4
Typical Figures of Merit
NF
~ 2dB
IIP3
~ -10 dBm
P-1dB
~ -20 dBm
Gain
~ 15 dB
Input and Output
Return Loss:
S11, S22
Reverse
Isolation:S12
Zin=Zout
< -15 dB
April 30, 2017
< - 30 dB
=50Ω
5
LNA Design






Input Matching Network
Noise and Linearity Consideration
Output Loading and Gain
Output Matching Network
Stability
Differential Design
April 30, 2017
6
Noise Figure of LNA

LNA, the first gain stage in the receive path
Noise figure directly adds to that of the system
its
Duplexer Noise Figure ~ 2dB
System Noise Figure=4dB
LNA noise Figure =2dB
SNRmin
S
 
N
 8dB    in
NBW  200 KHz
April 30, 2017
S
 
 N  out
 NF
S min  109dBm
8dB
7
Noise Figure of LNA

LNA=2dB using BJT:
=2KTgm (shot noise)
4KTrb
Vneq
2

Vneq
April 30, 2017
2
2 KTg m
 4 KTrb 
2
gm
&
Ic
gm  
VT
Vneq
2
Req
VT
 4 KT (rb 
)  NF 
1  1
2I c
4 KTRs
Rs
8
Noise Figure of LNA
VT
Req  rb 
2I c


For NF=2dB
Req < 29Ω
Q1 must be
relatively large and biased at a high current
Finger structure reduces rb but increases capacitance
Bandwidth reduction
April 30, 2017
9
Minimum Gain of LNA

Defined by Three parameters:



Loss of the image-reject filter
Noise Figure of mixer
IP3 of the Mixer
 For example:
 Filter loss=4~5 dB
 Mixer noise figure=10dB
Gain=20dB
 Mixer IP3=+5dBm
min.
 Input-referred noise is suppressed
 reasonable equivalent IP3 is maintained
April 30, 2017
10
Input and Output Matching

Input Impedance is 50Ω because it comes out of the
antenna
Output Impedance can be>=50Ω whether it goes to IC

The quality of the input matching is expressed by:

Input Return Loss=20log|Γ|
Γ=the reflection coefficient with respect
to a source impedance R0
For Impedance Matching: Γ<0.2
April 30, 2017
11
Measuring S11 and S21
April 30, 2017
12
Measuring S11 and S21
Z in  RO
S11   
Z in  RO
April 30, 2017
13
Input and Output Matching

Γ=0.2
Zin=35Ω_65Ω
|S11|35=((35-50)/(35+50))^2|dB=-15dB
|S11|65=((65-50)/(65+50))^2|dB=-17.6dB

In RF Circuits :




Impedance matching
Max Power Transfer
In LNA Design:

R
sopt
We accept mismatch in the first stage
But we try to select the device in a way to have
Matching
circuit
50Ω
50Ω
April 30, 2017
Rsopt~50Ω
Rsopt 50Ω 50Ω 50Ω
50Ω 50Ω
14
Input and Output Matching


In IC design when the receiver sensitivity is very
important e.g. GPS, external discrete LNA placed on the
PCB is desirable
In mass productive ICs e.g. for Mobile handsets, we try
to design input LNA,
Zin=Rsopt~50Ω

LNA output Impedance must also equal 50Ω to have the
minimum loss and ripple in driving Image-Reject Filter
April 30, 2017
15
LNA stability


Due to feedback from the output to input, the circuit
may become unstable for certain amounts of source and
load Impedance
The amount of feed-back can also set the reverse
isolation of the amplifier which is important for LO
radiation.
April 30, 2017
16
LNA stability

Stern Stability Factor :
1    S11  S 22
K
2 S 21 S12
2
2
2
  S11S 22  S12 S 21


If K>1 & Δ<1
The circuit is unconditionally stable
Difficulty: S parameters must be calculated for a wide
frequency range to ensure that K>1 at all frequencies
April 30, 2017
17
LNA stability

If S12
0 then:
K
Δ
∞
S11.S22<1
(both S11 & S22 inside the unit circle of the smith chart)

This function is called “Neutralization” of the return path
April 30, 2017
18
Stabilization by Neutralization

L1 and C1 actually tune out the parasitic capacitance
At a frequency thus S12=0
April 30, 2017
19
Stabilization by Cascoding

In IC design the feedback can be suppressed by
cascode configuration
Variation of the
node X
is small due to
Vb so the
effect on Vin
is low enough
to reduce S12
April 30, 2017
X
20
Is the LNA stable anyway?




Vcc and GND leakage paths and substrate of ICs still
have to be considered
Isolating Vcc and GND is a solution
Differential structure is useful for c.m. signal rejection
Problem:

Differential LNA design is not easy because of
matching constraints
April 30, 2017
21
Is the LNA stable anyway?
April 30, 2017
22
PCB Ground Consideration
April 30, 2017
23
Impedance matching in MOS LNA

A common-source stage in order to create 50Ω input
Impedance
April 30, 2017
24
Impedance matching in MOS LNA
Yin  Yinr  jYini
Yinr  RL C F  2
C F  g m RL (C L  C F )
2
RL (C L  C F ) 2  2  1
RL C L (C L  C F ) 2  1  g m RL
Yini  C F 
2
RL (C L  C F ) 2  2  1
2
if C L  C F & g m RL  1
1

RL C L
g m CF
Yinr 
.
2 CL
g m RL
Yini  C F  (1 
)
2
Proper selection of 2CL/gmCF makes 50Ω input resistance but the
drawback is the relatively low voltage gain at high frequencies due
To bandwidth limitation at the output node
April 30, 2017
25
Resistive Termination


In high frequencies, Capacitive part of the input
impedance must be cancelled by an external inductor
Noise figure is at least 3dB (NF=1+Rs/RP , Rs = RP)
April 30, 2017
26
Input Resistive Termination by Negative Shunt
Feedback

Low input impedance with a 50Ω real part can be obtained
April 30, 2017
27
Input Resistive Termination by Negative Shunt
Feedback

Drawbacks:


Active feedback injects noise in the input of the
circuit
Frequency stability can be ruined because of the
creation of a loop

April 30, 2017
Either compensation (BW reduction) or oscillation
risks should be accepted
28
Common-gate stage design

Trade-off between noise figure and input matching
April 30, 2017
29
Common-gate stage design

Input resistance of 50Ω is achieved by proper Bias
parameters
1
Rin 
g m  g mb

The drawback is worse Noise Figure:
4 KTg m

4 KTRs 
2
gm
gm
NF 
1
4 KTRs
Rs
if :
April 30, 2017
Rs ~ 1
gm

NF  1  
30
Common-gate stage design

Long channel devices (1-10μm)
γ=0.66

Short channel devices(0.18-0.5μm)
γ=3~4

High noise Figure in recent technology
April 30, 2017
31
Resistive termination by Inductive
Degeneration
LS
X
Vref
For Bias
April 30, 2017
32
Resistive termination by Inductive
Degeneration

Freedom in tuning Zin is obtained
g m L1
1
Z in 
 L1 S 
 LS S
CGS
CGS S





L1 is tuned to have 50Ω by the first statement
LS is added to reject the second and third statement
Vref is placed for Bias
The circuit is designed in an iterative process
L1 degenerates the gain
April 30, 2017
33
Bipolar LNA with Replica Biasing

I1 is passed through Q1 so thermal matching is obtained
April 30, 2017
34
Bipolar LNA

R1 & R2:




Compensate the effect of β (Base Current)
Reducing the value of C1 that rejects the Biasing
circuit’s Noise (Since the input Impedance is
increased, smaller capacitor can be used)
R2 causes approximately equal VBE for transistors so
thermal matching is obtained
Noise of R1 can not be rejected because the signal
will be grounded if the capacitor is placed before R1
April 30, 2017
35
Bipolar LNA

Noise Figure is considered as the following:
Shot noise of Collector
4KT/2gm
Rb
g m RS
1
NF  1  

RS 2 g m RS 2
 1  2 g m Rb 
Rb
g m RS
1
NFmin  

 RSOPT 
RS 2 g m RS 2
gm
 NFmin  1 
April 30, 2017
Shot noise of Base
4KTgm/2β
1  2 g R 
m
b

36
IP3 calculation
IC  I S

VBE  Vin 
exp
VT
2
3


 VBE 
Vin 1  Vin  1  Vin 
 1 
 I S exp 
       ...

 VT   VT 2  VT  6  VT 
4 1
iip 3 
 2 2VT
3 3
voltage
April 30, 2017
if Rin  50 then iip 3  12.3dBm
Power
37
Comparison



With MOS, better values of iip3 is considerable
MOS does not have shot noise so we do not have an
optimum value for noise
In order to have controlled NF, discrete circuit has to be
implemented because inside the IC, β and Rb are not
controllable
April 30, 2017
38
Some State-Of-The-Art LNAs

MEYER & MACK



Common-Base LNA
CMOS LNA: Karanicolas


IEEE Journal of Solid-State Circuits, Vol.29,
PP.350-355, March 1994
IEEE Journal of Solid-State Circuits, Vol.31,
PP.1939-1944, December 1996
LNA implemented with MESFETs
April 30, 2017
39
A 900MHz Bipolar LNA

MEYER & MACK
Defines DC level
of the output
Negative feedback
April 30, 2017
Opens the feedback at high frequencies
40
A 900MHz Bipolar LNA

First Stage:



Second Stage:




provides much of the gain
controls Noise Figure
Lower Gain
Controls Zout
Rf & RE effectively linearize the second stage
Le improves ip3 because of its re like effect

re is proportional to VT, ip3 (voltage)=2√2VT
April 30, 2017
41
A 900MHz Bipolar LNA

Thermal stability of the gain is considered as follows:
 Vb1  R1I c  VBE 3  VBE 2
Vb1  VBE 3  VBE 4
 0  I C1 
RC1
Vb1  VPTAT  2VBE
VPTAT
 I C1 
RC1
I C1
VPTAT
Gain of the first stage  g m1.RC1 
RC1 
 cte
VT
VT
April 30, 2017
42
A 900MHz Bipolar LNA

Le also provides conjugate matching of the input
g m Le
1
Z in  rb 
 Le S 
C
C S

With proper choice of gm, Le, CΠ:
g m Le
Z in  rb 
 50
C

The last two terms cancel
April 30, 2017
43
Common-Base LNA

The source resistance Rs linearizes the input-output
characteristic
Rin
April 30, 2017
44
Common-Base LNA

Rin is used to reduce current but it worsens the NF

Although BJT, but the circuit is very linear

1/gm<<Rs so in the voltage divider, the lower voltage
causes little variation and consequently better linearity
April 30, 2017
45
Common-Base LNA

With Rin=0
Rs=1/gm=50Ω
iip3≈-6.8dBm


High reverse isolation is achieved if the base bias is
properly bypassed
Relatively high noise figure is the drawback
April 30, 2017
46
MOS LNA

Karanicolas
M3
For Bias
April 30, 2017
47
MOS LNA



Vref and W/L of M3 changes the Bias current
The capacitor makes the gain for M1 otherwise
bypasses the feedback in AC
The bias current is reused to provide a higher
equivalent transconductance: (gm1+gm2)
 1
Gain  g m1  g m 2 
 g ds1

1  g m1  g m 2


g ds 2  g ds1  g ds 2
The circuit is followed by a similar stage so as to
drive a 50-Ω load
April 30, 2017
48
MOS LNA

900-MHz LNA & 2.7-V Vcc in CMOS 0.5μm technology




NFmin=1.9 dB
 External matching network
Gain=15.6 dB
iip3=-3.2 dBm
20mW power consumption
7mA
April 30, 2017
49
LNA implemented with MESFETs

Recently implemented with CMOS
April 30, 2017
50
LNA implemented with MESFETs

Both M1 and M2 use the same Bias current


Power is saved
Drawback

The parasitic bottom plate of C1 limits the RF gain at
node X or Y
April 30, 2017
51
BW enhancement

1.5GHz CMOS LNA
April 30, 2017
52
BW enhancement




On-chip and off-chip inductors are employed
Ls and L1 create conjugate matching at the input
At 1.5GHz, high gain is provided by the on-chip inductor
LD
Roles of using M2 by increasing the reverse isolation:



Reduces LO leakage of the following mixer
This Cascode device minimizes the feedback from
output to input
Inductive peaking is caused by LD

It can cause near 500MHz increase in BW
April 30, 2017
53
Mixer, general considerations

Multiplier
(Weak LO)
Mixer
(Large LO)
instrumentation

Passive
April 30, 2017
Active
54
active mixer




The circuit does not provide Gain
Otherwise
passive
Active
Sample of an active mixer on the next slide
The drain current of M1 multiplied by a square wave
routed to R1 and R2 alternately
LO signal is powerful thus either M2 or M3 is off

Cascode amplifier is obtained
April 30, 2017
55
Active mixer
April 30, 2017
56
Active Mixer
Gain   g m1 .R1
Fourier expansion of the pulse
 4  1 
VIF  VRF .g m1 .R1 .  
   2 
Multiplication of two sine waves
VRF
VIF
50Ω
e.g. 1500Ω
VLO
April 30, 2017
57
Active Mixer
G power
April 30, 2017
 VIF 2 
 1500 
VIF
 50 
  2   20 log
 10 log

VRF
 1500 
 VRF 
 50  dB
GVoltage
58
SSB and DSB Noise Figure


SSB: the desired signal spectrum resides on only one
side of the spectrum (a common case in heterodyne receivers)
DSB: the desired signal spectrum resides on both sides
of the spectrum (a common case in ZeroIF receivers)
April 30, 2017
59
SSB NF

Upon downconversion,
1.
2.
3.
the signal
the noise in the signal band
the noise in the RF band
Translated to ωIF
IF noise
April 30, 2017
60
SSB NF

If:
The input frequency response of the mixer is the same for:
1.
2.

The signal band
The image band
Then:
Output SNR=½ Input SNR
NFnoiseless mixer=3dB
April 30, 2017
61
DSB NF


The input and Output SNRs are equal
NFnoiseless mixer=0 dB
April 30, 2017
62
SSB NF vs. DSB NF
SSBNF  DSBNF  3dB
 RF noise components around 3ωRF, 5ωRF, …are downconverted
to the IF further increasing the output noise power
 Often negligible here but not in phase noise calculation
April 30, 2017
63
Single Balanced Mixers

Single Balanced: differential LO but a single-ended RF
April 30, 2017
64
Double Balanced Mixers

Both LO and RF signals are differential
April 30, 2017
65
SB vs. DB Mixers


In SB, M2 & M3 operate as a differential pair so LO
amplified. If I F not much lower than LO, the LPF following
the mixer may attenuate IF signal in order to suppress LO
feedthrough thus the large LO content desensitizes the IF
signal
In DB, M3-M4 and M5-M6, add the amplified IF with
opposite phases providing the first-order cancellation
April 30, 2017
66
Comparison


Single ended operation at the output ruins the
advantages of double balanced configuration
Low-frequency components in RF signal appear at the
output without attenuation called direct feedthrough



It also increases the noise figure of the mixer
Despite the advantages of differential output, singleended output is required because of IF SAW filter
present as the next stage
External LC network makes the conversion
April 30, 2017
67
Conversion of differential to single-ended
output

To reduce the effect of direct feedthrough and achieve
the maximum gain
April 30, 2017
68
Mixer Spurious Response



Mixer as a nonlinear device, generates various crossproducts of the RF and LO signals |mωRF ± nωLO |
Except for |ωLO-ωRF|, such components do not fall in the
IF band
Spurious response for different combination of m and n
must be analyzed in the design
April 30, 2017
69
BJT Mixers_a

RF applied to Base
April 30, 2017
70
BJT Mixers_b

RF applied to Emitter
I
April 30, 2017
71
Comparison

The nonlinearity in both of them is because of re
Vt
re 
I
VRE  IRE
to reduce nonlinearity :
RE  re  VRE  4Vt
April 30, 2017
RE
72
Comparison


Linearity of circuit b is better than a because in a, there
would be a large voltage drop due to increase of RE.
The presence of the capacitor in circuit b avoids DC so
larger values of RE is possible
I

VRF
1
RS  RE 
gm
increasing RE causes:


Lower Gain
More input noise
April 30, 2017
73
Comparison

RE reduces the effect of nonlinearity caused by 1/gm
but there are some other reasons for nonlinearity:

Two extremely nonlinear capacitors exist
Cb proportional to I
April 30, 2017
Cb proportional to I
74
Comparison


The equivalent capacitor of the upper tree (switches),
halt proper operation of the ideal switch
There some methods of reducing these capacitors with
their own drawbacks




Reducing transistor sizes (upper tree) but larger rb
increases noise
Shortening the transition time by larger LO
amplitude but reducing switching time
Designing a circuit to sense the voltage at point P
and providing the required current for the capacitors
at the moment
Deleting the current of the bottom transistor at the
switching time of the upper transistors
April 30, 2017
75
Comparison

Reverse Isolation of circuit b is better:


Zin of circuit b is controlled by RE but in a by βRE



Leakage of LO at point P transfers to the input
through Ccb in circuit a but in b, there exists no
collector-emitter capacitor so leakage is smaller
β is frequency dependent
Why is Zin important?
The behavior of external filters like SAW or Crystal ones
is defined by source impedance ZS and Load impedance
Zin.

If frequency dependent, there would be ripples in
passband and the attenuation frequencies vary
April 30, 2017
76
One Method of Linearization




Gilbert Cell, extensively used, allows linearization of RF
port
Different Emitter areas are used in differential pairs
Two such pairs are cross-connected
Transconductance Gm grows as a function of the input
voltage
April 30, 2017
77
One Method of Linearization

Gm vs. Vin
April 30, 2017
78
CMOS Mixers

Active Mixer
April 30, 2017
79
CMOS Mixer


The upper tree requires greater voltage swings to be able to
switch( at least VTH ) than its Bipolar counterparts
For lowering the swing for upper tree switching:



Increasing the ratio W/L
Lowering the upper tree’s current thus the current of M1
is decreased
gm of M1 decreases thus total gain is
reduced
For the purpose of linearizing M1:
 (VGS-VT)

transconductance
 noise figure
 conversion gain
 The trade-off between Gain and Linearity is
problematic
April 30, 2017
80
Passive CMOS Mixer

M1 and M2 are driven by complementary phases of LO
April 30, 2017
81
Passive CMOS Mixer

Advantages:

Higher ip3

if a large gate-source overdrive voltage
(VGS-VT) is used for M1 and M2 in the on state so
that VRF does not vary their on-resistance


No power is drawn from the supply voltage
Drawbacks:



Because of the gain below unity, the noise figure of
the following stages is magnified
The large width requirement of M1 and M2 for low
on-resistance leads to capacitive feedthrough from
LO to IF
The linearity advantage diminishes at low supply
voltages (sub micron new devices)
 because of being near subthreshold region, Ron is
severely nonlinear and VRF varies the switch onresistance, thus introducing distortion
April 30, 2017
82
Noise in Mixers

Sources of noise in a single-balanced mixer:
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83
Noise in Mixers
1.
2.
3.
4.
5.
6.
Thermal noise due to the base resistance of Q1
Collector shot noise of Q1
Thermal noise due to the emitter resistor RE
Collector shot noise of Q2 and Q3
Thermal noise due to the base resistance of Q2 and Q3
In the IF path, resistors RC1 and RC2 introduce thermal
noise
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84
Noise in Mixers







Noise 1, 2, 3, translated from RF to IF
Images of these noises also translated to IF
1/f noise here is not problematic because of the low
frequency. It is up converted. Going to LO frequency, it
is filtered
IF filter sets the BW, so only this value is taken from
noise (e.g. 30KHz in GSM)
When each of the two switches in on instantaneously,
noises 4 and 5 and their images contributes to IF
When Q2 and Q3 are on simultaneously for a part of a
period, the two transistors amplify noises 4 and 5 to the
output
Noise 6 directly appears at IF frequency
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85
Noise in Mixers

Spice Models would not be able to calculate noise of the
mixer so:





Sine wave sources are used as sources of noise with
the same frequency
Transient analysis calculates the gain
The process is also done at image frequencies
Noise gains are added
The blue highlighted statement of the previous side is
problematic
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86
Intuitive remedies to reduce noise




Increasing LO swing is the solution for Q2 and Q3 not
being on simultaneously
Trying to reduce Cp by reducing the size of Q1,Q2,Q3,
lowers noise sources 4 and 5

Cp is the parasitic capacitance arising from the
base-emitter junction of Q2 and Q3 and C-B
and C-substrate of Q1
For reducing noise 5, larger Q2 and Q3 are effective
because of lower rb
In Q1, the noise number 2 is equal to 2qIc1
I n  2qI C 1
2
Vn
April 30, 2017
2
2qI C 1
2qVT


2
I C1
gm
87
Intuitive remedies to reduce noise




Increasing the lower stage current is effective
This circuit increases
the lower transistor’s
current and lowers the
collector current
of Q2 and Q3
The upper transistors
switch better and Q1
introduces lower noise
DC source can be made a spike
and reject the noise of switching
at the switching instant.
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88
New methods to calculate noise of
mixers



Chris Hull method
Harmonic Balance
Physical model of “Darabi”
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89
Chris Hull method






The circuit is nonlinear when considered totally but at
the instant of taking a picture of it, it is linear
The circuit is periodically linear relative to LO signal
So the impulse response of each noise source is a
function of the instant of injecting it at the period of LO
For each source of noise there is a three dimensional
impulse response including the instant of applying the
impulse in LO period
After performing two dimensional FFT, for each
frequency, the gain is calculated for all of the noise
sources
The total noise is calculated
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90
Physical model of “Darabi”

In Zero-IF
1.
1/f noise of the upper tree leaks to the output with
gain
2.
1/f noise of the lower stage leaks to the output at
the same condition
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91
Physical model of “Darabi”


In Zero-IF, 1/f noise of the upper tree leaks to the output
with gain
The simultaneous switching of the transistors of the upper
tree can be modeled as a DC offset that leads to
appearing the RF frequency in the output:
COS t DC
RF
Offset
 ACOS  LO t 
The equivalent noise of the upper tree
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92
Physical model of “Darabi”

Added noise to the LO signal changes the switching
point so there will be a new zero-crossing
Vn
LO
+Vout -
+
LO
-
gm section
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93
Physical model of “Darabi”
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94
Physical model of “Darabi”
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95
Physical model of “Darabi”
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96
Physical model of “Darabi”
Δt
Vn
Vn
S 
t
New zero-crossing
A random function with the amplitude of 2IR or -2IR
is added to the output
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97
Physical model of “Darabi”
iON
t
2 I  T : the period of

T
2
V
V 
 4 I n  4 I n LO
ST
2 S
LO
If LO is a sin with the amplitudeA
S  2 A
 iON
LO    A sin t
LO    A sin t
Vn LO
IV
 4I
 n
2  2 A   LO A
Vn
i
 4I
4A
ON
April 30, 2017
98
Physical model of “Darabi”
upper tree as the source of noise:
2 g mVin
SNR  
Vn
4I
ST
ST g m Vin



2 I Vn
In this analysis, only low frequency noise (e.g. 1/f) is
considered because it is assumed that the variation of
noise is much slower than LO
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99
Physical model of “Darabi”
In BJT :
Long Channel
g m  I  cte
V
T
g
2
 m 
V
I
eff
In MOS :
Short Channel 
April 30, 2017
V
eff
 Esat L
g
2
m
 2
V
V  Esat L
I
eff
eff
100
Physical model of “Darabi”
Short Channel :
SNRMOS



Vin
ST
1



2 VGS  VT Vn
In order to reduce noise:
1. LO must have square wave shape
2. Veff of the lower transistor must be reduced:
3. For gm to remain unchanged, W/L must be increased
that causes Cp and 1/f noise of the lower transistor to
grow
1/f noise is not important in Low-IF but considerable in
Zero-IF
1/f noise of the lower transistor has to be considered as
a term added to 1/f noise calculated before
April 30, 2017
101
Physical model of “Darabi”

To consider the effect of 1/f noise of the upper tree:
LO feedthrough can be measured and the value of Voffset
that causes the LO feedthrough is calculated
Mixer gain
ion
1/f noise
VOS
 gm 
 Vni

2A
2
1
f
The ratio of equivalent offset voltage and the amplitude of LO
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102
Calculation of Indirect Noise
Vn locates itself on Cp and the resulting current is noisy that
directly appears at the output that is called “indirect noise”
Vn
LO+
April 30, 2017
LO-
103
Calculation of Indirect Noise
dVCP
2 T2
ion  0 iCP t dt , iCP  C P 
T
dt
2 T2
dVA
2
 T 

 ion  0 C P 
dt  C P  VA    VA 0
T
dt
T
 2

2
 ion  C P  Vn
T
: The noise is slow
The noise is called “indirect” because it is converted to the
current of capacitor and then transfers to output
April 30, 2017
104
Noise in mixers
Load noise at IF frequency
Thermal noise of the input tr.
2


1
4
KT

2
Vn2  8KTR  noise
 g   gm R   n
L f
L
m 
& thermal noise of the
Gain of mixer
intermedia te stage
The effect of Image frequencies+ thermal noise at harmonics
n: represents the effect of harmonics
2
1
1



n  2 1  2  2      
 3 5
 4
April 30, 2017
105
Noise in mixers
If thermal noise is more important than 1/f noise as in Low-IF:
IR 2
2


4
KT



Vn2  8KTR  8KT  L  g 2 gm R   n
L
L
m 
A
Thermal noise of upper tree calculated by direct calculation method
April 30, 2017
106
Contents
1.
2.
3.
4.
5.
6.
7.
8.
9.
Introduction
Basic concepts
Digital modulation, Spectral control, Detection
Multiple access standards, TDM, CDM, OFDM
TRx architecture
LNA and Mixer
Oscillator
Frequency Synthesizer
Power Amplifier
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107
Oscillator





LC vs. VCO Design
Phase noise considerations
Loop design
Inductor limitations
Quad signal generation
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108
General Oscillatory System

RF oscillator viewed as a feedback circuit
Y S 
H S 

X S  1  H  S 
if : H S   10
April 30, 2017

The feedback system oscillates
109
General Oscillatory System


The output spectrum on the spectrum analyzer looks
like:
A wideband oscillation will be present on the spectrum
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110
General Oscillatory System
Saturation limits the
amplitude of oscillation
average gain
small signal
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111
General Oscillatory System

1.
2.
For Oscillation:
A start-up signal is required
Noise growth has to be limited


noise
Average loop gain returns to unity
 Stable amplitude
A frequency-selective network called “resonator” is
required:
1.
2.
To set the frequency of oscillation
To reject the harmonics
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112
General Oscillatory System
50-10=40Ω
can not oscillate
Oscillates but its frequency is unknown
 a frequency selective circuit is required
 noise is the start-up signal
 in large amplitudes the negative resistance
reduces
50......  50
 60 55 50
oscillatio n condition
 nonlinear elements do the function of
limiting
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113
ALC

A mechanism to define the amplitude of oscillation:
April 30, 2017
114
ALC
April 30, 2017
115
ALC




A detector senses the output signal to be compared with
a reference voltage thus the gain of H(S) is controlled
The output of this oscillator is a pure sine with minimum
harmonics
The resonator in oscillating circuits rejects harmonics
but in this circuit, the gain is set to unity with control
circuit and no harmonic is produced
The drawback is that the complexity and phase noise
of the control circuit is high
April 30, 2017
116
Desired output of an RF oscillator



Previously analysis of mixers proved that square wave
is ideal as the output of an RF oscillator
generally the output of Oscillators are sine waves
because of bandwidth limitation
Consequently, a large-amplitude sine wave is required
to represent a square wave at zero crossing points
April 30, 2017
117
LC vs. VCO




Following the feedback model, a one-transistor LC
oscillator includes an LC tank at the collector with a
feedback to base or emitter
In resonance, the impedance of the LC tank is real so
the phase difference between its current and voltage is
zero.
For a total phase shift equal to zero, the feedback must
compensate for the transistor phase shift.
The important issue is that a low resistive load seen at
the emitter, 1/gm


Reduces the Q of the tank
The loop gain drops below unity and oscillation is
prevented
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118
LC vs. VCO

The solution is transforming the impedance to a higher
value before it appears in parallel with the tank
April 30, 2017
119
LC vs. VCO

A transformer can do the task:


The value “ n2⁄gm” is transformed
The loop gain is:
2


1
n
1
g m 
RP   g m RP
n  gm
n



Reduced loop gain lowers the required nonlinearity to come
to the conditions of oscillation
RP is the equivalent resistance of the resonator

Lower phase noise is obtained
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120
LC vs. VCO


Passive impedance transformation is achieved by
utilizing tanks with capacitive or inductive dividers
Colpitts and Hartley are the examples
Colpitts:
April 30, 2017
Hartley:
121
LC vs. VCO

Different models for implementation
C1
C2
C2
C1
April 30, 2017
Butler
122
VCO


The circuit in which the output frequency of an oscillator
is controlled by a voltage is called Voltage-Controlled
Oscillator (VCO)
In LC implementations (part of) the tank capacitance
can be provided by a reverse-biased diode
April 30, 2017
123
VCO


Each Diode is actually a varactor but in VCO IC, for
achieving higher capacitance a larger Diode is incorporated
The nonlinearity of the circuit should not be high

Mixing results in transmission of 1/f and thermal noise
to RF frequency
April 30, 2017
phase noise is generated
124
VCO

The operating region of the varactor is before the peak
operating region
of varactor
April 30, 2017
125
VCO

The nonlinearity of the varactor's capacitor generates
phase noise (the value of it changes in the period of the
sine)

Two Circuits to reduce the nonlinearity of the
varactor are as the following:
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126
LC vs. VCO


Colpitts is better accepted because of its only one
inductor usage
Both of them have two drawbacks:


To make the effect of the nonlinear g_m negligible
on the Q of the tank we need a large ratio in the
tapped inductors or capacitors.
Only a single-ended output is provided
April 30, 2017
127
VCO


The circuit in which the output frequency of an oscillator
is controlled by a voltage is called Voltage-Controlled
Oscillator (VCO)
In LC implementations (part of) the tank capacitance
can be provided by a reverse-biased diode
April 30, 2017
128
Phase Noise





Noise can influence both amplitude and frequency of
the oscillator but the latter is more important
Random deviation of the frequency is considered:
For a nominal periodic sine :
n t 
X t   A cos t  n t 
is the small random excess phase representing
variation in the period called phase noise
For :
n t   1  X t   A cos C t   An t sin C t 

That is the spectrum of  n t  is translated to ±ωC
exhibiting skirts around the carrier frequency
April 30, 2017
129
Phase Noise


We consider a unit bandwidth at an offset Δω with
respect to ωc and calculate the noise power in this
bandwidth and divide the result by the carrier average
power
Phase noise is dropping of the noise power per hertz
with respect to carrier
April 30, 2017
130
Importance of phase noise



Incorporating an oscillator with a finite phase noise, an
adjacent channel with a large interferer and the wanted
signal both downconvert with two overlapping spectra
The wanted signal is drawn at the skirt of the adjacent
channel
The wanted signal suffers from noise due to the tail of
the interferer
April 30, 2017
131
Phase Noise
April 30, 2017
132
Driscoll Circuit
VB
April 30, 2017
133
Driscoll Circuit

Minimum phase noise is achieved if:
1. Q of the resonator is high enough
2. Nothing loads the tank (transformer is used)
3. The differential pair acts as a limiter (the
whole current is switched to one of the
transistors of the differential pair
4. Q1 can become nonlinear but the limiter in diff
pair starts limiting long before that.
5. Oscillation is done at the point with maximum
slope
April 30, 2017
134
Driscoll Circuit
1.
2.
3.
4.

A buffer must separate the resonator and the
limiter to prevent the Upconversion of 1/f
noise
Transistors with low thermal and 1/f noise
must be selected
Symmetric limitation is done. (differential pair
is completely symmetric)
Soft
limiter
Sharp limiting is desirable
Soft
Limiter
Soft limiter functions at large
Hard Limiter
amplitudes causes the
Hard limiter
elements of the circuit to be
nonlinear and causes clipping
April 30, 2017
135
Driscoll Circuit

Another theory for phase noise reduction states that:
The transistor switches on instantly and injects a sharp
current in to the resonator thus injected noise is
reduced
April 30, 2017
136
Quadrature Signal Generation
Methods





RC/CR
+/Divider
LLL
Quadrature OSC (with feedback loop)
April 30, 2017
137
RC/CR

The advantage is its simplicity
I
Q
April 30, 2017
138
RC/CR

The drawbacks:


There is only one frequency in which the amplitudes
of I and Q are equal
Dependency to the mismatch of R’s and C’s
April 30, 2017
139
+/
If addition and subtraction of two vectors are equal then
the two vectors are in Quadrature phases
I
Q
April 30, 2017
140
+/
Soft Limiting equalizes the amplitudes without any
clipping
I
Q
April 30, 2017
141
divider


A master-slave flipflop which divides a signal at 2ω1 by
a factor 2, generates Quadrature periodic signals with
frequency ω1
Duty cycle is 50% otherwise phase error will happen
I
Q
April 30, 2017
142
divider

If the duty cycle of the input is not 50-50, the remedy
is:
I
2
2
Q

But to have the frequency equal to f, a VCO that
generates 4f is required
April 30, 2017
143
LLL: Level Lock Loop


For sine wave input
Vref increases up to the value that duty cycles reach to
50% and a 90° phase difference is obtained
in
+
-
I
÷2
Q
Vref
integrator
April 30, 2017
Phase
detector
144
Quadrature OSC (with feedback loop)


Coupling two oscillators in such a way to make them
oscillate with 90° difference in phase
Measuring the phase difference and controlling the bias
current leads to precise 90°-phase shift
April 30, 2017
145
Wide tune Range VCO

The characteristic curve of a varactor's capacitor looks:
C
10 pf
3pf
-10v
April 30, 2017
0v
VC
146
Wide tune Range VCO


CV is very nonlinear
Having the required voltage range on the IC is not easy.
(no -10V on the IC)
f 
1
2 LC

1
2 LC f  C v 
if
Cf  0
if
C f  C v  10% VCO  40% C v
April 30, 2017
 10% VCO  20% C v
147
Wide tune Range VCO


For wide ranges with no phase noise Cf is varied instead of
Cv
In the field of instrumentation, VCO‘s with high frequency
range is required

In these applications the whole band is
upconverted to a high frequency and then
multiplied by the next mixer
Mixing is done in several steps

0 – 10GHz

20 – 30GHz
April 30, 2017
20 GHz
#

20.2 GHz
200 MHz
#

21.4 MHz
#
221.4 MHz
148
Wide tune Range VCO

1.
2.
3.
4.
Different old IF frequencies:
455KHz : AM
10.7MHz: FM
21.4MHz: Spectrum analyzers
70MHz, 140MHz, 280MHz :Analog satellite
April 30, 2017
149