6.776
High Speed Communication Circuits
Lecture 17
Noise in Voltage Controlled Oscillators
Michael Perrott
Massachusetts Institute of Technology
April 12, 2005
Copyright © 2005 by Michael H. Perrott
VCO Noise in Wireless Systems
Zin
From Antenna
and Bandpass
Filter
PC board
trace
Zo
Mixer
RF in
Package
Interface
IF out
To Filter
LNA
LO signal
VCO
Reference
Frequency
Frequency
Synthesizer
Phase
Noise
fo
ƒ
ƒ
f
VCO noise has a negative impact on system performance
- Receiver – lower sensitivity, poorer blocking performance
- Transmitter – increased spectral emissions (output spectrum
must meet a mask requirement)
Noise is characterized in frequency domain
M.H. Perrott
MIT OCW
VCO Noise in High Speed Data Links
Zin
From Broadband
Transmitter
PC board
trace
Zo
Data
Package
Interface
In
Amp
Clock and
Data
Recovery
Clk
Data Out
Data In
Phase
Detector
Clk Out
Loop
Filter
VCO
ƒ
Jitter
VCO noise also has a negative impact on data links
- Receiver – increases bit error rate (BER)
- Transmitter – increases jitter on data stream (transmitter
must have jitter below a specified level)
ƒ
Noise is characterized in the time domain
M.H. Perrott
MIT OCW
Noise Sources Impacting VCO
Time-domain view Jitter
out(t)
t
Frequency-domain view
Sout(f)
PLL dynamics
set VCO
carrier frequency
(assume noiseless
for now)
vc(t)
Phase
Noise
Extrinsic
noise
Intrinsic
noise
vn(t)
vin(t)
ƒ
Extrinsic noise
ƒ
Intrinsic noise
fo
f
out(t)
- Noise from other circuits (including PLL)
Noise due to the VCO circuitry
M.H. Perrott
MIT OCW
VCO Model for Noise Analysis
Time-domain view Jitter
out(t)
t
Note: Kv units are Hz/V
Frequency-domain view
Sout(f)
PLL dynamics
set VCO
carrier frequency
(assume noiseless
for now)
vc(t)
ƒ
Phase
Noise
Extrinsic
noise
Intrinsic
noise
vn(t)
vin(t)
2πKv
s
Φvn(t)
f
fo
Φout
2cos(2πfot+Φout(t))
out(t)
We will focus on phase noise (and its associated jitter)
- Model as phase signal in output sine waveform
M.H. Perrott
MIT OCW
Simplified Relationship Between Φout and Output
PLL dynamics
set VCO
carrier frequency
(assume noiseless
for now)
vc(t)
Extrinsic
noise
Intrinsic
noise
vn(t)
vin(t)
2πKv
s
Φvn(t)
Φout
2cos(2πfot+Φout(t))
ƒ
Using a familiar trigonometric identity
ƒ
Given that the phase noise is small
M.H. Perrott
out(t)
MIT OCW
Calculation of Output Spectral Density
ƒ
Calculate autocorrelation
ƒ
Take Fourier transform to get spectrum
ƒ
- Note that * symbol corresponds to convolution
In general, phase spectral density can be placed into
one of two categories
- Phase noise – Φ (t) is non-periodic
- Spurious noise - Φ (t) is periodic
out
out
M.H. Perrott
MIT OCW
Output Spectrum with Phase Noise
ƒ
Suppose input noise to VCO (vn(t)) is bandlimited,
non-periodic noise with spectrum Svn(f)
- In practice, derive phase spectrum as
ƒ
Resulting output spectrum
SΦout(f)
Ssin(f)
1
-fo
fo
f
*
f
Sout(f)
1
dBc/Hz
M.H. Perrott
-fo
fo
SΦout(f)
f
MIT OCW
Measurement of Phase Noise in dBc/Hz
Sout(f)
1
dBc/Hz
-fo
ƒ
ƒ
fo
SΦout(f)
f
Definition of L(f)
- Units are dBc/Hz
For this case
- Valid when Φ
is small in deviation (i.e., when carrier
is not modulated, as currently assumed)
M.H. Perrott
out(t)
MIT OCW
Single-Sided Version
Sout(f)
1
dBc/Hz
fo
ƒ
ƒ
SΦout(f)
f
Definition of L(f) remains the same
- Units are dBc/Hz
For this case
- So, we can work with either one-sided or two-sided
spectral densities since L(f) is set by ratio of noise
density to carrier power
M.H. Perrott
MIT OCW
Output Spectrum with Spurious Noise
ƒ
Suppose input noise to VCO is
ƒ
Resulting output spectrum
SΦout(f)
Ssin(f)
1
-fo
fo
f
*
-fspur
fspur
1 dspur 2
2 fspur
f
Sout(f)
1 dspur 2
2 fspur
1
dBc
-fo
M.H. Perrott
fo
fspur
f
MIT OCW
Measurement of Spurious Noise in dBc
Sout(f)
1 dspur 2
2 fspur
1
dBc
-fo
ƒ
fo
f
fspur
Definition of dBc
- We are assuming double sided spectra, so integrate over
positive and negative frequencies to get power
ƒ Either single or double-sided spectra can be used in practice
ƒ
For this case
M.H. Perrott
MIT OCW
Calculation of Intrinsic Phase Noise in Oscillators
Zactive
Active
Negative
Resistance
Generator
Zres
Vout
Active Negative
Resistance Zactive
inRn
1
= -Rp
-Gm
Resonator
Zres
Vout
Resonator
Rp inRp
Cp
Lp
ƒ
Noise sources in oscillators are put in two categories
ƒ
We want to determine how these noise sources influence
the phase noise of the oscillator
- Noise due to tank loss
- Noise due to active negative resistance
M.H. Perrott
MIT OCW
Equivalent Model for Noise Calculations
Active Negative
Resistance
inRn
1
= -Rp
-Gm
Noise Due to Active
Negative Resistance
inRn
Zres
Zactive
Vout
Resonator
Rp inRp
M.H. Perrott
Lp
Compensated Resonator with Noise from Tank
1
= -Rp
-Gm
Vout
Rp inRp
Noise Due to Active
Negative Resistance Noise from Tank
inRn
Cp
inRp
Ztank
Vout
Cp
Lp
Ideal Tank
Cp
Lp
MIT OCW
Calculate Impedance Across Ideal LC Tank Circuit
Ztank
Cp
ƒ
Lp
Calculate input impedance about resonance
=0
M.H. Perrott
negligible
MIT OCW
A Convenient Parameterization of LC Tank Impedance
Ztank
Cp
Lp
ƒ
Actual tank has loss that is modeled with Rp
ƒ
Parameterize ideal tank impedance in terms of Q of
actual tank
- Define Q according to actual tank
M.H. Perrott
MIT OCW
Overall Noise Output Spectral Density
Noise Due to Active
Negative Resistance Noise from Tank
inRn
ƒ
inRp
Ztank
Vout
Ideal Tank
Cp
Lp
Assume noise from active negative resistance element
and tank are uncorrelated
- Note that the above expression represents total noise that
impacts both amplitude and phase of oscillator output
M.H. Perrott
MIT OCW
Parameterize Noise Output Spectral Density
Noise Due to Active
Negative Resistance Noise from Tank
inRn
ƒ
ƒ
Ztank
Vout
inRp
Ideal Tank
Cp
Lp
From previous slide
F(∆f)
F(∆f) is defined as
M.H. Perrott
MIT OCW
Fill in Expressions
Noise Due to Active
Negative Resistance Noise from Tank
inRn
inRp
Ztank
Vout
Ideal Tank
Cp
Lp
ƒ
Noise from tank is due to resistor Rp
ƒ
Ztank(∆f) found previously
ƒ
Output noise spectral density expression (single-sided)
M.H. Perrott
MIT OCW
Separation into Amplitude and Phase Noise
Noise Due to Active
Negative Resistance Noise from Tank
inRn
inRp
Ztank
Ideal Tank
Vout
Cp
Lp
Amplitude
Noise
Vsig
vout
A
t
ƒ
Vout
A
t
t
Phase
Noise
Equipartition theorem (see Tom Lee, p 534 (1st ed.))
states that noise impact splits evenly between amplitude
and phase for Vsig being a sine wave
- Amplitude variations suppressed by feedback in oscillator
M.H. Perrott
MIT OCW
Output Phase Noise Spectrum (Leeson’s Formula)
Output Spectrum
Noise Due to Active
Negative Resistance Noise from Tank
inRn
inRp
Ztank
Vout
SVsig(f)
Ideal Tank
Cp
Carrier impulse
area normalized to
a value of one
L(∆f)
Lp
f
fo
∆f
ƒ
All power calculations are referenced to the tank loss
resistance, Rp
M.H. Perrott
MIT OCW
Example: Active Noise Same as Tank Noise
Active Negative
Resistance
inRn
ƒ
1
= -Rp Vout
-Gm
Resonator
Rp inRp
Cp
Lp
Noise factor for oscillator in this case is
L(∆f)
ƒ
Resulting phase noise
-20 dB/decade
log(∆f)
M.H. Perrott
MIT OCW
The Actual Situation is Much More Complicated
Rp1
inRp1
Tank generated
noise
Cp1
Lp1
Lp2
Vout
A
inM1
Cp2
Vout
M1
M2
Rp2
inRp2
Tank generated
noise
A
inM2
Vs
Transistor generated
noise
ƒ
ƒ
Ibias
Vbias
M3
inM3
Transistor generated
noise
Impact of tank generated noise easy to assess
Impact of transistor generated noise is complicated
- Noise from M and M is modulated on and off
- Noise from M is modulated before influencing V
- Transistors have 1/f noise
1
2
3
ƒ
out
Also, transistors can degrade Q of tank
M.H. Perrott
MIT OCW
Phase Noise of A Practical Oscillator
L(∆f)
-30 dB/decade
-20 dB/decade
10log (
∆f1/f
ƒ
3
fo
2Q
2FkT
Psig
(
log(∆f)
Phase noise drops at -20 dB/decade over a wide
frequency range, but deviates from this at:
- Low frequencies – slope increases (often -30 dB/decade)
- High frequencies – slope flattens out (oscillator tank does
not filter all noise sources)
ƒ
Frequency breakpoints and magnitude scaling are not
readily predicted by the analysis approach taken so far
M.H. Perrott
MIT OCW
Phase Noise of A Practical Oscillator
L(∆f)
-30 dB/decade
-20 dB/decade
10log (
∆f1/f
ƒ
3
fo
2Q
2FkT
Psig
(
log(∆f)
Leeson proposed an ad hoc modification of the phase
noise expression to capture the above noise profile
- Note: he assumed that F(∆f) was constant over frequency
M.H. Perrott
MIT OCW
A More Sophisticated Analysis Method
Ideal Tank
Amplitude
Noise
Vout
iin
Vout
Cp
A
Lp
t
Phase
Noise
ƒ
Our concern is what happens when noise current
produces a voltage across the tank
- Such voltage deviations give rise to both amplitude and
phase noise
- Amplitude noise is suppressed through feedback (or by
amplitude limiting in following buffer stages)
ƒ Our main concern is phase noise
ƒ
We argued that impact of noise divides equally
between amplitude and phase for sine wave outputs
What happens when we have a non-sine wave output?
M.H. Perrott
MIT OCW
Modeling of Phase and Amplitude Perturbations
Ideal Tank
Amplitude
Noise
Vout
iin
Vout
Cp
A
Lp
t
Phase
Noise
Phase
iin(t)
Φout(t)
iin(t)
τo
hΦ(t,τ)
t
Amplitude
iin(t)
iin(t)
τo
ƒ
t
Φout(t)
τo
t
τo
t
A(t)
A(t)
hA(t,τ)
Characterize impact of current noise on amplitude and
phase through their associated impulse responses
- Phase deviations are accumulated
- Amplitude deviations are suppressed
M.H. Perrott
MIT OCW
Impact of Noise Current is Time-Varying
Ideal Tank
Amplitude
Noise
Vout
iin
Vout
Cp
A
Lp
t
Phase
Noise
Phase
iin(t)
iin(t)
τo τ1
t
hΦ(t,τ)
Amplitude
iin(t)
iin(t)
τo τ1
ƒ
Φout(t)
t
Φout(t)
τo τ1
t
τo τ1
t
A(t)
A(t)
hA(t,τ)
If we vary the time at which the current impulse is
injected, its impact on phase and amplitude changes
- Need a time-varying model
M.H. Perrott
MIT OCW
Illustration of Time-Varying Impact of Noise on Phase
T
iin(t)
Vout(t)
qmax
Vout(t)
qmax
qmax
ƒ
t
∆Φ
Vout(t)
qmax
t
t
Vout(t)
qmax
t4
ƒ
∆Φ=0
t
t3
iin(t)
t
Vout(t)
t2
iin(t)
∆Φ
t
t1
iin(t)
t
t
t0
iin(t)
∆Φ
t
∆Φ
t
High impact on phase when impulse occurs close to the zero
crossing of the VCO output
Low impact on phase when impulse occurs at peak of output
M.H. Perrott
MIT OCW
Define Impulse Sensitivity Function (ISF) – Γ(2πfot)
T
iin(t)
Vout(t)
qmax
Vout(t)
qmax
qmax
t
t
Vout(t)
t
t
∆Φ
t
qmax
T
Γ(2πfot)
Vout(t)
qmax
t4
ƒ
∆Φ=0
t
t3
iin(t)
t
Vout(t)
t2
iin(t)
∆Φ
t
t1
iin(t)
t
t
t0
iin(t)
∆Φ
∆Φ
t
ISF constructed by calculating phase deviations as
impulse position is varied
Observe that it is periodic with same period as VCO output
M.H. Perrott
MIT OCW
Parameterize Phase Impulse Response in Terms of ISF
T
iin(t)
Vout(t)
qmax
Vout(t)
qmax
iin(t)
M.H. Perrott
hΦ(t,τ)
t
∆Φ
t
∆Φ
Vout(t)
qmax
t4
τo
t
t
t3
T
Γ(2πfot)
Vout(t)
qmax
t
∆Φ=0
t
t2
iin(t)
t
Vout(t)
qmax
iin(t)
∆Φ
t
t1
iin(t)
t
t
t0
iin(t)
∆Φ
t
t
Φout(t)
τo
t
MIT OCW
Examples of ISF for Different VCO Output Waveforms
Example 1
Example 2
Vout(t)
Vout(t)
t
t
Γ(2πfot)
Γ(2πfot)
t
ƒ
t
ISF (i.e., Γ) is approximately proportional to derivative
of VCO output waveform
- Its magnitude indicates where VCO waveform is most
sensitive to noise current into tank with respect to
creating phase noise
ƒ
ƒ
ISF is periodic
In practice, derive it from simulation of the VCO
M.H. Perrott
MIT OCW
Phase Noise Analysis Using LTV Framework
in(t)
hΦ(t,τ)
Φout(t)
ƒ
Computation of phase deviation for an arbitrary noise
current input
ƒ
Analysis simplified if we describe ISF in terms of its
Fourier series (note: co here is different than book)
M.H. Perrott
MIT OCW
Block Diagram of LTV Phase Noise Expression
Input Current
Normalization
in(t)
1
qmax
ISF Fourier
Series Coefficients
2
co
2
Integrator
Φout(t)
1
j2πf
Phase to
Output Voltage
out(t)
2cos(2πfot+Φout(t))
2cos(2πfot + θ1)
c1
2
2cos(2(2πfo)t + θ2)
c2
2
2cos(n2πfot + θn)
cn
2
ƒ
Noise from current source is mixed down from different
frequency bands and scaled according to ISF coefficients
M.H. Perrott
MIT OCW
Phase Noise Calculation for White Noise Input (Part 1)
Note that
in2
1
(q ( 2∆f
∆f
n
max
is the single-sided
noise spectral density
of in(t)
in(t)
1
X
-3fo
-2fo
-fo
fo
-fo
0
B
1
1
-fo
fo
1
D
-fo
2fo
1
2 i2
( (
1
f
-3fo
2 i2
( (
1
2cos(3(2π)fot + θn)
1
SA(f)
0
SB(f)
fo
0
SC(f)
fo
0
SD(f)
fo
0
fo
f
f
n
2 q
max 2∆f
f
-2fo
2 i2
( (
2cos(2(2πfo)t + θ2)
C
f
3fo
n
2 q
max 2∆f
1
f
-fo
2 i2
( (
f
1
2fo
n
2 q
max 2∆f
2cos(2πfot + θ1)
M.H. Perrott
0
1
1
A
2
qmax
SX(f)
2 i2
3fo
f
n
2 q
max 2∆f
-fo
f
MIT OCW
Phase Noise Calculation for White Noise Input (Part 2)
2 i2
(1(
ISF Fourier
Series Coefficients
SA(f)
A
n
2 q
max 2∆f
-fo
1
2 i2
( (
0
SB(f)
fo
f
n
2 q
max 2∆f
-fo
1
2 i2
( (
0
SC(f)
fo
-fo
1
2 i2
( (
0
SD(f)
fo
M.H. Perrott
0
fo
c1
2
C
c2
2
D
c3
2
f
n
2 q
max 2∆f
-fo
B
f
n
2 q
max 2∆f
f
co
2
Integrator
Φout(t)
1
j2πf
Phase to
Output Voltage
out(t)
2cos(2πfot+Φout(t))
MIT OCW
Spectral Density of Phase Signal
ƒ
From the previous slide
ƒ
Substitute in for SA(f), SB(f), etc.
ƒ
Resulting expression
M.H. Perrott
MIT OCW
Output Phase Noise
SΦout(f)
Sout(f)
1
dBc/Hz
f
0
-fo
0
fo
SΦout(f)
f
∆f
ƒ
We now know
ƒ
Resulting phase noise
M.H. Perrott
MIT OCW
The Impact of 1/f Noise in Input Current (Part 1)
Note that
in2
1
(q ( 2∆f
∆f
n
max
is the single-sided
noise spectral density
of in(t)
in(t)
1
X
-3fo
-2fo
-fo
fo
(1(
f
-fo
0
1
B
1
1
-fo
fo
1
D
-fo
2fo
1
2 i2
( (
1
f
-3fo
2 i2
( (
1
2cos(3(2π)fot + θn)
1
f
SA(f)
0
SB(f)
fo
0
SC(f)
fo
0
SD(f)
fo
f
f
n
2 q
max 2∆f
f
-2fo
2 i2
( (
2cos(2(2πfo)t + θ2)
C
3fo
n
2 q
max 2∆f
1
f
-fo
2fo
n
2 q
max 2∆f
2cos(2πfot + θ1)
M.H. Perrott
0
2 i2
1
A
2
qmax
SX(f) 1/f noise
2 i2
3fo
f
n
2 q
max 2∆f
-fo
0
f
fo
MIT OCW
The Impact of 1/f Noise in Input Current (Part 2)
2 i2
(1(
ISF Fourier
Series Coefficients
SA(f)
A
n
2 q
max 2∆f
-fo
1
2 i2
( (
0
SB(f)
fo
f
n
2 q
max 2∆f
-fo
1
2 i2
( (
0
SC(f)
fo
-fo
1
2 i2
( (
0
SD(f)
fo
M.H. Perrott
0
fo
c1
2
C
c2
2
D
c3
2
f
n
2 q
max 2∆f
-fo
B
f
n
2 q
max 2∆f
f
co
2
Integrator
Φout(t)
1
j2πf
Phase to
Output Voltage
out(t)
2cos(2πfot+Φout(t))
MIT OCW
Calculation of Output Phase Noise in 1/f3 region
ƒ
From the previous slide
ƒ
Assume that input current has 1/f noise with corner
frequency f1/f
ƒ
Corresponding output phase noise
M.H. Perrott
MIT OCW
Calculation of 1/f3 Corner Frequency
L(∆f)
-30 dB/decade
(A)
-20 dB/decade
(B)
∆f1/f
3
10log (
fo
2Q
2FkT
Psig
(
log(∆f)
(A)
(B)
(A) = (B) at:
M.H. Perrott
MIT OCW
Impact of Oscillator Waveform on 1/f3 Phase Noise
ISF for Symmetric Waveform
ISF for Asymmetric Waveform
Vout(t)
Vout(t)
t
Γ(2πfot)
t
Γ(2πfot)
t
ƒ
ƒ
t
Key Fourier series coefficient of ISF for 1/f3 noise is co
- If DC value of ISF is zero, c
o
is also zero
For symmetric oscillator output waveform
- DC value of ISF is zero – no upconversion of flicker noise!
(i.e. output phase noise does not have 1/f3 region)
ƒ
For asymmetric oscillator output waveform
- DC value of ISF is nonzero – flicker noise has impact
M.H. Perrott
MIT OCW
Issue – We Have Ignored Modulation of Current Noise
Rp1
inRp1
Tank generated
noise
Cp1
Lp1
Lp2
Vout
A
inM1
Cp2
Vout
M1
M2
Rp2
inRp2
Tank generated
noise
A
inM2
Vs
Transistor generated
noise
ƒ
Ibias
Vbias
M3
inM3
Transistor generated
noise
In practice, transistor generated noise is modulated by
the varying bias conditions of its associated transistor
- As transistor goes from saturation to triode to cutoff, its
associated noise changes dramatically
ƒ
Can we include this issue in the LTV framework?
M.H. Perrott
MIT OCW
Inclusion of Current Noise Modulation
iin(t)
in(t)
α(2πfot)
hΦ(t,τ)
Φout(t)
T = 1/fo
α(2πfot)
ƒ
Recall
ƒ
By inspection of figure
ƒ
We therefore apply previous framework with ISF as
M.H. Perrott
0
t
MIT OCW
Placement of Current Modulation for Best Phase Noise
Best Placement of Current
Modulation for Phase Noise
Worst Placement of Current
Modulation for Phase Noise
T = 1/fo
T = 1/fo
α(2πfot)
0
α(2πfot)
t
Γ(2πfot)
0
t
Γ(2πfot)
t
t
ƒ
Phase noise expression (ignoring 1/f noise)
ƒ
Minimum phase noise achieved by minimizing sum of
square of Fourier series coefficients (i.e. rms value of Γeff)
M.H. Perrott
MIT OCW
Colpitts Oscillator Provides Optimal Placement of α
T = 1/fo
Vout(t)
L
I1(t)
Vbias
Ibias
t
Vout(t)
M1
α(2πfot)
I1(t)
C1
C2
0
t
Γ(2πfot)
t
ƒ
Current is injected into tank at bottom portion of VCO
swing
- Current noise accompanying current has minimal
impact on VCO output phase
M.H. Perrott
MIT OCW
Summary of LTV Phase Noise Analysis Method
ƒ
ƒ
ƒ
ƒ
ƒ
ƒ
Step 1: calculate the impulse sensitivity function of
each oscillator noise source using a simulator
Step 2: calculate the noise current modulation
waveform for each oscillator noise source using a
simulator
Step 3: combine above results to obtain Γeff(2πfot) for
each oscillator noise source
Step 4: calculate Fourier series coefficients for each
Γeff(2πfot)
Step 5: calculate spectral density of each oscillator
noise source (before modulation)
Step 6: calculate overall output phase noise using the
results from Step 4 and 5 and the phase noise
expressions derived in this lecture (or the book)
M.H. Perrott
MIT OCW
Alternate Approach for Negative Resistance Oscillator
Rp1
A
Cp1
Lp1
Lp2
Vout
Cp2
Vout
M1
Rp2
A
M2
Vs
Ibias
Vbias
ƒ
M3
Recall Leeson’s formula
Key question: how do you determine F(∆f)?
M.H. Perrott
MIT OCW
F(∆f) Has Been Determined for This Topology
Rp1
A
Cp1
Lp1
Lp2
Vout
Cp2
Vout
M1
Rp2
A
M2
Vs
Ibias
Vbias
ƒ
ƒ
M3
Rael et. al. have come up with a closed form
expression for F(∆f) for the above topology
In the region where phase noise falls at -20 dB/dec:
M.H. Perrott
MIT OCW
References to Rael Work
ƒ
Phase noise analysis
- J.J. Rael and A.A. Abidi, “Physical Processes of Phase
Noise in Differential LC Oscillators”, Custom Integrated
Circuits Conference, 2000, pp 569-572
ƒ
Implementation
- Emad Hegazi et. al., “A Filtering Technique to Lower LC
Oscillator Phase Noise”, JSSC, Dec 2001, pp 1921-1930
M.H. Perrott
MIT OCW
Designing for Minimum Phase Noise
Rp1
Cp1
Lp1
Vout
A
Vout
M1
Ibias
Vbias
ƒ
(B)
(C)
M2
Vs
ƒ
(A)
(A) Noise from tank resistance
(B) Noise from M1 and M2
M3
(C) Noise from M3
To achieve minimum phase noise, we’d like to
minimize F(∆f)
The above formulation provides insight of how to do
this
- Key observation: (C) is often quite significant
M.H. Perrott
MIT OCW
Elimination of Component (C) in F(∆f)
ƒ
Rp1
Cp1
A
Lp1
Vout
- Component (C) is
Vout
M1
Capacitor Cf shunts
noise from M3 away from
tank
eliminated!
M2
ƒ
Vs
Issue – impedance at
node Vs is very low
- Causes M
and M2 to
present a low
impedance to tank
during portions of the
VCO cycle
ƒ Q of tank is degraded
1
Ibias
Vbias
M.H. Perrott
M3
inM3
Cf
MIT OCW
Use Inductor to Increase Impedance at Node Vs
ƒ
Rp1
Cp1
Lp1
- Fundamental component
Vout
A
is at twice the oscillation
frequency
Vout
M1
M2
ƒ
Vs
High impedance
at frequency 2fo
Lf
T = 1/fo
M3
inM3
Place inductor between Vs
and current source
- Choose value to resonate
Ibias
Vbias
Voltage at node Vs is a
rectified version of
oscillator output
Cf
ƒ
with Cf and parasitic
source capacitance at
frequency 2fo
Impedance of tank not
degraded by M1 and M2
- Q preserved!
M.H. Perrott
MIT OCW
Designing for Minimum Phase Noise – Next Part
Rp1
Cp1
Lp1
(A)
Vout
A
(B)
(C)
Vout
M1
(A) Noise from tank resistance
M2
Vs
High impedance
at frequency 2fo
Lf
T = 1/fo
(B) Noise from M1 and M2
(C) Noise from M3
Ibias
Vbias
ƒ
M3
inM3
Cf
Let’s now focus on component (B)
Depends on bias current and oscillation amplitude
M.H. Perrott
MIT OCW
Minimization of Component (B) in F(∆f)
Rp1
Cp1
Lp1
(B)
Vout
A
Vout
M1
ƒ
Recall from Lecture 11
M2
Vs
Ibias
ƒ
So, it would seem that Ibias has no effect!
- Not true – want to maximize A (i.e. P
sig)
to get best phase
noise, as seen by:
M.H. Perrott
MIT OCW
Current-Limited Versus Voltage-Limited Regimes
Rp1
Cp1
Lp1
(B)
Vout
A
Vout
M1
ƒ
M2
Vs
Ibias
ƒ
ƒ
ƒ
Oscillation amplitude, A,
cannot be increased above
supply imposed limits
If Ibias is increased above the
point that A saturates, then
(B) increases
Current-limited regime: amplitude given by
Voltage-limited regime: amplitude saturated
Best phase noise achieved at boundary between these regimes!
M.H. Perrott
MIT OCW
Final Comments
ƒ
Hajimiri method useful as a numerical procedure to
determine phase noise
- Provides insights into 1/f noise upconversion and
impact of noise current modulation
ƒ
ƒ
Rael method useful for CMOS negative-resistance
topology
- Closed form solution of phase noise!
- Provides a great deal of design insight
Another numerical method
- Spectre RF from Cadence now does a reasonable job of
estimating phase noise for many oscillators
ƒ Useful for verifying design ideas and calculations
M.H. Perrott
MIT OCW