Multi-Mode and Wideband VCO Design
Prof. Ali M. Niknejad
Berkeley Wireless Research Center
University of California, Berkeley
UNIVERSITY OF CALIFORNIA, BERKELEY
Prof. Niknejad: Multiband and Multimode VCO Design
Outline
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Introduction
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Oscillator Start-up
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Basic Oscillator Topologies
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Simple Theory of Phase Noise
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Varactors (MOS, PN Junction, Switch)
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Switching LC Resonators
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Design Example: Wideband CMOS VCO
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Prof. Niknejad: Multiband and Multimode VCO Design
Introduction
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Multi-band synthesizer requires VCOs at multiple frequencies
Simple solution: Build multiple VCOs for each band and switch between
bands
Multiple VCOs can be physical large due to passives
Good frequency planning can re-use a single VCO by changing PLL divide
ratios
To accommodate various standards and to simplify frequency planning, a
wide tuning range is desirable
To keep noise low in PLL, the gain of the VCO should be small
UNIVERSITY OF CALIFORNIA, BERKELEY
Prof. Niknejad: Multiband and Multimode VCO Design
Oscillator Architecture
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Oscillators are non-linear circuits:
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Input: DC Power, Initial Condition
Ideal output: Sinusoidal oscillation
Real output: Harmonics, Phase Noise, Spurious Signals
Oscillators have inherent amplitude stability
Oscillators do not have phase stability (unlocked)
Linearized Picture:
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In steady-state, infinite gain (pos FB with loop gain = 1)
At start-up, the osc is excited by noise
Poles in RHP (unstable) cause perturbation to grow
Amplitude will grow until limiting mechanism kick in
Stable steady state amplitude is obtained
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Prof. Niknejad: Multiband and Multimode VCO Design
Oscillator Start-Up: Feedback Perspective
gm R
A l ,0=
1
n
Al =
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Gm R
=1
n
Positive feedback places poles at start-up in RHP
The loop gain determined by gm, feedback factor, tank impedance
Large signal Gm has limiting characteristics
Amplitude grows until loop gain is unity (infinite gain)
In steady-state, poles on jw axis
Any amplitude perturbation is rejected
UNIVERSITY OF CALIFORNIA, BERKELEY
Prof. Niknejad: Multiband and Multimode VCO Design
Oscillator Start-Up: Negative Resistance
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An oscillator is composed of a lossy tank and a regeneration circuit
that has net negative resistance
At start-up the negative resistance is larger than positive resistance for
start-up (RHP pole)
Steady-state negative resistance cancels the positive resistance of tank
(zero net loss)
Amplitude determined by large signal limiting of resistance
Equivalent to FB picture for 2-port devices
Possible to use 1-port “active” devices (Gunn Diodes)
UNIVERSITY OF CALIFORNIA, BERKELEY
Prof. Niknejad: Multiband and Multimode VCO Design
Oscillator Topologies
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Ring Oscillators
Tuned Ring Oscillators
Distributed Oscillators
LC Tank positive feedback circuits:
● Transformer feedback
● Capacitive transformer feedback
● Tapped inductor feedback
● LC feedback
Single-ended versus differential
Grounding options
FET versus BJT (1/f noise, amplitude of osc)
UNIVERSITY OF CALIFORNIA, BERKELEY
Prof. Niknejad: Multiband and Multimode VCO Design
Oscillator Topologies (2)
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Single ended
● Colpitts Oscillator has capacitive feedback
● Common base/gate: capacitor feedback has no phase inversion
● Hartley and Pierce (dual of Colpitts)
● Clap, Armstrong, ...
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Prof. Niknejad: Multiband and Multimode VCO Design
Oscillator Topologies (3)
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Differential
● Cross coupled diff pair (MOS can be better than BJT)
● Colpitts (capacitor feedback for higher swing in BJT)
● Colpitts with built-in buffer (take output at collector)
PMOS versus NMOS (lower 1/f noise since PMOS device is not a
surface device)
Advantage is disappearing in ultra-short channel devices (0.13mm)
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Prof. Niknejad: Multiband and Multimode VCO Design
Oscillator Topologies (4)
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Current source inject 1/f noise into “mixer”
DC and all even harmonics can form mixing products at fund.
Use a large PMOS device or even a resistor
Use filter at current source to suppress noise
Double-differential ... (PMOS and NMOS cross-coupled pair)
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Prof. Niknejad: Multiband and Multimode VCO Design
Resonators Quality Factor
U mU e
Av. Energy Stored
Q=
=
Power Loss
Pl
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The quality factor for a resonant system is defined as the product of the
resonant frequency times the energy stored per cycle over the power
loss.
From Poynting's Theorem we can find the power in the electromagnetic
field in a volume of space
P=
P0
 
P l 2
j U m−U e 

power crossing surface
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From circuit theory
P oP l
R=
1 2
∣I∣
2
power loss
V V I 2 P
Z i= = 2 = 2
I ∣I∣ ∣I∣
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power stored
4 U m−U e 
X=
1 2
∣I∣
2
Prof. Niknejad: Multiband and Multimode VCO Design
Simple Phase Noise Theory
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Since any real system has noise, the “input” to an oscillator is not zero
but finite (very small)
The noise spectrum is shaped by tuned positive feedback amplifier
Signals near tank resonance see very large gain due to positive feedback
with loop gain < 1
The actual loop gain never reaches unity but is very close to one
Integrate spectral power density to find loop gain
UNIVERSITY OF CALIFORNIA, BERKELEY
Prof. Niknejad: Multiband and Multimode VCO Design
Phase Noise Theory (2)
v
2
2, rms
=
v2n A2l n2
 
2

1−A l  4
Q2
0
2
∞
∫−∞
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●
d 
2
1a 
=/a
Compute transfer function for input referred voltage noise
Integrate expression to obtain total oscillator power
2
2
vn 2  1 A l
P osc = n
R 2 RC 1− A l
●
Loop gain is not unity (but nearly so):
2
vn
R  1
1−A l =
P osc 2 R C
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Prof. Niknejad: Multiband and Multimode VCO Design
Phase Noise Theory (3)
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This simple theory does not account for non-linear and noise mixing
effects
● 1/f noise from current source is mixed to RF (even harmonics)
● Gain compression (use steady-state gm)
● Oscillator can be approximated as a cyclostationary system (time of
noise injection is important [Kaertner] [ Hajimiri])
But it's a good first-order theory (Leeson equations) that highlight the
importance of tank Q
Oscillator Figures of merit can be defined accordingly
More Discussion of this approach can be found:
Phase noise in LC oscillators
Kouznetsov, K.A.; Meyer, R.G.;
Solid-State Circuits, IEEE Journal of , Volume: 35 Issue: 8 , Aug 2000
Page(s): 1244 -1248
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Prof. Niknejad: Multiband and Multimode VCO Design
Multi-Mode Resonators
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On-chip spiral inductor have multiple resonance frequencies (shorted Tline resonates at odd multiples of /4)
Why not use second harmonic for second band?
Transformer has two fundamental resonant modes (in phase and
differential):
1
2
2
U m=  L1 I 1 L2 I 2 ±M I 2 I 2
2
Leff =L1L2±2 M
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High frequency mode has lower Q (energy storage)
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Prof. Niknejad: Multiband and Multimode VCO Design
Wideband VCOs
V osc ≈2 I bias R T
R T ≈Q  L ∝
V osc ∝
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2
a
Challenge of realizing wide tuning range
● Loop gain must be high enough over entire range
● Must design for worse case (high current consumption)
● Amplitude of oscillation a function of frequency
Amplitude control loop (ACL) can provide just enough feedback to
keep loop gain = 1 over entire range
ACL subject to noise issues
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Prof. Niknejad: Multiband and Multimode VCO Design
Varactors for RF Applications
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Common technique for frequency variation is to vary the cap
PN junction diodes are ubiquitous, MOS capacitors good alternative
MOS capacitors have larger tuning range (2:1) but also higher “gain”
(achieve tuning range over a narrow voltage swing)
Many options for MOS varactors:
● n-type or p-type, triple well for isolation
● inversion mode versus accumulation mode
● body bias (inversion only or accumulation only)
Noise on control line and substrate reception an important consideration
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Prof. Niknejad: Multiband and Multimode VCO Design
Variable Inductors?
Variable current gain
v s = j  L1 i 1 j  M i 2= j  L1K M i 1
Leff =L1K M
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Transformer technique: sense primary current and amplify secondary
Active circuit sets linearity and noise limits
Active circuit must handle resonant current in secondary!
Resonant circuit current is Q times larger than oscillator current
Phase delay in secondary current can create loss
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Prof. Niknejad: Multiband and Multimode VCO Design
Varactors: PN Junction Diodes
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Forward bias issues limits swing
Biasing and noise requires AC isolation and filtering
High tuning voltage for wideband operation
Need extra process steps to optimize performance (high doping to
minimize series resistance due to substrate loss)
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Prof. Niknejad: Multiband and Multimode VCO Design
Varactors: MOS Capacitors
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Accumulation or inversion Mode
Accumulation mode preferred (higher electron mobility)
Tuning range is very large due to fast charge build-up
CV equation follows from solution of Poisson's equation:


 −
W0
e
2Vt
Vgb−V fb
2Vt
Cg
=
V −V
Cox
 − 2V
1W0
e
2Vt
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

gb
t


fb


(W0 is product-log function)
Prof. Niknejad: Multiband and Multimode VCO Design
Varactors: Switched-Capacitors
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MOS device is a pretty good switch (parasitic on resistance and off
capacitance)
PN Junction can also be switched between “low” and “high” cap
Why not switched inductor? Low inductor Q prevents use unless switch
has very low on-resistance
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Prof. Niknejad: Multiband and Multimode VCO Design
MOS Switched-Capacitor Topologies
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Binary weighted array of capacitors and switches
Can select discrete sub-bands and tune with variable capacitor
Band overlap by some safety margin
Tuning range limited by parasitic off capacitance
Quality factor limited by on-resistance
Device size chosen large enough such that the overall tank Q dominated by
inductor
Differential topology also possible
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Prof. Niknejad: Multiband and Multimode VCO Design
Switched-Capacitor Design Equations
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Size does matter:
● Series loss goes down with W
● Parasitic capacitance goes up with W
● Tuning Range and Q tradeoff
Max/min frequency of oscillation
1

1
1
max : 2
=C  ,min 2 −1

C dd C a
0, max L
 min :
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n
1
2
0, min L

−1
C p
n
=C  ,max 2 −1C a C p
Frequency overlap inequality:

1
1
C  ,max −C  ,min C a −

C dd C a
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
−1
Prof. Niknejad: Multiband and Multimode VCO Design
Switched Capacitor Equations...
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Let k > 1 be the safety margin
Overlapping tuning ranges provide robustness against process
In terms of overlap and capacitance ratio
=
C  ,max
C  ,min =
C  ,min
1
C a=

2
0, min
L
−Cp
k
n
2 −1
−1
[ 
k
1
1
C a−

C dd C a
−1
k
C  ,max =
−1
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[
1

2
0, min
L
]
−1
≈
k
C a−C dd 
−1
−Cp
k
n
2 −1
−1
−C dd
]
ox
=C ox = W⋅L
t ox
Prof. Niknejad: Multiband and Multimode VCO Design
Switched Capacitor Q Factor
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The on-resistance of a FET switch in triode region:
R on =
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The channel resistance of a MOS accumulation mode varactor (Factor
of 12 due to distributed effects):
Rc=
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L
1
W n C ox V gs −V t 
L
1
W 12  p C ox V gs −V t 
Switch-capacitor Quality Factor (independent of n)


Ron n
1
Qc=0
1 n 2 −1Ca
2
0 Ron Ca 2 −1
Qc≃ 1
0 Ron Ca
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Prof. Niknejad: Multiband and Multimode VCO Design
Example: CMOS Wideband VCO
Ref: Axel Berny et al. (to appear at CICC '03)
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M4
M3
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IB
M1
M2
Vo+
Vo-
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Vtune
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Vo4C
B2
4W/L
Vtune
2C
B1
2W/L
All PMOS to reduce 1/f noise
Only 2 gain devices to minimize
cap loading.
Large area tail device since main
1/f contributor
P+/Nwell varactors
Very compact integrated varactor
bias chokes
LB = 100nH at only 100μm/side!!
C
B0
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1W/L
LB
Prof. Niknejad: Multiband and Multimode VCO Design
CMOS Wideband VCO Die Photo
Tail device
Cap
array
chokes
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1600 x 1500 mm2
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VCO core
P+/nwell
varactor
Dimensions:
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Technology: IBM 0.25mm RF
CMOS process
5 Al metal layers
To appear at CICC '03
output buffer
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Prof. Niknejad: Multiband and Multimode VCO Design
Measured Performance
1.45
Frequency of Oscillation (GHz)
1.40
1.35
000
001
010
1.30
011
100
1.25
101
110
1.20
111
1.15
1.10
1.05
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Tuning Voltage (V)
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Measured tuning range:1.06-1.41 GHz or 28.3%
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Simulated tuning range: 1.06-1.46 GHz or 31.7%
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Prof. Niknejad: Multiband and Multimode VCO Design
Measured and Simulated Phase Noise
-80
-105
Vtune=1.5V, B2B1B0=011
Vtune=0.0V, B2B1B0=000
-90
-110
Phase Noise (dBc/Hz)
-100
L (dBc/Hz)
-110
-120
-130
-140
-120
-125
L(f=1 MHz)
-130
-150
-160 4
10
L(f=100 kHz)
-115
5
10
6
10
7
10
Frequency Offset (Hz)
8
10
-135
1.10
1.15
1.20
1.25
1.30
1.35
1.40
Frequency of Oscillation (GHz)
VDD = 2 V, Vtune = 0|1.5 V, Icore = 3.6 mA
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Prof. Niknejad: Multiband and Multimode VCO Design
Performance Summary
Technology
.25 μm CMOS
Supply Voltage
2V
Current (VCO Core)
3.6 mA
Tuning Range
Tuning Sensitivity (K )
28.00%
VCO
< 75 Mhz/V
Phase Noise (f = 1.244 Ghz, Δf = 100 kHz)
-111 dBc/Hz
Phase Noise (f = 1.244 Ghz, Δf = 600 kHz)
-127 dBc/Hz
Phase Noise (f = 1.244 Ghz, Δf = 1 Mhz)
-131 dBc/Hz
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Prof. Niknejad: Multiband and Multimode VCO Design
Summary
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VCO design is a careful tradeoff between power, noise, and
passive element design and optimization
Multi-band voltage controlled oscillators can be realized easily
with a switched capacitor array
Quality factor of switched capacitor array only a function of
technology (low on-resistance for fixed parasitics)
MOS varactors offer wide tuning range over small voltage
swings
Switch capacitor arrays decouple VCO gain K from achievable
tuning range
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Prof. Niknejad: Multiband and Multimode VCO Design