VCO Fundamentals
John McNeill
Worcester Polytechnic Institute
mcneill@ece.wpi.edu
Overview
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Functional Block Concept
Oscillator Review
Basic Performance Metrics
Methods of Tuning
Advanced Performance Metrics
Conclusion
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Overview
• Functional Block Concept
– Applications
– Specifications
• Oscillator Review
• Basic Performance Metrics
• Methods of Tuning
• Advanced Performance Metrics
• Conclusion
10
Functional Block Concept
• Input control voltage VTUNE
determines frequency of output waveform
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Applications: RF System
• Downconvert band of interest to IF
• VCO: Electrically tunable selection
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Applications: Digital System
÷N
• Clock synthesis (frequency multiplication)
J. A. McNeill and D. R. Ricketts, “The Designer’s Guide to Jitter in Ring Oscillators.” Springer, 2009
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Specifications
• from data sheet showing specs
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Overview
• Functional Block Concept
• Oscillator Review
– Frequency Control
– Amplitude Control
– Types of Oscillators
• Basic Performance Metrics
• Methods of Tuning
• Advanced Performance Metrics
• Conclusion
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Oscillator Review
• Types of Oscillators
– Multivibrator
– Ring
– Resonant
– Feedback
• Basic Factors in Oscillator Design
– Frequency
– Amplitude / Output Power
– Startup
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Multivibrator
• Conceptual multivibrator oscillator
– Also called astable or relaxation oscillator
• One energy storage element
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Example: Multivibrator
• Frequency: Controlled by charging current IREF ,
C, VREF thresholds
• Amplitude: Controlled by thresholds, logic swing
• Startup: Guaranteed; no stable state
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Ring Oscillator
• Frequency: Controlled by gate delay
• Amplitude: Controlled by logic swing
• Startup: Guaranteed; no stable state
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Resonant Oscillator
• Concept: Natural oscillation frequency
of resonance
• Energy flows back and forth between
two storage modes
fOSC =
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1
2π LC
Resonant Oscillator (Ideal)
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Example: swing (ideal)
Energy storage modes: potential, kinetic
Frequency: Controlled by length of pendulum
Amplitude: Controlled by initial position
Startup: Needs initial condition energy input
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Resonant Oscillator (Real)
• Problem: Loss of energy due to friction
• Turns “organized” energy (potential, kinetic) into
“disorganized” thermal energy (frictional heating)
• Amplitude decays toward zero
• Requires energy input to maintain amplitude
• Amplitude controlled by “supervision”
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LC Resonant Oscillator (Ideal)
• Energy storage modes:
Magnetic field (L current), Electric field (C voltage)
• Frequency: Controlled by LC
• Amplitude: Controlled by initial condition
• Startup: Needs initial energy input (initial condition)
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LC Resonant Oscillator (Real)
• Problem: Loss of energy due to nonideal L, C
– Model as resistor RLOSS; Q of resonator
• E, M field energy lost to resistor heating
• Amplitude decays toward zero
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LC Resonant Oscillator (Real)
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Problem: Loss of energy due to nonideal L, C
Requires energy input to maintain amplitude
Synthesize “negative resistance”
Cancel RLOSS with -RNEG
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Negative Resistance
• Use active device to synthesize V-I characteristic that
“looks like” –RNEG
• Example: amplifier with positive feedback
• Feeds energy into resonator to counteract losses in RLOSS
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Feedback Oscillator: Wien Bridge
Forward gain A=3
Feedback network with transfer
function β (f)
• At fOSC, |β
β |=1/3 and ∠ β =0
• Thought experiment:
break loop, inject sine wave, look at
signal returned around feedback loop
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Aβ
β=1
• “Just right”
waveform is
self sustaining
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Aβ
β=0.99
• “Not enough”
waveform
decays to zero
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Aβ
β=1.01
• “Too much”
waveform grows
exponentially
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Feedback oscillator
• Stable amplitude condition: Aβ
β =1 EXACTLY
• Frequency determined by feedback network Aβ
β =1 condition
• Need supervisory circuit to monitor amplitude
• Startup: random noise; supervisory circuit begins with Aβ
β >1
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Resonant Oscillator (Real)
|RNEG| < RLOSS
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|RNEG| = RLOSS
|RNEG| > RLOSS
Stable amplitude condition: |RNEG| = RLOSS EXACTLY
Frequency determined by LC network
Startup: random noise; begin with |RNEG| > RLOSS
Amplitude grows; soft clip gives average |RNEG| = RLOSS
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Clapp oscillator
f OSC =
1
2π LCeq
1
Ceq =
1
1
1
+ 
 +
C
C
C3 
 1
2
• L, C1-C2-C3 set oscillation frequency fOSC
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Clapp oscillator
• Circuit configuration
• Equivalent circuit
MiniCircuits AN95-007, “Understanding Oscillator Concepts”
Clapp oscillator
1
1
gm
Z eq =
+
− 2
jωC1 jωC2 ω C1C2
• Frequency: Determined by L, C1, C2, C3
• Amplitude: Grows until limited by gm soft clipping
• Startup: Choose C1, C2 feedback for | RNEG | > RLOSS
Oscillator Summary
• Typical performance of oscillator architectures:
BETTER
PHASE
NOISE
RESONANT
FEEDBACK
RING
MULTIVIBRATOR
kHz
MHz
GHz
FREQUENCY fOSC
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Overview
• Functional Block Concept
• Oscillator Review
• Basic Performance Metrics
– Frequency Range
– Tuning Range
• Methods of Tuning
• Advanced Performance Metrics
• Conclusion
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Basic Performance Metrics
• from data sheet showing specs
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Basic Performance Metrics
• from data sheet showing specs
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Basic Performance Metrics
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Supply: DC operating power
Output
– Sine: output power dBm into 50Ω
– Square: compatible logic
Frequency Range
Tuning Voltage Range
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Frequency Range
• Output frequency over tuning voltage range
• Caution: Temperature sensitivity
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Overview
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Functional Block Concept
Oscillator Review
Basic Performance Metrics
Methods of Tuning
Advanced Performance Metrics
Conclusion
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VCOs / Methods of Tuning
• Require electrical control of some parameter
determining frequency:
• Multivibrator
– Charge / discharge
current
• Ring Oscillator
– Gate delay
• Resonant
– Voltage control of
capacitance in LC
(varactor)
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Example: Tuning Multivibrator
IREF
4CVREF
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Frequency: Controlled by
IREF , C, VREF thresholds
fOSC =
•
Use linear transconductance
GM to develop IREF from VTUNE
IREF = GM VTUNE
fOSC
 GM 
=
VTUNE
4CV

REF 
+ Very linear VTUNE – fOSC characteristic
- But: poor phase noise; fOSC limited to MHz range
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Tuning LC Resonator: Varactor
Q
Cj =
dQ
dVR
Cj =
C j0
 VR m
1+ 
 Vbi 
• Q-V characteristic of pn junction
• Use reverse bias diode for C in resonator
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Example: Clapp oscillator
fOSC =
1
2π LCTUNE
1+
CTUNE CTUNE
+
C1
C2
• Tuning range fMIN, fMAX set by CTUNE maximum, minimum
• Want C1, C2 > CTUNE for wider tuning range
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Overview
Functional Block Concept
Oscillator Review
Basic Performance Metrics
Methods of Tuning
Advanced Performance Metrics
– Tuning Sensitivity
– Phase Noise
– Supply Pushing
– Load Pulling
• Conclusion
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Advanced Performance Metrics
• Tuning Sensitivity (V-f linearity)
• Phase Noise
• Supply/Load Sensitivity
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Tuning Sensitivity
• from data sheet showing specs
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Frequency Range
• Change in slope [MHz/V] over tuning voltage range
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Tuning Sensitivity
K d (θ i − θ o )
1+ sτ Z
sτ I
KO
s
ωL ≈
K d K Oτ Z
τI
• Why do you care?
– PLL: Tuning sensitivity KO affects control parameters
– Loop bandwidth ωL (may not be critical)
– Stability (critical!)
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Varactor Tuning
Cj =
C j0
 V
m
1+ TUNE 
Vbi 

fOSC =
fOSC
1
2π LC
V
m 2
1
TUNE
≈


2π LC j 0  Vbi 
m =1 2
• Disadvantages of abrupt junction C-V characteristic (m=1/2)
– Smaller tuning range
– Inherently nonlinear VTUNE – fOSC characteristic
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Hyperabrupt Junction Varactor
Cj =
C j0
 V
m
1+ TUNE 
Vbi 

fOSC =
fOSC
1
2π LC
V
m 2
1
TUNE
≈


2π LC j 0  Vbi 
m =1 2
m →2
• Hyperabrupt junction C-V characteristic (m ≈ 2)
+ Larger tuning range; more linear VTUNE – fOSC
- Disadvantage: Lower Q in resonator
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Phase Noise
• from data sheet showing specs
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Phase Noise
• Power spectrum “close in” to carrier
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Phase Noise: RF System
• Mixers convolve LO spectrum with RF
• Phase noise “blurs” IF spectrum
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Phase Noise: Digital System
÷N
• Time domain jitter on synthesized output clock
• Decreases timing margin for system using clock
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Shape of Phase Noise Spectrum
• LC filters noise into narrow band near fundamental
• High Q resonator preferred to minimize noise
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Phase Noise: Intuitive view
• Sine wave + white noise; Filter;
limit; Result:
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Phase Noise: Intuitive view
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Sine wave + white noise;
Filter; limit; Result:
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Phase Noise Description
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Symmetric; look at single sided representation
Normalized to carrier: dBc
At different offset frequencies from carrier
White frequency noise: phase noise with -20dB/decade slope
Other noise processes change slope; 1/f noise gives
-30dB/decade
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Phase Noise Specification
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Symmetric; look at single sided
Normalized to carrier: dBc
At different offset frequencies from carrier
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Sources of Phase Noise
White noise in
VTUNE signal path
Noise of
active
devices
Thermal noise: Losses in resonator, series R of varactor
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Supply / Load Sensitivity
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Ideally tuning voltage is the only way to change output
frequency
– In reality other factors involved
– Mechanism depends on specifics of circuit
Power supply dependence: Supply Pushing
Impedance mismatch at output: Load Pulling
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Supply Pushing
• Change in fOSC due to change in supply voltage
• Clapp oscillator: supply affects transistor bias condition,
internal signal amplitudes
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Load Pulling
• Change in fOSC due to impedance mismatch at output
• Clapp oscillator; reflection couples through transistor
parasitic to LC resonator
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Overview
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•
•
•
•
•
Functional Block Concept
Oscillator Review
Basic Performance Metrics
Methods of Tuning
Advanced Performance Metrics
Conclusion
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Summary: VCO Fundamentals
• First order behavior
– Tuning voltage VTUNE controls output frequency
– Specify by min/max range of fOSC, VTUNE
• Performance limitations
– Linearity of tuning characteristic
– Spectral purity: phase noise, harmonics
– Supply, load dependence
• Different VCO architectures trade frequency range,
tuning linearity, phase noise performance
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Questions?
Thank you to our presenter John McNeill and our
sponsor Mini-Circuits
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