VCO Fundamentals

VCO Fundamentals

John McNeill

Worcester Polytechnic [email protected]

Overview

• Functional Block Concept

• Oscillator Review

• Basic Performance Metrics

• Methods of Tuning

• Advanced Performance Metrics

• Conclusion

9

Overview


– Applications

– Specifications





• Conclusion

10

Functional Block Concept• Input control voltage VTUNE

determines frequency of output waveform

11

Applications: RF System

• Downconvert band of interest to IF

• VCO: Electrically tunable selection

12

Applications: Digital System

• Clock synthesis (frequency multiplication)

÷ N

13

J. A. McNeill and D. R. Ricketts, “The Designer’s Guide to Jitter in Ring Oscillators.” Springer, 2009

• from data sheet showing specs

Specifications

14

Overview



– Frequency Control

– Amplitude Control

– Types of Oscillators




• Conclusion

15

Oscillator Review

• Types of Oscillators

– Multivibrator

– Ring

– Resonant

– Feedback

• Basic Factors in Oscillator Design

– Frequency

– Amplitude / Output Power

– Startup

16

Multivibrator

• Conceptual multivibrator oscillator– Also called astable or relaxation oscillator

• One energy storage element

17

Example: Multivibrator

• Frequency: Controlled by charging current IREF ,

C, VREF thresholds

• Amplitude: Controlled by thresholds, logic swing

• Startup: Guaranteed; no stable state

18

Ring Oscillator

• Frequency: Controlled by gate delay• Amplitude: Controlled by logic swing• Startup: Guaranteed; no stable state

19

Resonant Oscillator

• Concept: Natural oscillation frequency of resonance

• Energy flows back and forth between two storage modes

20

fOSC =1

2π LC

Resonant Oscillator (Ideal)

• 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

21

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”

22

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)

23

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

24

LC Resonant Oscillator (Real)

• Problem: Loss of energy due to nonideal L, C

• Requires energy input to maintain amplitude

• Synthesize “negative resistance”

• Cancel RLOSS with -RNEG

25

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

26

Feedback Oscillator: Wien Bridge

• Forward gain A=3

• Feedback network with transfer

function ββββ(f)

• At fOSC, |ββββ|=1/3 and ∠ ββββ =0

• Thought experiment: break loop, inject sine wave, look at signal returned around feedback loop

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Aββββ=1

• “Just right”waveform is self sustaining

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Aββββ=0.99

• “Not enough”waveform decays to zero

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Aββββ=1.01

• “Too much”waveform growsexponentially

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Feedback oscillator

• Stable amplitude condition: Aββββ=1 EXACTLY• Frequency determined by feedback network Aββββ=1 condition• Need supervisory circuit to monitor amplitude• Startup: random noise; supervisory circuit begins with Aββββ>1

31

Resonant Oscillator (Real)

• 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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|RNEG| < RLOSS |RNEG| = RLOSS |RNEG| > RLOSS

Clapp oscillator

• L, C1-C2-C3 set oscillation frequency fOSC

33

fOSC =1

2π LCeq

Ceq

=1

1

C1

+1

C2

+1

C3

Clapp oscillator

• Circuit configuration • Equivalent circuit

MiniCircuitsAN95-007, “Understanding Oscillator Concepts”

Clapp oscillator

• Frequency: Determined by L, C1, C2, C3

• Amplitude: Grows until limited by gm soft clipping

• Startup: Choose C1, C2 feedback for | RNEG | > RLOSS

Zeq

=1

jωC1

+1

jωC2

−g

m

ω 2C

1C

2

Oscillator Summary

• Typical performance of oscillator architectures:

36

kHz MHz GHz

FREQUENCY fOSC

BETTERPHASENOISE

RESONANT

RING

MULTIVIBRATOR

FEEDBACK

Overview




– Frequency Range

– Tuning Range



• Conclusion

37


Basic Performance Metrics

38



39


• Supply: DC operating power

• Output

– Sine: output power dBm into 50Ω

– Square: compatible logic

• Frequency Range

• Tuning Voltage Range

40

Frequency Range

• Output frequency over tuning voltage range• Caution: Temperature sensitivity

41

Overview






• Conclusion

42

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)

43

Example: Tuning Multivibrator

• Frequency: Controlled by IREF , C, VREF thresholds

• Use linear transconductanceGM to develop IREF from VTUNE

+ Very linear VTUNE – fOSC characteristic

- But: poor phase noise; fOSC limited to MHz range

44

fOSC =IREF

4CVREF

fOSC =GM

4CVREF

VTUNE

IREF = GMVTUNE

Tuning LC Resonator: Varactor

• Q-V characteristic of pn junction

• Use reverse bias diode for C in resonator

45

C j =C j 0

1+VR

Vbi

m

C j =dQ

dVR

Q

Example: Clapp oscillator

• Tuning range fMIN, fMAX set by CTUNE maximum, minimum

• Want C1, C2 > CTUNE for wider tuning range

46

fOSC =1

2π LCTUNE

1+CTUNE

C1

+CTUNE

C2

Overview






– Tuning Sensitivity

– Phase Noise

– Supply Pushing

– Load Pulling

• Conclusion

47

Advanced Performance Metrics

• Tuning Sensitivity (V-f linearity)

• Phase Noise

• Supply/Load Sensitivity

48


Tuning Sensitivity

49

Frequency Range

• Change in slope [MHz/V] over tuning voltage range

50

Tuning Sensitivity

• Why do you care?

– PLL: Tuning sensitivity KO affects control parameters

– Loop bandwidth ωωωωL (may not be critical)

– Stability (critical!)

51

Kd θ i − θo( )1+ sτZ

sτI

KO

s

ωL

≈KdKOτZ

τI

Varactor Tuning

• Disadvantages of abrupt junction C-V characteristic (m=1/2)

– Smaller tuning range– Inherently nonlinear VTUNE – fOSC characteristic

52

C j =C

j 0

1+V

TUNE

Vbi

m

fOSC

=1

2π LC

fOSC ≈1

2π LC j 0

VTUNE

Vbi

m 2

m =1 2

Hyperabrupt Junction Varactor

• Hyperabrupt junction C-V characteristic (m ≈ 2)+ Larger tuning range; more linear VTUNE – fOSC

- Disadvantage: Lower Q in resonator

53

C j =C

j 0

1+V

TUNE

Vbi

m

fOSC

=1

2π LC

fOSC ≈1

2π LC j 0

VTUNE

Vbi

m 2

m =1 2 m →2


Phase Noise

54

Phase Noise

• Power spectrum “close in” to carrier

55

Phase Noise: RF System

• Mixers convolve LO spectrum with RF

• Phase noise “blurs” IF spectrum

56

Phase Noise: Digital System

• Time domain jitter on synthesized output clock• Decreases timing margin for system using clock

÷ N

57

Shape of Phase Noise Spectrum

• LC filters noise into narrow band near fundamental• High Q resonator preferred to minimize noise

58

Phase Noise: Intuitive view

• Sine wave + white noise; Filter; limit; Result:

59

Phase Noise: Intuitive view

• Sine wave + white noise;Filter; limit; Result:

60

Phase Noise Description

• 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

61

Phase Noise Specification

• Symmetric; look at single sided• Normalized to carrier: dBc• At different offset frequencies from carrier

62

Sources of Phase Noise

Noise of active devices

63

Thermal noise: Losses in resonator, series R of varactor

White noise in VTUNE signal path

Supply / Load Sensitivity

• 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

64

Supply Pushing

• Change in fOSC due to change in supply voltage

• Clapp oscillator: supply affects transistor bias condition, internal signal amplitudes

65

Load Pulling

• Change in fOSC due to impedance mismatch at output

• Clapp oscillator; reflection couples through transistor parasitic to LC resonator

66

Overview






• Conclusion

67

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

68

Questions?

69

Thank you to our presenter John McNeill and our

sponsor Mini-Circuits

Documents

VCO Fundamentals