VCO Fundamentals

John McNeill Worcester Polytechnic Institute [email protected] Overview

• Functional Block Concept • Oscillator Review • Basic Performance Metrics • Methods of Tuning • Advanced Performance Metrics • Conclusion

9 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 V TUNE determines frequency of output waveform

11 Applications: RF System

• Downconvert band of interest to IF • VCO: Electrically tunable selection

12 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

13 Specifications

• from data sheet showing specs

14 Overview

• Functional Block Concept • Oscillator Review – Frequency Control – Amplitude Control – Types of Oscillators • Basic Performance Metrics • Methods of Tuning • Advanced Performance Metrics • 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, V REF 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

1 f = OSC 2π LC

20 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 R LOSS ; 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 R LOSS 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 R LOSS

26 Feedback Oscillator: Wien Bridge

• Forward gain A=3 • Feedback network with transfer function βββ(f)

• At fOSC , | βββ|=1/3 and ∠βββ =0 • Thought experiment: break loop, inject sine wave, look at signal returned around feedback loop

27 Aβββ=1

• “Just right” waveform is self sustaining

28 Aβββ=0.99

• “Not enough” waveform decays to zero

29 Aβββ=1.01

• “Too much” waveform grows exponentially

30 Feedback oscillator

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

31 Resonant Oscillator (Real)

32 Clapp oscillator

1 f = OSC 2 π LC eq 1 C = eq  1 1 1   + +   C1 C2 C3 

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

33 Clapp oscillator

• Circuit configuration • Equivalent circuit

MiniCircuitsAN95-007, “Understanding Oscillator Concepts” Clapp oscillator 1 1 gm Zeq = + − 2 jωC1 jωC2 ω C1C2

• Frequency: Determined by L, C1, C2, C3 • Amplitude: Grows until limited by g m soft clipping • Startup: Choose C1, C2 feedback for | RNEG | > R LOSS Oscillator Summary

• Typical performance of oscillator architectures:

BETTER RESONANT PHASE NOISE

FEEDBACK

RING

MULTIVIBRATOR

kHz MHz GHz

FREQUENCY fOSC

36 Overview

• Functional Block Concept • Oscillator Review • Basic Performance Metrics – Frequency Range – Tuning Range • Methods of Tuning • Advanced Performance Metrics • Conclusion

37 Basic Performance Metrics

• from data sheet showing specs

38 Basic Performance Metrics

• from data sheet showing specs

39 Basic Performance Metrics

• Supply: DC operating power • Output – Sine: output power dBm into 50 Ω – Square: compatible logic • Frequency Range • Tuning Voltage Range

40 Frequency Range

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

41 Overview

• Functional Block Concept • Oscillator Review • Basic Performance Metrics • Methods of Tuning • Advanced Performance Metrics • 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

I • Frequency: Controlled by f = REF OSC 4 CV REF IREF , C, V REF thresholds

• Use linear transconductance IREF = GM VTUNE GM to develop IREF from VTUNE  G  f =  M V OSC  4CV  TUNE + Very linear VTUNE – fOSC characteristic REF

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

44 Tuning LC Resonator: Varactor

dQ C = j dV C j 0 R C = j m  V  1 + R   Vbi 

• Q-V characteristic of pn junction • Use reverse bias diode for C in resonator

45 Example: Clapp oscillator

1 C C f = 1+ TUNE + TUNE OSC 2 π LC TUNE C1 C2

• Tuning range fMIN , fMAX set by C TUNE maximum, minimum • Want C 1, C 2 > C TUNE for wider tuning range

46 Overview

• Functional Block Concept • Oscillator Review • Basic Performance Metrics • Methods of Tuning • Advanced Performance Metrics – 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

• from data sheet showing specs

49 Frequency Range

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

50 Tuning Sensitivity

K K τ ω ≈ d O Z 1 L + sτ Z KO τI Kd (θi − θ o ) sτ I s

• Why do you care? – PLL: Tuning sensitivity K O affects control parameters – Loop bandwidth ωωωL (may not be critical) – Stability (critical!)

51 Varactor Tuning

C 0 C = j j m  V  1 + TUNE   Vbi 

1 f = OSC 2π LC

m 2 1  V  f ≈  TUNE  m =1 2 OSC 2 π LC j 0  Vbi 

• Disadvantages of abrupt junction C-V characteristic (m=1/2) – Smaller tuning range – Inherently nonlinear VTUNE – fOSC characteristic

52 Hyperabrupt Junction Varactor

C 0 C = j j m  V  1 + TUNE   Vbi 

1 f = OSC 2π LC

m 2 1  V  f ≈  TUNE  m =1 2 2 OSC 2 m → π LC j 0  Vbi 

• Hyperabrupt junction C-V characteristic (m ≈ 2)

+ Larger tuning range; more linear VTUNE – fOSC - Disadvantage: Lower Q in resonator

53 Phase Noise

• from data sheet showing specs

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

÷ N

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

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

White noise in

VTUNE signal path

Noise of active devices

Thermal noise: Losses in resonator, series R of varactor

63 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

• Functional Block Concept • Oscillator Review • Basic Performance Metrics • Methods of Tuning • Advanced Performance Metrics • Conclusion

67 Summary: VCO Fundamentals

• First order behavior – Tuning voltage V TUNE controls output frequency – Specify by min/max range of fOSC , V TUNE

• 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?

Thank you to our presenter John McNeill and our sponsor Mini-Circuits