Signal Sources

Oscillators and PLLs

1

Oscillators • Properties

– Frequency range – Frequency Stability

• Drift • Phase Noise

• Active Circuit – Negative Z – Feedback

• Resonators – LC – Piezoelectric

• Quartz crystal • Ceramic • SAW

– YIG – Cavity

2

Oscillators

• Pumps and resonators • LC Oscillators • Quartz crystal oscillators • Tuning mechanisms • Phase noise • PLLs • Other resonators

– Ceramic – YIG – Cavity

• DDS • High precision and GPS Disciplined sources

3

An oscillator has two parts

Energy Resonator

4

The Energy source serves as a pump. A resonator alternates between two kinds of energy at a certain frequency.

5 https://www.facebook.com/VT/videos/259117811648536/?t=0

6

Capacitors

7

𝐸𝑛𝑒𝑟𝑔𝑦 = 1

2𝐶𝑉2

𝐸𝑛𝑒𝑟𝑔𝑦 = 1

2𝐿𝐼2

Inductors

+V 0

8

Capacitor Inductor

VC

Resonator Q

𝑄 = 𝑅𝐶

𝐿

𝜔0 =1

𝐿𝐶

𝐿 = 𝐶 =1

𝜔0

𝑄 = 𝑅

=1

2𝜋 ∙ 100MHz

For simplicity,

𝐿 = 𝐶 = 1.5915 ∙ 10−9

𝐿 = 𝐶 so

9

Response vs. Q

𝐵𝑊 =𝑓0𝑄

−𝜕𝜑

𝜕𝜔= 𝑡𝑔 =

2𝑄𝜔0

Gilmore & Besser, Practical RF Circuit Design For Modern Wireless Systems, V2, Eq 6.27, 2003 10

2𝑄

𝜔0=

200

2𝜋 ∙ 108≈ 318ns

𝑡𝑔 = −𝜕𝜑

𝜕𝜔=2𝑄

𝜔0

2𝑄

𝜔0=

2000

2𝜋 ∙ 108≈ 3.18μs

11

Open Circuit Resonator Response

Load

Vin

VoutG VinVout

Barkhausen Criteria for oscillation

𝐺 ≥ 1; N2

𝑉𝑜𝑢𝑡 𝑉𝑖𝑛

f

Adjust f so that 𝜙 = 0°

𝐺1 𝐺2

Adjust 𝐺1 and 𝐺2 so that 𝐺 > 1 at startup. 12

Flip the switch to make it an oscillator

Load

𝑉𝑜𝑢𝑡 𝑉𝑖𝑛

Now the closed-loop poles are in the right half plane until the amplifiers saturate.

No longer needed

f

13

Negative Z Oscillator

14

Source connected to a positive resistance load

15

Source connected to a negative resistance load

16

A Negative Resistance Oscillator

17

18

Remove R1

19

Turn it into a feedback oscillator

Hint: It’s the same circuit

<-Feedback

20

LC Oscillator Designs

• Hartley

• Colpitts

• Clapp

21

Hartley

https://www.electrical4u.com/hartley-oscillator/

22

Colpitts

https://www.electrical4u.com/colpitts-oscillator/ 23

Clapp

https://www.electrical4u.com/clapp-oscillator/ 24

Tuning an LC Oscillator

Pump

VTUNE

25

Broadband VCO – Synergy DCRO390670-5

https://synergymwave.com/products/vco/datasheet/DCRO390670-5.pdf

KV = 98 MHz/V

55 MHz/div

KV = 137 MHz/V

KV = 66 MHz/V

KV = 37 MHz/V

KV = 20 MHz/V

26

The Quartz Crystal

27

Motional Elements

The Crystal Equivalent Circuit

28

Resonator Equations

For a Series Resonant Operation,

29

S

S

S C

L

RQ

1

PS

PSEQ

CC

CCC

SS

SCL

1

S

S

S C

L

RQ

1

EQS

PCL

1

For a Parallel Resonant Operation,

https://www.radio-electronics.com/info/data/crystals/quartz-crystal-cuts-at-sc-ct.php 30

31

BT cut: Angle from z axis is 49 degree. It has operating frequency range from 0.5 to 200 MHz. It is similar to AT cut type. XY cut: This crystal cut type is widely used for low frequency of operation. It has range from 5 to 100 KHz. One common frequency used is 32.768KHz as used in many of micro-controllers as clock reference source. GT cut: This type has angle of 51o 7'. It has frequency range from 0.1 to 2.5MHz. IT cut: It is similar to SC cut type. It has operating frequency range from 0.5 to 200 MHz.

Other crystal cuts

32

http://www.crystek.com/documents/appnotes/pierce-gateintroduction.pdf 33

Implementation of Series Resonant Oscillator – The Butler Oscillator

34

The Butler Oscillator can be useful at

high frequencies but requires an

inductor to achieve the feedback gain.

This works well with overtone

oscillators where a tank circuit is

needed.

High Q→low RE or low RS → high device bias current.

Dm

SIg

R2

11

C

EI

mVR

25

Implementations

https://www.electronics-tutorials.ws/oscillator/crystal.html

Pierce Crystal Oscillator Colpitts Crystal Oscillator

CMOS Crystal Oscillator 35

Three categories of Crystal Oscillators

• OCXO -- Oven-controlled crystal oscillator

• VCXO – Voltage controlled crystal oscillator

– For fine tuning the frequency

– Uses a varactor diode

• TCXO – Temperature compensated crystal oscillator

– Uses a thermistor to bias a varactor diode

– Some models also allow for external fine tuning

36

https://coloradocrystal.com/applications/ 37

http://www.rfwireless-world.com/Terminology/AT-cut-vs-SC-cut-quartz-crystal.html 38

http://www.rfwireless-world.com/Terminology/AT-cut-vs-SC-cut-quartz-crystal.html

39

Benefits of SC cut ovenized oscillator

• SC stands for “stress compensated)

• Improved frequency stability

• Higher operating temperature (typ ~85°C)

• Improved aging (2-3x better than AT)

• Phase noise (Higher Q than AT)

• Less sensitive to vibration

https://blog.bliley.com/anatomy-of-an-ocxo-oven-controlled-crystal-oscillators 40

TCXO Example

http://www.nickc.com/uploaded/NIC_catalog.pdf 41

MT-008

TUTORIAL Converting Oscillator Phase Noise to Time Jitter by Walt Kester

https://www.analog.com/media/en/training-seminars/tutorials/mt-008.pdf 42

Leeson’s Oscillator Noise Model

43

Phase noise vs. offset

Log(Offset from carrier)

dB

re

lati

ve

to

ca

rrie

r

mS

3

2

0

2

mFS

Q

2

2

0

2

mFS

Q

Qm

2

0

Zone 1

Zone 2

Zone 3

m

S

FP

FkTS

2

m

Key parameters are Q, F, and PS

https://www.analog.com/media/en/training-seminars/tutorials/MT-086.pdf 44

Relevance of phase noise

• Virtually every communication receiver contains a local oscillator whose phase noise:

– adds to the noise of the incoming signal

– causes the down-converting mixer to add energy from adjacent-channel signals as noise.

– all of which causes deterioration of the Shannon

Channel Capacity Limit:

45

N

SBC 1log2

Effect of phase noise on a QAM Constellation

46

Baseband Upconverted, downconverted, with channel

impairments and equalized

-1.5 -1 -0.5 0 0.5 1 1.5-1.5

-1

-0.5

0

0.5

1

1.5Initial BB Constellation, EVM = 1.4866e-014%

Real

Imagin

ary

-1.5 -1 -0.5 0 0.5 1 1.5-1.5

-1

-0.5

0

0.5

1

1.5Equalized Rx Constellation, EVM = 5.8399%

Real

Imagin

ary

-1.5 -1 -0.5 0 0.5 1 1.5-1.5

-1

-0.5

0

0.5

1

1.5Equalized Rx Constellation, EVM = 1.2035%

Real

Imagin

ary

Including phase noise in the frequency converters

PLL (Phase Locked Loops)

• PLL Architecture

• Optimize system frequency stability

• Concept of phase noise multiplication

• Phase/frequency detector

• PLL Strategy

• PLL loop stability

47

PLL Concept

N

ø/f Detector

Loop Filter

VCO fREFERENCE

N*fREF

48

Phase noise is largely cause by timing variations between zero crossings of the sinusoid. The energy in that modulation at a particular offset frequency determines the spectral level in the phase noise and is proportional to the RMS magnitude of the phase variation at that rate.

49

Phase noise at low modulation rates refers to phase jitter of zero crossings relative to each other many cycles away. The lower the rate the more time there is between crossings so the more chance of greater phase jitter.

50

D FlipFlop

D

Clk

Q

Q 𝑓

𝑓2

Frequency can be divided with logic circuits

51

N Down- counter

Reload

Clk

Done

Done 𝑓

𝑓𝑁

Frequency Divided by N

52

Frequency can be multiplied with nonlinear harmonic circuits

𝑓 2𝑓

53

If you would prefer no DC Offset --

𝑓 2𝑓

90°

54

https://synergymwave.com/products/vco/datasheet/DXO10701095-5.pdf 55

https://www.vectron.com/products/ocxo/ox-205.pdf 56

https://www.vectron.com/products/ocxo/ox-205.pdf 57

58

59

~40.67 dB

60

61

62

Synergy 12.8 GHz PLL DRO, fref = 1.28 GHz

https://synergymwave.com/products/phase-locked-oscillators/datasheet/KSFLOD12800-12-1280.pdf 63

𝐾𝑑 PD

Phase Detector & Charge Pump

Loop Filter

𝐻 𝑠

1

𝑁

𝐾𝑣𝑠

VCO Ref

𝑓𝑅𝐸𝐹 𝑁 ∙ 𝑓𝑅𝐸𝐹

64

https://www.analog.com/media/en/training-seminars/tutorials/MT-086.pdf 65

𝑓𝑅𝐸𝐹

1

𝑁

VCO

VTune

66

(Bad idea!)

𝐾𝑑 PD

Phase Detector & Charge Pump

Loop Filter

𝐻 𝑠

1

𝑁

𝐾𝑣𝑠

VCO Ref

𝑓𝑅𝐸𝐹 𝑁 ∙ 𝑓𝑅𝐸𝐹

67

Insert a zero at 1 MHz

𝜔𝑍 = 2𝜋 ∙ 106

𝑋𝐶1 =1

𝜔𝑍𝐶1≈ 1.6k

68

Insert a pole at 4 MHz

𝜔𝑃 = 2𝜋 ∙ 4 ∙ 106

𝐶𝑃 =1

𝜔𝑃𝑅1≈ 25pF

Phase Margin 72°

69

Phase Margin ~42°

70

𝑓𝑅𝐸𝐹

1

𝑁

VCO

VTune

71

Insert a pole at 10 MHz

𝜔𝑃2 = 2𝜋 ∙ 10 ∙ 106

𝐶𝑃2 =1

𝜔𝑃2𝑅3≈ 1.59pF

𝑅2 = 10𝑘

Phase Margin 30°

Gain Margin 16dB

72

First Order Calculation Example

𝐾𝑑 PD 𝐻 𝑠

1

𝑁

𝐾𝑣𝑠

VCO Ref

𝑓𝑅𝐸𝐹 𝑁 ∙ 𝑓𝑅𝐸𝐹

𝐾𝑑 =𝑖𝐶𝑃2𝜋

A/rad

𝐻 𝑠 =1

𝑗𝜔𝐶𝑉𝐴

𝐾𝑣 =𝑑𝜔𝑉𝐶𝑂

𝑑𝑣rad

V ∙ 𝑠𝑒𝑐

𝐾𝑣𝑠=𝐾𝑣𝑗𝜔

=1

𝑗𝜔

𝑑𝜔𝑉𝐶𝑂

𝑑𝑣

𝐴𝑜 = 𝐾𝑑 ∙ 𝐻 𝑠 ∙𝐾𝑣𝑠∙1

𝑁

𝐴𝑜 =𝑖𝐶𝑃2𝜋

∙1

𝑗𝜔𝐶∙1

𝑗𝜔

𝑑𝜔𝑉𝐶𝑂

𝑑𝑣∙1

𝑁

𝐴𝑜 = −𝑖𝐶𝑃

2𝜋𝜔2𝐶∙𝑑𝜔𝑉𝐶𝑂

𝑑𝑣∙1

𝑁

At unity gain crossover:

𝐶 =𝑖𝐶𝑃2𝜋𝜔2

∙𝑑𝜔𝑉𝐶𝑂

𝑑𝑣∙1

𝑁

73

https://www.analog.com/media/en/training-seminars/tutorials/MT-086.pdf 74

https://www.analog.com/media/en/training-seminars/tutorials/MT-086.pdf 75

https://www.analog.com/en/education/education-library/videos/756428873001.html

https://www.analog.com/media/en/training-seminars/tutorials/adisimpll.pdf

76

Another Pump – the Gunn Diode

77

Other resonators • Ceramic • YIG • Cavity

78

https://nardamiteq.com/docs/D210B.PDF

https://nardamiteq.com/docs/D210B.PDF

79

MITEQ’s DRO circuits utilize both silicon bipolar transistors and GaAs MESFET devices. All microwave oscillators are designed by adding resonating elements (L, C or R) in various configurations to different ports of a transistor. These elements generate a negative resistance at a certain resonant frequency and set the device into oscillation. In the case of a DRO, the resonating element is the DR, which can be modeled electrically as an L, C, R network, as shown in Figure 1.

https://nardamiteq.com/docs/D210B.PDF 80

The Dielectric Resonator is made of a high dielectric constant (ε = 30 to 80) ceramic material, often barium titanate (Ba2Ti9O20). This material exhibits a high Q (9000 @ 10 GHz) and low temperature coefficient of frequency (TC to ±6 ppm/°C typical).

The cylindrical shape as shown in Figure 1 is the most popular. It has good separation between the desired TEδ(0,1) mode and other higher order resonant modes, making it easier to couple to microstrip circuits, as well as easy to mount. The resonator is magnetically coupled to one or more ports of the transistor using a transmission line, as shown in Figure 2.

https://nardamiteq.com/docs/D210B.PDF 81

FREQUENCY ACCURACY AND SETTABILITY The frequency accuracy of a free-running DRO is typically within 500 kHz and can be set to within 100 kHz. FREQUENCY STABILITY DROs are highly stable free-running oscillators exhibiting low temperature coefficient of frequency drift (typically 4 ppm/°C) and have better stability than free-running cavity oscillators, Gunn diode oscillators or VCOs. FREQUENCY PULLING FACTOR Pulling is an oscillators sensitivity to VSWR changes. Since the DRO is a high Q oscillator, its frequency pulling factor is better than other free-running sources. The frequency pulling figure for an unbuffered (at 10 GHz) DRO is typically less than 5 MHz peak-to-peak for a 1.5:1 VSWR varying through all phases. RF POWER OUTPUT A DRO exhibits good power efficiency compared to other oscillators, such as a Gunn oscillator or VCO, due to lossless coupling of dielectric resonator element. It also has less power variation over temperature. BANDWIDTH Mechanical tuning bandwidth is another limiting factor. Typically the bandwidth is 0.2% of center frequency, it can only be increased up to 3% of center frequency for special applications.

https://nardamiteq.com/docs/D210B.PDF 82

PHASE NOISE DROs typically offer excellent phase noise performance.

https://nardamiteq.com/docs/D210B.PDF

Miteq DRO Phase Noise Performance Previous VCO Phase Noise Performance

83

https://nardamiteq.com/docs/D210B.PDF

84

How Does YIG Work? YIG is a ferrite material that resonates at microwave frequencies when immersed in a DC magnetic field. This resonance is directly proportional to the strength of the applied magnetic field and has very linear “tuning” over multi-octave microwave frequencies

https://www.microlambdawireless.com/resources/ytodefinitions2.pdf 85

http://www.sjsu.edu/people/raymond.kwok/docs/project172/EE172_YIG_oscillator.pdf

86

It should be noted that with the advent of inexpensive frequency doublers, YIG oscillator manufacturers have discontinued making fundamental oscillators above 26.5 GHz.)

https://www.microlambdawireless.com/resources/ytodefinitions2.pdf 87

https://www.microlambdawireless.com/components/wide-tuning-range-oscillators/ 88

https://www.microlambdawireless.com/components/wide-tuning-range-oscillators/ 89

• 0.5 to 26 GHz FM Coils for Phase Locking • Low Phase Noise (best in industry) • Multi-Octave frequency bands • Flat Power Output over Temperature • Phase Lock & Modulation Capability • Small & TO-8 Package Styles • Excellent Linearity • Reduced Package Sizes (surface mount, 1” & 1.25”) • Analog and Digital drivers available

TMS YIG OSCILLATORS AT-A-GLANCE

90

http://www.teledynemicrowave.com/teledyne-yig-products/microwave-solutions-yig-oscillators#yig-oscillator-model-types 91

http://uspas.fnal.gov/materials/09UNM/ResonantCavities.pdf

Fields in Resonant Cavities

92

http://uspas.fnal.gov/materials/09UNM/ResonantCavities.pdf 93

http://web.mit.edu/22.09/ClassHandouts/Charged%20Particle%20Accel/CHAP12.PDF

94

https://www.analog.com/media/en/training-seminars/tutorials/MT-085.pdf 95

https://www.analog.com/media/en/training-seminars/tutorials/MT-085.pdf 96

https://www.analog.com/media/en/training-seminars/tutorials/MT-085.pdf 97

https://www.analog.com/media/en/training-seminars/tutorials/MT-085.pdf 98

99

100

101

102

Very high precision sources

103

GPS Disciplined OCXO

Bliley “New Reliance on GPS for Critical Infrastructure and the Need for GPS Disciplined Oscillators” 104