signal sourcesece.boisestate.edu/~bhay/ece413_513/lecturematerial/3-system/6 s… · •lc...
TRANSCRIPT
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