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This documents explain the basic equations governing the design of CMOS Oscillators. Thumb of rules are given to provide a good starting point. The work references work by Professor Behzad Razavi.
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1Oscillator Design
Behzad RazaviElectrical Engineering Department
University of California, Los Angeles
2Outline
z Introductionz Basic Ringsz Frequency Tuningz LC Oscillators
3Small-Signal View
4Ring Oscillators
5Linear Model
6Amplitude Limiting
7Basic Rings
8Other Rings
9Voltage-Controlled Oscillators
z Center Frequencyz Tuning Range:- Band of Interest- PVT Variations
z Gain (Sensitivity)
z Supply Rejectionz Tuning Linearityz Intrinsic Jitterz Output Amplitude
10
Two Schools of Thought
Use differential rings lower supply sensitivity
But Use inverters with supply acting as control line. wider tuning range
But
11
Differential Ring VCOs (I)
z But large swing variation across tuning range
z Ring with Replica Biasing
[Young, JSSC, Nov. 92]
12
Differential Ring VCOs (II)
13
Tuning by Interpolation
z Interpolation does not work well at low speeds.
14
Example of Wide-Range Tuning
[Maneatis, JSSC, Nov. 03]
15
Single-Ended VCOs
[van Kaenel, JSSC, Nov. 98]
[Mansuri, JSSC, Nov. 98]
16
CCO with Regulation
[Yan, ISSCC05]
17
But how to generate complementary outputs?
[Grozing, ESSCIRC 03]
z Synchronize two rings:
18
Other Examples
[Searles, ISSCC07] (AMD)
[Desai, ISSCC07] [Straayer, JSSC, April 09]
19
18-GHz Ring in 65 nm
[Gebara, ISSCC07]
20
Measured Tuning Range
[Gebara, ISSCC07]
21
Another Example
[Kossel, ISSCC05]
22
Delay Stage
[Kossel, ISSCC05]
23
Simulated Behavior
[Kossel, ISSCC05]
24
LC Oscillators
z Much lower phase noise than rings (for a given power budget and frequency)
z Much faster than ringsz Much narrower tuning range z Main entry barrier: accurate inductor and varactor models
25
Basics
26
MOS Varactors
Simpler to use than pn junctions. C/V characteristic scales with technology.
27
Q-Range Trade-Off
28
Symmetric Inductors
Inductors driven differentially have a higher Q.
29
Output Swing
Peak differential output voltage swing is given by:
30
One-Port View
Example of negative resistance:
31
3-Point Oscillator
32
Oscillation Condition
Convert series resistance to parallel:
33
Differential Topology
R1 appears in series with the parallel combination of L1 and L2, lowering their Q and avoiding CM oscillation.
34
Cross-Coupled Oscillator
Looks like a diff pair with positive feedback.
Oscillation freq is given by:
35
Problem of Swings
Peak Vds must not stress the transistors.
36
Supply Sensitivity
Voltage-dependent Cdb results in a finite Kvcofrom Vdd to output frequency:
37
One-Port View
Oscillation condition easier to meet than in 3-point topologies:
38
Frequency Tuning (Type I)
To maximize tuning range, we wish to minimize C1.
But C1 is given by:- Caps of M1 and M2 (including 4Cgd)- Cap of L1- Input cap of next stage
39
Use of Symmetric Inductor
Requires accurate model of inductor. cant begin design without a useful
inductor library.
40
Tuning Range Limitations
41
Effect of Varactor Q
Now include the varactor:
42
VCO Type II
Select device dimension to set the output CM level to about Vdd/2.
43
Varactor Modulation by IDD
Noise of current mirror becomes the dominant source.
Does this effect exist in Type I VCO?
44
VCO Type III
Tuning range:
With 5% bottom-plate parasitic cap:
45
VCO Type IV
Select device dimension to set the output CM level to about Vdd/2.
Output swing twice that of previous topologies.
But tail noise modulates varactors.
46
Oscillation Amplitude vs. Frequency
Suppose the tank inductor has only a series resistance:
Oscillation amplitude falls as freq is lowered.
47
Discrete Tuning
But on-resistance of switches lowers tank Q:
48
Use of Floating Switch
49
LC VCO Design Procedure
50
Application as Reference
[McCorquodale, ISSCC08]
51
Results
[McCorquodale, ISSCC08]
52
Mathematical Model of VCOs