ece 453 wireless communication systems oscillatorsemlab.uiuc.edu/ece453/oscillators.pdfwith...
TRANSCRIPT
ECE 453 – Jose Schutt‐Aine 1
Jose E. Schutt-AineElectrical & Computer Engineering
University of [email protected]
ECE 453Wireless Communication Systems
Oscillators
ECE 453 – Jose Schutt‐Aine 2
Feedback – Basic Concept
ECE 453 – Jose Schutt‐Aine 3
1. The closed-loop transfer function is a function of frequency
2. The manner in which the loop gain varies with frequency determines the stability or instability of the feedback amplifier
3. The frequency at which the phase of the transfer function is equal to 180o will be unstable if the magnitude is greater than unity
Feedback and Frequency Dependence
ECE 453 – Jose Schutt‐Aine 4
1 ( )f
A sA s
A s s
Feedback and Stability
When loop gain A(j)(j) has 180o phase, we have positive feedback
1 ( )f
A jA j
A j j
ECE 453 – Jose Schutt‐Aine 5
Nyquist Plot
- Radial distance is |A|- Angle is phase of - Intersects negative real axis at 180
ECE 453 – Jose Schutt‐Aine 6
Stability and Pole Location ( ) 2 coso ot tj t j t
nv t e e e e t
ECE 453 – Jose Schutt‐Aine 7
Oscillator
• Closed‐Loop Transfer function:
–
• Barkhausen’s criteria for oscillation:––
• = oscillation‐frequency.
ECE 453 – Jose Schutt‐Aine 8
Oscillator Topologies• Common‐base topology is usually preferred becauseFeedback within transistor is minimized (low Miller)External feedback is dominantCurrent gain has little phase shift and is constant with f
• Oscillator built around 2 major requirements:Oscillation frequency foPower Po that must be delivered to a load
• Other criteriaEfficiencySpectral purityFrequency stability
ECE 453 – Jose Schutt‐Aine 9
BJT – High-Frequency Model
ECE 453 – Jose Schutt‐Aine 10
Common-Collector Colpitts
• Minimize circuit dependence on transistor internal parameters
• Choose
1C C
2 oC C
ECE 453 – Jose Schutt‐Aine 11
rightZ
leftZ
For Oscillation, we want Zleft = ‐Zright
Incremental Model
ECE 453 – Jose Schutt‐Aine 12
2 2 2 2 4 2 2 21 2 1 2 1 2
1 1 1 1 0me e e
r gC r C R C C r R C C R
2 2 2 2 21 2 1 2
1 0m m
e
g grC C R C C
2 11 2
2
2
1
1e
ms
CC C rC Rg C
C
Oscillation Criteria
Term in ‐4 can be neglected. This gives
Gives transconductance to set net resistance to zero
Condition gives
ECE 453 – Jose Schutt‐Aine 13
2 11 2
2
1ms
e
Cg C C rC R
1 2 1
2
1oms
L e
C C CgQ C R
Oscillation Conditions
If gm << C1and assuming that is large
In terms of the inductor quality factor QL
gms is the trans-conductance needed to support steady-state oscillations
ECE 453 – Jose Schutt‐Aine 14
CC-Colpitts - Observation• To implement tunable oscillatorUse variable capacitor in parallel or is series with inductor
• To extract power from oscillatorPlace resistance in shunt with inductorAccount for loading effect in analysis and design
1. Oscillation amplitude builds up and vbe increases
2. Transistor moves out of linear range and operation becomes nonlinear. Transconductance decreases.
3. When transconductance reaches gms, steady state operation is achieved.
ECE 453 – Jose Schutt‐Aine 15
L pt L p
L p
R RR R R
R R
i e eR R r
Common-Base Colpitts
Cf: tuning capacitorC1 & C2: feedback ratioRFC: RF choke to prevent power dissipation in RE
1/i ig R
1/t tg R
DEFINITIONS
ECE 453 – Jose Schutt‐Aine 16
1 2 1
1 11
0
iiS
i t o f ot
g s C C sCVI
g sC g s C C C VsL
Setting the determinant to zero provides the criterion for the onset of oscillation.
CB-Colpitts - Incremental Model
ECE 453 – Jose Schutt‐Aine 17
21
3 21 0
i t t i a t i b t t a t i
t a b t
s g s L g g C s L g C L g C L C g
s L C C L C
1 2aC C C 1b o fC C C C
21Re 0i t b i a t ij g L C g C g C g
CB-Colpitts - Oscillation ConditionsSetting the determinant to zero gives.
Defining and
we get a complex conjugate pair of roots. This leads to 2 equations for real and imaginary parts that must be equal to zero separately
2 21Im 0t t i a t a bj L g g C L C C C
ECE 453 – Jose Schutt‐Aine 18
22
/t i a to
a b t
g g s C LC C C
2
1 2 1 2 1 2 1 2
1 1/o
t o f t i f o
LC tank circuit transistor and load
L C C C C C C R R C C C C C C
CB-Colpitts - Oscillation ConditionsFrom the equation for the imaginary part, we get
or
First term should predominate
ECE 453 – Jose Schutt‐Aine 19
1 2t t iL R R C C
2
1 2 1 2
1/o
t o fL C C C C C C
CB-Colpitts - Oscillation Conditions
In that case
which leads to
Circuit oscillates at frequency determined by Ltand equivalent capacitance.
ECE 453 – Jose Schutt‐Aine 20
2min 2
1 1 1
11 1f o i
t o t
C C R CC R C L C
2 2 2
min1 2 1 2 1 1
11 1 11 /
i i
t t
C R C R CC C R C C C R C
CB-Colpitts - Oscillation Conditions
The solution of the real part using gives
For oscillations to start, of the transistor should be greater than min.
ECE 453 – Jose Schutt‐Aine 21
Crystal Oscillator
• Quartz exhibits piezoelectric effectReciprocal relationship between mechanical deformation and appearance of electrical potentialDeforming crystal produces voltageApplying voltage produces deformation
• When applied voltage is sinusoidalMechanical oscillations that exhibit resonances at multiple frequenciesExtremely high Q that can reach 105 and 106
Do not work above 250 MHz
ECE 453 – Jose Schutt‐Aine 22
Crystal Resonator - Circuit Model Rq, Lq and Cq describe mechanical resonance behavior C0 is capacitance due to external contacting
- Cq/C0 can be as high as 1000- Lq ranges from 0.1 mH to 100H
ECE 453 – Jose Schutt‐Aine 23
01
1 /q q q
Y j C G jBR j L C
0 00 22
1 /0
1 /
q qo
q q q
L CC
R L C
Crystal Resonance FrequenciesAdmittance from terminals is
Resonance condition is expressed by
ECE 453 – Jose Schutt‐Aine 24
20
0 0 12q
S Sq
R CL
20
0 0 12q
P Pq
R CL
0 1 /S q qL C 0 0 0/P q q qC C L C C
Crystal Resonance FrequenciesSeries resonance frequency
Parallel resonance frequency
where
ECE 453 – Jose Schutt‐Aine 25
Crystal is characterized by Lq = 0.1H, Rq = 25, Cq
= 0.3pF, and C0 = 1 pF. Find series and parallel resonance frequencies and compare them against the susceptance formula.
Crystal Oscillator - Example
2 20 0
011 1 0.919
2 22q q
S Sq qq q
R RC Cf f MHzL LL C
2 200 0
00
11 1 1.0482 2 2q q q
P Pq q q q
R C C RC Cf f MHzL L C C L
ECE 453 – Jose Schutt‐Aine 26
Voltage Controlled Oscillator
ECE 453 – Jose Schutt‐Aine 27
1 2 1 2 0IN IN C IN C B C B Cv i X i X i X i X
11 1 1 0B B C IN Ch i i X i X
Voltage Controlled Oscillator
ECE 453 – Jose Schutt‐Aine 28
11 1 2 1 211 1
1 1IN C C C CC
Z h X X X Xh X
21 2 11 1 2
1 1 1 1INZ
j C C h C C
21 2
mIN
gRC C
1
ININ
Xj C
Voltage Controlled OscillatorFinding input impedance
Re-write as (assuming h11>>XC1)
Using gm = /h11
ECE 453 – Jose Schutt‐Aine 29
0 30 3 0 1 2
1 1 1 1 0j LC j C C
03 3 2 1
1 1 1 1 12
fL C C C
1 2
1 2IN
C CCC C
Resonance frequency follows from condition:
1 2 3 0X X X
which gives
and
VCO – Resonance Frequency
ECE 453 – Jose Schutt‐Aine 30
• Most important performance characteristicFrequency‐domain equivalent of jitterOriginates from thermal, shot and 1/f noiseRandom variation in phase angle of oscillatorAffects frequency stability
• Phase noise quantificationCompare phase noise power to carrier powerDetermine phase noise spectral densityCan be characterized in time or frequency domain
Oscillator Phase Noise
ECE 453 – Jose Schutt‐Aine 31
Phase Jitter in Time Domain
If the phase varies, the waveform V(t) shifts back and forth along the time axis and this creates phase jitter
ECE 453 – Jose Schutt‐Aine 32
( ) cos 2 ( )o oV t V f t t
(t) is a random noise process. The instantaneous frequency is
1 ( )2inst o
d tf fdt
1 ( )( )2
d tf tdt
( ) 1 ( )( )2o o
f t d ty tf f dt
Oscillator Phase NoiseOscillator operates as
Instantaneous frequency variation is
Fractional deviation in instantaneous frequency is
ECE 453 – Jose Schutt‐Aine 33
Phase, Period and CTC Jitter
ECE 453 – Jose Schutt‐Aine 34
Phase Noise in Spectral Domain
Phase noise appears as sidebands centered around the carrier frequency
ECE 453 – Jose Schutt‐Aine 35
Phase Noise Specification
( )( ) n
o
P fL fP f
: phase noise power (in watts) ( )nP f: carrier’s power (in watts) oP
: phase noise bandwidth (in hertz) f
1( ) ( )2
L f S f
Phase noise magnitude is specified relative to the carrier’s power on a per-hertz basis
: PSD of phase noise( )S f
10( )( ) 10log2
S fL f
or
ECE 453 – Jose Schutt‐Aine 36
Phase Noise to Phase Jitter
From the phase noise PSD, random jitter and deterministic jitter can be identified
Need: convert phase noise measured in the frequency domain to phase jitter for PLLs, clocks and oscillators
ECE 453 – Jose Schutt‐Aine 37
Phase Noise Impact on PLL
Phase noise is the key metric for evaluating the performance of a PLL system