Phase-Locked Loop

1
Phase-Locked Loop
2
Phase-Locked Loop in RF Receiver
Antenna
BPF1
BPF2
LNA
Mixer
BPF3
IF Amp
Demodulator
RF front end
LO
VCO
Ref.
PD
Loop Filter
Phase-Locked Loop
1/N
3
Functional Blocks in PLL
VCO
Ref
LO
PD
Loop Filter
Phase-Locked Loop
1/N

• Phase detector (PD) find difference between
  phases of two signals
• Loop filter provide appropriate control voltage
  for the voltage-controlled oscillator (VCO)
• VCO generate signals with phase determined by
  the control voltage
• Divide-by-N LO phase changes N times faster than
  Ref phase

4
Design Issues

• Tracking behavior
• Noise performance
• Jitter characteristics
• Jitter tolerance
• Jitter transfer
• Jitter generation
• Power consumption

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System Modeling
VCO
vd
vC
PD
F(s)
vRef
vLO

• vRef input reference signal
• vLO local oscillator (LO) output signal
• vd detector output
• F(s) transfer function of loop filter
• vC control voltage for VCO

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System Modeling
qRef
VCO
Kdqe
PD
F(s)
vRef
vLO
qLO

• Phase signals contain information
• qRef phase of reference signal
• qLO phase of local oscillator (LO) signal
• qe phase difference between qRef and qLO

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Jump in Phase
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Ramp in Phase
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Ramp in Phase
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Phase Detector
qREF
qe
vd
Kd
- qLO

• VdKdqeKd(qREF qLO)
• Kd gain of phase detector

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Loop Filter
vd
vC
F(s)

• VC(s) F(s) Vd(s)
• Low-pass filter
• Extract phase error
• Remove high frequency noises
• Passive filter for integrated PLL
• Active filter for discrete component PLL

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Passive Lag Filter
R1


R2
vd
vC
C

• Lag filter pole magnitude smaller than zero
• Passive components high linearity, gain lt 1

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Active Lag Filter
R1
R2
C2
C1



vd
vC

• Can adjust pole and zero locations
• Can have gain
• Op amp limitations

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Active Proportional-Integral (PI) Filter
R1
R2
C



vd
vC

• Large open loop gain at low frequency
• Op amp limitations
• Linearity
• Noise
• Open loop gain

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Voltage-Controlled Oscillator
vC
qLO

1/s
KVCO
w0

• KVCO gain of VCO

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Transfer Function of PLL
w0
qREF
qe
vd
vC
qLO

Kd
1/s
KVCO
F(s)
- qLO

• Open-loop transfer function from qe to qLO

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Transfer Function of PLL
w0
qREF
qe
vd
vC
qLO

Kd
1/s
KVCO
F(s)
- qLO

• Closed-loop transfer function from qREF to qLO

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Transfer Function from qREF to qe
w0
qREF
qe
vd
vC
qLO

Kd
1/s
KVCO
F(s)
- qLO

• Closed-loop transfer function

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Other TF of Interest
vCn
qREF
qe
vd
vC
qLO

Kd
1/s
KVCO
F(s)
- qLO

• Noise in control voltage

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Other TF of Interest
qn
qREF
qe
vd
vC
qLO

Kd
1/s
KVCO
F(s)
- qLO

• Phase noise of VCO

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Transfer Functions for Different Loop Filters

• Passive lag filter
• Active lag filter
• Active PI filter

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Normalizing Transfer Function

• Normalized denominator
• Passive lag filter
• Active lag filter
• Active PI Filter

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Normalized Transfer Function

• Passive lag filter
• Active lag filter
• Active PI Filter

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Normalized Transfer Function

• Passive lag filter
• Active lag filter

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Frequency Response of H(s)
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Frequency Response of He(s)
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Step Response of PLL

• Phase step
• Phase Error
• Steady state error (final value theorem)

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Step Response
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Ramp Response of PLL

• Phase ramp
• Phase Error
• Steady state error (final value theorem)

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Ramp Response
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General Steady State Error in Ramp Response

• High loop gain
• Low loop gain

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Stability of PLL

• Criterion for stability
• Closed-loop pole at left half plane
• Sufficient phase margin
• Control of pole location
• Open loop gain
• Open loop zero
• Check root locus

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Root Locus Method

• Closed-loop TF
• Closed-loop poles make
• K0, open-loop poles
• K infinity, open-loop zeros or infinity

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Root Locus for Passive Lag Filter
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Root Locus for Active Lag Filter
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Root Locus for Active PI Filter
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Root Locus for 1st-Order LP Filter
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Effects of Parasitics
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Effects of Zero
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Phase Noise and Jitter

• Phase noise
• Fluctuation in phase
• Frequency domain
• Discussed in RF circuits
• Jitter
• Error in clock edge (period)
• Time domain
• Significant in communications circuits
• Two concepts
• Related to each other
• Exact relationship not clear

41
Jitter Measurements
Agilent, Understanding Jitter and Wander
Measurements and Standards.
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Jitter Tolerance

• Ability of a PLL to operate with jitter
• Applied to its reference
• Various magnitudes
• Different frequencies
• Usually specified using an input jitter mask
• Jitter magnitude and corner frequencies
• BER requirement
• Various for standards

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PLL in Clock and Data Recovery
0 1 0 0 1 0 1 0 1
Ideal signal
Distorted signal
0 1 0 0 X 1 0 1 0
Ideal clock
0 1 0 0 1 0 1 0
Recovered clock
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Jitter Tolerance Mask
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Jitter Tolerance Measurement
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Jitter Tolerance Measurement
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Jitter Tolerance Measurement

• Error at corner frequency
• Insufficient clock recovery bandwidth
• Incorrect mask used

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Jitter Tolerance Measurement
Tolerance margin

• Excessive jitter tolerance margin

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Jitter Tolerance Measurement

• Occasional fail at specific frequencies
• Need extra settling time after jitter amplitude
  change
• Repeating with additional settling time
• Spot measurement

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Jitter Tolerance Measurement

• Limited clock recovery bandwidth
• Eye-width alignment noise

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Jitter Tolerance Measurement

• Limited buffer store

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Jitter Transfer

• Jitter transfer or jitter attenuation
• Output jitter vs. input jitter
• Input jitter with various amplitudes and
  frequencies
• Output jitter measured with various bandwidths
• Intrinsic jitter
• Typically specified using a bandwidth plot
• Amplitude
• Roll off speed
• Corner Frequency

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Jitter Transfer Mask
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Jitter Transfer Measurement

• Jitter tolerance mask used to set input jitter
  level
• Sinusoidal jitter at magnitudes and frequencies
• Narrow-band measurement

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Jitter Transfer Measurement

• Different test masks
• SONET mask additional amplitude at lower band

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Jitter Transfer Measurement

• Measurement set-up noise
• -40 dB sufficient

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Jitter Transfer Measurement

• Low-frequency phase noise
• Power-line crosstalk
• Short measurement time

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Jitter Transfer Measurement

• Incorrect filter characteristic
• Excessive peaking

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Jitter Transfer Plot
E. Barari, Jitter Analysis / Specification, May
2002.
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Measured Jitter Transfer Characteristic
E. Barari, Jitter Analysis / Specification, May
2002.
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Measured Jitter Transfer Characteristic
E. Barari, Jitter Analysis / Specification, May
2002.
62
Measured Jitter Transfer Characteristic
E. Barari, Jitter Analysis / Specification, May
2002.
63
Measured Jitter Transfer Characteristic
E. Barari, Jitter Analysis / Specification, May
2002.
64
Jitter Generation

• Intrinsic jitter produced by the PLL
• Thermal noise
• Drift in VCO
• Measured at its output
• Applying a clear reference signal to PLL
• Measuring its output jitter.
• Usually specified as a peak-to-peak period jitter
  value

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Jitter Generation Standard
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Jitter Generation Measurement

• Direct measurement of p-p jitter
• Phase noise measurement
• Eye diagram and histogram

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Jitter Generation Measurement
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Measurement Considerations

• Calibration
• Measurement range
• Measurement time
• Power
• Frequency offset

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TF from Noise in VCO Control Voltage
vCn
qLO

Kd
KVCO/s
F(s)
-1

• Can be viewed as low-pass filter

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TF from Noise in VCO Control Voltage
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TF from Phase Noise in VCO
qn
qLO

Kd
KVCO/s
F(s)
-1

• High-pass filter
• The same as He(s)

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Phase Error in VCO
qn
vCn
HC(s)
Hq(s)
qLO
qREF
qe
Kd
KVCO/s
F(s)
- qLO

• vCn dominate at low frequencies
• qn dominate at high frequencies