Spur Reduction in Wideband PLLs by Random
Positioning of Chargepump Current Pulses
2010 International Symposium on Circuits and Systems, Paris
Chembiyan Thambidurai
Nagendra Krishnapura
Department of Electrical EngineeringIndian Institute of Technology, Madras
Chennai, 600036, India
2 June 2010
Outline
• Reference spur in chargepump PLLs
• Randomization of chargepump current pulses
• Implementation details
• Spectrum after randomization
• Effect of non-idealities
• Simulation results
• Conclusions
Reference spurs
PFD
up
dn
CP
N
ref
div
R
Cz
Cp
20 MHz fouticp(t)fr =
fdiv
VCO
0 Tr 2Tr
icp(t)
Chargepump non-idealities
-IleakTr
Ift
-Ift
{ Trst
-Imis
Icp
Trst
{Icp
icp(t) icp(t)icp(t)
Tr
Tr
Vdd
Iup=Icp
Idn=Icp+
icp(t)
Cp
R
Cz
UP
DN
Ileak
Ift
-Ift
Imis
Reference spurs
PFD
up
dn
CP
N
ref
div
R
Cz
Cp
20 MHz fouticp(t)fr =
fdiv
VCO
fr 2fr
Icp(f)
fout fout+fr fout-fr
Sφ(f)
0
Spur vs bandwidth tradeoff
• The magnitude of the spur at a frequency offset fr (dBc)
Sφ(fr ) = 20 log
(
Icp(fr ) |Zlp(fr )|Kvco
2fr
)
• Low spur level ⇒ low bandwidth (large settling time)
(Loop filter with one pole and one zero assumed here)
Random pulse position modulation
0 Tr 2Tr 3Tr 4Tr 5Tr
-2fr -fr fr 2fr0f f
0
Time Domain
Frequency Domain
Random pulse
Periodic pulses
0 Tr 2Tr 3Tr 4Tr 5Tr
positioning
• Redistribute the spur energy to all frequencies.
Implementation
CPup
dn
Randomizer
Randomizer
upr
dnr
0 Tr 2Tr 0 Tr 2Tr
up(t) upr(t)
ir(t)
0 Tr 2Tr
ir(t)
• Chargepump current pulse position has to be randomized.
• Accomplished by randomizing up/dn pulses.
Randomizer
16 : 1
sel [3:0]
up
MUX
upr
}Td=Tr/n
1 2 n-2 n-1
• Randomly choose 1 of n delayed pulses
Random number generator
• The randomizing sequence sel [3 : 0] should have a
uniform distribution.
• Generated using PRBS(Pseudo Random Bit Sequence)
generator.
• A PRBS of longer length
• produces low in-band noise.• guarantees near uniform distribution.
• Length of PRBS chosen based on tolerable in-band noise.
PLL with random pulse positioning
PFD
up
dn
upr
dnr
RandomizerCP
N
ref
div
VCO
R
Cz
Cp
sel [3:0]
fr
fdiv
fout
Randomizer
ir(t)
• Control voltage not periodic
Mathematical analysis
• The periodic impulse train
x(t) =∞
∑
k=−∞
δ(t − kTr )
• The randomized impulse train
r(t) =∞
∑
k=−∞
δ(t − kTr −akTr
n)
(n: Number of possible pulse positions in a period)
Spectrum before and after randomization
• Power spectrum of a periodic impulse train
Sx(f ) =1
Tr2
∞∑
k=−∞
δ(f −k
Tr)
• Power spectrum of the randomized signal
Sr (f ) = Srd (f ) +1
Tr2
∞∑
k=−∞
δ(f − kn
Tr)
• Srd(f ) is the “redistributed noise”
Srd(f ) =1
nTr
[
(n − 1) −2
n
n−1∑
k=1
(n − k) cos(2πkfTrn
)
]
Simulated spectrum after randomization
0 1 2 3 4 5 6 7 8−80
−60
−40
−20
Ma
gn
itu
de
(d
B)
0 1 2 3 4 5 6 7 8−80
−60
−40
−20
Frequency (f/fr)
Ma
gn
itu
de
(d
B)
n=2
n=16
Noise shaping in the redistributed noise
0 0.5 1 1.5 2 2.5 3 3.5−80
−70
−60
−50
−40
−30
−20
Frequency (f/fr)
Magnitude (
dB
)
n=2n=16
Shaped noise
• The ‘redistributed noise’
is not white.
• For n=2 we can see that
Srd(f ) =1
Trsin2(
πfTr2
)
• Close-in phase noise
remains unaffected.
Delay sensitivity
• Delays prone to process variations (Td 6= Tr/n).
• Delay line may span more or less than a reference period
• The current after randomization (ir (t)) on an average can
be expressed as
ir (t) =1
n[icp(t) + icp(t − Td) + ..... + icp(t − (n − 1)Td)]
|Ir (f )| =sin(nπfTd)
sin(πfTd)|Icp(f )|
Delay sensitivity
• Thus the randomization behaves as a moving average filter
with frequency nulls at
fz =k
nTd
k ∈ [1, (n − 1)]
• If Td =Tr
n; nulls occur at reference harmonics.
• If Td 6=Tr
n; nulls do not occur at reference harmonics and
spurs appear at PLL output
Sensitivity to delay variations
−40 −30 −20 −10 0 10 20 30 40 50−25
−20
−15
−10
−5
Percentage variation in delay
Sp
ur
reje
ctio
n (
dB
)
n=2n=4n=8n=16n=32
Simulated PLL parameters
fref 20 MHz
fout 1 GHz
fBW 1 MHz
PFD Tri-state PFD
Charge-pump Icp = 50 µA
Loop-filter R = 21.7 k˙,Cz = 37.25 pF,Cp = 1.99 pF
VCO fvco = 1GHz, Kvco = 200MHz/V
Divider N=50
• 3-dB bandwidth of the PLL is ≈ 1 MHz.
• Charge pump current mismatch 10 %
• Charge pump and PFD: transistor level
• Other components: ideal
Simulation results
10−1
100
101
102
−180
−170
−160
−150
−140
−130
−120
−110
−100P
ha
se
no
ise
(d
Bc/H
z)
Frequency offset from carrier (MHz)
Before randomizationAfter randomization
19.9 20 20.1−140
−130
−120
20 dB
Effect of randomization at high frequencies
100
101
102
−180
−170
−160
−150
−140
−130
−120
−110
−100
Ph
ase
no
ise
(d
Bc/H
z)
Frequency offset from carrier (MHz)
Randomization noiseOpen loop VCO phase noiseVCO and resistor noise
10 MHz
< 20 dB
fb=1 MHz
Simulated sensitivity to delay variations
−40 −20 0 20 40 60−40
−35
−30
−25
−20
−15
−10
−5
0
Percentage delay variation
Sp
ur
reje
ctio
n (
dB
)
AnalyticalSimulated
Conclusions
• Pulse position randomization eliminates reference spur.
• Resulting spectrum shaped to high frequencies.
• Close-in phase noise remains unaffected.
• > 11.5 dB spur rejection for ±20% delay variation.
• Simple implementation.
References
Cicero.S.Vaucher, “An adaptive PLL tuning system architecture combining high spectral purity and fast
settling time.” IEEE Journal of Solid State Circuits, pp. 2131-2137, vol. 35, issue 4, April. 2000.
Che-Fu Liang et al., “Spur suppression techniques for frequency synthesizers,” IEEE Transactions on
Circuits and Systems-II:Express Briefs, pp. 653-657, vol. 54, issue 8, Aug. 2007.
Che-Fu Liang et al., “A digital calibration technique for charge pumps in phase-locked systems,” IEEE
Journal of Solid State Circuits, pp. 390-398, vol. 38, issue 2, Feb. 2008.
T. C. Lee, W. L. Lee, “A spur suppression technique for phase Locked frequency synthesizers.”, International
Solid State Circuits Conference, ISSCC 2006, pp.592-593.
Cameron T. Charles, David J Allstot, “A Calibrated Phase/Frequency Detector for Reference Spur Reduction
in Charge-Pump PLLs,” IEEE Transactions on Circuits and Systems-II:Express Briefs, vol. 53, issue 9, Sep.2006.
B. P. Lathi, Modern Digital and Analog Communication Systems., Third edition, New York:Oxford University
Press., 1998.
Mathematical representation
kTr
kTr+akTr/n
}
Tr/n(k+1)Tr
• The reference period (Tr ) is divided into equal time
intervals of Tr/n.
• The k th current pulse will appear at kTr + akTr/n instead of
kTr .
• ak is a uniform random integer ∈ [0, n − 1]
Random pulse positioning illustrated for n=4
a1=3
a2=1
0 Tr 2Tr
Tr+3Tr/4 2Tr+T
r/4
0 Tr 2Tr
{
Tr/4
x(t)
t
t
ak
(a)
(b)
a0=2
Tr+2Tr/4
,r(t)
