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Texas Instruments How to Calculate the Period Jitter from the SSCR for High-Speed ADCs Application notes
SLWA028 – DECEMBER 2003
How to Calculate the Period Jitter σT from the SSCR L(fn)
with Application to Clock Sources for High-Speed ADCs
Alfio Zanchi
Texas Instruments, Inc. – Wireless Infrastructure Data Converters
12500 TI Boulevard - 75243 Dallas, TX (U.S.A.)
alfio.zanchi@ieee.org
ABSTRACT
This document introduces a general formula to translate the phase noise of a clock source, rated via the Single Sideband to
Carrier Ratio (SSCR), to the cycle-to-cycle jitter of the oscillation period. The link allows to seamlessly aggregate the
external clock source phase noise, usually given in dBc/Hz, to the phase stability figure of the on-chip clock
synchronization circuitry, usually rated in ps-RMS. This permits in turn to evaluate their impact on the total aperture jitter
of a sampling circuit, finally enabling the determination of the SNR for systems like, as shown in this document, an analogto-digital converter.
The validity of the relationship between the time- and frequency-domain figures of merit has been first tested on the phase
noise spectrum featured by bipolar and CMOS integrated VCOs; thereafter, the most popular case of PLL-based frequency
synthesizers has been treated both by adopting time-to-amplitude conversion techniques, or dedicated phase-noise testing
equipment.
The optimal performance enabled by a state-of-the-art aperture jitter, optimized by making use of the formulas here
proposed and rigorously quantified in 250fs, is demonstrated on Texas Instruments ADS5420, a high-speed 14b 65MSps
ADC for 3G wireless infrastructure BTS applications.
INTRODUCTION
The increasingly challenging requirements posed on ADC performance by the newest CDMA multi-carrier standards, by lowIF single-heterodyne receivers, and by sophisticated power amplifier linearization techniques call for device flexibility in terms
of speed, gain, matching, and linearity, nowadays available primarily in very advanced technologies. At the same time, the
integration of RF front-end and IF A-to-D conversion potentially allowed by a common BiCMOS platform, or of the ADC with
a digital downconverter (DDC), could eliminate important bottlenecks in front of the final DSP. The main limitation to the
resolution of the system becomes the Signal-to-Noise Ratio (SNR) of the ADC, which is in turn limited by jitter when the
intermediate frequency (IF) of the receiver is pushed higher than 70MHz. The timing uncertainty is given by the RMS
combination of external clock synchronization source and on-chip clock conditioning and distribution network.
The unification of the figures of merit used for rating the phase noise of time reference circuits becomes essential exactly at the
boundary between external instrumentation and integrated circuit. While mixed-signal designers are more prone to adopt time
jitter as the figure of choice for assessing the stability of the sampling clock and ultimately the SNR, RF instrumentation data
sheets tend to rate the same phenomenon in terms of phase noise, expressed via the Single Sideband to Carrier Ratio (SSCR).
σTo is defined as the RMS standard deviation of the statistical distribution obtained by collecting the time duration of the
oscillation periods. The SSCR(fn), instead, is the spectral profile given by the ratio of the phase noise power found in a 1-Hz
bandwidth at the offset fn from the carrier, and the carrier power concentrated at f0.
In a previous work [1] the link between the time-domain and frequency-domain parameters used to evaluate the phase noise
(respectively jitter and SSCR) was demonstrated. Among the numerous definitions given for the jitter we will discuss the cycle
jitter of a periodical waveform, or period jitter σTo, since it is the parameter that determines the SNR in the well-known
expression [2]:
SNR = −20 ⋅ log(2πf IN σ To )
(1)
SLWA028 – DECEMBER 2003
With the aid of the formula presented hereinafter, Eqs. 14 or 16, the jitter can be derived from the phase noise spectrum via the
numerical computing of an integral, without any additional effort. From the experimental standpoint, the formula allows for the
estimation of the timing deviation without relying on jitter-specific test instrumentation, but only on a standard spectrum
analyzer, as shown in the last part of this discussion.
This study lead to the optimization of the total source+clock jitter in the design of a critical circuit: we will introduce a 14b
65MSps switched-capacitor pipeline ADC, whose specifications target base-stations for 3G wireless standards requiring IF
sampling capability of 70MHz to 220MHz. The ADC eventually showed a period jitter as low as 250fs, the best figures proven
to date for CMOS-based clocks, enabling excellent SNR of 69.3dBFS at 65MSps, 220MHz IF. The circuit has been designed
in Texas Instruments’ proprietary RFSiGe1 silicon-germanium very high-speed BiCMOS process.
DERIVATION OF THE GENERALIZED SSCR ↔ JITTER FORMULA
The formula developed in [1] (reported for convenience in Eq. 2) was obtained based on the assumption of a classical phase
noise profile featuring fn-2 tails around the carrier (Fig. 1a):
σ T20 =
f n2
⋅ SSCR ( f n )
f 03
(2)
However, a lot of practical situations exist which divert from such a behavior. For instance, the flicker noise of a CMOS VCO
transfers into a characteristic fn-3 slope in the output spectrum sidebands. More important, for a number of applications
synchronized to an external source, the spectrum synthesized by a PLL remains flat within the loop bandwidth BW centered at
f0 (Fig. 1b). Since the characteristics of phase stability of the PLLs found in instrumentation (e.g., the HP8644B source) are
usually rated in SSCR terms, or expressed in dBc/Hz @ offset fn from the carrier, a generalized equation linking any SSCR
profile to the period jitter σTo can be gained from the same standard derivation.
Sφ
Sf
0
a)
0
fn
0
Sf
0
fn
fn
0
f0
f
SV
Sφ
0
b)
SV
fn
f0
f
Fig. 1. Power spectral densities of frequency noise, phase noise, and output voltage noise in the case of a) a free-running oscillator, b) a
PLL frequency synthesizer
What represented in Fig. 1 can be easily obtained with an ad-hoc Matlab simulation, where for example the built-in vco()
function is fed with a white noise in the first instance, and with an highpass-shaped noise in the second case. The results
obtained when the PLL bandwidth is set to a broad 10% of the center frequency (100MHz vs. 1GHz) are represented in Fig. 2.
Of course, within the simulated environment it is also easy to retrieve the jitter from the definition (standard deviation of the
Gaussian distribution of the period’s durations), which yields 2.48ps for the VCO and 2.13ps for the PLL arrangement
respectively.
The following is a demonstration of the mathematical foundations and assumptions upon which the frequency-to-time domain
formula relies. The mathematical procedure leading to the generalized formula has been presented in [3] and is here reported
for the reader’s convenience; if only concerned with the final outcome, the reader can conveniently skip to Eq. 14 without loss
of logical continuity in the Application Note.
SLWA028 – DECEMBER 2003
PLL BW = 100 MHz
Fig. 2. Matlab simulated signals spectra in detail. The upper spectrum pertains to oscillators showing white frequency noise (free running
VCO), the lower one by highpass-filtered frequency noise (typical of PLL)
Let us consider two noise components at offset ±fn rotating in the frame of the phasor representing the carrier, which rotates at
frequency f0 (Fig. 3). In order to generate an orthogonal phasor to the carrier, which eventually perturbs the angle of the carrier
phasor and leads to phase noise (PM), these phasors must be equal in amplitude and be positioned as shown in Fig. 3. In this
case in fact, to a first order the composition of noise tones affects only the phase of the carrier without modifying its module,
which would translate into amplitude noise (AM).
fn
φ (t)
Vn
Vn
-fn
V0
Fig. 3. Phasor-plane representation of the carrier affected by the two side tones responsible for sole phase modulation
It is very common to deal with noise contributions that can be modeled with narrowband FM noise. The phase modulation due
to these components is therefore
φ ( t ) = 2Vn sin ( 2π f nt ) V0
(3)
Since dφ/dt = 2πf, the phase error φ(t) causes an instantaneous frequency deviation given by
∆f 0 = f n ⋅ 2Vn cos ( 2π f nt ) / V0
(4)
The phase disturbances affecting the carrier can be modeled as a random process, identified by the power spectrum Sφ, or Sfo as
an alternative. Spectra will be always considered bilateral throughout the derivation. The link between the two functions is
provided by the differentiation rule for the Fourier transform:
S f0 ( f n ) = f n ⋅ Sφ ( f n )
2
When considering only the two tones of Fig. 3, by taking the integration bandwidth df at offset fn it is:
(5)
SLWA028 – DECEMBER 2003
2
Vn
= SV ( f 0 ± f n ) df
4
(6)
1 4V 2 4 ⋅ SV ( f 0 ± f n ) ⋅ df
= 2 ⋅ SSCR ( f n ) ⋅ df 1Hz
φ 2 = ⋅ 2n =
2 V0
V02 2
(7)
φ 2 = 2 ⋅ Sφ ( f n ) df
(8)
Sφ ( f n ) = SSCR ( f n )
(9)
and therefore, according to Eq. 3:
But since, by definition:
by equating the two expressions above we get:
Thus the spectrum of the voltage noise observed on a spectrum analyzer does represent the spectrum of the phase of the signal,
for small deviations – which is by far the most common case. Let now σTo denote the RMS jitter of the single oscillation period
To = 1/fo. Since
∆T0 = −∆f 0 / f 0
2
(10)
Then, by applying the statistical definition of variance:
σ T20 = 1 f 04 ⋅ σ 2fo
(11)
where σfo is the RMS value of the frequency deviation observed over one period T0, i.e., the cycle jitter. Now it is possible to
evaluate σfo after Sfo(fn) by making use of the Wiener-Khintchine theorem. In particular, σ2fo can be determined after the
integration of the frequency noise over one single period T0. In the frequency domain, this means filtering the spectrum with
the sinc transfer function of a “gated integrator” spanning T0 over time. Therefore:
σ 2f0 =
+∞
∫ S ( f )⋅ W ( f )
f0
n
2
n
df n
(12)
−∞
where, as is well known, the weight function is the Fourier transform of a rectangle, or:
 f 
 f   f 
W ( f n ) = sin  π n   π n  = sinc  π n 
 f0   f0 
 f0 
(13)
Eventually, by recalling Eqs. 11 and 12 we obtain:
σ T2o =
1
= 4
f0
1
σ
f 04
2
f0
+∞
∫
f
2
n
Sφ
=
1
f 04
+∞
∫
S f0
( fn )⋅ W ( fn )
−∞
( fn )⋅ W ( fn )
2
df n =
(14)
2
df n
−∞
which constitutes the general link between the jitter of the period duration and the phase noise spectrum measured on a clock
signal.
Let us now consider the two cases in Fig. 1. For a free-running oscillator the noise density Sfo(fn) is white, therefore it can be
denoted simply by Sfo, and after straightforward processing the integral in Eq. 14 reduces to:
SLWA028 – DECEMBER 2003
S f0 ⋅1 T0 = S f0 ⋅ f 0
(15)
where the expression of the equivalent noise bandwidth of the gated integrator has been used. From Eq. 14 we essentially
recovered Eq. 1, otherwise to be obtained with way more complicated derivation. When the formula is applied to the simulated
Matlab cases reported in Fig. 2, the σTo of the distribution results about 2.50ps for the unlocked VCO, against the 2.48ps
obtained by the cycle jitter definition. As expected, the identity of the paradigm under which the formula has been derived and
the idealized simulation setup leads to a tiny error, only 0.8%.
In the case of an oscillator locked into a PLL instead, as shown in Fig. 1, the spectrum Sfo(fn) is highpass-filtered with a
bandwidth BW. No closed-form solution is given for Eq. 14; however, once the spectrum Sφ is known after the oscillator
simulation, the multiplication by the standard sinc filter profile followed by the integral between fn1 and fn2 becomes a
numerical expression:
σ T0 (T0 ) ≅
1
f 02
f n2

∑ 2 f
f n1

2
n

 f 
⋅ SSCR ( f n ) ⋅ sinc 2  π n  ∆f n 
 f0 

(16)
The formula (16) can be computed in an uncomplicated automated way, using built-in functions widely available in waveform
analysis software such as NI’s LabView. The numerical solution of Eq. 16 can be employed for example to obtain the
variance σ2To and, eventually, the RMS jitter for the second spectrum of Fig. 2: the jitter value calculated this way is 2.15ps.
Once again, the time jitter estimated from the spectrum Sφ(fn) matches within 1% the σTo value that would be obtained from the
direct – but lengthy... – statistical extraction of the jitter from the distribution of the occurrences of zero-crossings.
To summarize, the expression converts the phase noise spectrum into frequency noise spectrum (according to the Laplace
transform rule Sf = j ωSφ) and weights it through the sinc function, to account for the uniform jitter accumulation in the time
span 0→T (i.e., rectangular weight function h(t) ). The integral of the noise spectral density is extended from the reciprocal of
the total observation time f1=1/Tobs to the maximum offset frequency allowed by the spectrum analyzer instrumentation f2.
The formula in Eq. (16) is the practical tool that allows to pass from SSCR to jitter, and can be solved in closed form in a
number of cases (again, a VCO without flicker noise! whose solution is in [1]).
EXPERIMENTAL VALIDATION OF THE FORMULA
A lab apparatus suitable to characterize the time stability of the test oscillators is schematically represented in Fig. 4.
Ω POWER
50Ω
SPLITTER
INST.
AMP.
MCA
STOP
CF+TAC
START
DELAY
≈ 1.1GHz
REF≈
ZEM-4300
DUT
Fig. 4. Block diagram of the lab setup. A low-noise instrumentation amplifier can provide for image rejection, whereas the coaxial stub is
used to synchronize the operation of the zero-crossing detector [3]
In fact, by plugging in Eq. 2 the typical numbers featured by RF oscillators for communications – i.e., running at 1 GHz or so
and with SSCR below –110dBc/Hz @ 100kHz offset; or even worse, featured by crystal signal sources suitable to drive highIF performance ADCs – i.e. running at 100MHz with SSCR of –140dBc/Hz @ 1kHz, it can be recognized that we deal with
time jitters on the order of a picosecond, or lower. In the laboratory practice, this problem can be substantially relaxed by
rigidly translating the oscillation spectrum at lower frequencies. Intuitively speaking, working on a number of the original
periods allows for the jitter to build up with time, and eases the observation of it. After some mathematical processing (or,
SLWA028 – DECEMBER 2003
more heuristically, even using the simplistic Eq. 2 for the same SSCR profile at two different center frequencies) it turns out
that the jitter which will be observed after the downconversion is:
 f 
σ T21 = σ T20 ⋅  0 
 f1 
3
(17)
Of course, the device to be used to lower the frequency without affecting the spectrum is a low-noise mixer. Frequency
dividers would alter the spectrum, lowering the jitter and complicating the estimation, and are usually noisier. Nowadays an
increasing number of high-end oscilloscopes offer a high-frequency jitter characterization option; however, this alternative
method features a resolution that can be enhanced by selecting advantageous frequency ratios, and is very flexible.
The assessment of the time jitter of the slower waveform can be easily accomplished either via a cheaper oscilloscope card, or
through time-to-amplitude conversion. The blocks involved in implementation of the latter, as depicted in Fig. 4, were a zerocrossing detector (comparator) with standard square digital pulses as output, which also rejects any contribution of AM noise,
allowing for the only PM to pass through; a Time-to-Amplitude Converter (TAC), basically a ramp integrator whose voltage
output level is proportional in amplitude to the duration of the pulse received at the input; and a Multi Channel Analyzer
(MCA) storage system, constituted by a memory bank addressed by an input ADC, in order to sort into a histogram the
amplitudes of the pulses sampled at its input. Due to the limited speed of each module, the original oscillation signal frequency
must be shifted down to 50kHz maximum.
1. Free-running LC-tank VCO
The measurement system described above has been employed to prove the validity of Eq. (16) over a bipolar spiral-inductor
LC-tuned VCO used in a RF wireless DAB application [4], with 2.2GHz center frequency. The results of the test carried out on
the oscillator when operated “standalone” (actually, setting its PLL BW to a few 100Hz) are presented in Fig. 5. As emphasized
by the upper curve (diamonds) the VCO’s phase noise decays according to a fairly regular power law, dropping like 1/f2 all the
way after 500Hz.
-20
standalone
fn-2
VCO
30000
R=7.5Kohm C=220nF
Zero-crossing counts
SSCR (fn) [dBc/Hz]
-40
-60
-80
-100
1E+2
a)
1E+3
1E+4
Frequency Offset fn [Hz]
20000
FWHM=498nsec
b)
FWHM=660nsec
10000
0
-1000
1E+5
PLL
-500
0
500
1000
Cycle-to-cycle time jitter [nsec]
Fig. 5. a) Experimental SSCR curves for the LC-tuned VCO and PLL built around it. The discrepancy with the pure 1/f2 trend of the VCO
plot is due to a residual PLL action. b) Statistical distributions of the period duration as collected at the MCA of the setup in Fig. 4
The standalone condition is here effectively reproduced by using a very narrowband PLL in order to avoid the issues due to
jitter divergence (that would require the introduction of complex structure functions in the theory, see [5] or [6]) and thermal
drifts. The oscillation spectrum of Fig. 5a has then been downconverted to 50kHz, and the time occurrences of the waveform’s
zero-crossings were detected and memorized. Fig. 5b reports the histogram of the time period distribution as recorded by the
MCA apparatus. The wider plot shows a Gaussian-shaped profile with a standard deviation σTo = 280ns (that is, 30.3fs on the
original oscillation as computed through Eq. 17). The corresponding jitter estimation obtained when Eq. 16 is numerically
SLWA028 – DECEMBER 2003
applied to the phase noise spectrum, truncated at only 200kHz and thus leaving out a considerable part of the spectrum, gives
260ns - meaning a limited 7.1% error against the experimental data.
2. Phase-Locked Loop tests
The experiment described in the previous paragraph permitted to double-check the correctness of the proposed formula when
used for VCOs. A case of huge practical relevance is to be analyzed by locking the bipolar VCO into an integrated PLL, whose
principle scheme is depicted in Fig. 6. The loop filter consists of a standard charge-pump circuit driving an adjustable off-chip
passive network.
14.5MHz
VCO
8
2
PFD
R
1114M Hz
C1
C
615
Fig. 6. Scheme of principle for the integrated phase-locked loop used in the experimental validation
By adopting a simple R-C series filter (R = 7.6kΩ, C = 220nF, C1 = 0) the BW of the system was set to approximately 30 kHz.
In Fig. 5a, the superposition of standalone and locked-in (triangles) noise spectra testifies the prevalence of the VCO noise
beyond such a bandwidth. The numerical integration of the relationship given in Eq. 16 returns for the PLL a jitter estimate of
185ns at the 50kHz frequency. When weighted against the 260ns computed for the free-running VCO, the data highlights how
the PLL removed a considerable amount of close-in phase noise, as expected especially in integrated oscillators’
implementations.
The measurement performed on the output of the PLL still leads to a Gaussian-shaped histogram (Fig. 5b, narrower plot)
whose standard deviation is 195ns. The discrepancy with the prediction from the formula (16) still keeps to about 5.1%, even
though the integration was stopped to 200kHz only.
To make the analysis even more comprehensive, a 0.25µm LC-tuned CMOS VCO built for 5GHz operation has been locked in
a PLL using a phase noise analyzer (HP3048A). The instrumentation employed allows for the PLL bandwidth to be adjusted by
simply switching a filter bank: the BW values chosen for the test were 21, 43, and 92kHz, producing the spectra reported in Fig.
7a. As clearly appreciable from the slopes indicated inside the plot, and expected from the nature of the technology used to
fabricate the circuit, the flicker noise component is considerable for this kind of VCO under test. The jitter prediction based on
the computation of Eq. 16 for each of the spectra sketched in figure, when referred to the 50-kHz final oscillation, provides the
following RMS results: σT(T0) = 750ns @ BW = 21kHz, 519ns @ 42kHz, and 358ns @ 92kHz. The accuracy of the system
was as good as 7ppm, translating into a negligible 140ps uncertainty for a 50kHz input.
SLWA028 – DECEMBER 2003
SSCR (fn) [dBc/Hz]
-40
-80
-100
-2
fn
-120
-140 3
10
a)
fn
-60
BW = 21 kHz
BW = 43 kHz
BW = 92 kHz
-3
4
10
10
5
6
10
Frequency Offset fn [Hz]
7
10
b)
Fig. 7. a) Experimental SSCR plots for the CMOS PLL frequency synthesizer operated with different bandwidths. b) The jittering zerocrossings of the PLL output, as captured with an Agilent InfiniiumTM oscilloscope
Once the synthesized waveform is mixed down to 50kHz, the jitter analysis can be easily carried out – for sake of practicality,
this time via an Agilent InfiniiumTM oscilloscope. The trigger could be synchronized on the first oscillation crossing, and the
period test menu provided a very straightforward measurement of the variance. The deviations obtained by this method were
σT(T0) = 798ns, 526ns, and 361ns, respectively for the three PLL bandwidths BW mentioned above. The simpler setup, along
with the 10MHz extended span of the numeric integral, led to achieve relative errors even smaller than before: respectively,
6.0% @ BW = 21kHz, 1.3% @ 42kHz, and only 0.8% @ 92kHz. This complete series of validation test provides a full proof to
the SSCR-to-period jitter link proposed in this document, making it a valuable tool for both silicon and system design and
optimization.
APPLICATION: CLOCK SOURCE JITTER FOR HIGH-SPEED ADCs
The best proof and application of the formula’s validity has been accomplished in a very practical case: the measurement of the
clock jitter due to the external source driving TI’s ADS5420, a 14b 65MSps Analog-to-Digital converter. The case can be
viewed as a corollary of the situation described in paragraph C above, since pretty much every commercial synthesizer adopts a
PLL scheme inside, although it features way better specs than the ones reported in Fig. 7a.
To maximize the dynamic range required by wireless communication protocols, while containing the power consumption, a
multibit-per-stage architecture has been chosen. As shown in Fig. 8, the ADC is comprised of five 2.5b stages (2 effective bits
+ 1 bit redundancy for digital correction) followed by a 4b flash. Although a dynamic element matching (cap shuffling)
algorithm was initially designed in the ADC, the inherent matching of the passives of the TI technology used proves acceptable
to 14b level without need for dynamic shuffling, nor one-time trimming, nor calibration of any sort.
SLWA028 – DECEMBER 2003
-
Clock
3b
3b
+
x4
-
shuf
Flash
Flash
VREF
shuf
+
x4
x4
-
shuf
3b
3b
3b
Flash
3b
flash
-
+
x4
Flash
+
x4
Flash
+
T/H
Flash
AIN
4b
Output Delay Line + Digital Correction
14b
Output Drivers
DOUT
Fig. 8. Pipelined converter architecture (2.5 bit per stage), with integrated internal references and on-chip clock driver
The Analog Front-End (AFE) of the circuit is based on a Sample/Hold stage implemented with a flip-around architecture. This
block is where the sampling of the input occurs, storing the voltage signal on capacitors by means of a CMOS switch: hence
the phase stability of the clock signal opening the S/H switches is the main concern for the SNR at high IF. In fact, the sampled
input voltage will vary a lot if the sampling instant occurrence is undetermined by 1ps or more. Therefore, when experimental
data documenting the performance of the part are collected without optimizing the external reference source, the Signal-toNoise Ratio (SNR) featured by the circuit rapidly degrades at high input frequencies (> 100MHz). Since the noise is largely
dominated by jitter contributions at such an IF range, SNR can be determined via the well-known formula already reported in
Eq. 1. By the same token, the formula can be reversed and from the SNR a jitter figure can be inferred. When this exercise is
performed on the ADS5420 fed with non-optimized clock signal, featuring SNR @ 220MHz in the order of 55dBFS, the total
aperture jitter affecting the S/H block turns out to be in excess of 1.3ps - well above the designed spec! Same behavior affects
the performance of any other device based on the same sampling principle, even at the 12 bit level (see for example the case of
a 12b 80MSps device in [7]).
Final goal of the chip designer, as well as of the PCB-designer’s analysis, is to improve the clock circuit in order to reduce the
jitter figure and enhance SNR. This entails the discrimination of the jitter components due to the external clock source, and to
the internal clock conditioning and distribution tree. The first task can been accomplished in the lab by using a phase noise
measurement system, e.g. the PN9000 by Aeroflex Comstron Inc., targeted at avionics tests (VOR), operated in phase-lock
mode and fed with the clock source running at sampling rate fs (about 30MHz in the example illustrated in Fig. 9). The plot
represents the function of phase noise (SSCR or L(fn)) vs. offset frequency fn of the external source, as detected by this
instrument.
Fig. 9. SSCR vs. fn offset frequency profile of the external source at 30MHz, as obtained from the Aeroflex PN9000 phase noise analyzer
The phase noise profile shown in the figure can be exported in ASCII data stream to be processed in a math program such as
Matlab, and now be plugged into the formula (16), where the integral of the noise spectral density is extended from the inverse
of the total observation time, about 4kHz in this case, to the maximum frequency sensed by the PN9000, about 40MHz in our
setup. The experiment returns a cycle jitter as high as 1.36ps. Notice that, since the X-axis of Fig. 9 is logarithmic, the close-in
phase noise does not matter as much, whereas the flat spectrum range extends for 3+ decades to constitute the bulk of the noise.
SLWA028 – DECEMBER 2003
This is not usually the case in integrated oscillators, where the phase noise is way higher close to the carrier and swamps out
the white spectrum contributions. A clear indicator of the difference between the two situations is the absolute value of the
jitter: for the same center frequency, σTo can be tens of picoseconds in the first case, and sub-picosecond for a good, stabilized
quartz (OXCO).
Since the white floor cannot be abated, and since in the formula the 1/fn roll-off of the sinc is balanced by the fn term, the
contribution of a steady white floor becomes exponentially dominant on the logarithmic abscissa of Fig. 9. But by applying
again the link in Eq. 16 to the spectrum in Fig. 9 after a reasonably tight bandpass filter (4MHz bandwidth using a standard LC
filter) has been used after the source, the jitter is calculated in only 25fs. The equation provided then a unique insight about the
reason of this happening. Only a small fraction of the jitter (25fs against 1.36ps, or 1360fs!) actually comes from the 1kHz1MHz span, the remainder being contributed by the floor from 10MHz to 25MHz.
These state-of-the-art numbers emphasize both the accuracy, as well as the extreme difficulty of the measurement. The
contribution figured out above is to be discounted from the aperture jitter inferred from SNR by means of Eq. 1, to isolate the
additional aperture uncertainty introduced by the on-chip regeneration/distribution circuitry. Finally, the RMS subtraction
returns 250fs as the impact of the on-chip preamplifier / clock buffer circuit of Fig. 8, way closer to the designed-in specs. The
number is fully confirmed by the improvement in SNR shown by the plot in Fig. 10, where the overall noise performance taken
@ 61.44MSps and 220MHz increased dramatically from the ~54.5dBFS previously observed (w/o BP filter) to 69.3dBFS
(w/BP filter).
Such an excellent aperture jitter figure can be directly measured via a novel coherent sampling technique [8], and qualifies as
the best performance reported to date for CMOS-based (i.e., non-ECL/PECL) clock circuits. A figure of 250fs enables very
limited roll-off in SNR at higher input frequency, as corroborated by the very intuitive plot of SNR against the full IF axis in
Fig. 10. As a benefit of the jitter optimization, the low-IF performance of the ADC measured in 73.2dBFS SNR, 11.9 ENOB,
92dBc SFDR at 65Msps and 1MHz keeps to 69.3dBFS SNR, 10.7ENOB, 70dBc SFDR at 220MHz, making the ADS5420
uniquely suitable for aggressive single-downconversion receiver chains.
ADS5420 14b 65MSps - IF performance @ 2Vpp
Performance [dB]
95
SNR [dBFS]
90
SFDR [dBc]
SINAD [dBFS]
85
80
75
70
65
0
50
100
150
Fin [MHz]
200
250
Fig. 10. fIN sweep at 65MSps sampling rate on TI’s ADS5420 14 bit 65MSps A-to-D converter for wireless infrastructure applications
The characteristic concave profile of the SNR starting at 100MHz IF is the signature of the prevalence of jitter contributions on
the SNR from 100MHz onwards. The total power consumption of the ADC is about 1W at 65MSps, internal voltage reference,
dissipated from 3.3V analog and digital supply, and 3.3V output driver supply. The latter can be lowered to 1.8V achieving yet
better SNR performance, without putting in jeopardy the data capture window. When external voltage references are provided
to the circuit, the consumption is lowered to about 900mW.
SLWA028 – DECEMBER 2003
All data was collected with a sinusoidal input of –1dBFS amplitude, to avoid clipping. The chip is provided in standard 64-pin
TQFP package with PowerPad® TI technology, which guarantees minimal performance variations between –40°C and +85°C
of full temperature range operation, and from 2.7V up to 3.6V extended analog/digital supply range.
CONCLUSION
In conclusion, despite the variety of synthesizers tested and the simplicity of the final numerical tools employed, the matching
between jitter estimation and measurement keeps always below 7%. In force of this, the analysis proposed and the formulas
devised (Eqs. 14 and 16) become a powerful tool for the designer to interpret simulation results obtained after frequencydomain software (SpectreRF), and for the test engineer to interface SSCR specs with jitter specs in order to perform
calculations to dis/aggregate the data along the clock chain, and optimize the setup for best jitter parameter.
SPECIAL THANKS TO…
Prof. Carlo Samori and Prof. Andrea L. Lacaita (Politecnico di Milano) for many useful discussions about these topics
Salvatore Levantino and Andrea Bonfanti (Politecnico di Milano) for their precious help in both the development of the theory
and the experimental verification of it
Vito Boccuzzi and Sander Gierkink (Agere Systems) for their assistance in performing the measurements on the PLL
I. Papantonopoulos (Texas Instruments) for the tests with Comstron instrumentation.
TO PROBE FURTHER
[1] C. Samori, A.L. Lacaita, A. Zanchi, and F. Pizzolato, “Experimental verification of the link between timing jitter and phase noise”, IEE
Electronics Letters., vol. 34, no. 21, Oct. 1998, pp. 2024-2025.
[2] M. Shinagawa, Y. Akazawa, and T. Wakimoto, "Jitter analysis of high-speed sampling systems", IEEE Journal of Solid-State Circuits,
vol. 25, no. 1, Feb. 1990, pp. 220-224.
[3] A. Zanchi, A. Bonfanti, S. Levantino, and C. Samori, "General SSCR vs. cycle-to-cycle jitter relationship with application to the phase
noise in PLL", in Proceedings of the IEEE SSMSD, pp. 32-37, Austin, TX, Feb. 2001.
[4] G. Calì, G. Cantone, P. Filoramo, G. Sirna, P. Vita, and G. Palmisano, “A high-performance Si-Bipolar RF receiver for digital satellite
radio,” IEEE Transactions on Microwave Theory and Techniques, vol. 46, pp. 2568 - 2576, Dec. 1998.
[5] S.L.J. Gierkink, “Control linearity and jitter of relaxation oscillators”. Ph.D. dissertation, University of Twente, Enschede, The
Netherlands, 1999.
[6] J. Rutman, “Characterization of phase and frequency instabilities in precision frequency sources: fifteen years of progress”, Proceedings
of IEEE, vol. 66, no. 9, Sep. 1978, pp. 1048-1075.
[7] A. Loloee, A. Zanchi, H. Jin, S. Shehata, and E. Bartolome, “A 12b 80MSps pipeline ADC core with 190mW consumption from 3V in
0.18µm digital CMOS”, in Proceedings of ESSCIRC 2002, pp. 467-470, Florence (Italy), Sep. 2002.
[8] A. Zanchi, I. Papantonopoulos, and F. Tsay, “Measurement and Spice prediction of sub-picosecond clock jitter in A/D converters”, in
Proceedings of ISCAS 2003, May 2003, Bangkok (Thailand), vol. 5, pp. 557-560.
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