TDA1541 TDA1305T PE8001A PD2028 PD2028A (vagy PD2028B) PD2028B PD2028A PD2028A (vagy PD2028B) PD2026B PCM1700 PCM1700P PD0034 PCM56 PD2026A PCM58P PD2026A PCM63P PCM58 PD2028A AKM4321 PCM1716 PCM1716 PCM1716 PCM1702J PD2026A PD2026B PD2029A PE8001A PD2029A PD2029A PE8001A PD2028 PD2028B PD2028B PD2028B 4x PCM1704K AKM4324 4x PCM1702 PCM58P
PROTON AC423 PROTON AC424 QUAD66 QUAD77 REGA PLANET REVOX B225 REVOX B226 REVOX C221 ROKSAN ATTESSA DP3P ROKSAN CASPIAN ROTEL RCD-02 ROTEL DCM-9PRO ROTEL RCD-855 ROTEL RCD-856BX ROTEL RCD-865BX ROTEL RCD-870 ROTEL RCD-945AX ROTEL RCD-955AX ROTEL RCD-955 ROTEL RCD-961 ROTEL RCD-965BX ROTEL RCD-970BX ROTEL RCD-971 ROTEL RCD-975 ROTEL RCD-991 ROTEL RCD-1070 SANSUI CD V1000 SANYO CP489 SEG CD200 SHANLING CD-T80 SHANLING CD-T80UK SHARP DX112 SHARP DX650 SHERWOOD CD1 SHERWOOD CD1060C SHERWOOD CD1160R SHERWOOD CD1192R SHERWOOD CDC2000C SHERWOOD CDC2010RC
LC78820 TDA1311A TDA1541A CS4328 PCM1710U TDA1540 TDA1541 SAA7310 CS4328 TDA1305 PCM1732 PCM63 TDA1541 SAA7323 SAA7323 TDA1540 SAA7341GP T TDA1541A TDA1541 PCM1732U SAA7323GP T TDA1305T PCM63 TDA1305T PCM63P PCM1732 PCM56 LC7881 YM3020 PCM1738E PCM1738E IR 3K16BM LC7880 TDA1547 D6372 CX PCM56 YM4113B PD6376 PD6376
SHERWOOD CD4030R SIMAUDIO MOON ECLIPSE SONIC FRONTIERS SFCD1 SONY CDP-40 SONY CDP-101 SONY CDP-222ES SONY CDP-222ESD SONY CDP-227ESD SONY CDP-228ESD SONY CDP-302ES SONY CDP-303ESII SONY CDP-313 SONY CDP-315 SONY CDP-333ESA SONY CDP-333ESD SONY CDP-333ESJ SONY CDP-337ESD SONY CDP-338ESD SONY CDP-497 SONY CDP-501ES SONY CDP-502 SONY CDP-502ES SONY CDP-502ESII SONY CDP-520ESII SONY CDP-552 SONY CDP-552ESD SONY CDP-553ESD SONY CDP-555ESA SONY CDP-555ESD SONY CDP-555ESJ SONY CDP-557ESD SONY CDP-620 SONY CDP-650 SONY CDP-701ES SONY CDP-707ESD SONY CDP-770 SONY CDP-777ESA SONY CDP-M95 SONY CDP-MS1
SAA7350BS 4x PCM1704K UltraAnalog D20400A 1x PCM54 (S/H) CX20017 PCM56P J 1x TDA1541 TDA1541 PCM58P CX20152 CX20152 CXD2565M CXD2565M CXD2562 TDA1541 CXD2562 TDA1541 2x PCM58P CXD2561 CX20017 PCM54 CX20152 PCM53JP-V CX20152 PCM54 CX20152 PCM53JP-V K CXD2562 TDA1541A CXD2562 PCM58P PCM54 PCM54 CX20017 PCM58P PCM56P CXD2562Q TDA1541 CXD8594 + CXA8042AS
SONY CDP-R3 + DAS-R1a CXD2552Q + CXD2552 SONY CDP-X229ES CXD2562Q SONY CDP-X3000 CXD2562Q + CXA8042AS SONY CDP-X303ES CXD2562Q SONY CDP-X5000 CXD2562 + CXA8042 SONY CDP-X505ES CXD2562Q SONY CDP-X33ES CXD2552Q SONY CDP-X55ES CXD2552 SONY CDP-X777ES CXD2552BQ SONY CDP-X779ES CXD2562 SONY CDP-X77ES CXD2552 SONY CDP-X7ESD PCM58P S SONY CDP-X900 CXA8042 SONY CDP-XA20ES CXD8505BQ + CXA8042AS SONY CDP-XA30ES CXD2562Q + CXA8042AS SONY CDP-XA50ES CXA8042AS SONY CDP-XA55ES CXD8594Q + CXA8042S SONY CDP-XA5ES CXD2562Q + CXA8042AS SONY CDP-XA7ES CXD2562 + CXA8042AS SONY CDP-XB920 CXD8715 + CXA8355 SONY CDP-XB720E CXD8735N SONY CDP-XB930 CXD8735N SONY CDP-XE300 CXD8567 SONY CDP-XE310 CXD8567 SONY CDP-XE330 CXD2529Q SONY CDP-XE900 CXD8505 + CXA8055 SONY CHC-P11 (mini hifi) PCM1710U SONY DAS-R1 2x TDA1541A S1 (single crown) SONY PLAYSTATION SCPH-1002 AKM AK4310VM or AK4310AVM (late) SONY PLAYSTATION SCPH-5502 AKM AK4310AVM SONY PLAYSTATION SCPH-5552 AKM AK4310AVM SOUND WAVE CD1100 LC7881 SUDGEN OPTIMA TDA1543 SUDGEN SDA-1 TDA1541 SUDGEN SDT-1 TDA1541A S1 (single crown) T+A CD1210R SM5864AP TAG McLAREN CD20R CS4329 TALK ELECTRONICS THUNDER 3 CS4390 TASCAM CD201 MN6474

TEAC CPD3450SE TEAC PD155mk2 TEAC PD160 TEAC PD365 TEAC VRDS 7 TEAC VRDS 8 TEAC VRDS 9 TEAC VRDS 10SE TEAC VRDS 25 TEAC ZD5000 TECHNICS SL-P1 TECHNICS SL-P2 TECHNICS SL-P50 TECHNICS SL-P110 TECHNICS SL-P120K E TECHNICS SL-P272A TECHNICS SL-P520 TECHNICS SL-P555 TECHNICS SL-P720 TECHNICS SL-P770 TECHNICS SL-P990 TECHNICS SL-P999 TECHNICS SL-P1200 TECHNICS SL-PG480A TECHNICS SL-PJ28A TECHNICS SL-PS670D TECHNICS SL-PS700 TECHNICS SL-PS770A THETA DSP THOMSON LAD300 THULE CD100 THULE SPIRIT TOSHIBA XR40 UHER UCD-210 UNIVERSUM CD4682 USHER CD-100 WADIA 23 WADIA 850 WADIA 860
YDC103 Y3015 TC9218F YM7121B SAA7350 PCM1702 PCM1702 TDA1547 AD1862J PCM53 PCM53 PCM53 MN6474 PCM54HP PCM54HP MN6474 MN6618A MN6471 MN6618A 2x PCM56P + 2x PCM56P-J 4x PCM56P-J 4x PCM56P-J PCM54HP MN662713 MN6477 MN6474 MN6474 MN64733 PCM67 TD6720N CS4303 PCM1715U TD6705AP LC7882 PCM56 PCM1732 AD1865 PCM1702 4x PCM1702
WADIA 861 YAMAHA CD-2 YAMAHA CD-3 YAMAHA CD-2000 YAMAHA CDX-3 YAMAHA CDX-410 YAMAHA CDX-420 YAMAHA CDX-470 YAMAHA CDX-480 YAMAHA CDX-490 YAMAHA CDX-580 YAMAHA CDX-590 YAMAHA CDX-593 YAMAHA CDX-700 YAMAHA CDX-810 YAMAHA CDX-880 YAMAHA CDX-890 YAMAHA CDX-893 YAMAHA CDX-900 YAMAHA CDX-993 YAMAHA CDX-1100 YAMAHA CDX-2020
4x PCM1704 PCM53 PCM53 PCM54HP PCM54 PCM56 PCM56 YDC103 MN66271 MN66271R YAC514 YAC514 YAC514 PCM56 2x PCM56J YAC514 YAC514 YAC514 PCM56 YAC514F PCM56 PCM58

Noise and distortion in the data transmission and recording channel can cause jitter in the re-generated data stream and clock signal. In digital systems, the Bit Error Rate (BER) is one of the parameter that describes the reliability of the data. Mathematical models shows that there is a relation between jitter and BER.

Table of contents

Preface....2 Summary....Introduction.....Some jitter sources in digital audio systems...9 2.1 Data transmission and recording...9 2.1.1 Reading process of the channel..10 2.1.2 Effect of noise and distortion in the channel...10 2.1.3 Characteristic of the transmitted RF-signal..12 2.1.4 Data-to-clock jitter...14 2.1.5 Data-to-data jitter...15 2.2 Effect of the bandwidth...16 2.3 Timing recovery....21 2.3.1 Phase-Locked Loops...21 2.3.2 Noise performance of the oscillator..23 2.3.3 Noise spectrum at the oscillator output..24 2.3.4 Noise spectrum at the Phase-Locked loop output..Mathematical description of timing jitter...27 3.1 Sinusoidal wave timing errors...27 3.1.1 Modulation of the timing errors...27 3.1.2 Frequency spectrum jittered clock..28 3.1.3 Jittered clock frequency...29 3.2 Distribution of random timing errors...30 3.2.1 Spectral characteristics of an ideal clock..31 3.2.2 Statistical description of a jittered clock signal..34 3.3 The relation between noise and jitter...37 3.3.1 Spectral characteristics of random signals and noise..37 3.3.2 Noise-equivalent bandwidth...41 3.3.3 Spectral characteristics of a sinusoidal wave plus white-noise.42 3.3.4 Measuring the Signal to Noise Ratio...43 3.3.5 Jitter contribution due to noise...The influence of timing jitter on A/D- and D/A-conversion.48 4.1 Converter Basics...48 4.1.1 A/D-conversion...49 4.1.2 D/A-conversion...49 4.1.3 Sampling jitter...51 4.1.4 Timing errors....53 4.2 The influence PLL noise on converters...56 4.2.1 The effect of PLL noise on multibit D/A-converters..57 4.2.2 Noise power of a multibit D/A-converter...59 4.2.3 The effect of PLL noise on bitstream D/A-converters..62 4.2.4 Noise power of a bitstream D/A-converter..65 4.2.5 The effect of PLL noise on A/D-converters..67 4.3 Measuring the jitter performance on converters..71 4.3.1 Jitter measurement set-up for D/A-converters..72 4.3.2 Jitter measurement set-up for A/D-converters..73 4.3.3 Total Harmonic Distortion + Noise measurement..73 4.3.4 Measured performance of the TDA1541A..75 4.3.5 Measured performance of the TDA1547..76

2.1.1 Reading process of the channel The continuous sequence of pits and lands carried by an optical disc, represents a serial-bit line code, which is generally designated in literature as nonreturn-to-zero (NRZ) signalling. Following the media read-out, the recorded pattern NRZ sequence becomes, in the analogue domain, the RF-signal. The modulation of the RF-signal is read-back with an optical pick-up unit. The timing diagram of the RF-signal from an optical disc and the generated NRZ-signal is shown in Figure 2. This shows the amplitude of the RF-signal varying with pit length. Since the pit causes light scattering the loss in amplitude is greater the longer the pit, and similarly, the output increases to higher levels for larger lands between the pits.

pit RF

Intensity of the reflected light
land Tangential direction

Correct slicing level

t NRZ t
Figure 2 Timing diagram generation of the RF-signal and NRZ-signal
Channel bits carries the minimum amount of information which, for a digital signal, may only be either 0 or 1. When translated to the disc relief structure, the channel length represents a minimum physical length along the disc spiral. The channel-bit rate is equal to the proportion between the linear scanning velocity (= 1.30 m/s) and the channel-bit length (= 0.3 m). For CD, the period of the channel bit rate (T) is equal to 231.4 ns. The symbol- or runlength of de modulation pattern on the CD disc various between 3T to 11T. 2.1.2 Effect of noise and distortion in the channel The accuracy of pits and lands positioning determines quality of the retrieval of the original audio data. Especially for recordeble/rewriteble optical discs, such as CDR/RW, a large portion of noise and distortion introduced in the recording process can be attributed to data-dependent shifts in the effective positions of the recorded transitions. Bandwidth limitations of the write path and spot shape during write can be primary cause of such shifts. The readout laser beam may have imperfections known as aberrations. The physical cause of an aberration can for example be defocus, disc tilt or thickness error of the disc substrate, or an imperfection in the lens itself. Aberrations can be seen as a collection of noise sources that generates jitter. During read, the noise signal has both additive and multiplicative components. Noise sources including the medium, laser, detector and preamplifier. Laser noise is due essentially to fluctuations of the light intensity. It is usually multiplicative, i.e. it takes the form of random fluctuations of the amplitude of the

3.1.1 Modulation of the timing errors
Assume that the clock is modulated by a sinusoidal wave with time amplitude t. In this case the time axis of the ideal and the jittered clock are related by:
t n = t o + t sin ( jm t o ) [s]

Equation 21

in which: to = time-instant time axis of ideal clock [s]; tn = time-instant time axis of jittered clock [s]; jm = jitter-modulation frequency sinusoidal wave [rad/s]; t = jitter-modulation amplitude [s].
The clock is longitudinally modulated by a sinusoidal wave, which results in a phase modulation (PM) signal. The jittered clock signal is therefore mathematically described by:
u c (t ) = u c cos( c t o + t sin ( jm t o ) ) = u c cos( c t o + c

] t sin [ t ])

Equation 22
where c is the carrier amplitude. Equation 22 is called the zero order Bessel function of the first sort. In this (= ct) is the modulation-index in the unit radians. For simplicity in mathematics, the clock is assumed to be sinusoidal. Or in the notation normally used for phase modulation: u c (t ) = u c cos( c t o + sin jm t o

Equation 23

3.1.2 Frequency spectrum jittered clock
The frequency spectrum of the jittered clock is obtained by using < 1 (cos[x] 1 and sin[x] x with x is small), this means that the we consider a narrow bandwidth. This leads to:
u c (t ) = u c cos( c t o )cos( sin jm t o ) u c sin ( c t o )sin ( sin jm t o u c cos( c t o ) u c sin ( c t o )sin ( jm t o ) = uc cos( c t o ) u c (cos c jm to cos c + jm to ) 2

Equation 24

The clock is phase modulated but the higher order Bessel components are neglected in this approximation. The spectrum of the clock, according to Equation 24, is shown in Figure 22.
A [dB] 20log c JDF 20log c 2

[rad/s]

Figure 22 Frequency spectrum of a jittered clock
The output spectrum of the jittered clock contains a carrier at c with amplitude c and two side (jitter) distortion components at distance jm with equal amplitudes
(c/2) and opposite signs. The maximum phase and maximum time error are related by (= ct). The Jitter Distortion Factor (JDF) is equal to:
2 JDF = 20 log( f c t ) [dB]

Equation 25

From Equation 25, there can be conclude that the jitter distortion component amplitudes are proportional with the clock frequency c and proportional with the maximum time deviation t. Based on Equation 25, the relationship between the JDF, the maximum time deviation t and the clock frequency is plotted in Figure 23.

-20,00

JDF [dB]
20,00-40,00 0,00-20,00 -20,00-0,00 -40,00--20,00 -60,00--40,00 -80,00--60,00 -100,00--80,00 -100,400 fc=34MHz fc=26MHz 500 fc=18MHz fc=10MHz 100000 -80,00 -60,00 -40,00

t [ps]

Figure 23 The jitter transfer function for sinusoidal wave timing errors on the clock signal

Due to clock jitter the sample period (Ts) is not constant and in sub-paragraph 4.1.3 we have concluded that jitter is translated in amplitude errors at the output of the D/Aconverter. Firstly consider a jittered clock modulated by a sinusoidal wave, according to Equation 22. The effect of the clock jitter can be mathematically described to take from each sample the Fourier transformation. However, this is a very cumbersome method, therefore we are approximate the discrete output signal as a time continuous function. To substitute Equation 21 in to Equation 84, we found the influence of the sinusoidal timing errors on the converted output signal: u A (t ) = u A sin ( A t n ) = u A sin ( A t o A t sin jm t o

Equation 85

Looking at Equation 85, there can be seen that the jitter is phase modulated with the output signal uA. The modulation index is proportional with the signal frequency fA and the jitter amplitude t ( = A t). The frequency spectrum at the output of a multibit D/A-converter is obtained by using << 1 (cos[x] 1 and sin[x] x with x is small), because the signal frequency is much smaller than the sample frequency. This leads to: u A (t ) = u A sin ( A t )cos( sin jm t ) u A cos( A t )sin ( sin jm t = u A sin ( A t ) u A cos( A t )sin ( jm t ) = u A sin ( A t ) u A (sin A + jm t sin A jm t ) 2

Equation 86

The output signal of the multibit D/A-converter is phase modulated but the higher order Bessel components are neglected in this approximation. The spectrum of the output signal, according to Equation 86, is shown in Figure 48.
A [dB] 20log A JDF 20log A 2
Figure 48 Frequency spectrum of a multibit D/A-converter as a result of clock jitter
The output spectrum of the multibit D/A-converter contains a carrier at A with amplitude A and two side (jitter) distortion components at distance jm with equal amplitudes (A/2) and opposite signs. Notice that one jitter distortion component can be outside the audioband, if (A - jm) A(min) and (A + jm) A(max). The maximum phase and maximum time error are related by (= At).
The total jitter distortion factor (JDF) is equal to:
2 JDF = 20 log( f A t ) [dB]

Equation 87

From Equation 87, there can be conclude that the jitter distortion amplitudes are proportional with the signal frequency A and proportional with the maximum time deviation t. The amplitude of a jitter distortion component is increasing with 20 dB/decade when the signal frequency is increasing, because at higher frequencies the timing error causes a greater modulation index ( = At). For audio signals, the influence of jitter is biggest at the maximum frequency of the audio bandwidth (for CD; 20 kHz).
4.2.2 Noise power of a multibit D/A-converter
In a multibit D/A-converter the phase modulation gives a phase modulation of the analogous output. In sub-paragraph 4.2.1 we have calculated that the phase modulated output signal is equals to Equation 86. Substitution of the VCO time-dependence according to Equation 17 (see sub-paragraph 2.3.2) yields the general form for one noise component: en =

K 0 en ( RMS ) = 4 f c

f A B + f A ln (B f A ) B fA f min

Equation 106

in which B (= fmax fmin) is the audio bandwidth. The SNR of a bitstream D/A-converter is equal to:

= 10 log10

P SNR jitter = 10 log10 A P N 2 u A( RMS ) K 0 en ( RMS ) 4 f u c A ( RMS )
f A B + f A ln (B f A ) B fA f min

Equation 107

Figure 52 shows the relation between the SNR, according to Equation 107, and the signal frequency, for full scale (= 0 dBFS => PA= 0.5 W) input sinusoidal wave signals. The audio bandwidth was equal to 22 kHz, so it was possible to calculate the SNR at 20 kHz. Further, the clock frequency was equal to 16.9344 MHz and K0 was equal to 2108 rad/s/V.
100,0-120,0 80,0-100,0 60,0-80,0 40,0-60,0 20,0-40,0 0,0-20,0
40,nV/Hz 40 nV/Hz 80 nV/Hz 0,nV/Hz 600 nV/Hz nV/Hz 20000
Figure 52 The SNR versus the signal frequency and VCO-noise for a bistream D/A-converter
Looking at Figure 52, there can be seen that the SNR is almost flat over the audio bandwidth, for a given VCO-noise amplitude. This in contrast with a multibit D/Aconverter, where the SNR, due to jitter, at the output of the converter has a slope of 20 dB/decade (see Figure 50). Further, there can be also seen that in most circumstances the sensitivity of the bitstream D/A-converters to small timing errors (as a result of VCO-noise) is worse with respect to multibit D/A-converters. Only for high frequencies, the performance degradation due to timing errors is less small for bitstream D/A-converters with respect to multibit D/A-converters.
4.2.5 The effect of PLL noise on A/D-converters
In this sub-paragraph we examines the influence of the PLL jitter on the performance of an A/D-converter. Due to timing errors, the A/D-converter converted the input samples at wrong time instants, which results in small amplitude errors. The A/D-conversion process consists of sampling and quantization. Firstly the sampling process is examined, because the jitter only influences the sampling process. Assume that the input of the A/D-converter is a sinusoidal wave, which is sampled by Dirac-pulses with a period of Ts. The converted output signal us(t) is a continuous function, which is equal to: u s (t ) = u A (t ) (t ) =u A sin ( A t ) (t-mTs )

sin ( A mTs ) (t mTs ) [V]

Equation 108

Firstly, we approximate the clock is longitudinally modulated by a sinusoidal wave with time amplitude t. The effect of the clock jitter can be mathematically described to take from each sample the Fast Fourier Transformation (FFT). However, this is a very cumbersome method, therefore we are approximate the discrete output signal as a time continuous function. We can make this approximation by the assumption that the surface of the Dirac-pulse at t = mTs is equal to the value of uA(t) on the same instant. Equation 21 gives the relation between the ideal and the jittered time-axis. Substitution of Equation 21 into Equation 108 yields the sampling values:
= u A sin ( A t o )cos( A t sin jm t o ) + u A cos( A t o

Equation 109

u s (t o ) = u A sin ( A t o + t sin{ jm t o } ) = u A sin ( A t o + A t sin jm t o

]) )sin ( t sin[ t ])

A jm o
For low input frequencies At<<1, Equation 109 can be simplified by using cos(Atsin[jmt]) 1 and sin(Atsin[jmt]) Atsin(jmt) which yields:
u s (t ) u A sin ( A t ) + u A A t cos( A t ) sin ( jm t ) = sin ( A t ) + u A A t (sin A + jm t sin A jm t ) 2

Equation 110

From Equation 110, the frequency spectrum at the output of an A/D-converter is similar to the frequency spectrum at the output of a multibit D/A-converter (see Figure 48). It contains a carrier at A with amplitude A and two side (jitter) distortion components at distance jm with equal amplitudes (A At/2) and opposite signs. The VCO-noise results in a phase modulated spectrum of the discrete samples. Substitution of the VCO time-dependence according to Equation 17 (see subparagraph 2.3.2) yields the general form for one noise component:
u A K 0 en A sin ( A + jm )t [V/ Hz ] 2 c jm

Equation 111

Or as function of the frequency by substitution of = A + jm and jm = - A: en = u A K 0 en sin (t ) [V/ Hz ] 2 c A

Equation 112

The power of a single noise component is equal to: u A K 02 en e = 8 c2
A u A K 0 en ( RMS ) = 4 f c A

Equation 113

fA ff A
From Equation 113, there can be concluded that the noise power density depends on the noise performance of the VCO expressed by the PLLs electrical parameters K0, en(RMS) and fc, and the amplitude A and the frequency fA of the input sinusoidal wave. The A/D-converter treats the noise caused by the jitter as normal signal. During A/Dconversion the jitter signal is directly converted and the quantization operation adds the normal quantization noise expressed by eq (this quantization noise has the same power as in the unjittered case). The choice of the PLL loop filter bandwidth (PLL) greatly influences the noise density near the frequency of the converted sinusoidal wave. Figure 53 shows jitter and quantization noise densities after A/D-conversion.

A/D-converter spectrum

en eq c A

log uc PLL en

Figure 53 Noise spectrum from the clock and after A/D-conversion, which contains quantization noise eq and jitter noise en from the PLL. The jitter noise density rises near the sinusoidal wave frequency.
After A/D-conversion the noise consists of the normally observed quantization noise and the jitter noise from the PLL. The quantization noise (eq) is approximately white noise and its power is almost independent of the input signal at higher signal levels. The number of bits determines the quantization noise density and is equal to:
SNRquantization = 6.02 n + 1.76 [dB]

Equation 114

where n is the number of bits. The jitter noise (en) according to Equation 113 is increasing at higher input level or when the frequency of the input signal is increased. Observe that the jitter noise density rises near the input frequency. A PLL with a smaller bandwidth will have a higher jitter noise near the input frequency and will impose stronger requirements on the noise performance of the VCO. When the external clock is stable and its noise is low, the PLL can have a higher bandwidth, which reduces the jitter noise near the input frequency. For a general and a robust solution a good PLL with a small bandwidth is preferred. In Figure 53 it is assumed that the PLL has a first order loop filter, which results in a flat noise density inside the PLL bandwidth. When a second order loop filter is used, the noise density will decrease again when going towards the input frequency, which will yield somewhat less jitter noise in practical situations. The jitter noise contribution and the consequences for the VCO-noise specifications can be calculated when the noise is determined by means of a fast Fourier computation. This will yield the tightest specifications for the PLL. Its total jitter power is found by integration of the jitter noise over the audio bandwidth (B). The jitter spectrum can be divided into three parts, first it increases, afterwards it is constant and for higher frequencies it decreases. When the corner frequencies are f1 and f2, as shown in Figure 53, the total jitter noise contribution can be written as:

4.3 Measuring the jitter performance on converters
In the previous paragraph we have been deduced the noise spectrum at the output of a multibit-, bitstream D/A-converter and an A/D-converter. In this paragraph we describe a measurement method to measure the influence of a noisy clock on the converted output signal of a converter. The converter output contains besides the converted sinusoidal wave signal also jitter noise originating from the jittered clock. The jitter noise degrades the performance of the converter, which can be measured by the Total Harmonic Distortion + Noise (THD+N) figure. This distortion measurement
can be performed by professional measurement equipment, like the Audio Precision, which neglects the signals in a part of the output spectrum. The obtained previous theory of the performance degradation, due to a noisy clock, has been evaluated for the TDA1541A multibit D/A-converter, the TDA1547 bitstream D/A-converter and the TDA1309H codec (combination of an A/D- and D/A-converter.
4.3.1 Jitter measurement set-up for D/A-converters
Figure 56 shows the measurement set-up to measure the jitter sensitivity on the performance of D/A-converters. Most D/A-converters for audio applications operates on a system clock of 11.2896 MHz (fc = 256fs, where fs is equal to 44.1 kHz). The jittered system clock is generated by the TDA1315H Digital Audio Input/Output circuit (DAIO). In receiver mode the TDA1315H converts the AES/EBU serial format to IS parallel format with regeneration of the system clock (SCK). The internal PLL is used for clock recovery. The analogous generator, which can generates different signal waveforms and pseudorandom white noise, of the Audio Precision One has been used as jitter source and connected to the VCO-input (pin RCfil). On this way, the PLL is used as phase modulator to modulate the timing errors (according to the mathematical models described in the previous chapters) on the clock frequency. The digital generator of the Audio Precision One has generated the digital sinusoidal wave. The data signal (16 bits) is with help of the AES/EBU serial output connected with the test set-up. After the D/A-converter there was placed a third order Butterworth low-pass filter with a cut-off frequency of 23 kHz. This filter suppresses all the noise and distortion components above the audio bandwidth.

HP4395A TDS 784D

spectrum analyzer
AES/EBU TDA1315 input DAIO

DAC under test R-out

analog L-out analog R-out

f -3dB = 23 kHz

analog out digital out

system one

Figure 56 Measurement set-up for jitter measurements on D/A-converters

4.4.3 Conclusion of the listing test
After the listing test, we can make the following conclusions. It was hardly to hear the influence of jitter and it is hardly too say that jitter is the cause of distortion and the hardness in digital audio equipment. Our listing test shows that some music pieces sound better with jitter. On this moment I cannot give a good scientific explanation of this. Maybe the noise, causes by jitter, masked some negative distortion components within the recorded music piece. The used jitter amplitude during the listing test was very high comparing to practical situations. This is done too get a good perceptional observation of the influence of jitter on de audio performance. From this point of view, we can conclude that good practical circuit realizations, which is found in most low- and high-end CD-players, the audibility of jitter will be negligible with respect to the THD+noise performance of the converter itself. Also the mathematical jitter models have shown that most jitter noise is concentrated around the input signal where the perceptional masking effect of the ear is the largest. Lastly I would like to make the comment that listing to high-quality audio equipment is about subtle differences. There are in the first place difficult to determine, but are quite easy to differentiated in the long run. If this is the case with jitter, it can only determine by complete well-defined and well-thought listing tests on high-end audio equipment.
5 The influence of jitter on the decoding system
In paragraph 2.1 we have described that noise and distortion in the data transmission and recording channel can causes jitter in the re-generated data stream and clock signal. This may have a significant impact on the overall player playability performance. Unfortunately, the playability issue is far from being limited only to the read channel. These issues start at the media level, where badly manufactured or recorded discs substantially decrease the playability margin of the system. Temperature and humidity variations may affect the optical construction and give rise to aberrations or shift the laser specifications to unacceptable values, which in turn translated to distorted RF-signals. The capability of the servo loops to maintain the laser spot in focus and on track when scanning media with surface defects, substrate thickness variations, track eccentricity, or some other no uniformity contributes heavily to the quality of the regenerated audio data stream. This chapter examines the influence of jitter on the player playability performance.

uh ul h l

Equation 117
Here uh and ul are the mean values for u(t) RF-signal amplitude high and low without ISI, while h and l are the root mean square (RMS) of the additive white noise for each Gaussian distribution. In a practical receiver implementation, ISI exists due to receiver bandwidth limitation, baseline wander, or nonlinearity of the active components. If we monitor the RFsignal eye diagram before the data decision, we find that, in addition to random noise, the signal has a certain amount of bounded amplitude fluctuation caused by ISI, which exhibits strong pattern dependence. To estimate the ISI penalty on optical sensitivity, a simple solution is to consider a worst-case amplitude-noise distribution. This is done separately by shifting the mean value of the Gaussian distribution from uh and ul to the lower amplitude boundary (uh uISI) and (ul + uISI). It is assumed that uISI is the vertical eye closure caused by ISI (see Figure 66).
u(t) uh uh-uISI uTH ul-uISI ul
Figure 66 Worst-case amplitude-noise distribution in the presence of ISI facilitates estimation of the ISI penalty on optical sensitivity
Under this condition, the signal Q-factor can be obtained by calculating the BER from the worst-case noise distribution. Assuming the decision threshold is optimized for minimum BER, the Q-factor is related to vertical eye closure uISI as follows:

uh ul 2 uISI h + l

Equation 118

1 QBER BER = erfc

Equation 119

where:

erfc( x ) = 2
QBER is the minimum required Q-factor for a given BER. Based on Equation 119, the relationship between QBER and BER is plotted in Figure 67.
Figure 67 BER versus QBER
Usually the signal peak-to-peak differential swing (up-p = uh ul) are measured and assume h = l = NRMS, so the Q-factor becomes: 85

u p p 2 uISI

2 NRMS

Equation 120

Here NRMS is the equivalent RMS noise at the input of the limiting amplifier (or the decision circuit). Equation 120 demonstrates that Q-factor is a measure of the vertical eye opening to RMS noise ratio in the presence of ISI. The Q-factor reduction due to ISI causes optical power penalty or error floor in an optical receiver design.
5.2.2 Intersymbol interference penalty
In an optical receiver, ISI can result from the following sources: high-frequency bandwidth limitation, insufficient low-frequency cut-off caused by AC-coupling or DC-offset cancellation loop, in-band gain flatness or multiple reflection between the interconnection of the pre-amplifier and the limiting amplifier. Depending on the nature of the data pattern being received (for CD EFM and for DVD EFM+ encoding), the ISI distortion could differ. ISI results in eye closure in both amplitude and timing. This is illustrated in Figure 68.

Equation 130

p p = 2 QBER [s]

Equation 131

The relationship between the decoder minimum eye opening requirement and the Qfactor is illustrated in Figure 73. To achieve a specified BER, the corresponding minimum QBER can be found from Figure 67.

(BER = 10-12)

p-p/2 Q=Tb/2 Tb p-p/2
Figure 73 The relationship between decoder minimum eye opening and the Q-factor
When the jitter frequency at the decoder input is higher than the PLL bandwidth, the decoder jitter tolerance (noted as tp-p) is related to Topen as:

t p p = (Tb Topen ) [s]

Equation 132
To avoid degrading the optical sensitivity, the decoder high-frequency jitter tolerance should satisfy:
t p p 2 QBER + d p p [s]

Equation 133

Depending on the slope of the edge transition, the random jitter is generated from the additive white noise at signal transitions. Assuming that the signal rise/fall time (10% to 90%) before limiting is symmetrical and equal to tr, the random jitter can be estimated by:

tr [s] NRMS ) 0.8

Equation 134
Here tr is dependent on the overall receiver small-signal bandwidth BWtotal. Assuming a first-order low pass filter: tr 0.22 BWtotal

Equation 135

At the optical receiver input, it is assumed that the transfer function is linear. Therefore, random jitter can be expressed as a function of the peak-to-peak current to the total RMS noise ratio at the receiver input:

tr [s] Ntotal ) 0.8

Equation 136
Using Equation 136, the random jitter at the limiting-amplifier output is plotted in Figure 74 as a function of the receiver input current to noise ratio.
Figure 74 Random jitter and input-current-to-noise ratios are shown for different rise times
The decoder jitter tolerance penalty on optical sensitivity can be estimated by combining Equation 133 and Equation 136, then solving for Ip-p as:

I p p =

2 QBER tr d p p ) 0.8 Ntotal

Equation 137

Figure 75 shows the optical sensitivity achievable with different decoder jitter tolerance (BER = 10-12).
Figure 75 The relationship between optical sensitivity and decoder jitter tolerance

Modulation Resolution Asymmetry

slicer

Jitter

pick-up

RF ampl.

Phase det.

Loop filter

Recovered clock PLL

Figure 77 Example of a general diagram for jitter measurement
An example of the frequency characteristics for the equalizer and the low-pass filter is shown in Figure 78. The low-pass filter is a 6th order Bessel filter with a cut-off frequency of 8.2 MHz. The analogue equalizer is a 3-tap transversal filter with the following transfer function:
H ( z ) = 1.35 z 2.093 0.+ z 4.186

Equation 139

Figure 78 Frequency characteristic for the equalizer and the low-pass filter
According to the CD-standard the jitter must be less than 35 ns for each individual pit and land (3T.11T). The jitter is defined as the standard deviation of time length variations between leading and trailing edges (data-to-data) of specific 3T.11T pits or lands, measured at reference scanning velocity and at decision level of the RF-signal. According to the DVD-standards the jitter for DVD-ROM discs must be less than 8.0 % and for DVD+R/RW discs the jitter must not exceed than 9.0 % of the channelbit clock period. The jitter is defined as the standard deviation of time variation of the digitized data passed through the equalizer. The jitter of the leading and trailing edges is measured to the PLL clock (data-to-clock) and normalized by the channel-bit clock period.
Measurement recommendations:
for correct and reproducible measurement, it is recommended to select an area on the disc with random EFM-data (not digital silence); because defects on the disc may affect the pit and land length distribution, it is also recommended to select a clean area on the disc; the bandwidth of the RF-amplifier shall be greater than 20 MHz in order to prevent time-delay distortion (time-delay variation maximum 3 ns below 6.5 MHz); to avoid confusion about pit and land, a possible sign inversion in the RFamplifier should correctly be taken into account; the AC coupling (high-pass filter) shall be first order with a cut-off frequency of 1 kHz; for sufficient accuracy, following TIA settings are recommended: - number of samples 105 per measurement - time base 10 ns.
5.4 CD measurment results
In this paragraph, the results are described of the evaluation of four audio CD discs: three pre-recorded audio CDs with different reflection layer material and one CD-R disc based on a organic dye coating. The disc performance has been measured on the CD CATS SA3 from Audio Development. The CATS SA3 is a professional CD-Analyzer to measure all relevant disc parameters and are used in many CD manufacturing environments to control their production. For this test, only the jitter and error correction flags, e.g. BLER1) and BERL2), of the CDs are measured. Beside the data-to-data jitter (TIA), also the data-to-clock jitter (not specified in the CD-standard) has been measured with help of the Yokogawa TA320 Time Interval Analyzer, which was connected to the RF-output of the CATS SA3 CD-Analyzer. Also an oscilloscope was connected to this RF-output, to make the eye pattern visible. Before the measurement, the discs have been cleaned and there have been used discs that have a minimum of scratches. Remark: Block Error Rate (BLER); expressed as the number of blocks with at least 1 error against the total number of blocks processed. According to the CD-standard the BLER must be less than 220 counts/sec (averaged over any 10 seconds), Remark: Burst Error Length (BERL): local defects, like air bubbles, black spots, scratches and finger prints, can cause several successive frames to be erroneous. These errors are called burst errors. The specification for burst errors in the CDstandard is based on an error correction system with a single error correcting C1 decoder and a single error correcting C2 decoder. No errors are allowed that are uncorrectable for such a decoder. This means that the C2 decoder should not encounter more than 1 error in any C2 frame, or the C1 decoder should not detect a burst of 6 or more successive uncorrectable C1 frames ( 2 errors per frame).

Haykin, S., An Introduction to Analog & Digital Communications, Singapore/New York/Chichester/Brisbane/Toronto, 1989. Kearsey, B.N., Jitter in Digital Telecommunication Networks, Telecommunications Engineering, Volume 3, nummer 7, July 1984. British
Kup, B.M.J., E.C. Dijkmans, P.J.A. Naus, J. Sneep, A Bit-Stream Digital-to-Analog Converter with 18-b Resolution, IEEE Journal of Solid-State Circuits, Volume 26, nummer 12, December 1991, 1757 t/m 1763. Robinson, F.N.H., Noise and fluctuations (in electronic devices and circuits), Oxford, 1974. Shannon, C.E., Communication in the Presence of Noise, Proceedings of the I.R.E., January, 1949, 10 t/m 21. Talambiras, R., Limitations on the dynamic range of digitized audio, 1977. Wong, W.K., Optimization techniques for high order Phase-Locked Loop type jitter reduction circuit for digital audio, IEEE Transactions on Consumer Electronics, Volume 42, nummer 1, February 1996.