S/PDIF cable: technical documentation (jitter, AES/EBU)

Technical documentation of the metrics, formulas and physical models implemented in the application: line model, reflections, noise, jitter, receiver PLL filtering, eye mask and practical limits of cables on Spdif and AES/EBU links. The simplified guide covers the same ideas without formulas, and every quantity described here can be computed in the simulator.

Interfaces covered: consumer coaxial S/PDIF (IEC 60958-1 and IEC 60958-3, 0.5 V peak-to-peak on 75 ohm) and professional AES3 (AES3, IEC 60958-4-4, 110 ohm balanced). Channel code: Biphase Mark Coding (BMC).

Main standards and references (details in the bibliography):

• IEC 60958-1:2021 (edition 4.0): frame structure, BMC and, in §7.1.3 "Unbalanced line", electrical characteristics of the consumer interface, with figure 8 "Eye diagram" (only the table of contents of the public preview was consulted). The values quoted here (75 ohm, 0.5 V ±20%, input eye mask of 200 mV over 0.5 UI) are read from IEC 60958-3:2003 (§7.3), which contained them until the 2006 edition of part 3 removed them.
• IEC 60958-3: consumer application (channel status); the electrical values of the 2003 edition (§7.3) serve as a reference for jitter, edges and the eye mask
• AES3-2009, parts 1 to 4 (the electrical part is AES3-4-2009), equivalent to IEC 60958-4-4:2016 (which, with parts 4-1 and 4-2, replaces the former IEC 60958-4)
• EBU Tech 3250, 3rd edition (2004): AES3 interface, electrical characteristics in §6, eye mask in §6.3.3
• Pozar, D.M., *Microwave Engineering*, 4th ed., Wiley, 2011: transmission lines, reflections
• Ott, H.W., *Electromagnetic Compatibility Engineering*, Wiley, 2009: cable shielding (chapter 2, §2.13-2.14: qualitative ranking of constructions)

Table of Contents

• 1. Cable Model
• Input Parameters per Cable
• Available Cables and Sources
• 1.1 Bandwidth Limitation
• 1.1b Skin Effect
• 1.2 Attenuation
• 1.3 Impedance Mismatch Reflections
• 1.4 EMI Noise and Electromagnetic Environment
• Electromagnetic Environment (EMI)
• 1.5 ISI Jitter (Intersymbol Interference)
• 1.5b Triple Transit
• Echo delay and amplitude
• Effect on BMC jitter
• Triple transit calculator
• Impedance matching
• 1.6 Custom Cable
• 1.7 AC Coupling and Baseline Wander
• 1.8 Optical Links
• 2. Analysis Metrics
• 2.1 Cell Error Rate (CER)
• 2.2 RMS and Peak-to-Peak Jitter
• Receiver PLL filtering
• Jitter and audio signal-to-noise ratio
• 2.3 Voltages (high, low, P-P)
• 2.4 RMS Noise
• 2.5 Parity Errors
• 2.6 Eye Diagram
• 2.7 Waveform Comparison (overlay)
• 2.8 Automatic Interpretations
• 2.9 AES3 Eye Mask and Practical Limit
• 2.10 Sensitivity Matrix
• 2.11 Cable Ranking
• 3. Global Verdict
• Appendix: Global Constants
• Appendix: Conversion from Cells to Analog Signal
• CSV Capture Format
• File Structure
• Format Rules
• Automatic Time Unit Detection
• Recommended Duration and Sampling Rate
• Example File
• WAV File Import
• Appendix: Reference Simulation Results
• Main cables at 1.5 m (home hi-fi)
• Effect of Length - Generic RCA Cable (Hi-Fi)
• Effect of Environment - Belden 1694A, 10 m
• Appendix: S/PDIF and AES/EBU Connectors
• 1. RCA (Phono)
• 2. BNC 75 ohm
• 3. XLR (AES/EBU)
• 4. Toslink (optical)
• 5. Practical impact at BMC frequencies
• 6. Why connectors are not modeled
• Appendix: Scope, the Complete Chain up to the Receiver
• Appendix: Model Limitations
• Appendix: Validation Against the Literature
• Jitter vs. Distance (Belden 1694A, 75 ohm)
• Maximum Distance per Cable
• Comparison Sources
• Appendix: Audiophile Myths vs. Digital Signal Physics
• S/PDIF Data Are Binary, the Waveform Is Not
• Critical Distance by Sample Rate
• The Role of the Receiver PLL (DAC)
• When the Digital Cable Really Matters
• What the Model Establishes
• Appendix: Blind Listening Tests
• Complete Bibliography
• Standards and Specifications
• Reference Books
• AES Articles and Preprints
• Application Notes
• Manufacturer Datasheets
• Author Biographies

1. Cable Model

The model simulates what happens to a Spdif or AES3 signal between the transmitter output and the receiver input. The cable_sim() function chains four stages, all applied to the waveform:

1. Transmitter: optional duty-cycle distortion (DCD), then optional AC coupling (high-pass, section 1.7).
2. Line: losses $\alpha(f)$ fitted to the datasheet, applied in the frequency domain with the associated minimum phase (sections 1.1 to 1.2).
3. Reflections: exact response of a mismatched line between a source and a load at the reference impedance (section 1.3).
4. Picked-up noise: Gaussian, at an absolute level (section 1.4).

Steady state. An S/PDIF link transmits continuously. The simulation therefore precedes the signal with a copy of itself, which brings the line, the echoes and the AC coupling to steady state; only the second pass is analyzed. This removes the cold-start transient (first edges distorted on a long cable) and the circular wrap-around of the FFT, which falls into the copy instead of the analyzed part.

No jitter is injected by formula. Intersymbol interference (ISI), the mismatch echo and the effect of noise on transition times show up in the waveform, and jitter is then measured on it (section 2.2).

Input Parameters per Cable

Each preset is defined by the following parameters:

Bandwidth is not an input parameter: it follows from the losses (section 1.1).

Two frequencies appear throughout. The cell rate (BMC half-bit rate):

$f_{cell} = 128 \times F_s$, i.e. 5.6448 MHz at $F_s$ = 44.1 kHz ($T_{cell}$ = 177.2 ns).

A frame holds two 32-bit subframes; each BMC bit takes two cells, hence 128 cells per frame. The cell is the unit interval (UI) of the AES3 eye mask.

The loss reference frequency:

$f_{ref} = 64 \times F_s$, i.e. 2.8224 MHz at 44.1 kHz.

This is the highest fundamental of the BMC signal. Every bit starts with a transition; a 1 bit adds one in the middle. A run of 1s is therefore a square wave of period $2\,T_{cell}$ (fundamental $64 F_s$), a run of 0s a square wave of period $4\,T_{cell}$ (fundamental $32 F_s$ = 1.41 MHz). The spectrum contains these fundamentals and their odd harmonics; $f_{cell}$ does not appear in it as a fundamental.

Available Cables and Sources

Values from spdif_core/cables.py. The last two numeric columns are computed by the model: attenuation at $f_{ref}$ = 2.82 MHz and -3 dB bandwidth for 100 m.

Attenuation in dB/100m, shielding in dB. Legend:

• no mark: manufacturer datasheet value;
• \*: estimated value (cable construction, comparable cables), or a value the manufacturer does not publish (retailer value);
• \*\*: value interpolated or extrapolated from other datasheet frequencies ($\sqrt{f}$ law for extrapolations); for the Belden 1800F, value of the fit on the full table.

Notes on some data:

• Belden 1800F: the datasheet dated 30 April 2013 publishes a 16-point table, from 0.384 to 24.576 MHz (2.23 dB/100ft at 4.096 MHz, 2.89 at 5.645 MHz, 4.53 at 11.29 MHz...); the 2025 revision no longer has the frequency column. The loss law is fitted to this table (section 1.1); the 5 and 10 MHz columns give the values of the fit. The $f$ term of this fit is empirical: read as dielectric loss, it would imply a tan δ of the order of 0.05, impossible for foam PE. Impedance 110 ohm nominal, no published tolerance; velocity 76%.
• Gotham GAC-1 10070: the data come from the US distributor Gotham Audio (10070 "v2"): maxima of 0.80 dB/100m at 1 MHz and 1.5 dB/100m at 6 MHz, 75 ohm ±2%, C < 56 nF/km. The model uses 1.40 dB/100m at 5 MHz, interpolated between these two maxima, and 1.94 dB/100m at 10 MHz, extrapolated as $\sqrt{f}$; v = 79% is the lower bound of $1/(Z \cdot C)$. The manufacturer (Gotham AG) now sells the 10080 GAC-1 S/PDIF: same losses and capacitance, tinned copper braid, impedance tolerance not published.
• Canare L-3CFB: 3.7 dB/100m at 10 MHz and 5.9 at 30 MHz, 75 ±3 ohm (datasheet SAA127E Ver.2.3, 2021); 2.62 at 5 MHz is extrapolated. Double shield (foil + braid). Canare L-5CFB: 2.2 dB/100m at 10 MHz, 75 ±3 ohm (datasheet SAA103E Ver3.3, 2021), aluminium tape and braid of at least 93%.
• Sommer SC-Vector Plus 1.2/5.0: Sommer only publishes attenuation from 50 MHz (4.5 dB/100m; 8.6 at 200 MHz). A $\sqrt{f}$ extrapolation from 50 MHz underestimated the losses: 1.61 and 2.20 dB/100m are estimated by scaling the Belden 1694A, of similar construction. Velocity 0.80 (manufacturer).
• Sommer SC-Vector 0.8/3.7: 2.90 dB/100m at 10 MHz is a retailer value (Thomann), as Sommer publishes nothing below 200 MHz. Velocity 0.82 (datasheet 600-0161 dated 31.07.2024; the manufacturer's web page says 0.8); 100% foil + 85% braid, the effectiveness in dB is not published.
• Van Damme "Standard 75 Ohm Plasma Grade Video Coax" (datasheet v2, 05/2025): 4.21 dB/100m at 10 MHz, 75 ±3 ohm, velocity 66%; the 5 MHz value is extrapolated. Braid-only shield in bare copper, no foil.
• Mogami 2964: velocity is not published; it is computed as $v = 1/(Z \cdot C)$ with C = 65 pF/m (Mogami datasheet), about 68%. The published phase constant, 0.3 rad/m at 10 MHz, confirms it: $v = \omega/\beta \approx$ 69.9%. Single spiral (served) shield, the weakest of the common constructions.
• Canare DA206: Canare publishes a single point, 2.6 dB/100m at 3 MHz; 3.36 and 4.75 dB/100m are extrapolated from it as $\sqrt{f}$. This is uncertain: a growth like that of the Belden 1800F would give about 6.3 dB/100m at 10 MHz. Velocity, not published, is computed as $1/(Z \cdot C)$ with C = 48 pF/m (solid cross-linked PE): 63%. Canare states 360 m ("AES3 SR48kHz").
• Canare DA202: 6.58 and 9.31 dB/100m are extrapolated as $\sqrt{f}$ from 5.1 dB/100m at 3 MHz, with the same caveat. Velocity computed the same way: 63% with C = 48 pF/m (Canare Japan), 67% with the 45 pF/m of Canare US. Canare states 180 m at 48 kHz.
• Belden 8281 (RG-59): 1.90 dB/100m at 5 MHz is interpolated between 0.5 dB/100ft at 3.6 MHz and 0.8 dB/100ft at 10 MHz; velocity 66% (solid PE dielectric); double braid. Belden 1505A: 82%, foil + braid. Belden 1505F: 21 AWG stranded conductor (7x29), double braid.
• Belden datasheets give attenuation in dB/100ft; dB/100m = dB/100ft × 3.281.
• Impedance tolerances are listed only when published.

Two presets are not S/PDIF cables: the RCA "spaghetti" and the generic 75 ohm coaxial. They serve as points of comparison. No manufacturer datasheet describes them: all their parameters are estimated. The RCA "spaghetti" stands for a cheap audio RCA lead, of the kind bundled with equipment, whose impedance is not specified (a composite video lead, by contrast, targets 75 ohm). The estimated 42 ohm corresponds to thin PVC insulation ($\varepsilon_r \approx$ 3.3, diameter ratio $D/d \approx$ 3.6, hence C ≈ 144 pF/m); a real reference point: the Mogami W2524 instrument cable (130 pF/m and 0.2 µH/m published) is about 39 ohm.

Optical links (see section 1.8):

Shielding. Datasheets do not give shielding effectiveness in dB. Preset values are working estimates based on the shield construction. Ott (2009, §2.13 "Braided Shield" and §2.14 "Spiral Shields") allows these constructions to be ranked, treating them through their transfer impedance, but gives no scale in dB.

Measured reference point: per IEC 62153-4-4, on 50 ohm cables between 0.1 and 6 GHz (Köppendörfer, Leoni, IEEE 802.3dm, December 2024), a single braid gives about 46 dB and foil with braid 72 to 89 dB. In the model, the shield only matters if it is below the picked-up field (section 1.4), which reaches 65 dB at 100 m and 71 dB at 200 m (the application's maximum length) in an industrial environment: a shield of at least 72 dB has no effect there, the Mogami 2964 (70 dB) loses only about 1 dB of SNR at 200 m, and the differences between these estimates do not change the results.

1.1 Bandwidth Limitation

Phenomenon. Cable losses grow with frequency: conductor losses from the skin effect (as $\sqrt{f}$) and dielectric losses (as $f$). The cable behaves as a low-pass filter whose cutoff depends on its length.

Loss law. A single law, fitted to the two datasheet points (loss_coeffs() function):

$$\alpha(f) = a_s \sqrt{f} + a_d\, f \quad \text{(dB/m, } f \text{ in Hz)}$$

The two measurements at 5 and 10 MHz give a linear system in $a_s$ and $a_d$. The coefficients are constrained to be non-negative: if datasheet rounding gives $A_{10}/A_5 < \sqrt{2}$ (slower growth than pure skin effect), $a_d$ is set to 0 and $a_s$ is fitted by least squares on both points. This is the case for the Belden 1694A ($2.33/1.71 = 1.36$).

The Belden 1800F is the exception. A twisted pair does not follow $\sqrt{f} + f$ over the whole 0.4-25 MHz range: the law is therefore fitted to the full manufacturer table (16 points), in relative error, over the useful BMC band (1 to 12.3 MHz). The error stays below 1% at the 1.41 and 2.82 MHz fundamentals and within ±5% over the band. A fit on the 5 and 10 MHz points alone overestimated the fundamentals by 9 to 14%. The $f$ term of this fit describes the shape of the pair's loss curve, not dielectric loss (see the notes of the cable table).

The loss of a length $L$ at frequency $f$ is $A(f) = L \cdot \alpha(f)$.

-3 dB bandwidth. It is not a model parameter: it is the frequency where $A(f)$ reaches 3.01 dB, shown for information. In the pure skin-effect regime:

$$f_{-3dB} = \left(\frac{3.01}{a_s\, L}\right)^2$$

It therefore scales as $1/L^2$. For the Belden 1694A:

These values come from the model, fitted on the losses at 5 and 10 MHz and then extrapolated: the full table of the Belden datasheet gives about 2 GHz over 10 m, 85 MHz over 50 m and 17 to 18 MHz over 100 m.

With dielectric losses, $f_{-3dB}$ is found by solving $a_d x^2 + a_s x - 3.01/L = 0$ with $x = \sqrt{f}$.

Applying a separate low-pass filter on top would count the same phenomenon twice: bandwidth and attenuation are two readings of the same law $\alpha(f)$.

Application to the signal. The line response is applied in the frequency domain (line_response() function). Its magnitude comes from $\alpha(f)$; its phase is the associated minimum phase, computed by the folded cepstrum method. The response is therefore causal. For pure skin effect it matches, up to a pure delay, the classic response of a line with $\sqrt{f}$ losses:

$$H(f) = e^{-(1+j)\, k \sqrt{f}}$$

The exact form used is:

$$A(f) = A_{ref}\left[(1-d)\sqrt{f/f_{ref}} + d\,(f/f_{ref})\right], \qquad H(f) = \text{minimum phase of } 10^{-A(f)/20}$$

where $A_{ref}$ is the loss at $f_{ref}$ and $d$ the dielectric share of that loss (dielectric_frac); for the Belden 1800F, $d$ is the share of the empirical $f$ term.

1.1b Skin Effect

Phenomenon. At high frequency, current concentrates in a surface layer of the conductor of thickness $\delta$ (skin depth; Pozar, §1.4, plane waves in a good conductor):

$$\delta = \frac{1}{\sqrt{\pi f \mu \sigma}}$$

with $\mu = 4\pi \times 10^{-7}$ H/m and $\sigma = 5.8 \times 10^{7}$ S/m for copper. At 2.82 MHz, $\delta \approx 39\ \mu m$; at 28 MHz, $\delta \approx 12\ \mu m$. The effective resistance, and hence the loss, grows as $\sqrt{f}$. This is the $a_s\sqrt{f}$ term of the loss law.

Effect on the BMC signal. Odd harmonics of the fundamental $f_{ref}$ lose more than the fundamental (pure skin effect):

Edges spread out, and the shape of a transition depends on the bits before it: this is ISI. The minimum phase adds dispersion (frequency-dependent group delay), which contributes to the same effect.

"Skin effect" checkbox. When checked (default), the full model above applies. When unchecked, the line applies a flat loss equal to $A_{ref}$ at all frequencies, without dispersion. This simplified model is there for comparison: it reduces the amplitude without spreading the edges, so with almost no ISI. For a 100 m Belden 1694A, TIE jitter is 0.20 ns RMS with the full model and 0.015 ns with the flat loss (hi-fi noise; 0 without noise).

1.2 Attenuation

Phenomenon. Resistive conductor losses and dielectric insulation losses, proportional to length (in dB) and increasing with frequency.

Displayed value. The displayed attenuation is the loss at $f_{ref} = 64 F_s$:

$$A_{dB} = L \cdot \left(a_s \sqrt{f_{ref}} + a_d\, f_{ref}\right)$$

For the Belden 1694A: 1.25 dB/100m at 2.82 MHz. $f_{ref}$ follows the sample rate: at 96 kHz, $f_{ref}$ = 6.14 MHz and the loss is higher.

Interpretation.

• The nominal S/PDIF signal is 0.5 V peak-to-peak. 6 dB of loss brings it to 0.25 V, 8 dB to 0.2 V, the minimum height of the input eye mask: 200 mV over 0.5 UI, centered on the decision threshold (IEC 60958-3:2003 §7.3.3.3; covered in IEC 60958-1:2021 §7.1.3, figure 8, according to its table of contents; same mask for AES3, EBU Tech 3250 §6.3.3). It is not a peak-to-peak sensitivity: the mask applies to the eye opening, ISI and noise included.
• The loss at $f_{ref}$ gives an order of magnitude of the vertical eye closure. Runs of 0s (fundamental half as high) lose less; the eye is limited by the worst pattern, which is what the mask measures (section 2.9).

AES3. The transmitter is simulated at 5 V peak-to-peak (the waveform really is at 5 V). Attenuation stays that of the cable, uncorrected. The higher level gives 20 dB of extra margin against picked-up noise and against the 200 mV mask: an AES3 signal reaches that height at about 28 dB of loss, against 8 dB for S/PDIF. At the normative minimum of 2 V the advantage is only 12 dB. The "> 200 m" practical limits of AES3 cables (section 2.9) come from this 5 V level. At 2 V, the Belden 1800F holds about 189 m at 44.1 kHz and 179 m at 48 kHz, the Canare DA202 about 195 m at 48 kHz, the DA206 more than 200 m. This is consistent with Canare (180 m stated for the DA202) and with Belden bulletin TB65, which recommends at most 203 m of 1800F at 6 MHz for a drop from 2 V to 200 mV. The model remains optimistic: minimum mask with no margin, ideal receiver.

1.3 Impedance Mismatch Reflections

Phenomenon. A line of impedance $Z$ between a source and a load of different impedance reflects part of the wave at each end. The echoes add to the direct signal with a delay.

Modeled configuration. By default, source and load are at the interface reference impedance, $Z_{ref}$ = 75 ohm (S/PDIF) or 110 ohm (AES3); only the line is mismatched (the triple transit panel lets you change the source and the load). The reflection coefficients seen from the line are then equal (Pozar §2.3):

$$\Gamma_L = \Gamma_S = \frac{Z_{ref} - Z}{Z_{ref} + Z}$$

The interface displays $\Gamma = (Z - Z_{ref})/(Z + Z_{ref})$, the coefficient of the cable seen from a $Z_{ref}$ reference. It has the same magnitude and the opposite sign. What matters for the echo is the product:

$$q = \Gamma_L \cdot \Gamma_S = \Gamma^2 \geq 0$$

Exact response. A wave making one round trip in the line (delay $2L/v$, line loss applied twice) is reflected once at each end. The sum of all bounces is a geometric series. Relative to the matched case, with any source impedance $Z_S$ and load impedance $Z_L$ ($\Gamma_S = (Z_S - Z)/(Z_S + Z)$, $\Gamma_L = (Z_L - Z)/(Z_L + Z)$, $q = \Gamma_L \Gamma_S$):

$$H_r(f) = \frac{(1 - \Gamma_S)(1 + \Gamma_L)}{1 - q\, H_{line}(f)^2\, e^{-j 2\pi f \cdot 2L/v}}$$

where $H_{line}$ is the line response (section 1.1) and $v = V_\% \cdot c / 100$. When source and load have the same impedance ($Z_S = Z_L$, the case of the presets), $\Gamma_S = \Gamma_L$ and the numerator is $1 - q$: the DC gain is 1, as in the matched case. Otherwise (source and load set differently in the triple transit panel), it is $2 Z_L/(Z_S + Z_L)$, relative to the matched case. All bounces are included, and the delay is applied in the frequency domain, so it is not rounded to the sampling step.

The first echo arrives $2L/v$ after the direct edge, with relative amplitude $q$; the next one $4L/v$ after, with $q^2$, and so on.

Examples.

Interpretation.

• A cable at the reference impedance, between a transmitter and a receiver at that same impedance (75 ohm for S/PDIF, 110 ohm for AES3), produces no echo, whatever its length.
• The echo of a mismatched line is a few percent of the amplitude. It is visible on the waveform (a step after each edge) and on the eye (doubled traces).
• Its effect on jitter depends on its delay (section 1.5b).

The echo jitter values apply beyond the length $L_0$ defined in section 1.5b. Below it, echo jitter is negligible on a lossless line, but not on a lossy line, where the echo copies the ISI already present.

1.4 EMI Noise and Electromagnetic Environment

Phenomenon. The cable picks up ambient electromagnetic fields; the shield attenuates them. The picked-up noise adds to the signal.

The SNR model described below is an order-of-magnitude heuristic, not a measurement. It is meant to compare cables with each other (good or poor shield, short or long); absolute SNR values, and the practical limits that depend on them, are not predictions.

Electromagnetic Environment (EMI)

Three environments, each with a penalty $P_{EMI}$:

The 0, 10 and 25 dB values correspond to an approximate field ratio $P_{EMI} \approx 20 \log_{10}(E_{env}/E_{0})$: with $E_0 \approx 0.3$ V/m, a living room at 1 V/m gives ~10 dB, and an industrial site at 10 V/m (test level of the IEC 61000-4-3 industrial class) ~30 dB; the model uses 25 dB. These are modeling choices, not normative values. The IEC 61000-4-3 test levels (1, 3, 10 and 30 V/m) apply to radiated fields from 80 MHz to 6 GHz, far above the BMC spectrum; below 80 MHz, the reference is IEC 61000-4-6 (conducted disturbances induced by radio-frequency fields). They therefore only give an order of magnitude of the fields.

SNR formula (compute_cable_params() function):

$$SNR_{int} = 70 - 8 \log_{10}(1 + L)$$

$$E_{through} = \max\left(0,\ P_{EMI} + 20 \log_{10}(1 + L) - S_{dB}\right)$$

$$SNR = \max\left(20,\ SNR_{int} - E_{through}\right) + B_{AES} \quad \text{(dB)}$$

where:

• $S_{dB}$ is the cable shielding;
• $20 \log_{10}(1+L)$ represents pickup, growing with length (antenna effect);
• $B_{AES}$ = 20 dB for AES3, 0 for S/PDIF: noise is an absolute level evaluated for a 0.5 V signal, and AES3 launches 5 V, i.e. a 20 dB higher SNR whatever the origin of the noise (common-mode rejection of the balanced link is not modelled);
• the 20 dB floor bounds the model.

Examples:

With 90 dB of shielding, the 1694A is not affected by the environment in this model: the picked-up field stays below the shielding.

Noise application. Additive Gaussian noise, at an absolute level set relative to the nominal transmitted level, and limited to the receiver input bandwidth:

$$\sigma = \frac{V_{nom}/2}{10^{SNR/20}}, \qquad \lvert H_B(f)\rvert^2 = \frac{1}{1 + (f/B)^4}, \qquad B = 3\,f_{cell}$$

with $V_{nom}$ = 0.5 V (S/PDIF) or 5 V (AES3) and $f_{cell} = 128\,F_s$, i.e. B = 16.9 MHz at 44.1 kHz and 73.7 MHz at 192 kHz. White noise is drawn for each sample (deterministic seed), filtered in the frequency domain, like the channel, by this second-order low-pass filter (Butterworth, -40 dB per decade), then scaled back to the standard deviation σ: the level of the SNR model is preserved. The bandwidth B passes harmonics 1, 3 and 5 of the fastest pattern ($f_{cell}/2$, $1.5\,f_{cell}$ and $2.5\,f_{cell}$) and matches the transmitter edge (0.107 UI from 10 to 90%, i.e. $0.35/t_r \approx 3.3\,f_{cell}$): a receiver needs no more bandwidth than the signal it receives.

Unfiltered white noise drawn sample by sample extended up to half the sampling rate of the simulation ($16\,f_{cell}$, i.e. 90 MHz at 44.1 kHz and 393 MHz at 192 kHz). Its share in the useful band depended on the simulation step, and its fast components made the same edge cross the threshold several times: isolated errors appeared on an eye that was still open (RCA from 25 to 30 m at 96 kHz). Limited to the receiver bandwidth, the noise no longer depends on the step and no longer creates these spurious edges. The level σ itself remains the order-of-magnitude heuristic described above.

Picked-up noise does not depend on what happens to the signal in the cable: when the cable attenuates, the signal-to-noise ratio at the receiver input degrades by the same amount.

1.5 ISI Jitter (Intersymbol Interference)

Phenomenon. Losses spread each edge over several cells. The level reached before a transition then depends on the preceding bits (a long cell lets the signal rise higher than a short one), and the time at which the signal crosses the threshold depends on the data. This is intersymbol interference, the main source of jitter on long cables. Chris Dunn and Malcolm Hawksford (AES preprint 3360, 1992) modeled a band-limited link (first-order RC low-pass) and showed that this jitter depends on the data and stays correlated with the audio signal.

Model. ISI is not computed by formula. It appears in the waveform filtered by the line (section 1.1), and jitter is then measured as TIE (section 2.2). Jitter therefore depends on the actual cable losses, the length, the data pattern and the sample rate.

Orders of magnitude (Belden 1694A, 1 kHz sine, 32 frames, 44.1 kHz, no noise):

Half a UI is 89 ns at 44.1 kHz: even at 300 m, the ISI jitter of the 1694A is far from closing the eye horizontally.

Cliff effect. A digital link works without errors as long as the eye stays open above the receiver threshold, then errors appear quickly. The practical limit is not located with the CER but with the eye mask, with noise taken at a $10^{-12}$ error rate (section 2.9).

Transmitter jitter. It is not part of the cable. The "Transmitter jitter" option (off by default) adds it as wideband white jitter, combined in quadrature and filtered by the PLL equivalent noise bandwidth (section 2.2). The default field value (2 ns RMS) is a working order of magnitude, not a normative value.

1.5b Triple Transit

Echo delay and amplitude

The direct edge travels along the line and reaches the load at time $L/v$. Part of it is reflected ($\Gamma_L$), travels back to the source, is reflected again there ($\Gamma_S$) and reaches the load at time $3L/v$: this is the triple transit.

Source (Zref)        Line (Z, length L)           Load (Zref)
    │                                                  │
    ├──── transit 1 ────────────────────────────────>──┤ direct edge at L/v, reflection ΓL
    │<─── transit 2 ─────────────────────────────────── │
    │ reflection ΓS                                    │
    └──── transit 3 ────────────────────────────────>──┘ echo at 3L/v
          (2L/v after the direct edge, amplitude ΓL·ΓS)

Relative to the direct edge, the echo is therefore:

• delayed by $\tau_{echo} = 2L/v$;
• of relative amplitude $q = \Gamma_L \Gamma_S$.

Later bounces ($q^2$, $q^3$...) are included in the waveform simulation (section 1.3).

Effect on BMC jitter

To first order in $q$, an echo $q\, s(t - \tau)$ added to edge $k$ shifts its zero crossing by:

$$\Delta t_k = -\,q\, \frac{s(t_k - \tau)}{s'(t_k)}$$

where $s(t_k - \tau)$ is the signal level one echo delay before the edge, and $s'(t_k)$ the edge slope. Two regimes follow.

Echo shorter than a cell. If $\tau < T_{cell}$, the main echo falls on the flat level that precedes each edge (in BMC, two transitions are at least one cell apart). That level has the opposite sign to the edge, whatever the edge. On a lossless line, all edges are then shifted by the same amount: the echo only delays them, and jitter stays negligible (10 m line mismatched to $\Gamma^2$ = 0.04: 0.002 ns without losses; 0.016 ns with the small losses of the Belden 1694A). On a lossy line, the level reached before the edge depends on the preceding bits: the echo copies this ISI and its share is no longer negligible (RCA "spaghetti" at 10 m: about 0.57 ns peak-to-peak; 0.12 ns at 5 m). Later bounces ($q^2$ at $4L/v$...) also leave a residue. The condition reads $L < L_0$ with:

$$L_0 = \frac{v\, T_{cell}}{2}$$

The transition between the two regimes spans a duration of the order of the edge rise time.

Echo longer than a cell. Beyond $L_0$, the level $s(t_k - \tau)$ depends on the data: depending on the pattern, it has the same or the opposite sign as the edge. The echo then adds data-dependent jitter of about:

$$J_{pp} \approx \frac{2\, q\, A}{s'}$$

where $A$ is the signal half-amplitude and $s'$ the edge slope at the threshold. With the simulated transmitter edges (10-90% ≈ 19 ns at 44.1 kHz), this formula gives 0.74 ns for $q = 0.04$; the full calculation gives 0.78 ns. The slope, not the cell rate, sets the order of magnitude.

This jitter is computed by a full simulation (compute_triple_transit() function) on a probe signal: four frames of pseudo-random 16-bit data (fixed seed), preambles included, with the actual transmitter edges. The same line, with its losses, is simulated mismatched and then matched; the TIE difference between the two, edge by edge, isolates the share of the reflections, all bounces included.

Echo jitter is not added to the verdict: it is already present in the simulated waveform (section 1.3) and therefore in the measured jitter. The calculator is there to isolate and explain it.

Triple transit calculator

The dedicated panel lets you set the source and load impedance, then shows:

• $\Gamma_L$, $\Gamma_S$, the echo amplitude and its delay $2L/v$;
• $L_0$, the length from which the echo produces data-dependent jitter;
• the peak-to-peak jitter at the chosen length, raw and filtered by the selected PLL;
• the echo jitter curve versus length;
• a six-cell illustration of the direct signal, the echo and their sum.

The severity level compares the peak-to-peak jitter with AES3 values: below 0.025 UI (intrinsic output jitter allowed for a transmitter), between 0.025 and 0.25 UI, above 0.25 UI (high-frequency input tolerance). The comparison is cautious: the AES3 figure of 0.025 UI is a peak value measured through a 700 Hz high-pass filter, whereas the simulator compares an unfiltered peak-to-peak value.

Impedance matching

If $Z = Z_{ref}$, $\Gamma_L = \Gamma_S = 0$: no echo, at any length. This is the reason for the nominal 75 ohm (IEC 60958-1) and 110 ohm (AES3) impedances. For a short, lightly attenuated mismatched line ($L < L_0$), the echo mostly delays the edges; it slightly reduces the eye margin and adds only a small amount of jitter.

References:

• Pozar, D.M., *Microwave Engineering*, 4th ed., Wiley, 2011: §2.3 (terminated line, reflection coefficient), §2.5 (quarter-wave transformer, multiple-reflection viewpoint), §2.6 (generator and load mismatches) and §2.8 (transients on transmission lines)
• Ramo, S., Whinnery, J.R., Van Duzer, T., *Fields and Waves in Communication Electronics*, 3rd ed., Wiley, 1994 (lossy lines, forward and reflected waves)
• EBU Tech 3250, 3rd ed., 2004, §6 (electrical characteristics of the AES3 interface)

1.6 Custom Cable

The interface lets you define a cable by its physical parameters, to simulate a cable whose datasheet you have or to isolate the effect of one parameter.

The calculation is exactly the same as for presets (sections 1.1 to 1.5). A custom cable is simulated as an S/PDIF link (75 ohm reference).

1.7 AC Coupling and Baseline Wander

Phenomenon. Most S/PDIF and AES3 outputs are AC-coupled, through a pulse transformer or a series capacitor, to isolate grounds and block DC. This coupling is a high-pass filter. BMC has no DC component, preambles included ("like biphase code, these preambles are d.c. free", IEC 60958-1 §4.3). But the preambles deliberately violate the biphase code (that is how they are recognized): they contain a three-cell flat level, whereas the data never have more than two. Their low-frequency content therefore differs from that of the data, and the high-pass makes the baseline fluctuate (*baseline wander*): a periodic ripple at the subframe rate, plus a data-dependent part.

Effect on jitter. The receiver compares the signal with a fixed threshold; when the baseline fluctuates, the crossing times shift. This is deterministic jitter, partly correlated with the data, with spectral lines at multiples of the block rate $F_s/192$ (about 230 Hz at 44.1 kHz), including the frame rate and its harmonics.

Real cutoffs. Common parts put the cutoff between about 2 and 20 kHz:

• Pulse PE-65612 transformer, recommended by Cirrus Logic: magnetizing inductance of 2.5 mH ±20%, i.e. $f_c = (R_s \parallel R_L)/(2\pi L)$ ≈ 2.4 kHz on 75 ohm and 3.5 kHz on 110 ohm;
• Scientific Conversion transformers (2015 catalog): low band edge of 7 kHz (SC937-02, SC947-02), 15 kHz (SC979-03) or 20 kHz (SC982-04); the older SC916-01 went down to 700 Hz;
• Jon D. Paul (Scientific Conversion, AES 105th convention, 1998, preprint 4840) recommends a low cutoff of 1/5 to 1/20 of the 100 kHz lower limit of the AES/EBU specification, i.e. 5 to 20 kHz; his measurements show a good eye with a 4 kHz cutoff, which closes at 400 kHz;
• 100 nF series capacitor between two 75 ohm resistances: 10.6 kHz.

Model. First-order RC high-pass applied to the transmitted signal, with adjustable cutoff $f_{c,HP}$: 1, 2.5, 5, 10 (default) or 20 kHz (box unchecked: DC coupling, no effect). The effect on jitter is not added by formula: it appears in the waveform and shows up in the TIE measurement. Simulated orders of magnitude (Belden 1694A, 2 m, 1 kHz sine, 32 frames, hi-fi noise, seed 42):

In the usual range, the effect stays at a few tens to about a hundred picoseconds RMS: at 10 kHz, about 50 ps RMS and 250 ps peak-to-peak, the same order of magnitude as the ISI of a 100 m Belden 1694A (0.20 ns RMS) and far below audibility thresholds. On a short cable it nevertheless dominates interface jitter. The effect does not depend on the cable: it applies to both branches of the comparison.

References: patents US6408032 (PMC-Sierra) and US7738567 (Texas Instruments), high-pass model of baseline wander; Jon D. Paul, "The Effect of Transformers on Transmission of Digital Audio Signals", AES 105th convention, 1998, preprint 4840; Pulse PE-65612 datasheet; Scientific Conversion catalog.

1.8 Optical Links

An optical link (TOSLINK, glass fiber, AT&T ST connector) has no electrical impedance and no noise pickup. The receiver module regenerates a logic signal: fiber loss does not change the amplitude of this signal. Its timing, however, depends on the received optical power, within the pulse width distortion guaranteed by the modules (±15 ns for the TOTX147/TORX147 pair). The model applies no loss, reflection or noise.

Only modal dispersion is modeled, by a Gaussian filter of bandwidth $BW(L) = BW_{len}/L$, taken as a -3 dB electrical cutoff. Fibers are specified at -3 dB optical, i.e. -6 dB electrical: their -3 dB electrical cutoff is lower (about 0.7 times for a Gaussian response). The filter is therefore slightly less severe than the fiber, with no visible effect at useful lengths (800 MHz for 5 m of plastic fiber).

For plastic fiber, category A4a.2 of IEC 60793-2-40 requires at least 40 MHz over 100 m with restricted launch (as cited by Tsukamoto, IEEE 802.3 GEPOF SG, 2014), i.e. 4000 MHz·m in the model. Its attenuations are maxima: 18 dB/100m with EMD launch, 40 dB/100m with overfilled launch (OFL). A commercial fiber such as the Mitsubishi ESKA SH4001 is specified at 19 dB/100m at most at 650 nm (21 over the full temperature range). Velocity 67% (phase index of PMMA: 1.488; with the group index, 1.509, it gives 66%). For OM1 glass fiber: 200 MHz·km and 3.5 dB/km, the ISO/IEC 11801 maximum for cabled fiber; manufacturer maxima for the bare fiber range from 2.7 to 3.2 dB/km (Prysmian, Corning, Leviton). Velocity ~67% (group index 1.496). The 62.5/125 µm fiber of the AT&T ST connector loses about 3.2 dB/km at 820 nm (Broadcom, HFBR-14xxZ).

What is not modeled:

• The optical modules: neither their jitter, nor their maximum data rate, nor their range. The usable length of a TOSLINK link is set by the optical budget of the module pair, not by the fiber bandwidth. For the Toshiba TOTX147/TORX147 audio reference pair, this budget is 3 dB in the worst case, between -21 dBm minimum launched power and -24 dBm sensitivity, and the specified range is 0.2 to 5 m.
• The modules add jitter: the TOTX147/TORX147 pair allows a pulse width distortion of ±15 ns. The jitter value shown for an optical cable is therefore not that of a real TOSLINK link. The transmitter DCD option (scope appendix) can represent it.
• The same pair is rated for 15 Mb/s NRZ, i.e. 7.5 Mb/s in biphase. A 96 kHz stream (6.1 Mb/s) passes; a 192 kHz stream (12.3 Mb/s) exceeds its capability.

2. Analysis Metrics

After the cable simulation (or the import of an oscilloscope capture), the analyzer computes the following metrics in the full_analysis() function.

2.1 Cell Error Rate (CER)

Definition. The Cell Error Rate is the fraction of BMC cells decoded differently from the reference.

Correlation alignment. Before comparison, decoded cells are aligned on the reference:

1. Cells (0/1) are converted to ±1: $r'[n] = 2 r[n] - 1$, $c'[n] = 2 c[n] - 1$.
2. A segment of 256 captured cells is correlated with the reference: $\text{corr}[k] = \sum_{n} r'[n+k] \cdot c'[n]$. In a simulation, the line delay is first estimated by cross-correlating the sent and received waveforms (peak searched within ±32 cells, below one 64-cell subframe whose repetition would give an almost equal peak); $k$ is then searched within ±4 cells of that delay. For an uploaded capture, whose start is unknown, $k$ runs from -4 to 512 over the first 768 reference cells. A negative offset covers the extra cell the decoder puts at the start when the line delay exceeds half a cell.
3. The offset kept is $\arg\max_k \text{corr}[k]$. Without the narrow search, a nearly periodic stream (pure sine) could lead to a false offset: 37% errors counted while 15 samples out of 16 were correct.
4. Comparison then runs in blocks of 64 cells (one subframe). If the decoder inserts or drops a cell, the offset is realigned locally (±4 cells) and the slip is counted separately. Cells decoded wrong until the realignment are still counted.

Formula.

$$CER = \frac{E}{N}, \qquad E = \sum_{n=0}^{N-1} \mathbb{1}[r_{align}[n] \neq c[n]]$$

with $N$ the number of compared cells. The interface shows it as a percentage.

Interpretation.

• S/PDIF and AES3 have no error correction. Every subframe carries a parity bit (section 2.5). The professional (AES3) channel status also carries a CRCC in its byte 23; the consumer channel status has none. An uncorrected error on a most significant bit produces a click.
• At 44.1 kHz there are 5,644,800 cells per second: a CER of 0.01% means about 565 wrong cells per second.

2.2 RMS and Peak-to-Peak Jitter

Definition. Jitter is measured as time interval error (TIE): the deviation of each transition from an ideal clock. This is the quantity a receiver PLL filters and the one standards refer to (AES3, IEC 60958).

Method (jitter_stats() function).

Step 1. Threshold crossings by linear interpolation. The threshold is the midpoint of the levels, estimated from the 1% and 99% percentiles (robust to noise spikes):

$$V_{thr} = \frac{P_{1\%}(v) + P_{99\%}(v)}{2}, \qquad t_k = t[i] + \frac{V_{thr} - v[i]}{v[i+1] - v[i]}\, \Delta t$$

Step 2. Rank of each transition on the cell grid: $n_k = \sum_{m<k} \text{round}\left((t_{m+1} - t_m)/T_{cell}\right)$.

Step 3. Ideal clock fitted by least squares: $t_k \approx t_0 + T\, n_k$ (linear regression on the origin $t_0$ and the period $T$).

Step 4. TIE of each transition:

$$TIE_k = t_k - (t_0 + T\, n_k)$$

Formulas.

$$J_{RMS} = \sqrt{\frac{1}{K}\sum_k TIE_k^2}, \qquad J_{PP} = \max_k TIE_k - \min_k TIE_k$$

The analyzer also plots the histogram (50 bins) of $TIE_k$. A clean signal gives a narrow distribution; ISI gives a wider distribution, often with several modes tied to data patterns; an echo beyond $L_0$ gives two peaks.

Orders of magnitude (Belden 1694A, 1 kHz sine, 32 frames): peak-to-peak TIE 0.05 ns at 10 m, 0.76 ns at 100 m, 4.7 ns at 300 m (section 1.5). The cell period is 177.2 ns at 44.1 kHz.

What is included. The measured jitter contains ISI, the mismatch echo, the effect of noise on crossing times, and baseline wander and DCD when enabled. None of these contributions is added separately.

Limit. This is interface jitter, not converter clock jitter. How one becomes the other depends on the receiver (next section).

Receiver PLL filtering

The receiver PLL tracks input jitter below its bandwidth and rejects it above. Its jitter transfer function is modeled in two ways:

• for presets other than the CS8412, a Butterworth low-pass of order $n$, without peaking:

$$\lvert H(f)\rvert^2 = \frac{1}{1 + (f/f_c)^{2n}}$$

• for the CS8412, a type 2 PLL (one zero and a pair of poles), with peaking:

$$\lvert H(f)\rvert^2 = \frac{1 + (2\zeta x)^2}{(1 - x^2)^2 + (2\zeta x)^2}, \qquad x = f/f_n$$

It is fitted to the curve of figure 3 of the DS61F1 datasheet (Crystal, 1998): $f_n$ = 10.8 kHz and $\zeta$ = 1.65, i.e. +0.6 dB around 6 kHz, -3 dB around 38 kHz, -9.5 dB at 100 kHz, then -20 dB per decade. The zero, at $f_n/2\zeta$ = 3.3 kHz, is that of the prescribed external filter (1 kΩ and 47 nF). The deviation from the published curve stays below 0.25 dB up to 600 kHz (about 1.3 dB near 1 MHz). The 1993 datasheet (DS61PP4) stated attenuation "from ~25 kHz", another pole at 80 kHz and 50 dB at 1 MHz; the 1998 revision removes that sentence.

A real PLL can show peaking (jitter gain above 0 dB near its cutoff), which the Butterworth model ignores: AES3 and IEC 60958-4 (2003) allow 2 dB, the CS8416 datasheet shows about +2 dB, and Dunn (Audio Precision AN-5) measures about 1 dB near 700 Hz on a converter, followed by a second-order slope. Some receivers, such as the CS8416, update their PLL on the preambles only, which do not depend on the data; the model, for its part, filters the TIE of all edges.

Three contributions are combined in quadrature (independent sources):

1. Cable jitter, filtered on its actual spectrum (pll_filter_tie() function): the TIE is resampled on a uniform grid, filtered by $\lvert H(f)\rvert$, and its RMS value is taken. Low-frequency limit: the ideal clock of the TIE measurement is fitted in origin and period; this fit removes the mean and the slope of the TIE, and acts as a high-pass around 1/duration, about 1.4 kHz for 32 frames at 44.1 kHz. Slower jitter is therefore removed from the interface TIE itself, not only after the PLL.
2. White transmitter jitter (option). Convention: continuous white jitter, limited to the band 0 to $64 F_s$. The PLL passes the fraction $\sqrt{B_n / (64 F_s)}$, where $B_n$ is the equivalent noise bandwidth of the filter (integral of $\lvert H\rvert^2$):

$$B_n = f_c \cdot \frac{\pi/2n}{\sin(\pi/2n)} \quad \text{(Butterworth)}, \qquad B_n = \pi f_n \left(\zeta + \frac{1}{4\zeta}\right) \quad \text{(type 2)}$$

For a first order ($n = 1$), $B_n = f_c \cdot \pi/2$. Jitter independent from one edge to the next, sampled at the mean edge rate, would pass from 15% (as many 1s as 0s) to about 40% (digital silence) more, depending on the edge density.

1. Receiver floor $J_{floor}$, the intrinsic jitter of its clock.

$$J_{DAC} = \sqrt{J_{cable,filtered}^2 + \left(J_{tx}\sqrt{B_n/(64F_s)}\right)^2 + J_{floor}^2}$$

Presets.

The floors are not of the same nature: RMS clock jitter for the CS8412, period jitter for the WM8805, orders of magnitude for the others. A datasheet may give period jitter, cycle-to-cycle jitter or TIE, quantities that do not compare directly; the model adds them all in quadrature as a TIE. Presets marked "typ." in the interface do not correspond to a published value.

ASRC. An asynchronous sample rate converter estimates the ratio between input and output rates through a very narrow filter. The preset represents the AD1890 as a 3 Hz first-order filter. The Analog Devices AD1890 datasheet states jitter rejection above about 3 Hz in slow mode (12 Hz in fast mode), with a first-order slope; Adams (*The Audio Critic* no. 21) mentions a cutoff "as low as 3 Hz" at -6 dB/octave. More recent ASRCs are more selective: the servo loop of the SRC4392 (Texas Instruments) rolls off at 80 dB per decade. Interface jitter is very strongly attenuated but not removed: the residue becomes a small amplitude error on the converted samples.

Word Clock. The converter clock is locked to an external reference: jitter received over the S/PDIF cable does not reach it. The 10 ps floor is an optimistic assumption (quality VCXO): the jitter of the word clock signal itself also goes through the converter PLL, and it is not modeled.

Example (Belden 1694A, 100 m, no transmitter jitter): interface jitter 197 ps RMS; after CS8412, 204.9 ps (the 200 ps floor dominates); after VCXO, WM8805, ASRC or Word Clock, mostly the floor (80, 50, 20, 10 ps). Limit: 32 frames last 0.73 ms, and the clock fit removes slower components (jitter correlated with the 1 kHz sine, block line at fs/192 = 230 Hz). They do exist: with the J-test and a simulated cable, Dunn (AN-5, fig. 22 and 23) observes an ISI jitter line at 125 Hz (384-cycle J-test, at 48 kHz), which a converter with no in-band jitter filtering lets through. His simulated cable is heavily degraded (19.9 ns RMS at 125 Hz); in our model, the ISI jitter of a 100 m 1694A is only 0.8 ns peak-to-peak, and these slow lines stay of that order at most.

Jitter and audio signal-to-noise ratio

Sinusoidal jitter of RMS value $J_{RMS}$ on the converter clock, applied to a signal of frequency $f$, limits the signal-to-noise ratio to:

$$SNR_{jitter} = -20 \log_{10}(2\pi f\, J_{RMS}) \quad \text{(dB)}$$

This is equation 1 of Dunn (1992), which gives each sideband as $20 \log_{10}(J_{pp}\,\omega/4)$ with $J_{pp}$ peak-to-peak: both sidebands together, expressed in RMS, give this formula. This is a worst case (full-scale 20 kHz signal); physically, it concerns the jitter that reaches the converter clock (after the PLL). Applied to raw interface jitter, as the interpretations do, it only gives a pessimistic bound.

Published detection thresholds.

• Benjamin & Gannon (Dolby, AES preprint 4826, 105th convention, 1998) studied sinusoidal jitter. On a full-scale 20 kHz sine with jitter at 17 kHz, the mean threshold is 10 ns RMS; on a 4 kHz sine (jitter at 2 kHz), 100 ns RMS. On music, the vast majority of programs do not make jitter audible. On excerpts chosen to be revealing (8 subjects, self-administered test), individual thresholds range from about 20 ns to 370 ns.
• Ashihara et al. (Acoust. Sci. & Tech. 26(1), 2005) studied random jitter on music: the detection threshold is at several hundred nanoseconds (6 listeners out of 23 detect it at 500 ns RMS, none at 250 ns).

Theoretical criteria, much stricter. Other authors do not measure what listeners detect: they compute the jitter that would stay inaudible in the worst case.

• Dunn (AES preprint 3361, 1992, §3.3) starts from masking, for playback at no more than 120 dB SPL and sidebands assumed audible from 0 dB SPL. Sampling jitter must stay below 20 ps peak-to-peak at 20 kHz; the limit rises by 6 dB per octave up to about 1 ns near 500 Hz, and below 200 Hz jitter may reach 500 ns. He also recalls the target of Meitner and Gendron: 250 ps RMS of white jitter for a 16-bit signal, that is an error of at most 1 LSB on a full-scale 20 kHz sine.
• Siau and Burdick (Benchmark Media Systems) start from the fact that a tone can be heard 25 dB below A-weighted white noise. They consider jitter totally inaudible only if its sidebands stay at least 23 dB below the A-weighted system noise. For their converter (-117 dBFS), the sidebands must stay below -140 dBFS, that is a few picoseconds at the clock (below 5 ps at 6 kHz, according to their measurement).

The two approaches do not answer the same question. Theoretical criteria set a design target: below it, no signal and no listener can reveal the jitter. Listening tests measure what listeners actually detect, on test signals or on music. Between the two, opinions differ: Katz (2007) considers the ear sensitive to minute amounts of jitter, without giving a figure. The application does not settle the matter.

Thresholds measured in listening tests are far above the jitter produced by a matched coaxial cable, before as well as after the PLL. After the PLL, what remains is mostly the receiver floor (10 to 200 ps depending on the preset), to be compared with the theoretical criteria. The automatic interpretations place the jitter at the converter clock on a scale drawn from listening tests: below 10 ns, below published thresholds; from 10 to 500 ns, within the range of published thresholds (depending on the signal and the listener); above 500 ns, beyond published thresholds. The source note shown under the chart recalls the theoretical criteria.

References:

• Adams, R.W. (1994). "Clock Jitter, D/A Converters, and Sample Rate Conversion." *The Audio Critic*, No. 21. biline.ca
• Dunn, J. (1992). "Jitter: Specification and Assessment in Digital Audio Equipment." AES preprint 3361, 93rd convention. Author's PDF
• Dunn, J. (2001-2004). "Measurement Techniques for Digital Audio." Audio Precision, Application Note 5. archive.org
• Katz, B. (2007). "Jitter." Digital Domain. digido.com
• Macadie, D. (2005). "Jitter performance of S/PDIF digital interface transceivers: is meeting standards enough?" Wolfson Microelectronics, white paper, rev. 1.1.
• Crystal Semiconductor. CS8412 datasheets: DS61PP4 (1993) and DS61F1 (1998).
• Benjamin, E. & Gannon, B. (1998). "Theoretical and Audible Effects of Jitter on Digital Audio Quality." AES preprint 4826, 105th convention. aes.org
• Ashihara, K. et al. (2005). "Detection threshold for distortions due to jitter on digital audio." *Acoustical Science and Technology*, 26(1), pp. 50-54. doi.org
• Siau, J. & Burdick, A.H. (Benchmark Media Systems). "Jitter and Its Effects." benchmarkmedia.com

2.3 Voltages (high, low, P-P)

Definition. Voltage levels of the received signal, to assess attenuation and symmetry.

Method. The signal is split into two populations around the threshold $V_{thr} = (\max(v) + \min(v))/2$:

$$V_{high} = \frac{1}{\lvert H\rvert} \sum_{v[n] \in H} v[n], \qquad V_{low} = \frac{1}{\lvert L\rvert} \sum_{v[n] \in L} v[n], \qquad V_{PP} = \max(v) - \min(v)$$

with $H = \{v[n] > V_{thr}\}$ and $L = \{v[n] \leq V_{thr}\}$.

Interpretation.

• The nominal S/PDIF signal is 0.5 V peak-to-peak (IEC 60958-1), the simulated AES3 signal 5 V. The model places the S/PDIF reference between 0 and 0.5 V.
• Attenuation brings both levels closer to the threshold. When the level gap falls below 200 mV, the eye can no longer contain the input mask (200 mV over 0.5 UI, section 2.9) and decoding is no longer guaranteed.
• An asymmetry between $V_{high} - V_{thr}$ and $V_{thr} - V_{low}$ indicates a DC offset, for instance from AC coupling.
• $V_{PP}$ includes noise spikes and echoes: it can exceed 0.5 V with a noisy cable.

2.4 RMS Noise

Definition. Noise measured on the flat levels, separately for the high and low levels. Samples close to a transition (±4 samples) are excluded, so that edges are not counted as noise. The differences $d[n] = v[n+1] - v[n]$ between successive samples of the same level are taken, and their median absolute deviation:

$$\sigma = \frac{1.4826 \cdot \operatorname{med}\lvert d - \operatorname{med}(d)\rvert}{\sqrt{2}}$$

The factor 1.4826 turns the median absolute deviation into a standard deviation for Gaussian noise, and $\sqrt{2}$ corrects for the difference of two samples. The difference removes the slow shape of the level; the median ignores the few edge samples that might remain.

Validation. The measurement is zero on the ideal reference and stays within 1% error for white noise from 20 to 60 dB. Simulated noise is limited to the receiver bandwidth (section 1.4): neighbouring samples are correlated (coefficient $\rho_1$ = 0.87 at 32 samples per cell) and the difference only sees $\sqrt{1-\rho_1}$ of it, i.e. 36%. For a simulated signal, the measurement is divided by this factor; a capture keeps the white-noise assumption. The former standard deviation of the levels counted the edges: it gave 12 mV on a noiseless reference.

Interpretation.

• Noise reduces the usable gap between the two logic levels.
• Measured signal-to-noise ratio: $SNR \approx 20 \log_{10}\left(V_{PP} / \max(\sigma_{high}, \sigma_{low})\right)$. This measured SNR, referred to $V_{PP}$, exceeds by about 6 dB (more at low SNR) the model's SNR parameter, where noise is referred to half the amplitude: that parameter is what represents shielding in the sensitivity matrix and the ranking (sections 2.10 and 2.11).
• The reference noise is subtracted by the interpretations; it is zero for the ideal reference.
• An asymmetry between $\sigma_{high}$ and $\sigma_{low}$ points to an effect specific to one level.

2.5 Parity Errors

Definition. Every subframe (32 bits, i.e. 64 cells) ends with a parity bit, chosen so that bits 4 to 31 hold an even number of 1s (IEC 60958-1, AES3). Numbering these 28 bits from 0 to 27, the check is:

$$P_{check} = \left(\sum_{i=0}^{26} b[i]\right) \bmod 2, \qquad \text{error if } P_{check} \neq b[27]$$

$$N_{perr} = \sum_{sf} \mathbb{1}\left[b_{sf}[27] \neq \left(\sum_{i=0}^{26} b_{sf}[i]\right) \bmod 2\right]$$

Interpretation.

• Parity detects errors affecting an odd number of bits in a subframe; an even number of errors goes unnoticed.
• S/PDIF and AES3 both have this parity bit. The professional (AES3) channel status adds a CRCC in its byte 23, computed over each channel status block; the consumer channel status has none.
• Parity errors indicate a signal that is already clearly degraded.

2.6 Eye Diagram

Definition. Overlay of all signal segments two cells long (2 UI). The eye opening shows the voltage and timing margins directly.

Construction (eye_diagram() function).

1. Samples per cell: $SPC = \text{round}(T_{cell}/\Delta t)$.
2. Alignment on the measured clock: the window origin comes from the TIE regression (section 2.2). Transitions thus fall at 0, 1 and 2 UI, whatever the line delay.
3. Window of $W = 2\,SPC$ samples, shifted by one cell for each segment: $\text{seg}_k = v[s_0 + k \cdot SPC : s_0 + k \cdot SPC + W]$, where $s_0$ is the aligned origin.
4. Horizontal axis normalized from 0 to 2 UI.
5. Persistence display, as on an oscilloscope: a regular sample of windows (360 at most) is drawn as thin overlaid traces, and density reads as intensity.
6. AES3 mask overlaid in each opening: a rectangle 200 mV high and 0.5 UI wide, centered on the decision threshold.

The decision threshold is at the level midpoint. The 200 mV of the mask is a minimum eye height around this threshold, not an absolute level.

Reading.

• Vertical opening: gap between levels at the eye center, reduced by attenuation, ISI and noise.
• Horizontal opening: width of the stable region, reduced by jitter.

The AES3 eye mask and the practical limit derived from it are described in section 2.9.

2.7 Waveform Comparison (overlay)

Definition. Three synchronized panels overlay the signals of both cables and the reference:

Choice of the zoom region.

1. Combined absolute difference: $D[n] = \lvert v_A[n] - v_{ref}[n]\rvert + \lvert v_B[n] - v_{ref}[n]\rvert$.
2. Moving-average smoothing (window of at most 3000 samples).
3. Zoom centered on the maximum of the smoothed difference.

The three panels share the time axis: zooming on one zooms the others. For AES3, the 5 V signals are shown on a secondary axis, or normalized depending on the chosen display mode.

2.8 Automatic Interpretations

Under each chart, a text summarizes what the metrics show.

Eye diagram: based on the CER (scale of section 2.1) and on the eye height, measured on the probe signal and compared with the 200 mV mask, noise included at a BER of $10^{-12}$ (section 2.9).

Causes identified automatically: reflections ($\lvert\Gamma\rvert > 0.05$), cable noise ($\sigma$ > 5 mV above that of the reference), attenuation (noiseless eye height below 70% of the nominal level). When the margins are not available, the opening is estimated by $O_{eye} = (V_{high} - V_{low}) - 6 \times \max(\sigma_{high}, \sigma_{low})$ (3 sigma on each side) and attenuation by $V_{PP}$ < 0.35 V. For an optical link, the text notes that only the fiber is simulated.

Overlay: based on the amplitude difference $\Delta V_{PP} = \lvert 0.5 - V_{PP}\rvert$ (S/PDIF scale).

Jitter: based on RMS interface jitter, with the jitter SNR at 20 kHz (pessimistic bound, no PLL).

When a PLL is selected, the text adds the filtered jitter, the cable share compared with the receiver floor, and where the residue sits relative to published detection thresholds: below them (under 10 ns), within their range (10 to 500 ns), beyond them (over 500 ns) (section 2.2). For an optical link it notes that module jitter is not modeled.

Each interpretation links to the matching section of this documentation.

2.9 AES3 Eye Mask and Practical Limit

Mask. EBU Tech 3250 (§6.3.3) defines the minimum eye at the input of an AES3 receiver: height $V_{min}$ = 200 mV over a width $T_{min}$ = 0.5 UI, with $UI = T_{cell} = 1/(128 F_s)$ = 177.2 ns at 44.1 kHz. The rectangle is centered on the decision threshold (level midpoint): 200 mV is a minimum height, not an absolute level. The consumer interface has the same mask (IEC 60958-3:2003 §7.3.3.3, figure 9; covered in IEC 60958-1:2021 §7.1.3, figure 8, according to its table of contents). A note in IEC 60958-3 states that this mask does not define the tolerance to zero-crossing deviations: that belongs to the jitter tolerance template, which requires a pulse of at least 0.8 UI. The simulator applies this mask to both interfaces and, for S/PDIF, also requires a pulse of at least 0.8 UI (peak-to-peak TIE of at most 0.2 UI); for AES3, the minimum opening stays 0.5 UI.

Margin measurement (link_margins() function). The probe signal (section 1.5b) goes through the cable without noise (line and reflections). Then:

• eye height: twice the smallest distance to the threshold in the central half of each cell (from 0.25 to 0.75 UI);
• width: $1 - J_{PP}/UI$, with $J_{PP}$ the peak-to-peak TIE;
• noise: the eye loses $2\,Q\,\sigma$, with $\sigma$ the absolute noise of section 1.4 and $Q$ = 7.03 (error rate of $10^{-12}$ for Gaussian noise).

The link meets the mask if the width reaches 0.8 UI for S/PDIF (0.5 UI for AES3) and the height, noise deducted, reaches 200 mV. The cause of a failure is shown: pulse < 0.8 UI or opening < 0.5 UI (jitter), eye < 200 mV (loss), eye < 200 mV at BER $10^{-12}$ (noise). Noise is only reported as the cause if it clearly shortens the limit: if, without noise, the mask already fails at a length 10% longer, the limit is attributed to losses.

Practical limit. Largest length, up to 200 m, that meets the mask: coarse sweep (0.5 to 200 m) then bisection. The search assumes that degradation grows with length, which holds since losses and picked-up noise increase with it. "> 200 m" means "beyond 200 m", the search limit. Examples in the Hi-Fi environment, at 44.1 kHz:

For the Van Damme, the Mogami 2964 and the generic coaxial, noise only takes 8 to 9 mV off the eye height: these limits depend little on the noise model, which is heuristic. Only the RCA "spaghetti" limit depends on it; it only gives an order of magnitude. AES3 cables exceed 200 m because the transmitter is simulated at 5 V: at the normative minimum of 2 V, the Belden 1800F holds about 189 m (179 m at 48 kHz), the Canare DA202 about 195 m at 48 kHz and the DA206 more than 200 m (section 1.2). For an optical link, the limit is set by the modules, not by the fiber (section 1.8): 0.2 to 5 m for the TOSLINK TOTX147/TORX147 pair; beyond 5 m, the result is not meaningful.

AES3 normative reference points (EBU Tech 3250).

• Input jitter tolerance (§6.3.6): 0.25 UI peak-to-peak above about 8 kHz, up to 10 UI below 200 Hz.
• Intrinsic output jitter of a transmitter (§6.2.5.1): less than 0.025 UI peak, measured through a 700 Hz high-pass filter.
• Equalization (§6.3.4): optional, at the receiver, for cables longer than 100 m ("Optional equalization can be applied in the receiver"). The reach of AES3-4 and IEC 60958-4-4 without equalization is 100 m, for frame rates up to 50 kHz. Dunn (AN-5) obtained reliable operation over 100 m without an equalizer on the BBC analog pair, and 250 m with one.

Consumer reference points (IEC 60958-3:2003, §7.3): cable of 75 ohm ±35% from 0.1 MHz to 128 times the frame rate; intrinsic output jitter below 0.05 UI peak, measured through the same 700 Hz filter; input tolerance of 0.2 UI peak-to-peak above 400 kHz, 0.25 UI from 200 Hz to 400 kHz and up to 10 UI below 5 Hz; rise and fall times below 0.4 UI; eye mask of 200 mV over 0.5 UI (§7.3.3.3).

2.10 Sensitivity Matrix

The matrix shows which cable parameter has the most influence on which metric, around the configuration chosen in the interface.

Method (compute_sensitivity_matrix() function). Each parameter is swept alone over 8 values, the others staying at their base value (that of cable A):

For attenuation, the list 0, 0.5, 1, 2, 4, 8, 12, 20, 25 dB is completed with the cable's own attenuation (rounded to 0.1 dB). If the latter does not exceed 12 dB, the sweep takes the 8 smallest values: it stops at 12 dB, or at 20 dB when the cable's value is already in the list (0 dB for a short cable, for example a 2 m Belden 1694A). Above 12 dB, it keeps 0 to 8 dB, the cable's value and 25 dB.

Measured metrics: CER, RMS jitter, amplitude $V_{PP}$, measured SNR, eye opening. For each pair, sensitivity is the range divided by the absolute mean value, then each column is normalized between 0 and 1. The calculation uses 4 frames and all the comparison options (skin effect, AC coupling, DCD).

Bandwidth is not swept: it follows from the losses and is not an independent parameter. Velocity has no effect on a matched cable, which is physical: it only sets the echo delay when there is an echo. For an optical link, only length and velocity are swept.

2.11 Cable Ranking

The ranking compares the presets (excluding generic and optical cables) at the chosen length and environment, in two categories (75 ohm coaxial, 110 ohm AES3), and keeps the top three of each.

• Viability: the eye mask of section 2.9 is met (noise included, BER $10^{-12}$). A non-viable cable is ranked last.
• Score (heuristic weighting):

$$S = 0.5\,\max\left(0,\ 1 - \frac{J_{PP}}{J_{tol}}\right) + 0.3\,\min\left(1,\ \frac{SNR}{80}\right) + 0.2\,\min\left(1,\ \frac{h_{eff}}{V_{nom}}\right)$$

with $J_{PP}$ the peak-to-peak TIE on the probe signal, $J_{tol}$ the required horizontal margin, that is 1 UI minus the minimum opening (0.2 UI for S/PDIF, pulse of at least 0.8 UI; 0.5 UI for AES3, eye mask), $SNR$ the model's SNR (shielding parameter) and $h_{eff}$ the eye height with noise deducted. The 50/30/20 weights are a presentation choice, not a standard.

3. Global Verdict

Each cable gets a verdict combining the CER and the RMS interface jitter. Conditions are evaluated in order:

The jitter used is the one measured on the waveform; it already includes the mismatch echo. The verdict gives a quick reading; the detailed metrics and the eye remain the reference.

Appendix: Global Constants

Appendix: Conversion from Cells to Analog Signal

Before simulation, BMC cells are converted into a waveform by cells_to_analog():

1. Each cell is repeated $OVS = 32$ times and scaled by 0.5 V.
2. Gaussian smoothing gives finite rise times:
3. kernel standard deviation $\sigma_k$ = 4/3 sample, i.e. a 10-90% rise time of $2.563\,\sigma_k$ = 0.107 UI;
4. $\sigma_k$ is increased if needed so that this time does not fall below 5 ns, the AES3 minimum (EBU Tech 3250 §6.2.4), which only happens at 176.4 and 192 kHz;
5. normalized Gaussian kernel, evaluated over $\pm \lceil 3\sigma_k \rceil$ samples.
6. 10-90% rise times measured on the sampled waveform (slightly more than 0.107 UI, because of discretization): 19.4 ns at 44.1 kHz, 17.8 ns at 48 kHz, 8.9 ns at 96 kHz, 5.2 ns at 176.4 and 192 kHz. For comparison, Dunn (Audio Precision AN-5) measures 15 to 20 ns on a real AES3 output, and IEC 60958-3:2003 requires less than 0.4 UI.

CSV Capture Format

The analyzer imports oscilloscope captures in CSV format.

File Structure

# Comment (optional, lines starting with #)
time_s,voltage_V
1.000000e-07,2.50000000e-02
2.000000e-07,4.80000000e-01
3.000000e-07,4.75000000e-01
...

Format Rules

Automatic Time Unit Detection

If the header gives the unit of the time column (ns, us or µs, ms), it is used. Otherwise, the unit is inferred from the range of the values:

Recommended Duration and Sampling Rate

At 44.1 kHz the cell rate is 5.6 MHz and edges last about twenty nanoseconds. 50 MSa/s or more allows accurate interpolation of threshold crossings for jitter measurement.

These minimums are recommendations: the import only rejects a file with fewer than 10 numeric points or covering less than 885 ns.

Example File

A sample CSV file can be downloaded from the interface ("Download sample CSV" button): a current reference S/PDIF signal (by default, 1 kHz sine, 44,100 Hz, 16 bits) after a 3 m Belden 1505A cable; the noise is drawn at random on each download.

WAV File Import

The analyzer also accepts WAV captures (8/16 bits, mono or stereo). The signal is normalized between 0 and 0.5 V. This format suits USB oscilloscopes that export to WAV.

Appendix: Reference Simulation Results

1 kHz sine, 44,100 Hz, 16 bits, 32 frames, fixed random seed (42), skin effect on, no AC coupling. Jitter is the measured TIE, noise included.

Main cables at 1.5 m (home hi-fi)

At 1.5 m, all cables transmit without errors, with jitter from a few picoseconds to about a hundred picoseconds. At 1.5 m the RCA "spaghetti" is below its $L_0$ length (14.6 m): the main echo falls on the flat level before each edge, and its jitter comes mostly from its higher losses, which the echo partly copies.

Effect of Length - Generic RCA Cable (Hi-Fi)

The simulated window shows no errors up to 30 m, but the practical limit from the eye mask, with noise taken at BER $10^{-12}$, is about 20 m. Beyond 14.6 m, the echo adds its data-dependent jitter.

Effect of Environment - Belden 1694A, 10 m

With 90 dB of shielding, the picked-up field stays below the shielding in all three environments: the SNR only depends on the length term.

Appendix: S/PDIF and AES/EBU Connectors

Values from manufacturer datasheets (Neutrik, Kings Electronics), standards (IEC 61169-8, IEC 61754-2) and a calculation of the reflection of a short plug (ABCD matrices), except those marked "order of magnitude (not verified)". No independent measurement was made for this project.

1. RCA (Phono)

A connector with no specified impedance: designed for analog audio, adopted by convention for consumer coaxial S/PDIF.

The value of ~32 ohm often quoted for an RCA plug comes from forums; it could not be verified.

Effect on the signal. A 2 to 4 cm discontinuity has a transit time of 0.1 to 0.2 ns. Seen by a ~19 ns edge, it is electrically short: an ABCD-matrix calculation gives a reflection of 0.2 to 0.6% for a 30 to 50 ohm plug on a 75 ohm line, and up to ~2% with 5 ns edges. The transmitted wave is delayed by 7 to 46 ps, by the same delay for every edge: this delay produces no jitter. These values do not depend on cable length. The "Belden 1694A + 50 ohm RCA plugs" preset therefore keeps a 75 ohm line. An oxidized plug mainly adds series resistance and intermittent contact.

2. BNC 75 ohm

Controlled-impedance connector. IEC 61169-8 describes the 50 ohm BNC; the 75 ohm version only appears in its annex A, for interface dimensions, with an unspecified reflection factor. Performance figures therefore come from manufacturer datasheets, for example the Kings 2065 series (bulletin 313A):

A 36 dB return loss corresponds to a reflection coefficient below 0.016, over a length of about one centimeter: negligible effect.

3. XLR (AES/EBU)

Balanced 3-pin connector (IEC 60268-12, cited by EBU Tech 3250 §6.4; IEC 61076-2-103), for example Neutrik NC3MXX and NC3FXX.

The controlled impedance is that of the cable (110 ohm). The connector is about 30 mm long (0.10 to 0.15 ns transit): even with $\lvert\Gamma\rvert$ = 0.3, its reflection stays below 0.5% for 19 ns edges.

4. Toslink (optical)

The optical connector has no electrical reflection. The jitter of an optical link comes from the transmitter and receiver modules (see section 1.8), not from the connector or the fiber.

5. Practical impact at BMC frequencies

6. Why connectors are not modeled

At these frequencies a connector is an electrically short discontinuity, whose reflection is negligible compared with that of a whole mismatched line. Only a contact defect (oxidation) has a noticeable effect, and it does not lend itself to a generic model.

Appendix: Scope, the Complete Chain up to the Receiver

Hysteresis is not modeled. When symmetric, it delays rising and falling edges by similar amounts, which depend on their slope; its effects (fewer multiple crossings caused by noise, a little extra jitter when the edge slope varies) depend on the receiver.

To compare two cables, device-specific options (transmitter jitter, DCD) can stay off: they apply identically to both branches. For an absolute estimate of the chain, turn them on.

Appendix: Model Limitations

The simulator is an educational tool and does not replace a measurement.

Appendix: Validation Against the Literature

Jitter vs. Distance (Belden 1694A, 75 ohm)

Simulated values (1 kHz sine, 32 frames, Hi-Fi environment, noise included, seed 42):

These values come from the published cable losses. They are not fitted to published jitter measurements: published link jitter measurements include the transmitter and the receiver, and are not directly comparable.

Maximum Distance per Cable

Comparison Sources

• EBU Tech 3250, 3rd edition (2004), §6: AES3 electrical characteristics, eye mask, optional equalization at the receiver beyond 100 m. tech.ebu.ch
• Canare: DA202 and DA206 specifications (stated maximum lengths).
• Belden: 1694A and 1800F cable datasheets; bulletin TB65 (*Digital Studio Cable Guide*, 4th ed., p. 8), recommended maximum distances for the 1800F.
• Dunn, J., *Measurement Techniques for Digital Audio*, Audio Precision AN-5: practical lengths for AES3 and consumer links.

Appendix: Audiophile Myths vs. Digital Signal Physics

S/PDIF Data Are Binary, the Waveform Is Not

The waveform travelling in the cable is an analog signal: it degrades gradually (losses, echo, noise). The receiver compares it with a threshold, and each cell is read right or wrong. As long as the eye stays open, a cable therefore does not gradually degrade the audio content; either the bits arrive intact, or errors appear.

Two cables that both give CER = 0 deliver the same bits. Without an ASRC or an external clock, however, the receiver derives the converter clock from the received signal: interface jitter, filtered by the PLL, reaches the DAC clock. Between two error-free cables, the only differences that can remain are therefore differences in filtered jitter, very small for matched cables (see section 2.2), and, for an electrical cable, the effects of a ground loop or of noise conducted to the receiver's analog ground, which the model does not cover.

Critical Distance by Sample Rate

For a mismatched cable, the length from which the echo produces data-dependent jitter is $L_0 = v\,T_{cell}/2$ (section 1.5b):

Below it, the main echo falls on the flat level before each edge: it mostly delays the edges, with a jitter residue that grows with the line losses. A cable at the right impedance, between a transmitter and a receiver at 75 ohm (110 ohm for AES/EBU), produces no echo, whatever its length.

The Role of the Receiver PLL (DAC)

The receiver locks its clock to the received signal through a PLL, which passes slow jitter and rejects fast jitter. The attenuation depends on the receiver: a wide-band PLL (CS8412, -3 dB around 38 kHz) passes all audio-band jitter, a narrow PLL (WM8805, rejection above 100 Hz according to Wolfson) rejects it strongly, an ASRC or a Word Clock remove it almost entirely. The receiver clock floor (10 to 200 ps depending on the preset) often dominates the result.

A residual jitter of 1 ns RMS at the DAC clock limits the SNR to 78 dB for a 20 kHz signal: $-20 \log_{10}(2\pi \times 20\,000 \times 10^{-9}) \approx 78$ dB.

When the Digital Cable Really Matters

What the Model Establishes

For a cable at the right impedance, shorter than 5 m:

• the loss at $f_{ref}$ stays below 0.1 dB for quality 75 ohm coaxial cables (Belden, Canare, Sommer, Gotham: from 0.05 to just under 0.1 dB at 5 m); it reaches 0.13 to 0.27 dB at 5 m for AES3 pairs, whose 2 to 7 V level leaves a much larger margin;
• interface jitter stays at a few hundredths of a nanosecond peak-to-peak;
• the CER is zero;
• there is no echo.

The received bits are identical from one cable to another, and jitter differences sit orders of magnitude below published detection thresholds, before as well as after the PLL.

The model does not cover ground loops or noise conducted by the shield of an electrical cable to the receiver's analog ground: these are the paths through which two error-free cables can still differ, and which an optical link removes.

Appendix: Blind Listening Tests

We found no peer-reviewed study comparing, blind, two digital cables that carry the same bits (search of the AES e-library, OpenAlex, Crossref and Semantic Scholar, September 2026). The available data concern the audibility threshold of jitter and double-blind comparisons of other links in the chain; the only controlled test in which an S/PDIF digital cable changes does so together with other elements.

Method. Two older reviews put these results in context. Clark (AES preprint 3167, 1991) summarises ten years of ABX tests: differences perceived in sighted listening are often not confirmed blind. Nousaine (AES preprint 3177, 1991) shows that, in the published tests he could analyse, listeners readily report a difference between two identical alternatives: a test without blinding or control trials overestimates differences.

Orders of magnitude. Without noise, a 10 m Belden 1694A adds 0.05 ns peak-to-peak of TIE; with the default hi-fi noise, the application shows 0.07 ns peak-to-peak and 0.014 ns RMS. The other 75 ohm coaxial cables stay between 0.01 and 0.04 ns RMS at 10 m (less than 0.2 ns peak-to-peak), and a good coaxial cable stays below one nanosecond peak-to-peak at 100 m, before any filtering by the receiver PLL. Published thresholds are 10 ns RMS on average in the worst case (full-scale 20 kHz sine, sinusoidal jitter at 17 kHz, Benjamin and Gannon), a few tens to a few hundred nanoseconds on selected music excerpts (sinusoidal jitter, 20 to 370 ns depending on the subject), and several hundred nanoseconds for random jitter on music (Ashihara: 6 listeners out of 23 at 500 ns, none at 250 ns). The gap is several hundred to several thousand times.

Limits. A negative test does not prove that a difference is inaudible for every listener and every system. None of these studies tests an S/PDIF digital cable on its own. Finally, an electrical cable can carry conducted noise and form a ground loop that reaches the analog part of the receiver; an optical link removes that path. This is an electrical effect, distinct from carrying the bits, that the simulator does not model.

Complete Bibliography

Standards and Specifications

Reference Books

AES Articles and Preprints

Application Notes

Manufacturer Datasheets

Author Biographies

• Robert W. Adams: Analog Devices. Author of "Clock Jitter, D/A Converters, and Sample Rate Conversion" (*The Audio Critic*, No. 21, 1994).
• John Siau and Allen H. Burdick: Benchmark Media Systems. Authors of the application note "Jitter and Its Effects".
• Bob Katz: Digital Domain, mastering engineer. Author of the article "Jitter" (2007).
• Eric Benjamin and Benjamin Gannon: Dolby Laboratories. Authors of AES preprint 4826 (1998).
• Julian Dunn: Prism Sound, then Nanophon. Author of AES preprint 3361 (1992) and of "Jitter and Digital Audio Performance Measurements" (1994).
• Chris Dunn and Malcolm O.J. Hawksford: University of Essex. Authors of AES preprint 3360 (93rd convention, October 1992).
• David M. Pozar: University of Massachusetts Amherst. Author of *Microwave Engineering*.
• Henry W. Ott: Bell Laboratories, then Henry Ott Consultants. Author of *Electromagnetic Compatibility Engineering*.
• Kaoru Ashihara and co-authors: National Institute of Advanced Industrial Science and Technology (AIST), Japan, for the lead author. Authors of the study published in *Acoustical Science and Technology* 26(1), 2005.