The Sound of a Digital Cable: Bandwidth and Jitter

DonH50

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Jun 23, 2010
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#1
Can your digital cable impact the sound of your system? Like most things, the answer is “maybe”… Reading some of the cable advertisements I see all kinds of claims. Some make no sense to me, such as “use of non-ferrous materials isolates your cable from the deleterious effects of the Earth’s magnetic field”. Hmmm… Some appear credible but describe effects that I have difficulty believing have any audible impact, such as “the polarizing voltage reduces the effect of random cable charges”. True, a d.c. offset on a cable can help reduce the impact of trapped charge in the insulation, but these charges are typically a problem for signals on the order of microvolts (1 uV = 0.000001 V) or less. Not a problem in an audio system even for the analog signals (1 uV is 120 dB below a 1 V signal), let alone the digital signals. But, there are things that matter and might cause problems in our systems.

Previously we discussed how improper terminations can cause reflections that can corrupt a digital signal. This can cause jitter, i.e. time varying edges, that are dependent upon the signal, which is really an analog signal from which we extract digital data (bits). As was discussed, this is rarely a concern for the digital system as signal recovery circuits can reject a large amount of jitter and extensive error correction makes bit errors practically unknown. The problem is when the clock extracted from the signal (bit stream) is directly used as the clock for a DAC. The DAC will pass any time-varying clock edges to the output just as if the signal was varying in time. It has no way of knowing the clock has moved, and the result is output jitter. Big enough variation and we can hear it as distortion, a rise in the noise floor, or both.

One thing all cables have is limited bandwidth. Poorly-designed cables, or even well-designed cables that are very long, may limit the signal bandwidth. This causes signal-dependent jitter. How? Look at the figure below showing an ideal bit stream and after band limiting. I used a 1 us bit period (unit interval) for convenience; this is a little less than half the rate of a CD’s bit stream.

time_small2..JPG

There is almost no difference between the ideal and 10 MHz cases. Since 10 MHz is well above 1/1 us = 1 MHz we see hardly any change. Dropping to 1 MHz, some rounding of the signal has occurred, and at 0.25 MHz we see that rapid bit transitions (rapidly alternating 1’s and 0’s) no longer reach full-scale output. Looking closely you can see that the period between center crossings (when the signal crosses the 0.5 V level) changes depending upon how many 1’s or 0’s are in a row. With a number of bits in a row at the same level, the signal has time to reach full-scale (0 or 1). When the bits change more quickly, the signal does not fully reach 1 or 0. As a result, the slope is a little different, and the center-crossing is shifted slightly in time. This is signal-dependent jitter.

A better way to see this is to “map” all the unit-intervals on top of each other. That is, take the first 1 us unit interval (bit period) and plot it, then shift the next 1 us to the left so that it lies on top of the first, and so forth. This “folds” all the bit periods into the space of a single unit interval to create an eye diagram (because it looks sort of like an eye). See the next figure.

eyes_small2..JPG

The top (ideal) plot shows a wide-open eye with “perfect” edges. As the bandwidth drops to 10 MHz we see the edges now curve somewhat, but there is effectively no jitter seen. That is, the lines cross at the center at one point, no “spreading”. With 1 MHz bandwidth the slower (curving) edges are very obvious, but still the crossing happens essentially at a single point. In fact jitter has increased but it is not really visible.

At 0.25 MHz there is noticeable jitter, over 41 ns peak-to-peak. That is, the center crossings no longer fall at a single point in time, but vary over about 41 ns in time. Why? Look at the 1 MHz plot and notice when the signal changes, rising or falling, it still (barely) manages to reach the top or bottom before the next crossing begins. That is, the bits reach full-scale before the end of the 1 us unit interval (bit period). However, with only 0.25 MHz bandwidth, if the bits change quickly there is not time for the preceding bit to reach full-scale before it begins to change again. You can see this in the eye where the signal starts to fall (or rise) before it reaches the top or bottom (1 V or 0 V) of the plot. This shifts the time it crosses the center (threshold). If the DAC’s clock recovery circuit does not completely reject this change, the clock period will vary with the signal, and we get jitter that causes distortion at the output of our DAC.

How bad this sounds depends upon just how much bandwidth your (digital) cable has (a function of its design and length) and how well the clock recovery circuit rejects the jitter. It is impossible to reject all jitter from the clock recovered from the bit stream, but a good design can reduce it significantly. An asynchronous system that isolates the output clock from the input clock can essentially eliminate this jitter source.

HTH - Don
 
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RogerD

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May 23, 2010
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BiggestLittleCity
#2
Last edited:
#3
About digital Coaxial versus digital Optical (Toslink), Don?

And what is the prefered digital Coaxial cable's impedance?

Connectors, do they have an influence on the overall sound quality?
...In relation to Jitter, or other type of spurious noise? ...Contact noise?

Dither noise? Thermal noise? About elevation?
 
Apr 3, 2010
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Seattle, WA
#4
It is great to have those simulations Don! And wonderful way to explain how it can be data dependent. Thanks so much for writing and posting it.
 

LL21

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Dec 26, 2010
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#5
Transparent Ref and Nordost Valhalla digicables were very different on my system. I am a big Transparent fan, use nearly all transparent...and i wanted so much to buy the Tranp Ref...i returned it after 3 fruitless hours of listening. On a lark, i went for the Nordost Valhalla since it was second-hand and in the store that day. i bought it that day, and i still listen to it every day after 2 years with no regrets.
 

DonH50

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Jun 23, 2010
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#6
Thanks guys. I tweaked the figures so they might be easier to see. I have yet to find an easy way to optimize for legibility...

Bob (Northstar):
  1. This is about coax. Optical uses a fiber link. The same sort of bandwidth issues can happen in the transmit/receive electronics, of course.
  2. Coax is typically 75 ohms though 50 ohms is used sometimes. This analysis was independent of coax impedance.
  3. Connectors don't usually impact the system unless they are poorly attached or the wrong type (impedance).
  4. Dither is random noise intentionally added to "scramble" the quantization spurs. It is mentioned in other threads but does not apply here. Dither does not impact bandwidth limitations.
  5. Thermal noise is not included and for a cable in audio systems is out of the picture.
  6. Elevation? I don't know what you mean. My house sits at about 7500', does that matter? :)

Amir: Figured you'd like the sims! Took waaay longer than it should to get them right. Tried a couple of ways before getting a source I liked (went with random), then had to generate a little impulse sampler (basic T/H did not work) and comparator circuit, then futz with various parameters. I swear it was easier to design at the transistor level than to gen up an ideal circuit for this...
 
#7
Thank you Don for your clear reply.

1. I got you; I was just wondering if it could make a difference.
2. I asked because some people use 100 Ohms digital Coax cables.
3. By the connectors I meant their built, material use; metal, gold, copper, brass, silver, etc.
And XLR Balanced versus RCA Unbalanced.
4. Got you, thanks.
5. Good to know, thanks again.
6. Elevation because at sea level versus 5,000 to 15,000 feet high (or more) can perhaps make a difference (just asking). But my guess is; no, it wouldn't affect the audio transmission through digital Coaxial cables.
- But low bass frequencies are certainly affected, but this has to do with sound pressure being different at various altitudes.

Thanks again, and your first post is a source of great info. Very much appreciated.
 

Ronm1

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Feb 21, 2011
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wtOMitMutb NH
#8
Nice work...

As likely a place as any to add....

When I first started getting into digital, issues I had were power related. My coax spdif hookups would be affected by diff devices turning on causing noise thru xports/players to external dac. Aes/Ebu, I2s or optical did not, only coax had issues. Eventually a Stealth shielded cable with proper gnd eliminated the coax symptom. It was an older house without a gnd to outlets except where new outlets, circuits had been added. I eventually added a dedicated 20a line and a power conditioner. Heating system turning on, fluorescent lights, dimmers were all culprits at the time.
 

bblue

New Member
Apr 26, 2011
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San Diego, CA
#10
Excellent, Don!

One other element which is often overlooked is proper resistive termination of the coax. I.E., 75 ohms. I would think that lack of proper resistive termination would have varying effects depending on the length of the run. For S/PDIF or Word Clock runs I use only 75 ohm quad shielded RG-6 with crimp-on BNC or RCA connectors (though I prefer BNC as a true 75 ohm connector) and have had zero problems with digital or WC connections.

AES/BSU is probably a safer alternative if your equipment has it.

--Bill
 

DonH50

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Jun 23, 2010
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#11
Excellent, Don!

One other element which is often overlooked is proper resistive termination of the coax. I.E., 75 ohms. I would think that lack of proper resistive termination would have varying effects depending on the length of the run. For S/PDIF or Word Clock runs I use only 75 ohm quad shielded RG-6 with crimp-on BNC or RCA connectors (though I prefer BNC as a true 75 ohm connector) and have had zero problems with digital or WC connections.

AES/BSU is probably a safer alternative if your equipment has it.

--Bill
See here: http://www.whatsbestforum.com/showthread.php?2746-Reflections-and-DACs
 

DonH50

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Jun 23, 2010
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#12
Nice work...

As likely a place as any to add....

When I first started getting into digital, issues I had were power related. My coax spdif hookups would be affected by diff devices turning on causing noise thru xports/players to external dac. Aes/Ebu, I2s or optical did not, only coax had issues. Eventually a Stealth shielded cable with proper gnd eliminated the coax symptom. It was an older house without a gnd to outlets except where new outlets, circuits had been added. I eventually added a dedicated 20a line and a power conditioner. Heating system turning on, fluorescent lights, dimmers were all culprits at the time.
Power certainly can be a factor, and coupled noise... Most cables have decent shielding so I neglected that for this since we are talking digital cables. A common weak link is the ground return path, which can be very poor in a lot of systems (analog and digital). USB is notorious for having lousy (noisy) grounds. Topic for another thread....
 

DonH50

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Jun 23, 2010
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#13
Thank you Don for your clear reply.

1. I got you; I was just wondering if it could make a difference.
2. I asked because some people use 100 Ohms digital Coax cables.
3. By the connectors I meant their built, material use; metal, gold, copper, brass, silver, etc.
And XLR Balanced versus RCA Unbalanced.
4. Got you, thanks.
5. Good to know, thanks again.
6. Elevation because at sea level versus 5,000 to 15,000 feet high (or more) can perhaps make a difference (just asking). But my guess is; no, it wouldn't affect the audio transmission through digital Coaxial cables.
- But low bass frequencies are certainly affected, but this has to do with sound pressure being different at various altitudes.

Thanks again, and your first post is a source of great info. Very much appreciated.
Thanks! Glad to know somebody reads my drivel...

100 ohms is used for many balanced (differential) digital systems, including the PCIe and SAS/SATA cables in your computer. I have not heard of using 100 ohms for a single-ended digital coax link, however. Maybe HDMI (did not look, lazy, lunch is waiting)?

The connector material has almost no influence (unless it is nonconductive). A poor design will not capture (attache) well and/or introduce an impedance discontinuity. Connectors are so short they are rarely problems, but if you get a bad one it is a pain.

Elevation has essentially no impact on the speed of electrons or transmission line characteristics. Cables using air dielectrics might vary a hair but you'd be hard-pressed to measure it. Sound waves are a totally different story since they travel through the air, not the metal... The speed of sound, attenuation, etc. is a function of the medium, and air density changes with altitude (and temperature, and humidity -- I think those are the primary first-order effects).
 
#15
If I may; http://wiki.answers.com/Q/What_parameters_determine_bandwidth_of_coax_cable

And Optical Fiber is faster (the fastest); speed of light.

* I also read that Glass Optical Fiber has more of a wider range of colors for real good bandwidth.
...Over Optical Plastic Fiber.

And, correct me someone please if I'm wrong:
The higher the frequency, the wider the bandwidth, and the increased ability to pass more data.
 
Apr 3, 2010
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Seattle, WA
#16
What determines the bandwidth of a cable?
The cable is essentially a low pass filter. Here is what a filter looks like:



There is a thing called a "cut off frequency" in such a filter:



For a filter like above, that cut off frequency is:



So if resistance or capacitance is increased, then the cut off filter gets lower and we are getting rid of more high frequencies.

The cable can be modeled using electronic elements of resistance, capacitance and inductance:



As you see, it has an "RC" low pass filter as shown above. Cable companies provide all of these parameters so you can compute the cut off frequency from them. Both are given as amount/foot (or meter) so the longer the cable, the more of a low pass filter the cable becomes.
 

DonH50

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Jun 23, 2010
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#17
What determines the bandwidth of a cable?
Primarily resistance, inductance, and capacitance for cables operating under perhaps 5 - 10 GHz, which I believe includes all cables used in audio and audio digital transmission systems. Cable parameters (below mmW) are expressed in values per unit length, e.g. capacitance per foot.

Pure resistance impedes current flow equally across all frequencies. Inductors pass LF and block HF, so series inductance reduces flow (and increases impedance) at HF. Capacitors pass HF but block LF, so parallel (shunt) capacitance also rolls off HF. Resistance working into the series L and shunt C reduces bandwidth.

Series resistance is a function primarily of wire cross-sectional area (diameter, gauge). Bigger is better. Adding wires in parallel, or more wires in a bundle (not insulated from each other), reduces the resistance.

Series inductance comes into play as frequency goes higher and becomes a function of surface area, which in turn is related to cross-sectional area, so again bigger is better. Wires in parallel again help, but since the current tends to flow more at the surface as frequency goes up and less in the middle, the wires must be insulated from each other to reduce inductance.

Capacitance is caused by the electric field between two conductors. It is a function of close the conductors are, so increasing the spacing between conductors lowers the capacitance.

A key point is that for digital audio (and any RF cables), if the transmitter, receiver, and cable are all the same impedance (perfectly matched) then the Rx and Tx do not "see" the impedance, only the delay through the cable. See the aforementioned thread on reflections.

HTH - Don

edit: I see Amir beat me to it with a better description, thanks Amir!
 

bblue

New Member
Apr 26, 2011
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San Diego, CA
#20
Power certainly can be a factor, and coupled noise... Most cables have decent shielding so I neglected that for this since we are talking digital cables. A common weak link is the ground return path, which can be very poor in a lot of systems (analog and digital). USB is notorious for having lousy (noisy) grounds. Topic for another thread....
But the USB signal wires are floating balanced twisted pairs that don't reference ground. The ground level is only the shield and +5 supply return. Is that what you're talking about, the supply return, and not the signal lines?

--Bill
 

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