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What is the difference between common mode and differential mode noise?

It is thought that both wires in a twisted pair wire pick up a great deal of noise, which is picked up by DSL modems at the same time. This seems simple enough since both wires are located together in close proximity, and twisted together tightly. If an electric field passes through one wire it will pass through the other with (ideally) equal strength. If this field causes interference in one wire it causes the same interference in the other. This signal is common to both wires, and it is called a "common mode" signal. In telephone company terminology it is known as "longitudinal mode", but let us stick with common mode here.
A DSL receiver is coupled to the twisted pair line via a transformer. If both pairs of the twisted pair wire have the same signal on them, this puts no signal across the transformer winding at all, and so nothing is coupled to the other side of the transformer. So any interference caused by a common mode signal is completely cancelled out by the receive transformer.
That is how it is supposed to work, and for many signals over quite a wide frequency range, it can be made to work that way up to a point. But of course, no signal is coupled EXACTLY the same to both wires, and the wires themselves are not EXACTLY the same, and the termination at the modem does not have equal impedance (to ground) at all frequencies, so the common mode signal actually is translated into differential mode signal at the receive transformer. And this interferes with the DSL signal, which is transmitted down the telephone line in differential mode.
Up to now, all signals specified by Standards bodies such as ITU have been differential mode signals, but there have been rumblings for a long time that "it would be nice if" common mode signals could be generated and applied to dsl modems.
The DLS 5410DC injector that applies common mode signals as well as differential mode signals, but so far I don't think that it has been used very much because there are no standards for this! With VDSL2 it is probably coming, because service providers are very worried about the pick up of RF noises in common mode, which could convert too easily into differential mode.
However, common mode signals in the RF range are extremely difficult to apply accurately. (It is very easy to apply them -- but very difficult to apply them accurately). So for the moment, standards are still based on differential mode impairments, and work on common mode impairments seems to be very slow.
Spirent is working with several common mode noise experts and will present new contributions to the standards later this year, to address Applying common mode noise injection in to the VDLS Wireline simulator.
Noise injection 
  Noise Definition
Common Mode Noise is when the noise is injected across both wires and the interference is common between both wires in the pair thus the term common mode noise. If you were to view the noise both waveforms would be in phase with respect to one another and have the same shape.
Differential mode Noise is when the noise is injected across both wires and the interference is
Differential between both wires in the pair thus the term differential mode. If you were to view
The noise both waveforms would be out of phase with respect to one another.
Effects of Noise on xDSL Modems
If the noise exceeds the receive input sentivity the DSL modem may exhibit the following conditions
The modem may not be able to train to the remote end device.  
The modem may operate fine then due to impairment conditions the DSL modem may have to retrain and downspeed to maintain error free operation.
The effects of common mode noise on a DSL modem may cause errored transmission conditions
Since any mismatch in the receive cct impedance of the DSL modem causes common mode noise to be changed into differential mode noise.
As we are dealing with high frequencies Common mode noise becomes more of a problem as the standards move to VDSL and VDSL2.  Common mode noise is applied with the DLS-5410DC noise injector. Spirent is continually contributing to the standards to improve the standards and to ensure that wireline products meet the latest evolving standards.

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