Crosstalk Crosstalk is the electromagnetic coupling between conductors that are close to each other. Crosstalk is an EMC concern because it deals with the design of a system that does not interfere with itself. Crosstalk is may affect that radiated/conducted emission of a product if, for example, an internal cable passes close enough to another cable that exists the product. Crosstalk occurs if there are three or more conductors; many of the notions learnt for two-conductor transmission lines are easily transferred to the study of multi-conductor lines.

Crosstalk in three-conductor lines Consider the following schematic: reference conductor generator conductor receptor conductor near end terminal far end terminal The goal of crosstalk analysis is the prediction of the near and far end terminal voltages from the knowledge of the line characteristics. There are two main kinds of analysis Figure 1

This analysis applies to many kinds of three-conductor transmission lines. Some examples are: receptor wire reference wire generator wire receptor wire generator wire reference conductor (ground plane) receptor wire reference conductor shield generator wire generator conductor receptor conductor reference conductor Figure 2 (a)(b) (c) (d)

As in the case of two-conductor transmission lines, the knowledge of the per-unit length parameters is required. The per-unit length parameters may be obtained for some of the configurations shown as long as: 1) the surrounding medium is homogeneous; 2) the assumption of widely spaced conductors is made. Assuming that the per-unit-length parameters are available, we can consider a section of length of a three-conductor transmission line and write the corresponding transmission line equations. It turns out that by using a matrix notation, the transmission line equations for a multi-conductor line resemble those for an ordinary two-conductor transmission line.

Let us consider the equivalent circuit of a length of a three-conductor transmission line. The transmission line equations are: (1) (2) Figure 3

The meaning of the symbols used in (1) and (2) is: and (7) (8)

Per-unit-length parameters We will consider only structures containing wires; PCB-like structures can only be investigated using numerical methods. The internal parameters such as r G, r R, r 0 do not depend from the configuration, if the wires are widely separated. Therefore we only need to compute the external parameters L and C. It is important to keep in mind that for a homogeneous medium surrounding the wires, two important relationships hold: and (9) (10)

The elements of the L matrix are found under the assumption of wide separation of the wires. In this condition the current distribution around the wire is essentially uniform. We recall a previous result for the magnetic flux that penetrates a surface of unit length limited by the edges at radial distance and as in the following. (11) + surface 1m Figure 4

Then we consider a three-wire configuration: For this configuration we can write: (12) or (13) Figure 5

Using the result of (11), we obtain (14) (15) (16) And from these elements, we obtain the capacitance using the relationship: (17)

Frequency-domain solution Consider the following circuit: The closed form expression for the near and far end voltages and are very complex so we will introduce additional simplifications: 1) the line is electrically short at the frequency of interest; 2) the generator and receptor circuits are weakly coupled, i.e.: (18) Three-conductor line Figure 6

Under these assumptions, the near end voltage simplifies to: (19) and the far end voltage becomes: (20) In (19) and (20) (21) and (22) (23)

The meaning of (19) and (20) is that for electrically short and weakly coupled lines the voltage due to the crosstalk are a linear combination of the inductance l m and capacitance c m between the two circuits. In addition, inductive coupling is dominant for low-impedance loads (high currents), whereas capacitive coupling is dominant for high- impedance loads (low currents). It turns out that (we skip the proof) if losses are included a significant coupling results at the lower frequencies. This phenomenon is called common-impedance coupling. Time-domain solution: exact solutions are more difficult to derive for multiple transmission lines, so we will not consider them.