This is exactly written in the book “Signal Integrity and Power Integrity – Simplified” written by Eric Bogatin.

The following text is taken from **Chapter 11: Differential Pairs and Differential Impedance**

**Even and Odd Modes**

There are two special voltage patterns we can launch into the pair that will propagate down the line undistorted.

The first pattern is when exactly the same signal is applied to either line; for example, the voltage transitions from 0 v to 1 v in each line.

The second special voltage pattern that will propagate unchanged down the differential pair is when the opposite-transitioning signals are applied to each line; for example, one of the signals transitions from 0 v to 1 v and the other goes from 0 v to –1 v.

To distinguish these two states, we call the state where the same voltage drives each line the even mode and the state where the opposite-going voltages drive each line the odd mode.

**Velocity of Each Mode and Far-End Cross Talk**

The description of the signal in terms of its components propagating in each of the two modes is especially important in edge-coupled microstrip because signals in each mode travel at different speeds.

The velocity of a signal propagating down a transmission line is determined by the effective dielectric constant of the material the fields see. The higher the effective dielectric constant, the slower the speed, and the longer the time delay of a signal propagating in that mode.

In the case of a stripline, the dielectric material is uniform all around the conductors and the fields always see an effective dielectric constant equal to the bulk value, independent of the voltage pattern.

The odd and even-mode velocities in a stripline are the same.

However, in a microstrip, the electric fields see a mixture of dielectric constants, part in the bulk material and part in the air. The precise pattern of the field distribution and how it overlaps the dielectric material will influence the value of the resulting effective dielectric constant and the actual speed of the signal. In the odd mode, more of the field lines are in air; in the even mode, more of the field lines are in the bulk material. For this reason, the odd-mode signals will have a slightly lower effective dielectric constant and will travel at a faster speed than do the even mode signals.

In a stripline, the fields see just the bulk dielectric constant for each mode. There is no difference in speed between the modes for any homogeneous dielectric interconnect.

In an edge-coupled microstrip, a differential signal will drive the odd mode so it will travel faster than a common signal, which drives the even mode.