Differential Pairs in PCB Transmission Lines: Differential Impedance, Even or Common Mode

Differential Pair series - Sierra Circuits

This article follows our explanation of differential and common mode signals in differential pairs in PCB transmission lines.

We will cover:

  • Differential impedance
  • Even or common mode

Differential impedance

The differential impedance is the impedance seen by a purely differential (ie. odd mode) signal over a differential pair. As:

Equation 9

Thus, the differential impedance is twice the odd mode impedance. Or the odd mode impedance is half of the differential impedance.

Most often, the only specified requirement of a differential pair is its differential impedance. Typical values for most common differential signal types are 90 ohms differential, 100 ohms differential or 120 ohms differential. In some cases, we can also use 75-ohm differential impedance.

Even or common mode

Let’s now take the case when both the lines of the differential pair are excited by a common signal:

Equation 9 bis

Since ‘V1 – V2 = 0’, there is no differential mode signal. As ‘V1 = V2’, ‘I1 = I2’ and the equations (3) and (4) become:

Equation 9 bis bis

Therefore, we can define the even mode impedance ‘Zeven’ as the ratio of the even mode voltage to the even mode current in each line:

Equation 10

As:

Equation 10a

And the common mode signal current in the differential pair is ‘I1 + I2 = 2I1’ so that the common mode impedance of the differential pair is:

Equation 11

Thus, the common mode impedance of the differential pair is half of the even mode impedance of one line. It basically equals two even mode impedances in parallel.

From the equation (10), it is clear that ‘Zeven’ is greater than ‘Zse’. Greater the coupling between the two lines of the pair is, larger will ‘Zeven’ be compared to ‘Zse’.

Recap: Odd and even mode impedances

Odd and even mode impedances of a differential pair lines are fundamental characteristics of the pair. We can evaluate all other impedances from their values, as illustrated below:

Since:

Equation 11 bis

Equation 12a 12b 12c

To these, we can add:

Equation 12 bis

In our next article, we will dive a little deeper into the physical parameters of a differential pair.

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