Sierra Circuit Certification

How to design differential pairs in PCB transmission lines

A pair of lines can be modeled as shown on this image. We will assume here that both of the lines of the pair are identical and uniform. And that they have the same separation from each other along the entire length of the line. These are precisely the characteristics of a pair of lines to be designated as a differential pair.

When we have a pair of lines close to each other, it is fair to say that the presence of a current in line 2 will induce some voltage in line 1 and a current in line 1 will induce some voltage in line 2. Thus, the voltage ‘V1’ at line 1 will not only depend on current ‘I1’ in line 1 (through impedance ‘Z0’ of line 1). It will also depend on current ‘I2’ in line 2 through coupling or mutual impedance ‘Zm’ between lines 1 and 2.

This e-book will give you the keys to better diff pair designing, explain differential and common mode signals and offer a detailed analysis in terms of line inductances and capacitances.


Odd and even modes

Let ‘V1’ and ‘V2’ be the signal voltages and ‘I1’ and ‘I2’ be the signal currents in the two lines of a differential pair characterized by impedances ‘Zse’ and ‘Zm’. We know these six quantities are related through our previous equations.

The difference in signal voltage ‘V1’ and ‘V2’ is called the differential signal ‘Vdiff’. Half of it is also called the odd mode signal.


Differential signaling analysis

These equations indicate the universal fact that any two arbitrary signal values ‘V1’ and ‘V2’ can always be expressed as and therefore analyzed in terms of a common (or even) mode signal and a differential (or odd) mode signal.

They also allow us to think that ‘Vcom’ or ‘Veven’ part of the signals in ‘V1’ and ‘V2’ are a kind of ‘’bias’’ on top of which the differential mode (or odd mode) signals ‘+Vodd’ and ‘-Vodd’ ride to result in ‘V1’ and ‘V2’.

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