I took various computer classes in high school and always wondered why the conductors in Ethernet cables were twisted around each other. Little did I know that this was a simple design method that ensured signals reached their destination without interfering with each other. Sometimes, the best solutions to complex problems are actually the simplest.

Differential routing of conductors is not limited to Ethernet cables; it is one of the key topologies in PCBs. Circuit board designers often discuss transmission line impedance in terms of single-ended traces rather than differential traces.

Some designers have a tendency to treat each member of a differential pair as its own single-ended trace. This ignores the natural coupling that exists between each trace, and the impedance of a differential pair is much different from their single-ended counterparts.

## Do I Really Have Transmission Lines?

Whether a trace behaves as a transmission line depends on the transmission delay over a given trace. When the rise time of the digital signal, or one quarter the oscillation period of the analog signal, is less than double the round-trip transmission delay along the trace, then the trace should be treated as a transmission line.

A more conservative industry-standard rule is to treat a trace as a transmission line if the transmission delay of the trace is greater than 10% of the critical round-trip transmission delay defined by the rise time or the oscillation period. When in doubt, it is safer to match impedance in order to prevent problems from signal reflection.

Coupling in a differential pair, which determines the differential impedance.

## Differential vs. Single-Ended Impedance

Impedance mismatch in high-speed/ high-frequency PCBs can wreak havoc on your signals. Problems like ringing due to signal resonance arise when there is a significant impedance mismatch in a single-ended trace. Impedance matching is not normally required at low-frequency signals unless the mismatch between a trace and its upstream and downstream components is large. Impedance should always be matched in high speed and high-frequency PCBs.

Single-ended trace impedance is normally calculated by ignoring any neighboring traces, regardless of whether they contain a propagating signal. In differential pairs, where we assume that a neighboring trace propagates a return current in the opposite direction as the signal trace, the signal in one line couples to the other through induction. The lines also have parasitic capacitance between them due to the substrate dielectric.

Differential pair routing and vias on a PCB

Aside from suppressing crosstalk, coupling between differential traces actually decreases the impedance of each trace. Designers should be aware that a simple single-ended trace impedance calculator should not be used to calculate the impedance of differential traces.

For digital signals, we also need to take the frequency spectrum of the signal into account when calculating differential impedance. For the mathematicians out there, the frequency content in a digital signal can be represented as a sum of analog frequencies. This means that coupling in a differential pair that carries digital signals depends largely on the entire frequency spectrum of the digital signal.

Most of the intensity in digital signals is concentrated at frequencies below the knee frequency, which is equal to approximately one-third the inverse of the rise time. All frequencies between the operating frequency and the knee frequency will be the primary contributors that determine impedance.

## Differential Impedance Calculators

Striplines and microstrip differential pairs have different impedance values due to the presence of the substrate. Symmetric and asymmetric striplines or embedded microstrips also have different impedance values compared to a surface microstrip. The substrate dielectric and geometry modify the effective dielectric constant of the trace, which also modifies the critical delay time determining whether the trace acts as a transmission line.

Working with many differential impedance calculators requires that you know the effective dielectric constant of the trace beforehand. This requires another calculator tailored to your specific geometry.

Once you have your effective dielectric constant and you’ve chosen your geometry, you are ready to start running calculations. You can play with the geometric parameters until you achieve the desired impedance level, or you can constrain the geometry and use the calculated impedance value for impedance matching in your PCB.

The differential impedance value that is returned from most calculators is equal to the sum of the impedance from each trace. Taking this value and dividing by 2 gives you the odd-mode impedance value of each trace. This is the value that needs to be considered when impedance matching. As a limiting case, setting the separation between the traces to a very large value causes the impedance of a trace to converge to the single-ended impedance value.

One drawback of many online differential impedance calculators is that they do not allow you to calculate the impedance as a function of frequency. Some RF calculators only perform calculations at a specific frequency, usually 2.4 GHz. The S-parameters in a trace are frequency dependent, and differential pair impedance calculators should take this into account. Most calculators use the approximation that the differential impedance is the square root of impedance divided by capacitance.

In the frequency domain, the impedance spectrum has a minimum at mid-range frequencies due to resonance and then increases both at lower and higher frequencies. In the time-domain, there is a minimum at a particular oscillation period/rise time, followed by a monotonic impedance rise as the signal period/rise time increases up to the round-trip delay time. This is where powerful design software and excellent simulation tools become important.

A great piece of PCB layout software like Altium Designer makes it easy to layout differential pairs in your next high-speed or high-frequency design. The ActiveRoute tool, xSignals tool, and built-in simulation tools can help you easily route differential pairs and avoid signal problems due to impedance mismatch. Talk to an Altium expert today if you’re interested in learning more about Altium Designer.

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