# Differential Pair Impedance: Using a Calculator to Design Your PCB

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 pair routing is not limited to Ethernet cables; it is one of the key routing and design techniques in high speed PCBs. Circuit board designers often discuss transmission line impedance in terms of single-ended traces rather than differential pairs traces, but a clear understanding and calculation or differential pair impedance is critical to ensuring controlled impedance throughout your circuit board. Things like reactance, inductance and impedance, can often be brought down to a simple solution.

## When Does Differential Impedance Matter?

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. The same applies to different pairs; the exception is end-terminated pairs connected to a load with high input impedance (e.g., LVDS). Just like single-ended impedance, differential pair impedance matters when the trace behaves as a differential transmission line, which then depends on the transmission delay over a given trace.

In the case where the signal rise time is very short, then the differential pair impedance should be matched to the source and load components. Impedance matching is not normally required unless the mismatch between a trace and its upstream and downstream components is large. You'll need to determine the critical length beyond which impedance matching is performed by looking at the allowed impedance mismatch for your signalling standard. This effective length can be converted back to a rise time for a digital signal, or to a fraction of the wavelength on the pair for an analog signal.

If the signal rise time is less than double the round-trip transmission delay along the trace, then the trace should be treated as a transmission line.If you want to be conservative, then you should always impedance match in high speed and high-frequency PCBs when bandwidths extend into the GHz range, simply because your signal wavelengths/propagation delay lengths will be on the order of a few cm. 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.

*Differential pair routing and vias on a PCB*

## Calculating Differential vs. Single-Ended Impedance

Trace impedance (single-ended and differential) is normally calculated by ignoring any neighboring traces, regardless of whether they contain a propagating signal. In addition, the single-ended impedance is normally calculated as the characteristic impedance rather than the input impedance; we aren't worried about what type of component (short, open, or load) the trace is connected to. In differential pairs, where we assume that a neighboring trace propagates a return current in the opposite direction as the signal trace, the differential impedance value is determined by capacitive and inductive coupling between each trace in the pair.

Stripline and microstrip differential pairs have different impedance values due to the presence of the substrate, just like in single-ended traces. Symmetric and asymmetric striplines or embedded microstrips also have different impedance values compared to a surface microstrip or single stripline. The substrate dielectric and geometry determine the effective dielectric constant seen by signals on a microstrip trace, which also modifies the critical delay time and determines whether the single-ended trace acts as a transmission line.

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

For differential pair impedance, there are some simple formulas you can use to estimate the impedance of the pair (when it is not connected to any load) using only the characteristic impedance and coupling strength. Take a look at this webinar with Ben Jordan to learn more about this calculation and to see a simple formula for differential microstrips.

For digital signals and wideband analog signals, we 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, and each analog portion of a digital signal will see slightly different dielectric constant due to chromatic dispersion in the dielectric. This means that coupling in a differential pair that carries digital signals varies throughout the frequency spectrum of a digital signal or a wideband analog signal.

These facts make calculation of differential pair impedance and single-ended trace impedance rather difficult unless you have a model defining dispersion in the dielectric. If you're not a fan of solving coupled partial differential equations (see the Telegrapher's equations), the right differential impedance calculator can help you determine the right trace width, separation, and distance from the reference plane for your desired differential impedance value.

## Differential Impedance Calculator

Working with many differential impedance calculators requires that you know the dielectric constant of the trace beforehand. This requires another impedance calculator tailored to your specific geometry, or you'll need to manually work out the dielectric constant at each frequency in your PCB substrate. Once you have the dielectric constant and you’ve chosen your trace arrangement, you are ready to start running calculations to determine the right geometry. 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 (including contributions from coupling). Taking this value and dividing by 2 gives you the odd-mode impedance value of each trace. 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 characteristic impedance of a single-ended trace with the same geometry.

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, or they force you to specify a single frequency of your choice. The differential pair impedance and its S-parameters are frequency-dependent due to dispersion (as mentioned above) and due to the effect of a load component on input impedance in moderately long traces. All the differential pair impedance calculators I've seen online do not take these facts into account; they are simply calculating the impedance of an isolated differential pair.

For complex impedance matching, the input impedance is important as this is the impedance seen by a signal as it enters the differential pair. In the frequency domain, the input 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.

## Control Differential Pair Impedance with an Integrated Field Solver

When your routing tools are built on top of an integrated field solver, you'll be able to define a single-ended or differential impedance profile for your traces. You'll also be able to check your differential pair routing against your complex impedance tolerances as you create your layout. You won't have to manually calculate trace dimensions or spacing; these are determined as a function of frequency as you create your circuit board stackup.

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 integrated field solver can help you easily route differential pairs with controlled impedance. You'll have the tools you need to analyze and prevent signal problems that can arise due to impedance mismatch. Talk to an Altium Designer expert today if you’re interested in learning more about Altium Designer.