# Differential Pair Signal Analysis: Clarifying Signals and Routing

June 19, 2019

Have you ever tried to convince yourself to go to sleep by thinking about quantum physics? Well, I haven’t either; but, I wish that I could. After all, quantum physics is all about cool stuff like string theory and antimatter. Positrons and antiprotons seem like the long-lost brothers of electrons and protons. Unfortunately, each has opposite electrical charges and magnetic properties and—when they get together for a family picture—find that they’re different and disappear in a science fiction-like-flash of energy.

Maybe, just maybe, that flash of energy leads to an alternate universe where PCB design teams never worry about differential pairs and impedance matching. Here, though, in our reality, we need to cast our differences aside and work with differential signals.

## Differential Pair Signal Analysis: Moving Past Our Differences

Differential signaling transmits information down a pair of coupled traces on a PCB. Routing the traces establishes a balanced transmission system that carries the equal and opposite differential signals across the PCB. One line carries the signal while the other line carries a complementary, equal, and opposite image of the signal. As a result, differential traces always carry complementary voltages and currents while having equal propagation delays. Any receiving circuit responds to the difference between the two signals.

From a design perspective, differential signaling offers several key benefits. With the second trace acting as a reference for the first, the circuit does not require a reference voltage. The use of differential pairs also eliminates the shared-impedance coupling that can occur if your design places the transmitter and receiver in the same package. In addition, differential signaling minimizes electromagnetic interference generated from the signal pair and remains immune to common mode electrical noise.

Signal propagation for a symmetrical, coupled transmission line pair occurs in even and odd modes. While even—or common--mode signals have an equal phase and the same polarity, odd mode signals have the opposite phase and different polarities in both lines. In both instances, the amplitude of the signal remains the same. With the odd mode, a signal couples from one line into the other line of the transmission pair and moves from the source to the matched load. Although some signal flows back to the source, no signal returns from the far end of the matched loads. Even mode signals between the conductor carrying the same polarity and the common ground between the traces.

## Looking Through Impedance

Before going further, let’s take a fresh look at impedance. In terms of any transmission line, impedance looks like a resistor and remains independent of length. We consider impedance from two perspectives. Instantaneous impedance represents the impedance that a signal sees as it propagates along a transmission line. If we drew a transmission line and marked intervals along the line, we could see a different value of instantaneous impedance at each interval. However, a transmission line that has a uniform cross section produces a constant instantaneous impedance at each interval.

Ensuring impedance with differential pairs is an important task in your design

The characteristic impedance represents the single value of instantaneous impedance that characterizes the entire, uniform transmission line. In other words, the signal sees one value of instantaneous impedance as it propagates along the line. The impedance of a transmission line is the characteristic impedance.

We can view the input impedance of a transmission line in two different ways. If we view the input impedance in the time domain, we see an impedance that varies with time and according to the source impedance, rise time of the signal, and with the time delay of the transmission line. In the frequency domain, impedance remains steady at any single frequency at a time.

When we design PCBs that operate with high frequencies and differential signals, we must use a precise approach for trace widths, thickness, and routing to account for single-ended impedance, differential impedance, and common-mode impedance.

Single-ended impedance represents the trace impedance referenced to ground. Differential impedance refers to the inductive and capacitive impedance found between two differential traces and equals the ratio of voltage to current on the differential pair. The impedance of each trace of the differential pair references to ground. Common-mode impedance occurs with the pair driven in parallel from a common-source.

## Matching Differential Impedances

Now, let’s go just a step further as we consider the behavior of odd mode and even mode impedances. Dividing the differential impedance by two yields the odd-mode impedance value for each trace that becomes relevant when we consider how to match impedances. Odd mode mode impedance always has a lower value than the even mode impedance.

The even mode impedance equals the impedance of one line with the pair driven by a common signal. Decreasing the distance between the traces increases the odd mode current but decreases the odd mode impedance. When we work with even mode signals, decreasing the distance between the traces decreases the even mode current and increases the even mode impedance.

Unbalanced impedances allow common-mode current to flow in the reference line. In turn, though, precise balancing counteracts the flow of common-mode current in your PCB design. This balancing act occurs through the use of traces that have the identical widths, lengths, thickness, and heights.

Matching the impedances throughout the circuit yields a desired low voltage standing wave ratio (VSWR). Circuits with a low VSWR transfer the maximum amount of power from the source to the load. If you achieve a characteristic impedance of 50-Ω in your circuit design, RF signal power transfers efficiently from the source to the load. Few signal reflections occur. Any impedance mismatch causes problems such as ringing and reflections in traces and decreases the capability of the circuit to transfer energy.

## Frequencies and Trace Thickness for Differential  Routing

A wide range of factors underlines the impact that high frequencies have on impedance. Let’s consider a quick example. One centimeter of a 0.25-millimeter thick trace in a circuit operating at 10 MHz has an impedance of approximately 0.55 ohms. Although small, the impedance introduces a 1% error into a system that has a characteristic impedance of 50Ω. However, you can control the impact of high frequencies on impedance by working with the thickness and width of trace conductors, the thickness of the dielectric substrate, and the dielectric constant of the substrate impact impedance.

Set up your differential traces for success.

Sudden changes in trace direction can cause changes in impedance or the dielectric constant can change across the length or width of a PCB. Changes in frequency and temperature also cause the dielectric constant to change. Each variance affects the characteristic impedance of an RF circuit.

Rather than require a specific differential impedance, PCB routing for differential signals has the objective of ensuring that the intact signal arrives at the target. The lack of proper termination in circuits that handle data or clock signals allows reflections to occur. Series termination works only with clock signals and places the termination at the near end. Using near-end series termination causes the driver to see the circuit as a voltage divider. The amplitude at the driver decreases to one-half after the termination. When the signal reaches the end of the transmission line, the entire signal reflects and restores the amplitude.

As you work with your PCB design, you can place parallel terminations on both ends of the differential pair. Since the differential pair work as a transmission line, you can also place terminations only at the far end of the transmission line. Regardless of the location, you should place the termination as close as possible to the source or the destination.

Don’t settle for anything less than success when designing and analyzing with differential pairs. Utilize OrCAD PCB Designer in order to get the most accurate layout and analysis results and ensure matched impedance along with any other design needs you need verified.