Back in the 1980’s, design issues like impedance control, termination, control over parasitics, and unique interconnect architectures were something of an afterthought. According to the great Rick Hartley, designers at the time were placing band-aids on their boards; they were doing little to understand the complex signal integrity problems that arise from uninformed routing decisions.

Fast-forward to today’s high speed/high frequency data center environments, upcoming 5G architecture, high performance computing, and other applications at high speeds/high frequencies. If you look at the routing specifications used in these applications and with many high-performance SOCs, you’ll find that these devices make copious use of differential pair routing with impedance control throughout the board. Even single ended signalling, such as MIPI C-PHY signaling with two-wire lanes and three-phase symbol encoding, still requires precise impedance control with length coupling/matching to prevent reflections. This puts impedance control in PCB design at even greater importance and brings it into the mainstream.

Once you consider the need for impedance control in PCB design, you’ll also need to consider the level of noise in your board. With multilevel signalling schemes at low signal levels, ringing, crosstalk, jitter, and other noise sources can cause a signal to blow past the noise margin at the receiver, causing a bit to be misinterpreted. Channel compensation schemes like equalization are useful for estimating and recovering data, but the error rate will still be high if ringing is intense. Similarly, transmission line ringing is a source of conducted and radiated EMI, so it should be reduced to prevent interference in other circuits. This is why you need to consider the need for impedance control when designing high speed digital interconnects in PCB design.

The same idea applies to differential impedance control and crosstalk in PCB design, but you need also need to account for the spacing between traces as this defines the differential impedance. In other words, you need to adjust the characteristic impedance of each line in the pair, as well as the coupling between pairs in order to adjust the ringing/damping and crosstalk susceptibility while maintaining a constant differential impedance. This is because differential signalling standards typically specify a specific differential impedance value rather than a characteristic impedance for routing.

This process can be difficult with differential transmission lines unless you know the coupling coefficient for the two lines in the pair. However, for single-ended microstrip or stripline transmission lines, you can use Wadell’s equations for the characteristic impedance alongside the approximate propagation delay, impedance in terms of parasitics, and propagation constant from the Telegrapher’s equations to size trace dimensions to maintain impedance while minimizing noise sources.

Example with Microstrip Traces

Let’s take a look at an example with single-ended microstrips and striplines. I’ll run through an example with microstrips, but you can take the same approach with single-ended striplines. To start, we need an accurate equation for the impedance of a single-ended microstrip trace. Wadell’s equations are widely regarded as the most accurate equations for describing the impedance of microstrip traces:

 

 

Next, we need the signal velocity, which simply involves a conversion from the speed of light in vacuum to the speed of light in our particular substrate. Note that the dielectric constant seen by the signal is an effective dielectric constant due to the geometry of the microstrip, which is exposed to air at the top side.

 

 

Finally, we need two equations from the standard circuit model for transmission lines. Here, we are using the parasitic capacitance and inductance per unit length to define the trace impedance and signal velocity:

 

 

As the damping in the line (according to RLC circuit theory) is inversely proportional to the parasitic inductance per unit length, your goal in reducing ringing as part of impedance control in PCB design is to maximize damping while minimizing the inductance per unit length in Eq. (3). This is done under the constraint that the characteristic impedance is held constant. Note that there are many other factors determining damping of any transients, as well as susceptibility to crosstalk and coupling strength to other lines.

This is a rather complex nonlinear optimization problem with three variables (the trace dimensions) and two constraints. One of these constraints is that the characteristic impedance be held constant, while the other depends on the ratio of the width of the trace to its height above the substrate (see Eq. (1)). This type of problem may be amenable to gradient descent methods, although my preferred method for this type of problem is to use an evolutionary algorithm. This type of algorithm is slower than gradient descent methods (e.g., generalized reduced gradient), but it is adaptable to strongly nonlinear problems. It can also be customized as a self-adaptive optimization algorithm, where the algorithm chooses among different population generation strategies as the algorithm runs.

• Read more about this transmission line optimization problem in this article.

 

Impedance control in PCB design can be difficult if you do not have the right tools and experience, and the same goes for transmission line ringing reduction. If you’re looking for a knowledgable firm that offers cutting-edge PCB design services and technology research services for innovative electronics companies, contact NWES for a consultation.

 

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