Optimal Track Impedance for a Digital Design

Charles Eidsness

Dr. Howard Johnson wrote an interesting article that appeared in the September 2000 edition of EDN; Why 50 Ohms. The first four paragraphs essentially conclude that for a high speed digital PCB the lower the characteristic impedance of the interconnect the better. It will result in signals with less cross-talk, less radiation, and less susceptibility to issues related to capacitive loading. He touches on the reasons why but the conclusions are not entirely intuitive (to me at least). To better understand his conclusions I performed some of my own analysis.

For simplicity (and due to laziness) I'm limiting my analysis to a strip-line transmission line but a micro-strip transmission line will produce similar results. The characteristic impedance of a strip-line is dependent on both the width of the track and the height of the track above and below the two reference planes. The impedance varies in a non-linear fashion with respect to these two variables. It's possible to plot these dependencies on a cool looking (but admitting not very useful) 3D graph:

Track width and height vs. Impedance

In most high-density digital designs (especially designs with devices in BGA packages) very thin tracks are be required. For example, if using a 1mm-pitch BGA package it's generally not possible to use tracks that are much wider than 5mil without either using micro-vias or impacting the PCB's manufacturability. It's also very difficult to manufacture a PCB with a track width less than 4mil and a dielectric width less than 4mil. For the purposes of this analysis I will use a fixed track width of 5mil and assume that the only variable that can be used to adjust a track's impedance is it's height above / below the reference planes.

1. Less Radiation from Loop Antenna Effect

The first benefit from using a lower impedance transmission line is less radiation. The radiation from a current loop is linearly dependent on both the loop's surface area and the current flowing through the loop. The lower the track impedance the higher the current but also the smaller the loop area. With a fixed track length and track width the loop area is completely dependent on the track's height above the reference planes, as is the characteristic impedance of the track. The following figure shows the relative radiation from a current loop created by a strip-line vs. the strip-line's dielectric thickness.

Relative Radiation vs. Impedance

2. Less Cross-Talk

The lower characteristic impedance of a transmission line the less the transmission line is susceptible to cross-talk. Crosstalk is proportional to the distance between the aggressor and victim traces and the height of the traces above the reference plane. The figure below demonstrates the relationship between the amount of cross-talk and the two track's characteristic impedance.

Cross-Talk vs. Track Separation and Impedance

3. Impedance Mismatch at Load Has Less Impact

Parasitic capacitance lowers the impedance of a transmission line at the location of the load, creating an impedance mis-match. This will create a short voltage droop on a signal when the signal arrives at the load. This droop is reflected back down the line. Pure load capacitance has a very small effective impedance. The lower the track impedance the closer it is to the impedance of the load capacitance and the smaller the reflected voltage droop.

If a track with a lower impedance will radiate less and have superior signal integrity when compared with a higher impedance track why wouldn't we use a track impedance of say... 1O Ohms? There are physical limitations of the PCB. As discussed earlier track widths can't be much less than 4mils, and dielectric thicknesses can't be much lower than 4mil. (unless you're willing to pay) It's generally not physically possible to design a strip-line with a characteristic impedance much lower than 45 Ohms. The driver's also have current drive limitations. Though few IC manufacturers specify the lowest track impedance that their driver can drive most modern drivers are designed to drive at least 50 Ohms. If you want to use an impedance lower than 50Ohms it's probably prudent to run some simulations using IBIS models (in fact even if you are using 50Ohm T-Lines it's prudent to run simulations).