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64 DESIGN007 MAGAZINE I JUNE 2023 top, ground plane on bottom), with a 5-mil thick dielectric material that has a Dk of 3, the length of the wave on that circuit when oper- ating at 2 GHz is approximately 3.9 inches (99.1 mm). If the frequency doubles to 4 GHz, the length of the wave will be twice as small and would be ~ 1.95" (49.5 mm). A higher frequency will give a wave of shorter length. When considering 60 GHz for this example, the wavelength is about 0 . 1 3 " ( 3 . 3 m m ) . Here is another way to think about wave- length: If the circuit has a special conduc- tor feature that is 0.26" (6.6 mm) in length, then at 60 GHz that circuit feature will have two full waves propagat- ing on it and it can be said the circuit length is two wavelengths. If the circuit feature is changed to be much shorter and is 0.065" (1.65 mm) in length, that conductor can be defined in terms of wave- length as a half-wavelength conductor when operating at 60 GHz. As a quick reminder, the waves that propa- gate on the PCB can be thought of as sine waves; a sine wave is made up of 360 degrees. If the propagating wave on a circuit encoun- ters an anomaly, like a circuit etching defect, some portion of the wave will be affected by that anomaly. If the anomaly is small and it only affects 10 degrees of the propagating wave, then the wave will not be distorted much, and the circuit will perform as expected. If the anomaly is much larger and can affect 90 degrees of the propagating wave, the wave will have some distortion and the circuit will prob- ably not perform as expected. e idea of the physical length of the con- ductor, as it relates to the physical length of the wave (wavelength), is critical for understand- ing why mmWave circuits need to be manufac- tured with much more precision than circuits operating at lower frequency. Again, looking at some of the example comparisons, if a cir- cuit is operating at 2 GHz with a wavelength of about 3.9" (99.1 mm) and the circuit has an etched anomaly about 0.033" (0.84 mm) in length, that will equate to about 3 degrees of the wave being affected and that will not cause a difference in the overall wave performance. However, that same anomaly for a circuit operating at 60 GHz will be equivalent to about 90 degrees of the propagating wave, which is a significant portion of the wave. e wave proper- ties will be distorted, and the circuit will not perform as expected. e examples given here are rela- tively simple and meant to help the thought process. However, there are a lot of spe- cial conductor geometries which the RF engineer will purposely design for the cir- cuit performance they want. e propagating wave will be much more sensitive to some of these special conductor geometries and very small differences in the geometry can make big differences in circuit performance. For radar circuits operating at 77 GHz, there have been notable RF performance differences due to certain circuit geometry varying as little as just a few mils. e PCB designer working with applica- tions at different frequencies should be mind- ful of circuit feature sizes as it relates to the wave size (wavelength) and consider the pos- sible variations of circuit geometry due to the PCB fabrication process. DESIGN007 John Coonrod is technical marketing manager at Rogers Corporation. To read past columns, click here. A higher frequency will give a wave of shorter length.