Issue link: https://iconnect007.uberflip.com/i/1457913
MARCH 2022 I DESIGN007 MAGAZINE 45 on a PCB that is a quarter or half or multiples of a quarter wavelength, they too can be reso- nant and exhibit very good radiation at specific frequencies, and at every quarter wavelength above that: half, three-quarters, full wave- length, etc. is is what we see in Figures 4, 5, and 6. We may have assumed that the copper pours are ground, and they are at DC and low frequen- cies. However, at a sufficiently high frequency, they will resonate as has been shown in Figures 5 and 6. What we have unwittingly made with the structure of Figure 3 is an edge-coupled bandpass filter 4 , not a trace shield. Rules of Thumb A common rule of thumb is that a signal prop- agates on a typical FR-4 type PCB at about half the speed of free space 5 . Hence a wavelength at a given frequency is given as Equation 1. Equation 1 Where λ is the full wavelength in inches. Rearranging the equation above to give us the critical, quarter wavelength frequency terms of frequency and length results in Equation 2. Equation 2 And re-arranging again, as a function of length, Equation 3 For example, knowing that the copper pours in Figure 4 are 1 inch long, Equation 2 predicts that the quarter wavelength frequency is 1.6/1 = 1.6 GHz and the half wavelength is 3.2 GHz, which is exactly where we see the peak reso- nance of our Sonnet simulation in Figure 5. e upper equation above can predict the critical trace length based on the frequency of operation. For example, if a trace is carrying a Figure 6a: It is interesting to look at the resulting current densities of the model in Figure 4 when excited. In this plot at 100 MHz there are no resonances present. As can be seen, all the high current is in the aggressor trace and along the edges of the copper pour as would be expected. Red is high-current density while blue is the lower-current density. Figure 6b: At a frequency of 3.2 GHz, the resonance can clearly be seen. The victim trace has picked up a lot of current and that copper pour between the traces that we may have assumed was ground is anything but ground now. As can be seen, there is more current flowing in our pour than the signal traces themselves! Red is high-current density while blue is the lower-current density.