Published by Eric Bogatin on 05 Oct 2009 at 09:15 pm
10/6/09 The single-ended impedance of a closely coupled line.
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Our last webinar, “Stack up Design of Differential Pairs”, had over 600 registered viewers. If you missed it, you can still watch the recording for free. The positive response was overwhelming. Surprisingly, most of the emails I got back were about a comment I made in passing.
“The single-ended impedance of one line does not change as an adjacent, grounded line is brought closer.” This is in contrast to the odd mode impedance of one line which will decrease as an adjacent line is brought closer.
Many people said they did not think the single-ended impedance would really be constant- it should decrease. Colin Warwick and Steve Martin, independently, went to the effort of running a simulation to check this out.
Steve did a super analysis and sent me the plot to the left which shows what is going on. In his example of two coupled microstrips, the line widths were 300 microns, which is 12 mils. The dielectric thickness he used was 254 microns, or 10 mils. This comes out as a relatively high impedance line, about 70 Ohms, single-ended.
He calculated the odd mode impedance, the even mode impedance and the single-ended impedance of one line as the other line was brought closer.
The center trace in the plot, the green line, is the single ended impedance. It is absolutely constant until a spacing of about 300 mils, which is the line width. Closer than this tight a coupling, the single-ended impedance begins to drop. But, as long as the spacing is greater than the line width, what we would call tightly coupled, the single-ended impedance is constant.
It is only when the two lines are much closer together than tightly coupled, does the single-ended impedance drop. Up until this extreme tight coupling, the single-ended impedance of a line really is constant.
Hope to see you in cyber space at our next webinar!