90 degree bends in microstrip

I was digging through some old reports from 1989 and found this text

Microstrip Discontinuity Capacitances and Inductances

A paper of this title was written by Peter Anders and Fritz Arndt

and published in the IEEE Transactions on Microwave Theory and Techniques

MTT-28 (11) pages 1213-17 (November 1980).

Amongst other things it discusses 45 and 90 degree junctions in microstrips.

My reading of the conclusions is that

  1. The problem is worst for 50R microstrip; the reflection

from a junction will be roughly at factor of three less from the same junction in 75R track and another factor of three

down again for l00R track.

  1. The reflection from a 45 degree junction is about a third of that from

a 90 degree junction, so there is a small advantage in making a

90 degree change in direction as two 45 degree junctions.

  1. The discontinuity can be reduced by about an order of magnitude by bevelling (they use the term mitering) the outside edge of the junction. For 90 degree junctions, the scale of the trim decreases with decreasing impedance, while for 45 degree junctions there in a smooth maximum in the trim around 75R.

Gigabit Logic's Application note 2 at Fig. 5, gives a figure of 1.8 times the track

width as the optimum length for the trimming cut for 90 degree junctions.

Applying the Anders and Arndt results, I get closer to 1.55 for a 50R track on PTFE,

1.77 for a 75R track, and about 2.2 for a l00R track, all for 90 degree junctions.

For 45 degree junctions in 50R track the equivalent figure is 0.91 of the width of the

track. For 75R track this increases to 1.5 of the track width, and for l00R track it goes

down a bit to 1.46 track widths.

Note that while our CAD system puts a radius on the outside corner of all track corners,

the area trimmed off by this feature is at least an order of magnitude less than that

removed by any of the trimming cuts specified above.

It is also worth noting that a via or a test pad inserted into a "constant impedance"

microstrip will introduce much larger reflections than an untrimmed 90 degree junction.

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The "trimming cut" is just ths 45 degree cut off the outside of the cormer - for 90 degree

bends, and 22.5 degrees for 45 degree bends.


Bill Sloman, Nijmegen
Reply to
Bill Sloman
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Below several GHz, risetimes above maybe 100 ps, square corners don't matter.


Reply to
John Larkin



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er -

correct. everything in Bill's post may be true at 10 GHz but irrelevant below a few GHz.


Reply to

But at least he posted something about electronics, for which we can be grateful.


Reply to
John Larkin




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ormer -

And John did express his gratitude with just the sort of graceful courtesy I've come to expect from him -

"Below several GHz, risetimes above maybe 100 ps, square corners don't matter."

In fact the whole point of the post was the reference to published paper on the subject

Microstrip Discontinuity Capacitances and Inductances by Peter Anders and Fritz Arndt IEEE Transactions on Microwave Theory and Techniques MTT-28 (11) pages 1213-17 (November 1980).

and the salvaged text was thrown in to give an indication of the content. But John Larkin doesn't seem to read the electronics literature, and that aspect of the post would not have got his attention.

-- Bill Sloman, Nijmegen

Reply to





cormer -

You expected gratitude? You believe in courtesy? Funny and funnier.

And all I stated in that post were facts. You find facts to be discourteous? Funnier yet.

Your post didn't mention frequency at all. I wouldn't want people going to the trouble of clipping trace corners and worrying about vias when it makes no sense... which it usually doesn't. [1]

Right, I don't read all those 30-year-old old journals, but I do have a few pretty good books about such stuff. More important, I *do* occasionally add to my boards test traces and SMA connectors into power/ground planes, so I can measure capacitances and resistances and TDR things. That's reality.




On the TDR display, the junk at cm 2-3 is the SMA/pcb transition. The two right angles start at cm 4 and the capacitive bump at cm 5 is the via. On regular boards, right angles are down in the noise, buried in trace width variations and fiberglass weave.

This is on a scope with a 30 ps reflected TDR risetime. At 100 ps, things would be a lot flatter.

TDRing power pour/ground plane structures is fascinating. It blows away all sorts of popular dogma about planes and bypassing.


[1] Corner clipping is a legacy of hand-taped layouts anyhow; CAD makes nice smooth curves, which lots of olden-days layout people forbade because it contributed to tape creep.
Reply to
John Larkin

You did claim to be grateful.

All I was saying that your initial reaction doesn't read like a grateful response. I did find the contrast funny.

The reference to Gigabit Logic's application notes would make it clear enough to anybody who could remember Gigabit Logic.

And they aren't going to do it if the application notes for the logic that they are using don't make a fuss about track impedance.

It is, if you've got a time domain reflectometer. Of the places where I've worked, only EMI Central Research and the Nijmegen University electronics workshop had their own, and even there they weren't easy to get at.

Even a smooth curve adds extra capacitance to the track. A 90 degree corner with a right-angle on the inside and a quadrant of a circle on the outside has 0.79 track widths squared in the quadrant. A 1.4142 long mitre has only 0.5 trackwidths squared, and the rule of thumb 1.8 track widths long 45 degree mitre gets rid of half of that.

In an ideal world, you'd want to narrow the track in according to the tightness of the bend.

Bill Sloman, Nijmegen
Reply to
Bill Sloman

I remember GBL. I threw away their databook during an over-enthusiastic cleanup. Pity... it's a collector's item now. I do still have a couple of samples of their wonderful (expensive, power hog) pin driver chip.

But - irony - none of their parts had edges fast enough to bother about trace corners.


Reply to
John Larkin

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