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.



2. 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.



3. 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.





l l

l l

l l

\ --------------

\

\----------------



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


.