Miller Technology Inc TN063 Microstrip Right Angle Bends
Introduction and Summary:
One of the more persistent
myths about PCB layout is that a right angle bend is to be avoided because a
right angle band is supposed to:
1. Reduce signal integrity.
2. Create radiated emissions.
This technical note discusses
why this myth is generally untrue, and under what conditions a right angle bend
will matter in a PCB layout. In short,
for most modern PCB layout designs where the dielectric thickness is less than
10 mils, the impact of a single right angle bend is negligible. Multiple right angle bends can produce signal
integrity problems, especially when clumped in near proximity on a line. Right angle bends should be avoided for very
high frequency signals (>10GHZ), or achieving the highest possible signal
integrity and minimizing DDJ.
Model of a Right Angle Microstrip
The transmission line
discontinuity due to a right angle bend can be modeled by the TEE equivalent
circuit below (or optionally a PI network
– see Appendix A):
Where the model values are
given by the two equations [1] below:
in picofarads
in nanohenrys
Notes on the above equations:
1. Microstrip width w, and microstrip height
(dielectric thickness) h are in mm.
2. The formula for Cbend applies for relative dielectric
constants of 2 to 13, and for 0.2 < w/h < 6.0.
3. The formula for Lbend is applicable for w/h
< 1, and tends to underestimate the inductance value for w/h > 1. This is not a significant detriment in most
applications, since the inductive part of the discontinuity is small in
comparison to the capacitive discontinuity.
Evaluating the above
expressions for a microstrip width of 8 mils, dielectric thickness of 4 mils,
and relative dielectric constant of 4.353, results in Cbend = 0.024pf, and Lbend
= 3.5ph.
Since the major effect of the
right angle bend discontinuity is capacitive in nature, we will ignore the
inductive part for evaluating the signal integrity impact for the remainder of
this note.
By way of example, let us
assume that we are interested in 50 ohm microstrip on FR4 like material
(relative dielectric constant of 4.35), which results in a w/h ratio of 2.0
. Note that the formula for Cbend can
then be simplified to:
where the dielectric height
hi is in inches, and Cbend is in picofarads, as shown in the graph below:
Note: For most non-trivial multilayer boards, with
dielectric thicknesses of the outer two layers less than 10mils, the
capacitance of a right angle 50 ohm microstrip bend will be less than 0.06pF.
Verification of extracted
lumped right angle bend parameters via field solver simulations
An electromagnetic field
solver simulation as performed on a simple right angle microstrip bend, total
microstrip length of approx 400mils:
(Microstrip width = 8mils, dielectric
thickness = 4mils, relative dielctric constant = 4.353.)
When the microstrip current
is viewed at 1GHz, we can see the skin effect pushing the current to the
outside edges of the microstrip, and the current crowding towards the inside
edge of the bend:
Note that the reflection
(S11) from the single right angle bend is less than 3% up to 15GHz:
When the measurement
reference planes are moved to the area of the discontinuity:
We can use the field solver to
extract the equivalent lumped parameters of the bend:
Note that the capacitance
value agrees very well with the Cbend formula given above. The Lbend formula does tend to underestimate
the inductive parasitics, although this has a negligible impact on the signal
integrity.
Approximate reflection
magnitude vs rise time:
For digital signals, the
impact of the right angle bend capacitive discontinuity will be proportional to
the signal’s edge rates. We can use the
approximate relationship [3] below:
and, if we only care about
the proportional reflection (rho), this becomes:
Thus, in a Zo = 50 ohm
system, we can relate the reflection from a single right angle microstrip bend as
a function of the dielectric thickness and edge risetime:
In summary, the impact of a
single right angle microstrip bend will be negligible (less than 20mrho) for
digital signals with a risetime of >100ps, and a dielectric thickness
<10mils. Measurements on a limited
number of evaluation boards are consistent with the graph above.
The impact of a right
angle microstrip bend on RF emissions:
Montrose [2], compares the
emissions from a number of evaluation PCB cases, and microstrip bends, and concludes
that for dielectric thicknesses of
10mils or less, the added emissions are less than 5dB (within the measurement
uncertainty), and only significant above 750MHz.
Thus, for typical modern
multilayer stackups, moderate usage of right angle bends will not compromise
emissions compliance. This does presume
that the right angle bends are used selectively, and do not occur near the edge
of the board, or edge of the reference ground plane – in which case there could
certainly be substantial increases in the radiated emissions.
Historical note: Since the capacitive discontinuity of a right
angle microstrip bend increases with the dielectric thickness, perhaps the fear
of right angle bends began when thick dielectrics (32 to 62.5 mil) were used,
and thus the effects seen were larger.
References:
1. Kirschning, M., et al, “Measurement and
Computer-Aided Modeling of Microstrip Discontinuities by an Improved Resonator
Method,” IEEE MIcrowave Theory and Techniques Symposium Digest, 1983, pp.
495-497.
2. Montrose, M. I. “Right Angle Corners on Printed Circuit
Board Traces, Time and Frequency Domain Analysis” IEEE
International Symposium on Electromagnetic Compatibility, 1998. pp. 551-556 .
3. Lee, Thomas A., Planar
Microwave Engineering.
Appendix A:
Summary of Tee and Pi Section Key Equations
Given the two simple
equivalent networks below (often used as discrete approximations to a quarter
wave section of transmission line):
Characteristic Impedance
(Zo):
Time Delay thru the
Section (Td):
Cutoff Frequency (-3dB
amplitude Fc):
