Here's a follow-up to last week's posting regarding questions using
microstrip in RF design for high power apps.
1.) Microstip Line impedance calculation tool:
First, a simple impedance calculator can be found at:
http://www.hta-be.bfh.ch/~dellsper/PartInterests.htm
Click the Download button in the "Synthesis and Analysis of Planar Lines"
section. You can either synthesize a line, or calculate impedance based
on material parameters. FR4 and other substrates are available as
default materials.
I ran a few line width calcs and these checked against know quasi-static
approximations. Unu
Impedance Substrate Thickness (in)
.0625 .125
(ohms) (width, in) (width, in)
25 .313 .627
50 .111 .227
70.7 .057 .117
100 .0 23 .049
2.) Voltage breakdown:
PCB voltage breakdown is not a limiting factor in HF design. Most
printed circuit board laminates are rated safely for 1000V/mm thickness,
or 1000V/40 mils. Note that this breakdown is determined at low
frequency or DC where dielectric losses are of no consequence. At
microwave freqs, voltage becomes a more severe problem because dielectric
losses will cause very high heating internally in the PCB. This is a
more difficult problem and can't be handled as a generic rule-of-thumb
issue. Open-ended stubs with high Q can generate high voltages at
microwave frequencies, whereas the dimensions of these features at HF
make them impractical, thus needing it is a non-issue. Again, I'd advise
.125" thick board for high power HF use. Note that PCB processing issues
such as bonding films and chemical contaminants will come into play. I
will say from experience that I had not sustained any ill effect in
microstrip antennas in the 6 GHz range running 100W pulse power. These
were Rogers Duroid (teflon) based designs where the material thickness
was 20 mils. Dielectric heating in FR4 materials should be low at 1KW
levels, but I did not run an analysis. Here is a website with more info:
http://www.empf.org/empfasis/july04/help704.htm
3.) Heating due to line currents:
Heating in conductors is often the limiting factor long before dielectric
heating (except high uwave freq). I'll refer you to a 1987 applications
note from Rogers Corp, RT 3.3.2.
The rise in heating due to current in a microstrip line is approximated
as:
dT = (I/W)^2 G H /(2 A C)
where:
dT= Temp rise in Kelvin
I = RMS current in amps
W=Line width in meters
G=resistivity of the conductive trace ohm*meter
H=dielectric thickness (meters)
A=Thermal conductivity of the dielectric (watt/meter/kelvin)
C=conductor thickness (meters)
Examples in their app note 3.3.1 demonstrate the following 196 mil wide
stripline (buried line, NOT microstrip) cases where 250 watts average at
5.5 GHz was applied continuously for 5 minutes:
.063" Dielectric Thickness .125"
Dielectric Thickness
Ground plane heat rise: 90C 62C
Stripline conductor final temp: 222C 166C
The melting point of the teflon bonding film was 260C, but the high temps
in the .063" case caused solder re-flow. Copper foil thickness was not
given, but it was described as electro-deposited, implying a thickness of
probably 1 mil or less. Note that a stripline heating case is much more
severe than microstrip, since the center line is buried and cannot take
advantage of free air convection.
Note that in considering line thickness, a better approximation is the
skin effect. Beyond that thickness, the current density is very low.
Also note that the current density will be on the line facing the
dielectric - not air - where the E field is concentrated between the line
and the groundplane. The skin effect knee for a 2 mil thick line is 31
MHz; therefore, below this frequency, the current density is fairly
constant, and the current density is constant in the z axis. Note though
that a 4 mil line presents a knee at 8 MHz; the line resistance will
multiply (2)^.5 for every octave increase in frequency. Therefore, the
resistance of a 4 mil line at 32 MHz is twice the value it presents at 8
MHz (the resistance will still be very low).
Anyways, I'll refer you to the PCB material vendors
(http://www.rogerscorporation.com/acm/index.htm) where there is an
abundance of application notes and data for determining PCB config for HF
power. Roughly, if your plating your lines at least 2 mils, and using
the characteristic impedance lines with .125" material, KW power is well
within reach.
73,
Steve Fraasch, K0SF
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