On 8/1/2014 8:50 PM, Jim Lux wrote:
On 8/1/14, 9:22 AM, Richard (Rick) Karlquist wrote:
FR-4 dielectric is quite lossy, comparable to the copper
loss.
At HF?
I worry about it "a little" at 3GHz, but not much, but then, I'm doing
fairly casual low performance designs.
I found one reference that gives 0.008 loss tangent at 100-3000 MHz.
I believe a good loss tangent number to use for design with FR-4 is
0.04. (4% dissipation factor). Certainly, it is way more than 0.008.
It is fairly constant from audio to microwave.
Dielectric loss (in dB/meter) is given by:
(27.3)(loss tangent)[sqrt(relative permittivity)]/(wavelength),
where wavelength is the free space wavelength in meters
Reference: Eq 5.03-3, Matthaei, Young, and Jones:
Microwave Filters, Impedance Matching Networks, and Coupling Structures.
For FR-4 with permittivity of 4.5, this works out to 2.3 dB per
wavelength, or 0.0055 dB per inch at 28 MHz, or 0.l3% per
inch, or 1.9 watts per inch at 1500W. Add copper loss to that
and double it for 2:1 SWR and you see the problem. BTW, the
high permittivity of FR-4 roughly doubles the copper loss vs
air. Just say no to FR-4 lines in legal limit designs.
It is interesting to simplify Eg 5.03-3 to:
Dielectric Loss = (loss tangent) X 100% percent/radian,
where electrical length is radians in the FR-4 (as opposed
to free space). IOW, there is a 4% power loss in an FR-4
line of electrical length 1 radian. On the 10 meter band,
a radian is about 30 inches.
Rick N6RK
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