[TowerTalk] Circuit Board Question

[Richard (Rick) Karlquist]

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