[TowerTalk] Circuit Board Question

[Jim Lux]

On 8/2/14, 8:26 AM, Richard (Rick) Karlquist wrote:
> 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.

OK..
I can certainly believe that... 0.008 was just the first number I found


>
> 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.

Interesting.. I was thinking more about the "loss" issue than the 
"heating in an area" aspect.  those milliBels add up.


Here's a question.. is the 2:1 really going to double it.  the 
dielectric loss is voltage related and the copper loss is current 
related. With a mismatch, the ratio between current and voltage changes 
from the matched case, so at a place the voltage is high, the current is 
low, etc.

your typical line (or wire in point to point wiring) is << wavelength at 
HF, so maybe it could be worse or better, depending on whether you are 
lucky?



>
> 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
>