Question about loss tangent calculation

if x=0.01, then loss tangent tan(x)=?. when you use the calculator to do the
tan calculateion, you use rad, deg or grad for the 0.01? 0.01 is rad? what is
grad?

The loss tangent is the ratio at any particular frequency between the real and imaginary parts of the impedance of a capacitor.

Short for grade, a unit of angle 100 grad is a right angle. Rad is short for radian - 2(Pi) radian is a full circle. So 360degrees=2(Pi)radian=400grad. The choice of units is imaterial when using a calculator designed to work in any of those units.

In the case you cite in your question, there isn't enough information to decide whether the loss tangent is 0.01, or you are trying to find the loss tangent from an angle that is 0.01 in some undisclosed units.

i am doing homework from the textbook"an introduction to radio frequency engineering" by christopher coleman. Chapter6 Exercises(2).
The problem says"For FR4 PCB material (relative dielectric constant er=4.4 and delta=0.01) with substrate thickness 3mm, find the width of microstrip(assumed to be made of copper) that yields a 50 ohm characteristic impedance. Find the loss per meter at a frequency of 2GHz." according to the book, tan(delta) is the loss tangent of the substrate. So what is the unit of delta=0.01? rad, degree or grade?

BTW, anybody know how to do the homework part two? how to find the loss per meter?

Normally, the angle is in degrees. For your problem, loss tangent = tan(.01deg).

A reasonable approximation of the loss can be found as:

Dielectric loss(dB/in) = 2.3 x freq(Ghz) x tan(delta) x sqrt(Er)

This relationship assumes that the metallic losses are much less than the dielectric losses - a reasonable assumption at 2Ghz on FR4.

I would expect that a relationship similar to this would be found in your text, or they wouldn't be asking the question as a review.

A more complete answer for the loss per unit length would include the skin effect loss in addition to the dielectric loss - but, as I said above, the dielectric loss is likely to be dominant for the material and frequency you are working with.

hi.

tan(delta) is the loss tangent given from the manufacturer?

is it for surface microstrip?
and what is the equation at striplines, and assymmetrical striplines?

do you know loss equations for skin effect and via-loss?

Some manufacturers will give you the loss tangent, and some will give you delta.

Loss tangent or delta is independent of the geometry. It is the ratio of the real part of capacitance to the imaginary part.

Skin effect losses are resistive, caused by the narrowing of the conduction path. There are several references on line that describe skin effect, a couple are:
http://www.sigcon.com/Pubs/news/dielectricloss.pdf

and

http://www.microwaves101.com/encyclopedia/calsdepth.cfm

The effect of vias on a high frequency circuit depend on the geometry of the via, and the frequencies involved. For skin effect resistive loss, you would calculate the width and thickness of an equivalent track. For inductive and capacitive effects, see:
http://www.sigcon.com/Pubs/news/ViaCapacitance.pdf

and

http://www.sigcon.com/Pubs/news/6_08.htm

thanks

so, see the vias as traces, and calculate the same copper-loss and dielectric loss?

ok, what about the stub-caused return loss? S12.

The loss caused by the stub of a via is primarily from the added parasitic capacitance. The capacitance of the stub would have to be calculated, or you would have to use the Teradyne results and interpolate (see the second reference below).

Note that the capacitance of a stub is only significant in the case where the unused stub passes through a plane.

References:
http://www.fairchildsemi.com/ms/MS/MS-569.pdf
and
http://www.sigcon.com/Pubs/news/ViaCapacitance.pdf

The only other effect from a stub could be if the unused stub is long enough to approach resonance at your operating frequency. For most boards, that would mean you are operating in the tens of gigahertz range. The stub would have to work out to be some sub-multiple of the signal wavelength - it seems very unlikely.

i saw a diagram, where stub-loss was 3dB at 9GHz, so at the knee frequency of the PCIe and SATA, its significant for the total loss budget.

in that article, they were talking about via-stubs, and there was this diagram. unfortunatelly i dont remember where did i see that.

i want to make a loss budget calculator in excell, so thats why i am interested.

The diagram you saw must have been for some specific number of vias on a specific signal path. There is no way to make a generalized calculation for via stub loss.

As I said, the loss from a via stub comes from the parasitic capacitance added by the unused portion of the via stub passing through a plane, or near another metallic structure. It is the capacitance resulting from the barrel of the via in proximity to the other metal plate (plane) that contributes to the loss.

If the via stub is simply "hanging", and not passing through a plane or near another structure, there is no measurable loss that you can assign to it. It then becomes a liability only from the standpoint of being an unterminated transmission line. Either the via would have to be exceptionally long, or the frequency would have to be exceptionally high for that to be a problem in most practical circuits.