I am trying to design a planar circular spiral antenna with a certain (pretty wide) beamwidth.This will mean I have to sacrifice gain –however, I don’t know from what direction the radio waves will come from so I need the wide beamwidth.

The maths for a spiral seems easy. –One would use a polar coordinate system and plot lines with points at a = k(theta) and b=[k(theta) – x]……The spiral “trace” would then simply be the area in between these lines……(the width of the trace being “x”)

My problem is that I do not know of a graphics package which allows me to plot this spiral. –I would be grateful if anybody knew of a package that I could use to plot this mathematical function. –The package would also (hopefully) have the facility to allow me to “shade in” the area between my two lines so as to give me a spiral trace. –I would then proceed to printing this spiral shape on to cooper clad dielectric and eventually etching away the copper that wasn’t needed for the spiral.

My next problem would be to find the relationship between beamwidth and the following spiral parameters:-

Width of spiral trace.

Gap length between adjacent spiral traces.

Number of curls.

Diameter of outer curl.

Thickness (depth) of spiral trace.

There must be some mathematical relationship between my spiral equations given above and the beamwidth….

Alternatively, does anybody know of any spiral antenna software which can allow me to do all this without going through all of the long prototype testing operations which I will inevitably need to go through?