Transformer

A transformer, comprising:

• a first substantially octagonally-shaped planar coil having a plurality of successive vertices defined by respective angled intersections of adjacent segments of the first planar coil, having two input ends disposed, respectively, at two of the successive vertices of the first planar coil, with a distance between the two input ends, wherein each input end is in electrical communication with a series of adjacent segments and successive vertices that complete two full turns;
• and
• a second planar coil, having two output ends disposed at a side substantially opposite the two input ends;
• wherein, the second planar coil has two points relative to the two input ends of the first planar coil, and an exclusively planar coil path length between the two points on the second planar coil is substantially equal to the distance of the two input ends, and
• wherein the two points on the second planar coil relative to the two input ends of the first planar coil have substantially equal impedances, such that two input signals at the two input ends inducts equal energy at the two points on the second planar coil and the two output ends produce two output signals with substantially equal signal strengths.