This paper examines the effect of coil length on the
turn ratio and coupling coefficient of an on-chip transformer with
multiple metal layers. This paper develops a transformer layout
that utilizes one winding loop in a metal layer with a ladder where
the pieces of metal between two coils crossed. According to the
relevant analytical formula, a transformer is properly arranged
with two coil locations to ensure high performance. To demonstrate
the proposed algorithm, a total of five devices are fabricated
using 0.13-μm CMOS technology. Measurements reveal that the
proposed transformer has a turn ratio of n = 5.59, a coupling coefficient
of k = 0.7, and an inductance density of 1052 nH/mm
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