  We describe the design, fabrication, and testing of a broadband log-periodic
antenna coupled to multiple cryogenic bolometers. This detector architecture,
optimized here for astrophysical observations, simultaneously receives two
linear polarizations with two octaves of bandwidth at millimeter wavelengths.
The broad bandwidth signal received by the antenna is divided into sub-bands
with integrated in-line frequency-selective filters. We demonstrate two such
filter banks: a diplexer with two sub-bands and a log-periodic channelizer with
seven contiguous sub-bands. These detectors have receiver efficiencies of
20-40% and percent level polarization isolation. Superconducting
transition-edge sensor bolometers detect the power in each sub-band and
polarization. We demonstrate circularly symmetric beam patterns, high
polarization isolation, accurately positioned bands, and high optical
efficiency. The pixel design is applicable to astronomical observations of
intensity and polarization at millimeter through sub-millimeter wavelengths. As
compared with an imaging array of pixels measuring only one band, simultaneous
measurements of multiple bands in each pixel has the potential to result in a
higher signal-to-noise measurement while also providing spectral information.
This development facilitates compact systems with high mapping speeds for
observations that require information in multiple frequency bands.
