  LiteBIRD, a forthcoming JAXA mission, aims to accurately study the microwave
sky within the 40-400 GHz frequency range divided into 15 distinct nominal
bands. The primary objective is to constrain the CMB inflationary signal,
specifically the primordial B-modes. LiteBIRD targets the CMB B-mode signal on
large angular scales, where the primordial inflationary signal is expected to
dominate, with the goal of reaching a tensor-to-scalar ratio sensitivity of
$\sigma_r\sim0.001$. LiteBIRD frequency bands will be split among three
telescopes, with some overlap between telescopes for better control of
systematic effects. Here we report on the development status of the detector
arrays for the Low Frequency Telescope (LFT), which spans the 34-161 GHz range,
with 12 bands subdivided between four types of trichroic pixels consisting of
lenslet-coupled sinuous antennas. The signal from the antenna is bandpass
filtered and sensed by AlMn Transition-Edge Sensors (TES). We provide an update
on the status of the design and development of LiteBIRD's LFT LF1 (40-60-78
GHz), LF2 (50-68-89 GHz) pixels. We discuss design choices motivated by
LiteBIRD scientific goals. In particular we focus on the details of the
optimization of the design parameters of the sinuous antenna, on-chip bandpass
filters, cross-under and impedance transformers and all the RF components that
define the LF1 and LF2 pixel detection chain. We present this work in the
context of the technical challenges and physical constraints imposed by the
finite size of the instrument.
