<inline-formula><tex-math notation="LaTeX">AC</tex-math></inline-formula> power filters play an important role in limiting the high-frequency current harmonics injected by grid-tied voltage source converters (VSCs). Amongst the various types of filters, <inline-formula><tex-math notation="LaTeX">LCL</tex-math></inline-formula> filters with integrated <inline-formula><tex-math notation="LaTeX">LC</tex-math></inline-formula> traps have become popular due to their ability to achieve a size reduction of the grid side inductor while demonstrating a similar current harmonic mitigation performance as a traditional <inline-formula><tex-math notation="LaTeX">LCL</tex-math></inline-formula> filter. In this article, a passively damped filter network with a partially rated <inline-formula><tex-math notation="LaTeX">LC</tex-math></inline-formula> trap (also referred to as the <inline-formula><tex-math notation="LaTeX">L\text{-}PT\text{-}L</tex-math></inline-formula> filter) is proposed and delineated. The proposed <inline-formula><tex-math notation="LaTeX">L\text{-}PT\text{-}L</tex-math></inline-formula> filter provides a <inline-formula><tex-math notation="LaTeX">-60\;\text{dB/dec}</tex-math></inline-formula> roll-off characteristics at frequencies greater than switching frequency. Additionally, it is also demonstrated that this proposed <inline-formula><tex-math notation="LaTeX">L\text{-}PT\text{-}L</tex-math></inline-formula> filter has smaller voltage ratings for two of its shunt-connected capacitor components due to the specific placement of the damping resistor. A systematic analysis of the proposed <inline-formula><tex-math notation="LaTeX">L\text{-}PT\text{-}L</tex-math></inline-formula> filter is elucidated to design and select the component parameters. Steady-state and transient experimental results captured from a grid-tied 2-Level, 3<inline-formula><tex-math notation="LaTeX">\phi</tex-math></inline-formula> VSC prototype are provided to validate the grid current harmonic filtering capability, reduced voltage ratings of the two shunt capacitors and passive damping performance of the proposed <inline-formula><tex-math notation="LaTeX">L\text{-}PT\text{-}L</tex-math></inline-formula> filter. The proposed approach can achieve 19% and 36% filter shunt branch volume reduction for low voltage (208 V, 60 Hz) and medium voltage (4.16 kV, 60 Hz) grid-tied inverter systems, respectively, compared to state-of-the-art <inline-formula><tex-math notation="LaTeX">LCL</tex-math></inline-formula> filters with integrated <inline-formula><tex-math notation="LaTeX">LC</tex-math></inline-formula> traps.