RTR: A Transformer-Based Lossless Crossover with Perfect Phase Alignment

This paper proposes a transformer-based lossless crossover method, termed Resonant Transformer Router (RTR), which achieves frequency separation while ensuring perfect phase alignment between low-frequency (LF) and high-frequency (HF) channels at the crossover frequency. The core property of RTR is that its frequency responses satisfy a linear complementary relation HLF(f)+HHF(f)=1. so that the original signal can be perfectly reconstructed by linear summation of the two channels. Theoretical derivation and circuit simulations demonstrate that RTR provides superior energy efficiency, phase consistency, and robustness against component tolerances. Compared with conventional LC crossovers and digital FIR/IIR filters, RTR offers a low-loss, low-latency hardware-assisted filtering solution suitable for high-fidelity audio and communication front-ends. The core theory behind this paper's work, lossless crossover, is based on a Chinese patent [CN116318117A] developed from the previous research of one of the authors, Jianluan Li. We provide a comprehensive experimental validation of this theory and propose a new extension.