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We present an innovative implementation of the solid-state-biased coherent detection (SSBCD) technique, which we have recently introduced for the reconstruction of both amplitude and phase of ultra-broadband terahertz pulses. In our previous works, the SSBCD method has been operated via a heterodyne scheme, which involves demanding square-wave voltage amplifiers, phase-locked to the THz pulse train, as well as an electronic circuit for the demodulation of the readout signal. Here, we demonstrate that the SSBCD technique can be operated via a very simple homodyne scheme, exploiting plain static bias voltages. We show that the homodyne SSBCD signal turns into a bipolar transient when the static field overcomes the THz field strength, without the requirement of an additional demodulating circuit. Moreover, we introduce a differential configuration, which extends the applicability of the homodyne scheme to higher THz field strengths, also leading a two-fold improvement of the dynamic range compared to the heterodyne counterpart. Finally, we demonstrate that, by reversing the sign of the static voltage, it is possible to directly retrieve the absolute THz pulse polarity. The homodyne configuration makes the SSBCD technique of much easier access, leading to a vast range of field-resolved applications.