Polarimetric surveys of the microwave sky at large angular scales are crucial in testing cosmic inflation, as inflation predicts a divergence-free $B$-mode angular power spectrum that extends to the largest scales on the sky. A promising technique for realizing such large surveys is through the use of rapid polarization modulation to mitigate variations in the atmosphere, coupling to the environment, and drifts in instrumental response. VPMs change the state of polarization by introducing a controlled, adjustable delay between orthogonal linear polarizations resulting in transformations between linear and circular polarization states. VPMs are currently being implemented in experiments designed to measure the polarization of the cosmic microwave background on large angular scales because of their capability for providing rapid, front-end polarization modulation and control over systematic errors. Despite the advantages provided by the VPM, it is important to identify and mitigate any time-varying effects that leak into the synchronously modulated component of the signal.In this paper, we consider and address the emission from a 300 K VPM on the system performance. Though instrument alignment can greatly reduce the influence of modulated VPM emission, some residual modulated signal is expected. We consider VPM emission in the presence of system misalignments and temperature variation. We use simulations of TOD to evaluate the effect of these residual errors on the power spectrum. The analysis and modeling in this paper guides experimentalists on the critical aspects of observations using VPMs as front-end modulators. By implementing the characterizations and controls as described front-end VPM modulation can be very powerful. None of the systematic errors studied fundamentally limit the detection and characterization of B-modes on large scales for a tensor-to-scalar ratio of $r=0.01$.
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