The time-modulated array (TMA) is a simple array architecture in which each antenna is connected via a multi-throw switch. The switch acts as a modulator switching state faster than the symbol rate. The phase shifting and beamforming is achieved by a cyclic shift of the periodical modulating signal across antennas. In this paper, the TMA mode of operation is proposed to improve the resolution of a conventional phase shifter. The TMAs are analyzed under constrained switching frequency being a small multiple of the symbol rate. The presented generic signal model gives insight into the magnitude, phase and spacing of the harmonic components generated by the quantized modulating sequence. It is shown that the effective phase-shifting resolution can be improved multiplicatively by the oversampling factor ($O$) at the cost of introducing harmonics. Finally, the array tapering with an oversampled modulating signal is proposed. The oversampling provides $O+1$ uniformly distributed tapering amplitudes.