The advantages of exploiting the harmonic patterns in a time-modulated linear array (TMLA) is presented in this paper through mathematical validation and also applied for real-world applications like beam scanning. The inherently generated harmonics or sideband radiations (SRs) in TMLAs are normally considered as a loss of power in unwanted direction. The effect of SRs at the multiple harmonic frequencies is mathematically modeled and presented in this paper. Time sequences with symmetrically and asymmetrically oriented pulses are studied (ON-time duration of array element is generally termed as ‘pulse’). The symmetrically oriented non-shifted switching scheme is equivalent to a simple ON–OFF switching, where all the switches connected with array elements are turned ON at the same time. On the other hand, an asymmetrically oriented shifted switching scheme has different switch-ON instants for different elements of an array. Closed-form expressions of radiated power in the main beam and sideband patterns are derived for both cases. The comparison of the shifted and non-shifted pulse is mathematically derived, and the advantages of shifted pulse for exploiting the sidebands are well established. To further discuss the advantages and limitations of these time schemes, phase-centered motion based TMLAs are investigated for electronic beam scanning, and the radiated power by fundamental and sideband patterns are calculated using closed-form equations.