In this work, we present a modification for the classic and phasor extremum seeking control algorithms in order to improve the accuracy by removing or reducing the convergence error. The modulation signals were replaced by a sum of sinusoids in order to remove the equilibrium shift in the controlled variable of the averaged system. The convergence error is calculated as a function of the number of sinusoids used in the modulation signal. A simulation example is presented to illustrate the improvement.