The implementation of a large number of single-phase phase-locked loops (PLLs) involves creating a fictitious quadrature signal.Apopular approach for this purpose is using a second-order generalized integrator-based quadrature signal generator (SOGIQSG) because it results in an acceptable speed/accuracy tradeoff. The SOGI-QSG-based PLL (or briefly the SOGI-PLL), in its standard form, involves a frequency feedback loop for adjusting the SOGI resonance frequency under frequency drifts. Some recent research works have reported that the speed/accuracy tradeoff of the SOGI-PLL can be considerably enhanced by removing the frequency feedback loop. In these methods, the SOGI resonance frequency is fixed at the nominal frequency, and a compensation strategy for correcting errors caused under off-nominal frequencies is employed. The main aim of this letter is to provide a critical analysis of frequency-fixed SOGI-based PLLs to highlight their real advantages and disadvantages.