A semiconductor device includes a time-to-digital converter (TDC) that receives a reference frequency signal and a feedback frequency signal, and outputs a first digital signal indicating a time difference between the reference frequency signal and the feedback frequency signal; a digital loop filter (DLF) that outputs a second digital signal generated by filtering the first digital signal; a multiplier circuit that outputs one of a third digital signal and a final test signal, the third digital signal generated by performing a multiplication operation on the second digital signal using a multiplication coefficient; a digital-controlled oscillator (DCO) that generates an oscillation signal having a frequency based on the output one of the third digital signal and the final test signal; and a loop gain calibrator (LGC) that receives the oscillation signal, generates a pair of test signals, and determines the multiplication coefficient using the pair of test signals.