Semiconductor devices and methods of operating the same

A method of operating a semiconductor device, comprising:

• receiving a first signal of a digital-controlled oscillator (DCO), the first signal having a first signal frequency;
• generating a first test signal, a frequency of the first test signal being a first test signal frequency different from the first signal frequency by as much as a first frequency;
• generating a second test signal, a frequency of the second test signal being a second test signal frequency different from the first signal frequency by as much as the first frequency;
• counting rising edges of the first test signal while maintaining the first test signal at the first test frequency using a first parameter during a output duration using a second parameter;
• counting rising edges of the second test signal while maintaining the second test signal at the second test frequency using the first parameter during the output duration using the second parameter;
• and
• identifying a gain of the DCO by a digital value,
• wherein the digital value is generated based on a difference of a first result of the counting rising edges of the first test signal and a second result of the counting rising edges of the second test signal.

A method of operating a semiconductor device, comprising:

• receiving a first signal set to half of an upper limit value of a digital output signal of a digital loop filter by performing a first calibration operation on an oscillation signal of a digital-controlled oscillator (DCO);
• generating a first test signal, a frequency of the first test signal being a first test signal frequency different from a signal frequency of the first signal;
• generating a second test signal, a frequency of the second test signal being a second test signal frequency different from the signal frequency of the first signal and the first test signal frequency;
• identifying a gain of the DCO using the first test signal and the second test signal;
• determining a multiplication coefficient using the gain of the DCO;
• and
• selectively providing one of a multiplied digital signal and a final test signal to the DCO using a multiplexer, the multiplied digital signal being obtained by performing a multiplication operation on a digital signal using the multiplication coefficient, the digital signal being obtained from the digital loop filter.