<![CDATA[This study analyzes the performance of a Butterworth active low-pass filter and a voltage divider circuit using Laplace Transform and Fourier Transform approaches validated through MATLAB/Simulink simulations. An RC-circuit-based Butterworth active low-pass filter with an operational amplifier and a 110 V DC input shows that the dominant capacitor impedance at low frequencies keeps the intermediate voltage close to the input value. The op-amp configuration produces a gain of approximately 2.5 times, while the frequency response displays maximum gain at low frequencies and damping at high frequencies with a cutoff frequency in the kHz range. Fourier Transform is used to emit a sinusoidal signal in a voltage divider circuit with inductive components. The output signal has the same waveform and frequency as the input signal, but its amplitude is reduced to approximately 0.258 times the input amplitude according to the resistance ratio. Frequency domain analysis shows energy concentration at the fundamental frequency, and the inverse Fourier successfully reconstructs the original signal. MATLAB simulations show high agreement with theoretical calculations.]]>
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