EDA (Electronic Design Automation) software, also known as circuit analysis software, lets you solve complex AC circuits problems that would take days to calculate by hand in just a few minutes. Use EDA software to compute AC circuit voltages, currents, impedances, frequency responses and power consumption when the AC circuit contains many components and there are many AC electrical parameters to solve for. Using EDA software, however, requires you to learn how to use it. How long it takes to learn EDA software will depend on the EDA software you choose. Select EDA software designed for AC circuit analysis problems and for the AC components that you are using in your design.
You can use complex numbers, numbers that represent the phase and magnitude of AC voltage, current, power and impedance in terms of rectangular or polar coordinates to solve AC circuits. However, they are generally only practical to use when the circuit contains no more than 10 electronic components and you need to solve for just a few AC electrical parameters. The complex number method of solving AC circuits requires you tp compute the magnitude and phase impedance of each AC component at a specific frequency and then analyize the circuit with Kirchhoff's current and voltage laws. The mathematics of complex numbers is often taught in high school Algebra 2 classes and in technical mathematics courses for electronic technicians.
The Laplace transform is a method used to solve for currents, voltages, impedances and power within an AC circuit at specific points in time. Because of this, the Laplace transform is referred to as AC time domain solution. Once the transfer function (the mathematical equation that describes the ouput response in relation to the input response) of the circuit is derived, the Laplace transform can be used to find any of the AC electrical parameters of the circuit for any type of AC electronic waveform applied. The mathematics of Laplace transform require that you have the ability to simplify complex algebra equations. Laplace transforms mathematics is often taught in advanced engineering mathematics classes after a student has taken two years of college calculus.
The Fourier transform solves AC electrical parameters, such as current, voltage, impedance and power at a specific input frequency. The Fourier transform obtains the frequency response of an AC circuit, such as a filter or an audio amplifier. The mathematics requires that you be able to write a transfer equation of the AC circuit and then convert it to the Fourier transform. Once the transfer function is written, the frequency response of the AC circuit can be solved using different types of periodic waveforms. The mathematics of Fourier transforms is often taught in advanced engineering mathematics classes after a student has had two years of college calculus.
Differential equations are also used to solve AC circuits. Using differential equations to solve for AC circuit parameters such as current, voltage and impedance, however, can be more time-consuming than other AC circuit techniques and requires mathematics training in differential equations. Using differential equations to solve AC circuit problems is often not done in practice because it it is impractical when compared with other methods. However, the use of differential equations to solve AC circuit problems does help reinforce one's understanding of electronic and other physical systems to mathematics.