Specifically for periodic functions, Fourier showed us how to decompose any periodic function into a sum of a possibly infinite set of sine and cosine functions. Any periodic function can be represented as a series of sinusoids He developed the Fourier Transform, which is an operation that decomposes a general function into trigonometric components, and the inverse Fourier Transform that synthesizes the components into a general function. He determined that pretty much any general function can be represented by sums of trigonometric functions, which are simpler and can be processed individually. Joseph Fourier was a French mathematician who lived from 1768 to 1830, and developed some mathematics that are very important for signal analysis and manipulation. All of these component signals can be addressed and minimized in different ways so that the receiver can reliably pick up the digital data signal out of that mess. This carries the digital data signal, but also cross-talk from nearby signals, ground plane and power plane noise from driver and receiver, reflected signals from transmision line effects. It is very helpful to think of any signal as a composite of component signals and that you can manipulate those components individually, at least to some extent. Think of any signal as a compositeĮven when signals are not intentionally mixed, no signal is entirely clean in the practical world, always having some “noise” from a variety of sources. The Superposition Principle is you friend. For example, you can implement a low-pass filter that filters out just the high-frequency components of a signal. Also, you can implement circuits that modify just some of the components of a composite signal. You can use techniques to subtract out signals that you don’t care about, so you can see the signal(s) of interest. For electrical engineers, this means that at a particular location, if there are signals present that are driven by mutliple sources, they add to create the resulting signal.įor exmple, if you drive a voltage sine wave of one amplitude and frequency onto a conductor, and you drive another voltage sine wave of a different amplitude and frequency onto that same conductor, what you would measure would be the sum of the two sine waves.Īnd, the Superposition Principle works in reverse too. The Superposition Principle in general form states that the total response at a particular place and time to two or more stimuli is the sum of the responses from each individual stimulus. The Superposition Principle holds for the most part for electromagnetic signals, and it provides help with understanding and manipulating signals. This is basically what the Superposition Theorem states.Electrical Engineering educational website But V 1/R has a value i 1 and the other term is i 2 this gives equation 3. If some simple algebra is used then equation 2 is reached. In Figure 1 (c) with independent voltage sources, V1 and V2, and resistor, R, a current i flows. Similarly in Figure 1 (b) with independent voltage source, V2, and resistor, R, a current i 2 flows. The current i 1 has a value according to Ohm’s Law. In Figure 1 (a) with independent voltage source, V 1, and resistor, R, a current i 1 flows. Linear elements are circuit elements which follow Ohm’s Law. Most basic electronic circuits are composed of linear elements. Superposition Principle įigure 1: The circuits showing the linearity of resistors.
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