By Don Johnson
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Extra info for Fundamentals of Electrical Engineering
7 Circuits with Capacitors and Inductors 41 What we have discovered is that source(s) equaling a complex exponential of the same frequency forces all circuit variables to be complex exponentials of the same frequency. Consequently, the ratio of voltage to current for each element equals the ratio of their complex amplitudes, which depends only on the source’s frequency and element values. This situation occurs because the circuit elements are linear and time-invariant. For example, suppose we had a circuit element where the voltage equaled the square of the current: v (t) = Ki 2(t).
Pass our circuit’s output to a sink. For most applications, we can represent these measurement devices as a resistor, with the current passing through it driving the measurement device through some type of display. In circuits, a sink is called a load; thus, we describe a system-theoretic sink as a load resistance R L . Thus, we have a complete system built from a cascade of three systems: a source, a signal processing system (simple as it is), and a sink. 6 f33g, works. Rather than defining eight variables and solving for the current in the load resistor, let’s take a hint from our previous analysis.
In short, linear circuits are a special case of linear systems, and therefore superposition applies. In particular, suppose these component signals are complex exponentials, each of which has a frequency different from the others. The transfer function portrays how the circuit affects the amplitude and phase of each component, allowing us to understand how the circuit works on a complicated signal. Those components having a frequency less than the cutoff frequency pass through the circuit with little modification while those having higher frequencies are suppressed.