Significance
Because they obey the superposition principle, linear circuits can be analyzed with powerful mathematical frequency domain techniques, including Fourier analysis and the Laplace transform. These also give an intuitive understanding of the qualitative behavior of the circuit, characterizing it using terms such as gain, phase shift, resonant frequency, bandwidth, Q factor, poles, and zeros. The analysis of a linear circuit can often be done by hand using a scientific calculator.
In contrast, nonlinear circuits usually don't have exact solutions. They must be analyzed using approximate numerical methods by electronic circuit simulation computer programs such as Spice, if accurate results are desired. These can give solutions for any specific circuit, but not much insight into the operation of the circuit in general with different component values or inputs. The behavior of such linear circuit elements as resistors, capacitors, and inductors can be specified by a single number (resistance, capacitance, inductance, respectively). In contrast, a nonlinear element's behavior is specified by its detailed transfer function, which may be given as a graph. So specifying the characteristics of a nonlinear circuit requires more information than is needed for a linear circuit.
Linear circuits and systems form a separate category within electronic manufacturing. Manufacturers of transistors and integrated circuits divide their product lines into 'linear' and 'digital' lines, for example. In their linear components, manufacturers work to reduce nonlinear behavior to a minimum, to make the real component conform as closely as possible to the 'ideal' model used in circuit theory.
Read more about this topic: Linear Circuit
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—Alasdair Chalmers MacIntyre (b. 1929)