Linear circuits are circuits that contain linear components such as resistors, capacitors, inductors, ideal voltage and current sources, transformers, operational amplifiers, etc. Table 1 presents a list of linear components together with their current-voltage characteristics. The current-voltage characteristics completely define the component for an electrical standpoint and, once these characteristics are measured for a particlar device, one can completely predict how that device will behave in a more complex electric circuit. Notice here that, in this course, we are focussing only on ideal components that do not break at higher voltages (in which case they would be considered non-linear).

Linear components of linear devices are those devices that have linear current-voltage characteristics. Intuitively, the current-voltage characteristic of a device is linear if it can be represented graphically by straight line on a current-voltage ($V(I)$) or voltage-current ($I(V)$) plot. Mathematically, a component is linear if $$\begin{equation} V(aI_1+bI_2)=aV(I_1)+bV(I_2) \end{equation}$$ or $$\begin{equation} I(aV_1+bV_2)=aI(V_1)+bI(V_2) \end{equation}$$ where $a$ and $b$ are any real constants. It turns out that the analysis of linear circuits requires solving linear systems of equations, which can be algebraic equations with real or complex coefficients or linear ordinary differential equations. Linear equations are generally much easier to solve than systems of nonlinear equations that appear in the case of nonlinear circuits.

Nonlinear circuits are circuits that contain at least one nonlinear component, which is a component in which the current-voltage characteristic is nonlinear. Examples of nonlinear components are diodes, transistors, and nonlinear sensors or actuators. Most often, real (practical) linear components such as voltage and current sources, resistors, transformers, etc. can be treated as linear on a small range of applied voltages and currents and they can become nonlinear if we increase this range. Nonlinear circuits can also be analyzed unsing Kirchhoff's laws, however, they will lead to systems of nonlinear equations that are usually more difficult to solve than systems of linear equations.

Linear circuits are important because they do not distort the input signal. For this reason they can be used as amplifiers, voltage or current reduction, linear sensors, etc.

Linear circuits are also easier to understand and analyze. Sine they are linear, linear circuits are governed by linear algebraic or differential equations, and can be analyzed using powerful mathematical frequency domain techniques, such as Fourier analysis and Laplace transforms.