What Is a Linear Circuit?

A linear circuit is a circuit that consists entirely of linear components, independent sources, or linearly controlled sources. The element characteristics of a circuit element are characterized by two physical quantities. If the algebraic relationship that characterizes the element is a linear relationship, then the element is a linear element, and if the algebraic relationship that characterizes the element is a non-linear relationship, the element is a non-linear element.

A linear circuit is a circuit that consists entirely of linear components, independent sources, or linearly controlled sources. The element characteristics of a circuit element are characterized by two physical quantities. If the algebraic relationship that characterizes the element is a linear relationship, then the element is a linear element, and if the algebraic relationship that characterizes the element is a non-linear relationship, the element is a non-linear element. ^[1]

Judging linearity and non-linearity: Non-linear circuits are circuits that contain non-linear components other than independent power supplies. The non-linearity of certain components is often used in electricians. For example, the non-linear characteristics of a lightning arrester appear as a decrease in resistance value at high voltages, which can be used to protect electrical equipment under lightning.

Non-linear circuits have six characteristics:

Steady state is not unique. When the DC circuit is disconnected with a knife switch, due to the non-linearity of the arc, the circuit at this time has two steady states determined by different starting conditions-one has an arc, so there is current in the circuit; the other arc is extinguished, so the circuit No current.

Self-excited oscillation. In some non-linear circuits, although the independent power supply is a DC power supply, the steady-state voltage (or current) of the circuit can have a periodic variation component, and self-excited oscillations appear in the circuit. The self-excited oscillation circuit of the audio signal generator has a non-linear element such as an amplifier, which can generate periodic oscillation whose waveform is close to a sinusoid.

Harmonics. When a sine excitation is applied to a non-linear circuit and the circuit has a periodic response, the response waveform is generally non-sinusoidal and contains higher harmonic components or subharmonic components. For example, currents in rectifier circuits often have higher harmonic components.

Jump phenomenon. In a non-linear circuit, when the parameters (resistance, inductance, amplitude, frequency, etc.) are changed to the bifurcation value, the response changes abruptly, and a jump phenomenon occurs. Current hopping occurs in ferromagnetic resonance circuits.

Frequency capture. When sinusoidal excitation is applied to the self-excited oscillation circuit, if the difference between the excitation frequency and the self-excited oscillation frequency is small, the response will be synchronized with the excitation.

Chaos. In the 1920s, the Dutchman B. van der Pol described the equation of the tube oscillation circuit, which became the precursor to the study of chaos. ^[2]