Inductance is a fundamental property of an electrical conductor, representing its ability to oppose any change in the electric current flowing through it. This opposition arises because a changing current generates a changing magnetic field, which, by Faraday’s law of induction, induces a voltage that works against the current change. This characteristic is often described as electrical inertia. While a true, passive component with negative inductance is physically impossible, the effect of negative inductance is achieved in specific, non-passive systems.
Defining Inductance and Its Positive Nature
The definitive answer for a standard, passive electrical component is that self-inductance (\(L\)) must always be a positive value. This constraint is rooted directly in the law of conservation of energy. Inductance quantifies the ability of a coil or conductor to store energy within its generated magnetic field, defined by the relationship \(E = \frac{1}{2} L I^2\).
Since energy must be a non-negative quantity, \(L\) cannot be less than zero. If \(L\) were negative, the component would constantly supply power back into the circuit, violating the passivity principle. The physical construction of an inductor, including its geometry and core material, ensures this positive value.
Inductance is proportional to the magnetic flux linked per unit of current. The magnetic flux is a measurable quantity that cannot be inherently reversed to represent a negative storage capacity. The induced voltage across an inductor is \(V = -L \frac{dI}{dt}\), where the negative sign reflects Lenz’s law, meaning the induced voltage always opposes the change in current.
The inductance value, measured in Henrys (H), is a measure of the component’s physical structure, not the direction of the opposing voltage. Therefore, for any standard, two-terminal coil or wire, the self-inductance \(L\) remains a fixed, positive characteristic.
The Role of Mutual Inductance
While self-inductance is always positive, the sign of mutual inductance (\(M\)) can be defined as positive or negative within circuit analysis. Mutual inductance describes the magnetic coupling that occurs when a changing current in one coil induces a voltage in a separate, nearby coil. It measures how effectively the magnetic flux from one coil links with the windings of the other.
The sign convention is determined by the relative winding directions and current flow, typically visualized using the “dot convention.” If currents in both coils enter or leave the dotted terminals simultaneously, the magnetic fluxes are additive, and \(M\) is positive (additive coupling).
Conversely, if the current enters the dotted terminal of one coil but leaves the dotted terminal of the other, the magnetic fluxes oppose each other. In this subtractive coupling scenario, the mutual term (\(M\)) is treated as negative in the circuit equations. \(M\) itself is a positive magnitude, but the sign indicates whether the induced voltage aids or opposes the self-induced voltage in the other coil.
Simulating Negative Inductance Using Active Circuits
The practical realization of negative inductance occurs through active circuits that employ external power sources, not passive components. These circuits synthesize the behavior of a negative inductor, even though no such physical component exists. This simulated behavior is often referred to as non-Foster impedance, as it violates Foster’s Reactance Theorem, which governs the behavior of all passive components.
Two common circuit topologies used are the Negative Impedance Converter (NIC) and the gyrator. A NIC uses active devices, such as operational amplifiers, to invert the voltage-current relationship of a passive load. If a NIC is terminated with a positive inductor, the input impedance of the overall circuit appears as a negative inductance (\(-L\)).
The gyrator circuit is a device that can transform a capacitive load into a simulated inductive impedance. By strategically configuring the gyrator, it can be made to exhibit a negative inductive reactance. This mimics a circuit node that supplies power as current increases, the opposite of a real inductor that absorbs and stores energy.
These simulated negative inductors are valuable in specialized applications, such as canceling parasitic inductance in high-frequency circuits or increasing the bandwidth of small antennas. However, because they require a power supply to maintain their non-physical behavior, these active implementations are inherently unstable. They are typically only suitable for small-signal or narrow-band applications.