Inductance, symbolized by \(L\), is an intrinsic property of an electrical conductor that describes its opposition to a change in the electric current flowing through it. This opposition arises because a changing current creates a changing magnetic field, which induces a voltage that works against the initial current change. The standard unit of measurement for inductance in the International System of Units (SI) is the Henry (H), named after Joseph Henry. One Henry is defined as the measure of inductance in a closed circuit where an electromotive force of one volt is produced when the electric current is changing at a rate of one ampere per second.
Dedicated Tools for Inductance Measurement
The most common and precise instrument for measuring inductance is the LCR meter, an electronic device designed to analyze Inductance (\(L\)), Capacitance (\(C\)), and Resistance (\(R\)). LCR meters do not directly sense inductance but calculate it based on the component’s complex impedance. They operate by applying a small, known alternating current (AC) signal across the component under test.
The meter precisely measures the resulting voltage, the magnitude of the current, and the phase angle difference between the two signals. By processing these three measured values—voltage, current, and phase—the meter determines the total impedance. Specialized benchtop LCR meters offer high accuracy and a wide range of selectable test frequencies, while portable handheld versions prioritize convenience for basic checks.
The LCR meter separates the reactive component (inductance or capacitance) from the resistive component present in real-world components. This calculation relies on the principles of alternating current circuits. The meter calculates the complex impedance and then uses the known test frequency to mathematically derive the inductance value, often displayed in millihenries (\(\text{mH}\)) or microhenries (\(\mu\text{H}\)).
Measurement Principles Using Alternating Current
The foundation for measuring inductance relies on the behavior of an inductor when subjected to Alternating Current (AC). Unlike direct current (DC), AC continuously changes direction and magnitude, forcing the inductor to oppose the flow. This opposition to AC is quantified as inductive reactance, symbolized as \(X_L\), and is measured in Ohms (\(\Omega\)).
Inductive reactance is mathematically related to the inductance (\(L\)) and the frequency (\(f\)) of the applied AC signal by the formula \(X_L = 2\pi fL\). This relationship shows that the component’s opposition to current flow is directly proportional to both its inductance and the frequency of the test signal.
A measurement device determines the inductance by first calculating \(X_L\) from the measured voltage, current magnitude, and phase shift. In a purely inductive circuit, the voltage across the component leads the current by \(90\) degrees. By measuring this phase difference and the overall impedance, the device isolates \(X_L\). Once \(X_L\) is known, the equation is rearranged to solve for the unknown inductance: \(L = X_L / (2\pi f)\), using the known test frequency \(f\).
Practical Methods and Laboratory Setups
While dedicated LCR meters offer the highest convenience, inductance can also be determined using common laboratory equipment. One common non-dedicated method is the resonance technique, which utilizes a simple inductor-capacitor (\(LC\)) circuit. The unknown inductor is placed in parallel or series with a capacitor of a known value.
The circuit is excited by a variable-frequency signal, and the frequency at which the circuit’s impedance peaks (parallel) or dips (series) is measured as the resonant frequency (\(f_r\)). The inductance \(L\) is calculated by rearranging the formula for resonant frequency: \(L = 1 / (4\pi^2 f_r^2 C)\). This method is effective because the resonant frequency can be measured precisely using an oscilloscope or frequency counter.
Another practical method, the I-V (current-voltage) method, uses a function generator and an oscilloscope to analyze the component’s impedance. The inductor is placed in series with a precision resistor, and a sine wave of a known frequency is applied. The oscilloscope measures the voltage across the entire series combination and the voltage across the known resistor, which is proportional to the current.
By comparing the amplitude and phase of these two voltage waveforms, the total impedance and the inductive reactance (\(X_L\)) can be calculated, allowing for the determination of \(L\). For simple coil geometries, such as an air-core solenoid, inductance can also be estimated via calculation using physical dimensions. This calculation involves factors like the coil’s cross-sectional area, length, number of turns, and the magnetic permeability of the core material. However, this calculated value is often less accurate than a direct measurement.
The Impact of Test Frequency on Measured Inductance
Inductance is not a fixed value; the measured result depends strongly on the frequency of the test signal used. This variation arises because no real-world inductor is purely inductive, and all possess parasitic elements that affect performance as frequency increases. The most significant element is parasitic capacitance, which exists between the individual turns of the wire coil.
This unintended capacitance acts electrically in parallel with the component’s primary inductance. At lower frequencies, the inductive effect dominates the component’s behavior. As the test frequency rises, the impedance of the parasitic capacitance drops, and its influence on the overall circuit behavior grows.
When the applied test frequency reaches a specific point, the inductive reactance and the capacitive reactance cancel each other out, a phenomenon known as self-resonance. At frequencies above this self-resonant point, the component behaves as a capacitor rather than an inductor. Consequently, to obtain an accurate measurement, the test frequency must be specified and ideally match the frequency at which the inductor will operate in its intended circuit application.