What is the formula for measuring inductance?

Measuring Inductance: A Simple Oscilloscope-Based Approach

Inductance, a fundamental property of electronic circuits, quantifies a component's ability to store energy in a magnetic field. While various methods exist for measuring inductance, utilizing an oscilloscope offers a straightforward and practical approach, especially for in-circuit measurements. This article details a simple technique to determine inductance using readily available oscilloscope data.

The underlying principle leverages the relationship between voltage, current, and inductance in an inductor during the "on-time" of a switching cycle. When a voltage is applied across an inductor, the current through it ramps up linearly. This linear relationship is governed by the following equation:

V = L * (di/dt)

where:

• V is the applied voltage across the inductor
• L is the inductance
• di/dt represents the rate of change of current with respect to time

During the on-time (Ton) of a switching cycle, assuming a constant applied voltage and a starting current of zero, the equation simplifies to:

V = L * (Ipk / Ton)

where:

• Ipk is the peak current reached at the end of the on-time

Rearranging this equation allows us to solve for inductance (L):

L = (V * Ton) / Ipk

This simple formula provides a direct method for calculating inductance using three parameters easily obtainable from an oscilloscope:

1. V (Voltage): Measure the voltage across the inductor during the on-time. Ensure the oscilloscope probe is connected directly across the inductor terminals.
2. Ton (On-Time): Measure the duration of the on-time. This is typically the period during which a switching element is conducting, allowing current to flow through the inductor. Accurate cursor placement on the oscilloscope is crucial for precise Ton measurement.
3. Ipk (Peak Current): Measure the peak current flowing through the inductor at the end of the on-time. This requires a current probe, or a small series resistor of known value, from which the voltage drop can be measured and used to calculate the current (I = V/R).

By plugging these values into the derived formula, L = (V * Ton) / Ipk, one can readily calculate the inductance.

Advantages of this method:

• Simplicity: The formula is straightforward and requires minimal calculations.
• Direct Measurement: The method utilizes in-circuit measurements, eliminating the need for specialized inductance meters or complex bridge circuits.
• Real-world Application: This approach is particularly useful for evaluating inductance in real-world circuit conditions, where parasitics and other factors can influence measurements.

Considerations:

• Waveform Shape: This method assumes a relatively constant voltage applied across the inductor during the on-time. Significant voltage variations during the on-time may introduce inaccuracies. Ideally, a square wave excitation is preferred.
• Current Probe Calibration: If using a current probe, ensure accurate calibration for reliable Ipk measurement.
• Series Resistance: If using a series resistor for current measurement, ensure its value is small enough to minimize its impact on circuit operation.

This oscilloscope-based technique provides a convenient and effective way to measure inductance. By understanding the underlying principles and carefully measuring the required parameters, engineers and hobbyists can accurately determine inductance values for a wide range of applications.