**Objective**

In this section, we will discuss the measurement of inductance, which is a fundamental property of electrical circuits. Inductance is a measure of an object’s ability to store electrical energy in a magnetic field, and it is expressed in henries (H). Inductance measurement is essential in many areas of electrical engineering, including power transmission, signal processing, and electronic circuit design. Inductance measurement can be challenging due to various factors, including stray inductance, parasitic inductance, and measurement instrument limitations.

**Inductors**

Inductors are essential passive electronic components used in a variety of applications, such as power supplies, filters, and oscillators. They store energy in the form of a magnetic field when an electrical current flows through them and release that energy when the current changes. In this introduction to inductors, we will explore the basic principles, types, and applications of inductors in electronic circuits.

**Basic Principles of Inductors**

An inductor consists of a coil of wire, usually wound around a magnetic core. When an electric current flows through the coil, it generates a magnetic field around it. This magnetic field stores energy, and when the current changes, the energy is released back into the circuit. The inductor’s ability to store and release energy is determined by its inductance, which is measured in henrys (H). The inductance value depends on factors such as the number of turns in the coil, the coil’s dimensions, and the core material.

Source:electronics-tutorials.ws

Inductance measurements are made to determine the inductance value of a coil, which directly relates to the coil's ability to store magnetic energy. The inductance of a coil is influenced by factors such as the number of turns in the coil, the cross-sectional area of the coil, the length of the coil, and the type of core material used (if any).

The basic formula to understand inductance 𝐿*L* in a coil is given by:

where:

- 𝜇 is the magnetic permeability of the core material,
- 𝑁 is the number of turns of the coil,
- 𝐴 is the cross-sectional area of the coil,
- 𝑙 is the length of the coil.

### Types of inductors

There are several types of inductors:

**Air-Core Inductors** As the name suggests, air-core inductors do not have a magnetic core. They consist of a coil of wire wound in a helical or spiral shape, often used in high-frequency applications due to their low parasitic capacitance and low loss.

**Iron-Core Inductors** These inductors have a core made of iron or a ferromagnetic material, which increases their inductance and energy storage capacity. Iron-core inductors are commonly used in power supplies and other low-frequency applications.

**Ferrite-Core Inductors** Ferrite-core inductors use a core made of a ferrite material, which has high magnetic permeability and low electrical conductivity. These inductors are suitable for a wide range of applications, including radio frequency (RF) circuits and noise suppression.

**Toroidal Inductors** Toroidal inductors have a doughnut-shaped core, which provides a closed magnetic path, resulting in high inductance and reduced electromagnetic interference (EMI). They are often used in power supply filters and other applications requiring compact, high-performance inductors.

**Applications of Inductors**

Inductors play a crucial role in various electronic circuits and systems:

**Filters** Inductors can be used in combination with capacitors to create low-pass, high-pass, and band-pass filters to control the flow of signals with specific frequencies in a circuit.

**Power Supplies** In power supply applications, inductors help stabilize the output voltage by smoothing out current ripples and transient voltage spikes.

**Oscillators** Inductors, in combination with capacitors and resistors, can create oscillating circuits that generate specific frequencies for applications like signal generation and frequency synthesis.

In summary, inductors are fundamental passive components in electronic circuits, characterized by their ability to store and release energy in the form of a magnetic field. They come in various types and are used in a wide range of applications, from filters and power supplies to oscillators and noise suppression. Understanding the principles, types, and applications of inductors is essential for anyone working with electronic circuits and systems. But there are types of inductances that we don’t want in our circuits.

**Stray and Parasitic Inductance: Common Obstacles in Inductance Measurement**

Parasitic and stray inductances are unintentional and often undesirable inductive effects that occur in electronic circuits. They can lead to performance issues, inaccuracies in measurements, and signal degradation. Both types of inductance arise from the physical layout and design of a circuit, including the arrangement and proximity of conductive traces, components, and wiring. In this brief introduction, we will discuss the origins and potential impacts of parasitic and stray inductances on electronic circuits.

**Stray Inductance and its Impact on Circuit Performance**

Stray inductance is an unintended and often undesirable inductive effect that occurs in electronic circuits, causing potential performance issues and inaccuracies in measurements. This phenomenon is primarily caused by the physical layout of a circuit, including the spacing and arrangement of conductive traces, components, and wiring. In this brief introduction, we will discuss the origins of stray inductance and its potential impact on circuit performance.

**Stray Inductance in High-Frequency Applications**

Stray inductance is particularly troublesome in high-frequency applications, such as radio frequency (RF) circuits, because the rapid changes in current can exacerbate the effects of stray inductance. Signal loss, reflections, and crosstalk can occur, reducing the overall performance of the circuit. Designers can mitigate the impact of stray inductance by using specialized components, such as air-core inductors or ferrite beads, which exhibit low magnetic permeability and eddy current losses. Additionally, arranging components and conductive traces to minimize mutual inductance and coupling can further reduce the impact of stray inductance on high-frequency circuits.

**Minimizing Stray inductance in Measurements**

Calibration is a crucial process that can help minimize the effect of stray inductance on measurement accuracy. By using a known reference object, the inductance meter or network analyzer can account for the presence of stray inductance and correct the measurements accordingly. This process involves comparing the measured value of the reference object to its known value, calculating the difference, and adjusting the measurement system to account for this discrepancy. Calibration should be performed periodically to maintain the highest level of measurement accuracy and account for any drift in the instrument’s performance over time.

**Guard Traces for Isolation from External Influences**

Guard traces are an effective technique for isolating the object being measured from external conductive objects that may introduce stray inductance. By surrounding the measurement area with a conductive shield connected to a low-impedance ground, the guard trace can intercept stray magnetic fields and prevent them from affecting the measurement signal. This technique is especially useful in low-frequency applications, where the shield’s inductance can be made sufficiently large to effectively isolate the measurement area from external influences.

**Parasitic Inductance and Techniques to Minimize its Effects**

Parasitic inductance is an undesired phenomenon in electronic circuits, stemming from unintentional inductance present in conductive traces, components, and other circuit elements. It arises due to the physical layout and design of a circuit and can cause a range of issues that degrade circuit performance, such as signal distortion, reduced bandwidth, and diminished signal-to-noise ratio. In this brief introduction, we will explore the origins of parasitic inductance, its impact on electronic circuits, and methods to minimize its effects.

**Utilizing Low-Inductance Components**

To reduce the impact of parasitic inductance on circuit performance, designers can use components with low inductance values. Surface-mount inductors and multilayer ceramic inductors offer lower parasitic inductance due to their compact size and minimal lead length. By using these components in high-frequency applications, designers can minimize the impact of parasitic inductance and reduce signal distortion, bandwidth limitations, and other performance issues associated with this phenomenon.

**Implementing Ground Planes and Power Planes**

Ground planes and power planes are essential elements of circuit layout design that can help minimize the effect of parasitic inductance. These large conductive planes serve as low-inductance paths for current flow, reducing the inductance of conductive traces and improving signal integrity. Designers should carefully consider the placement and routing of ground and power planes to optimize their performance and ensure that they effectively reduce parasitic inductance.

**Employing Simulation Tools for Circuit Optimization**

Simulation tools like SPICE can be invaluable for predicting the impact of parasitic inductance on a circuit and identifying potential issues before fabrication. By creating a virtual model of the circuit, designers can analyze the performance, identify areas of concern, and optimize the layout and component selection to minimize the effects of parasitic inductance. This proactive approach can save time, resources, and reduce the likelihood of errors in the final design.

**Methods for measuring inductance**

**LC Resonance Method**:- The LC resonance method involves setting up a circuit where the unknown inductance is part of a resonant circuit, typically with a known capacitor. The resonant frequency ($f_0$) of this circuit, where the inductive and capacitive reactance's are equal, is used to calculate the inductance.
- The formula for resonant frequency is: $f_0 = \frac{1}{2\pi\sqrt{LC}}$
- From this, the inductance can be rearranged to: $L = \frac{1}{(2\pi f_0)^2 C}$
**Impedance Method**:- This method involves applying an AC signal to the inductor and measuring the resulting voltage and current to calculate impedance. The inductance is then calculated from the impedance at a known frequency.
- The impedance of an inductor at a specific frequency (
*f*) is: $Z = j\omega L$ - Inductance can be extracted by: $L = \frac{\text{Im}(Z)}{\omega}$
**Bridge Circuits**:- Bridge circuits, such as the Maxwell-Wien bridge, are used for precision measurements of inductance. The unknown inductance is balanced against known values of other inductances, resistances, and capacitors until the bridge reaches a null point.
- At the balance condition, the relationship between the circuit elements is used to calculate the unknown inductance.
**Time Domain Reflectometry (TDR)**:- TDR involves sending a pulse along a transmission line and measuring reflections caused by impedance discontinuities. If the line terminates with an inductor, the reflection can provide information about the inductance.
- The change in impedance Δ
*Z*causes a reflection coefficient Γ, which can be related to inductance: $\Gamma = \frac{Z_L - Z_0}{Z_L + Z_0}$ **Frequency Response Analysis**:- By analyzing how an inductor responds to different frequencies, one can deduce its inductive properties. This method is useful for characterizing inductors in terms of their self-resonant frequency and quality factor.
**Stray and Parasitic Inductances**: These are unwanted inductances that can arise from the circuit layout, including the wiring and connections. They can significantly affect high-frequency measurements.**Core Materials**: The type of core material used in an inductor (air, iron, ferrite) affects its inductance and can introduce nonlinearities and losses, especially at high frequencies.**Temperature and Environmental Effects**: Inductance can vary with temperature, and environmental conditions can affect the magnetic properties of the core materials.

where $\omega=2 \pi f$ and ** j** is the imaginary unit

where 𝑍𝐿 is the load impedance at the end of the line,

$Z_0$ is the characteristic impedance of the line.

**Common Challenges in Inductance Measurement**

Inductance measurement can be influenced by several factors that may introduce errors or difficulties:

Understanding these principles and techniques is essential for effectively measuring inductance and using inductors in electronic designs and applications.

**Advanced Techniques for Measuring Inductance**

Expanding on the basic methods, these advanced techniques can provide more accurate and efficient ways to measure inductance, particularly in challenging environments or specialized applications.

**Automated Test Equipment (ATE) for Inductance Measurement**

Automated Test Equipment setups can rapidly and accurately measure inductance, resistance, and capacitance of inductors in production-line environments. ATE systems often integrate sophisticated measurement techniques and are capable of handling large volumes of components under tightly controlled conditions, providing consistent and reliable data.

**Nonlinear Inductance Measurement**

Some applications require understanding how inductance changes with varying current levels, especially in power electronic devices like inductors in switching regulators. Nonlinear inductance measurements involve applying a range of currents and measuring the corresponding inductance, which can be crucial for applications involving high power or variable load conditions.

**Thermal Effects on Inductance Measurement**

Temperature can significantly impact the magnetic properties of inductors, particularly those with ferromagnetic cores. Discussing how to measure inductance across a range of temperatures can be essential for applications in harsh environments or where temperature fluctuations are common. This may involve using temperature-controlled chambers during measurements.

**Advanced Concepts in Inductance Measurement**

Introduce more complex theoretical concepts that can deepen understanding and improve measurement approaches:

**Skin Effect and Proximity Effect in AC Inductance Measurements**

At high frequencies, the skin effect and proximity effect can significantly impact the effective inductance and resistance of an inductor. Discussing how these effects are accounted for in measurements can be crucial for applications involving AC power or signal processing.

**Magnetic Hysteresis and Its Impact on Inductance Measurements**

Magnetic hysteresis can affect the accuracy of inductance measurements, especially in materials with significant ferromagnetic properties. Understanding how hysteresis influences inductance and how to mitigate its effects during measurements can be an advanced topic for detailed exploration.

**Modeling and Simulation of Inductive Components**

The use of computational modeling and simulation to predict the behavior of inductive components before physical measurement can save time and resources in the design phase. This section can explore the software tools and methodologies used in simulating inductors.

By expanding on these topics, the discussion on inductance measurement can provide a comprehensive view that encompasses the latest techniques, challenges, and applications, making it a valuable resource for students and professionals in the field of electrical engineering.

**Conclusion**

The accurate measurement of inductance is crucial across various domains in electrical engineering, impacting everything from power transmission to RF circuit design. As technology progresses, so too do the methods for measuring inductance, which now incorporate advanced tools like vector network analyzers and automated test equipment. These innovations not only enhance measurement precision but also expand the practical applications for inductors in modern electronics.