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Parallel Resonance

Parallel Resonance

The parallel RLC circuit is an arrangement where the resistor (R), inductor (L), and capacitor (C) are all connected to the same nodes and, as a result, share the same voltage across them. The parallel RLC circuit is analyzed in terms of admittance (Y), which reflects the ease with which current can flow. The admittance is given by:

Design Example: Underdamped Parallel RLC Circuit

Design Example: Underdamped Parallel RLC Circuit

Consider designing an oscillator circuit, a crucial component in various electronic devices and systems. The objective is to create an oscillator circuit with specific characteristics: a damped natural frequency of 4 kHz and a damping factor of 4 radians per second. To accomplish this, a parallel RLC circuit is employed, known for its ability to sustain oscillations at a resonant frequency. In this case, the damping factor is pivotal in achieving the desired performance.
Starting with a fixed...

Series Resonance

Series Resonance

The RLC circuit impedance is defined as the ratio of the supply voltage to the circuit current. Resonance in such a circuit occurs when the imaginary part of this impedance equals zero. This specific condition means that the inductive reactance is exactly equal to the capacitive reactance. The frequency at which this happens is known as the resonant frequency. Mathematically, the resonant frequency is inversely proportional to the square root of the product of the inductance (L) and capacitance...

Characteristics of Series Resonant Circuit

Characteristics of Series Resonant Circuit

Series resonance occurs in a circuit containing inductive (L), capacitive (C), and resistive (R) elements connected sequentially. At the resonance frequency, the inductive and capacitive reactances are equal in magnitude but opposite in sign, effectively canceling each other. This causes the circuit's impedance is minimal, primarily determined by the resistance R. The resonant frequency of an RLC circuit is defined as:

Series RLC Circuit without Source

Series RLC Circuit without Source

Within the field of electrical circuits, source-free RLC circuits present an intriguing domain. These circuits comprise a series arrangement of a resistor, inductor, and capacitor, operating independently of external energy sources. Their initiation hinges upon utilizing the initial energy stored within the capacitor and inductor to instigate their functionality. Their mathematical equation, a second-order differential equation, sets these circuits apart. This equation captures how the...

Mutual Inductance

Mutual Inductance

Inductance is the property of a device that tells us how effectively it induces an emf in another device. In other words, it is a physical quantity that expresses the effectiveness of a given device.
When two circuits carrying time-varying currents are close to one another, the magnetic flux through each circuit varies because of the changing current in the other circuit. Consequently, an emf is induced in each circuit by the changing current in the other. Therefore, this type of emf is called...

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Balancing of Resonant Differential Coils for Broadband Inductive Sensor Systems.

Liam A Marsh¹, Adam D Fletcher¹, Anthony J Peyton¹

¹Department of Electronic and Electrical Engineering, University of Manchester, Manchester M13 9PL, UK.

Sensors (Basel, Switzerland)

|September 28, 2024

Summary

This study presents a new analytical model for resonant differential coils used in inductive sensing. The model effectively balances coil pairs, significantly enhancing bandwidth for applications like metal detection.

Keywords:

NDT broadband sensor systems differential coil pair gradiometer inductive sensor systems magnetic induction spectroscopy metal detection resonant coils

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Area of Science:

Electrical Engineering
Electromagnetics
Sensor Technology

Background:

Differential coils are crucial in inductive sensing for minimizing background coupling.
Achieving perfect coil balance across wide bandwidths is challenging when subcoils are not electrically identical.
Improved signal-to-noise ratio (SNR) and dynamic range utilization are benefits of balanced differential coils.

Purpose of the Study:

To present an analytical model for balancing arbitrary resonant differential coil pairs.
To apply and validate this model on a planar metal detector for detecting buried objects.
To demonstrate the model's capability in enhancing operational bandwidth.

Main Methods:

Development of an analytical model for resonant differential coil pairs.
Testing and application of the model on a planar metal detector system.
Characterization of coil balance and bandwidth before and after applying the model's correction.

Main Results:

The analytical model successfully balances arbitrary differential coil pairs.
Application to a planar metal detector resulted in a stable balance across an enhanced bandwidth.
The experimental system's bandwidth was increased from 20 kHz to 90 kHz.

Conclusions:

The presented analytical model provides a robust method for balancing differential coils.
This technique broadens the applicability of inductive sensors in metal detection and non-destructive testing.
The model significantly improves the performance of inductive sensing systems by enhancing bandwidth and balance stability.