Designing a Rogowski coil with particle swarm optimization

Rogowski coils are inductive sensors based on Faraday’s Law to measure currents through conductors without galvanic contact. The main advantage of Rogowski coils when compared with current transformers is the fact that the core is air so they never saturate and there is no limit in the frequency of the primary current. These characteristics makes Rogowski coils ideal candidates to measure high amplitude pulsed currents. On the contrary, there are two main drawbacks. On the one hand, the output voltage is the derivative of the primary current so it has to be integrated; and, on the other hand, the transfer function is resonant due to the turn-to-turn capacitance and the self-inductance of the coil. The solution is the use of a passive integration with a terminating resistor at the output of the sensor that splits the two complex poles and gives a constant transfer function for a determined bandwidth. The downside is a loss of sensitivity. Since it is possible to calculate the electrical parameters of the coil based on its geometrical dimensions, the geometry can be adapted to design sensors for different applications depending on the time characteristics of the input current. This paper proposes the design of Rogowski coils based on their geometric characteristics maximizing the gain-bandwidth product using particle swarm optimization and adapting the coil to the specific requirements of the application.