## How does it work?

An alternating or pulsed current in a conductor develops a magnetic field and the interaction of this magnetic field and the Rogowski coil local to the field gives rise to an induced voltage within the coil which is proportional to the rate of change of the current being measured.
Provided the coil constitutes a closed loop with no discontinuities, it may be shown that the voltage **E** induced in the coil is proportional to the rate of change of the encircled current I according to the relationship **E=H.dI/dt**, where **H**, the coil sensitivity in (Vs/A), is proportional to **NA**.

To obtain an output voltage **V**_{OUT} proportional to** I** it is necessary to integrate the coil voltage **E**; hence an electronic integrator is used to provide a bandwidth extending down to below 1Hz.

The op-amp integrator, in its simplest form, with an input resistor **R**_{sh} and feedback capacitor **C** has an output **V**_{out}=(1/CR)∫ Edt. The overall transducer gain is therefore given by, **Vout=R**_{sh}I, where **R**_{sh}= H/CR is the transducer sensitivity (V/A).

The relationship **V**_{out} proportional to **I** is valid throughout the transducer bandwidth. The bandwidth is defined as the range of frequencies from **f**_{L} to **f**_{H} for which sinusoidal currents can be measured to within 3dB of the specified sensitivity **R**_{sh}.

At low frequencies the integrator gain increases and in theory will become infinite as the frequency approaches zero. This would result in unacceptable dc drift and low frequency noise; hence the integrator gain has to be limited at low frequencies. This limitation is achieved by placing a low pass filter in parallel with the integrating capacitor. The low pass filter sets the low frequency bandwidth **f**_{L}, typically this is less than 1Hz.