Rogowski coil

[nForce]

I was reading about Rogowski coil on wikipedia: https://en.wikipedia.org/wiki/Rogowski_coil

I don't understand under formulae where did this equation came:


Doesn't Rogowski coil work from the principle of Faraday's induction law? U = d(psi)/dt?

[orolo]

Yes, using Faraday + Ampère, and being a bit careful couting the number of turns involved.

\$ \displaystyle \mathcal{E} \ = \ -\frac{\mathrm{d}\Phi}{\mathrm{d}t} \$

The coil has N turns and you can approach the flux by A·B, so:

\$ \displaystyle \mathcal{E} \ = \ -N\cdot A\cdot \frac{\mathrm{d}B}{\mathrm{d}t} \$

Now use Ampère's law for the current of the wire you are measuring, assuming the wire passes along the center
of the ring and generates a perfectly radial magnetic field. Integrating along the center of the toroid:

\$ \oint B \,\mathrm{d}\mathcal{l} \  = \ \mu_0\cdot I\$

\$ \mathcal{l} \cdot B \ = \ \mu_0\cdot I \quad \Rightarrow \quad B \ = \ \frac{\mu_0 I}{\mathcal{l}} \$


Introduce B into Faraday above, and you get the formula:

\$  \displaystyle \mathcal{E} \ = \ -\frac{\mu_0\cdot N\cdot A}{\mathcal{l}} \cdot \frac{\mathrm{d}I}{\mathrm{d}t} \$


Edit: added missing `dl´ in the path integral. Spotted by den. Thanks .

[nForce]

I have one other question regarding Rogowski coil:

How can we reduce the offset voltage at the integrator circuit? So we measure some voltage, and then we have to integrate to get the current. But how do we reduce the offset voltage before integration?

[MrAl]

I have one other question regarding Rogowski coil:

How can we reduce the offset voltage at the integrator circuit? So we measure some voltage, and then we have to integrate to get the current. But how do we reduce the offset voltage before integration?

Hi,

Use a low input offset op amp and employ a feedback resistor to reduce DC gain.