Cirrus Logic AN365 - Manual (Page 2)

AN365
2 AN365REV1
The voltage v(t) that is induced in the Rogowski coil is proportional to the rate of the charge of current (di(t)/dt) and
is based on Faraday's law. The voltage v(t) produced by a Rogowski coil is calculated using Equation 1:
where,
A = Area of each small loop
N = Number of turns
l = 2 R and is the length of the winding
µ
0
= Permeability of free space
When the AC line current, I, is a 50Hz or 60Hz sinusoidal, Equation 1 can be simplified to Equation 2.
where
k = Sensitivity constant that represents the output voltage per ampere at 50Hz or 60Hz.
Most Rogowski coil manufacturers provide a sensitivity constant for the coil. See Table 1:
3. Rogowski Coil Support
Since the output of a Rogowski coil is proportional to the derivative of the instantaneous primary current, an
integrator is required to retrieve the original current signal. The CS5480 incorporates selectable digital integrators
for both current channels. The integrators have the frequency responses illustrated in Figure 2 to compensate for
the 90 degree phase shift and 20dB/decade gain generated by the Rogowski coil.
Model Manufacturer Output Voltage/Ampere at 50Hz
PA3201NL Pulse 416µV/A
TR9L Taehwatrans 1.7mV/A
Mobius Sentec 80µV/A
Table 1. Rogowski Coil Parameters
v t  
AN 
0
–
l
------------------
 
  di t  
dt
-----------
 
 
= [Eq. 1]
V kI = [Eq. 2]