Method for calibrating a Rogowski coil of fast time response

Method for calibrating a Rogowski coil of fast time response Rui Liu,Xinxin Wang,Xiaobing Zou,Jianqiang Yuan,Naigong Zou,and Luya He

Department of Electrical Engineering,Tsinghua University,Beijing100084,China

͑Received30May2007;accepted1July2007;published online3August2007͒

A new method was designed for calibrating a Rogowski coil of fast time response.The method is

based on the cable pulser method except that the voltage signal pick-off output was moved to a position with a distance l from the load.If2l/v is longer than the time duration of the forward voltage pulse u f͑t͒,the reflected voltage pulse u r͑t͒could be separated from u f͑t͒and directly ing the formula i͑t͒=͓u f͑t͒−u r͑t͔͒/50to calculate the primary current of the Rogowski

coil,the coil could be more accurately calibrated.©2007American Institute of Physics.

͓DOI:10.1063/1.2764373͔

I.INTRODUCTION

A series of pulsed power generators with their currents having a magnitude exceeding100kA and a rise time of a few tens of nanoseconds were constructed for Z-pinch and X-pinch studies.1,2As the most frequently used sensors for measuring these fast and high current pulses,Rogowski coils should be calibrated before using.The direct method of cali-bration is the cross calibration against a coil of known sen-sitivity and response time.3However,a Rogowski coil for measuring a high current of nanosecond rise time is usually not commercially available and therefore the cross calibra-tion often becomes impossible.In this case,the most conve-nient method of calibration is so called“cable pulser method”which uses a cable pulser that consists of a high voltage charged cable as pulse forming line͑PFL͒coupled to a cable as pulse transmission line͑PTL͒through a pressur-ized spark gap of nanosecond rise time and delivers a rect-angular voltage pulse u͑t͒onto the load.4–6The calibration was made by threading the inner conductor of the coaxial cable of PTL through the loop center of the calibrated coil and then connecting a load,a short,or a resistor of50⍀that is matched to the impedance of PTL.It was assumed that the current into the load of the50⍀resistor is u͑t͒/50,and the current into the load of a short is2u͑t͒/50.However,this assumption is not always correct if the effect of the stray inductance of the load could not be neglected for the fast rising pulses.It was confirmed in the experiment that the load should be equivalent to a short piece of mismatched transmission line,hence,reflections occur.6In this article,we present a method for calibrating Rogowski coils of fast re-sponse time.The method is based on the cable pulser method,and the reflection from the load is also measured to more correctly determine the primary current of the cali-brated coil.

II.DESCRIPTION OF THE METHOD

Figure1shows the schematic diagram for the calibration of a Rogowski coil.The diagram is very similar to those in previous reports4–6except that the voltage signal pick-off output was moved from a position close to the load to a position with a distance l from the load.

As we know,the electromagnetic wave propagates along

the PTL at a velocity that could be calculated by using the formula v=1/ͱ␮␧and is about20cm/ns for the cable using polyethylene as insulation.It takes the forward voltage pulse

u f͑t͒a time of l/v from the position where the resistive di-vider is to the load and takes the reflected voltage pulse u r͑t͒one more time of l/v from the load to the resistive divider.If 2l/v is longer than the time duration of u f͑t͒,u r͑t͒could be separated from u f͑t͒and directly measured with the resistive divider.The primary current of the calibrated coil could be determined by the formula

i͑t͒=i f͑t͒+i r͑t͒=

u f͑t͒

50

−

u r͑t͒

50

.͑1͒If the effect of the stray inductance of the load can be ne-glected,i͑t͒=u f͑t͒/50is derived from formula͑1͒due to no reflection for the load of the50⍀resistor and i͑t͒=2u f͑t͒/50due to negative reflection for the load of a short.

It is easy to understand that the resistive divider needs to have a very fast response time,about1ns,and that the re-sistance of the divider must be much higher than the PTL impedance,otherwise reflections will occur at the position of resistive divider.

It should be indicated that the rise time of u f͑t͒will be slowed down when it goes a long distance of l and then arrives at the load.6In this case,the slow down effect on the rise time by cable length should be taken into account.This effect could be easily checked by the comparison of u f͑t͒and u r͑t͒when the end of PTL is open.

III.CALIBRATION AND DISCUSSION

The Rogowski coil to be calibrated was made with40 turns of0.44mm copper wire that is uniformly wound on a polyethylene ring of86mm in diameter and with a pitch of 6.8mm between turns.The ring,4.8mm diameter in cross section,is made from a polyethylene-insulated cable with its outer conductor being removed.The integration of the coil output was performed on a low inductance0.1⍀resistor fabricated from a foil of stainless steel.The coil together with the integrating resistor was put inside a shielding box made from copper.In this case,the sensitivity of the

REVIEW OF SCIENTIFIC INSTRUMENTS78,084702͑2007͒

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