Electrical Diagnostics For Pulsed Power

ELECTRICAL DIAGNOSTICS FOR PULSED POWER

R. Verma, R. S. Rawat, P. Lee, S. V. Springham, T. L. Tan NSSE, NIE, Nanyang Technological University 1 Nanyang Walk, 637616, Singapore

M. Krishnan Alameda Applied Sciences Corporation, San Leandro, CA 94577, USA

Abstract

Pulsed power systems are integral part of any pulsed plasma radiation device and hence the associated electrical diagnostics plays vital role in investigating the overall device performance and its characteristics. The typical diagnostic parameters of interest in any pulsed power system are linked with the measurement of high frequency, high voltages and currents. There is wide range of available diagnostics being used by practicing researchers for the measurement of mentioned parameters but even though they operate on simple laws of electromagnetics and the conceptual understanding is clear; the bandwidth response of such diagnostics is often limited by various parasitic effects that impairs the factual measurement of parameters. The scope of the paper is to introduce various invasive and non-invasive electrical diagnostics used in pulsed power systems and highlight the concealed causes that affect their behavioral response.

International Workshop on Plasma Diagnostics and Applications, Singapore

July 2 – 3, 2009

Purpose  This talk is meant to provide an overview of standard electrical diagnostic techniques used in pulsed power systems driving pulsed plasma devices.

 The main focus will be on pulsed electric and magnetic field (Voltage & Current) measurement techniques having bandwidth response in ns to ms regimes.

 Parasitic effects that impairs the factual measurement of parameters will be discussed.

 Overview of design methodology.

 Noise and Shielding. International Workshop on Plasma Diagnostics and Applications, Singapore

July 2 – 3, 2009

Categorization Pulsed Power Electrical Diagnostic Tools

Current measuring devices

Non-intrusive

Voltage measuring devices

Intrusive

Intrusive

Non-intrusive

Rogowski Coils Current Transformers

Current Shunt Simple resistive dividers Compensated dividers Capacitive Voltage dividers International Workshop on Plasma Diagnostics and Applications, Singapore

July 2 – 3, 2009

Rogowski Coils “most effective, economic and extensively used diagnostic”   i   H .dl Amperes Law It is an air-cored toroidal coil that surrounds the conductor carrying the current to be measured.

Faraday’s Law

Vcoil

International Workshop on Plasma Diagnostics and Applications, Singapore

d  n dt

July 2 – 3, 2009

Sensitivity of Rogowski Coil The current to be measured is related to the induced voltage by a proportionality constant i.e. the mutual inductance of the coil.

Vcoil

di   M 21  dt

M  0 nA

M = Coil Sensitivity (Vs/A) (depends on the coil winding design) di/dt = rate of change of current (A/s) n & A = design and geometry parameters International Workshop on Plasma Diagnostics and Applications, Singapore

July 2 – 3, 2009

Sensitivities for different cross-sections

Rectangular Cross-section

Circular Cross-section

Oval Cross-section

International Workshop on Plasma Diagnostics and Applications, Singapore

July 2 – 3, 2009

Time response consideration Differentiating / Integrating ! - depends on circuit parameters dI c I c d L  dt dt R 1 d L dI c   Ic R dt R dt

Self-Integrating

Differentiating L dI c  I c R dt

R  L

d Ic  dt

L dI c  I c R dt

L  R

International Workshop on Plasma Diagnostics and Applications, Singapore

Ic   July 2 – 3, 2009

Realistic lumped circuit model

I(t)

- solution is complex ! High frequency response (bandwidth) is determined by :

 Coil inductance (Lc)  Stray capacitance of winding (Cc)  Coil resistance (Rc)  Termination impedance (Z) International Workshop on Plasma Diagnostics and Applications, Singapore

July 2 – 3, 2009

High bandwidth issues 1. The rise time (tr) of the measuring pulse is limited by the wave transit time (T) in the coil winding. tr >T always

2. Role of termination impedance (Z) is very important. R  L L  R

20 ns/div 5 ns/div

International Workshop on Plasma Diagnostics and Applications, Singapore

July 2 – 3, 2009

High bandwidth issues 3. Highest frequency 4. Non-uniform excitation measurement limited by due to dislocation of resonant frequency (LC) current centroid may lead of the coil. to strong oscillations in “distributed capacitance the sensor signal due large no. of turns”

http://www.pemuk.com International Workshop on Plasma Diagnostics and Applications, Singapore

July 2 – 3, 2009

High bandwidth issues 5. High voltage consideration

6. Shielding - is placing the Rogowski coil inside the slotted metallic housing.

“Some times coupling capacitance b/w the winding and shielding may affect the signal response” International Workshop on Plasma Diagnostics and Applications, Singapore

July 2 – 3, 2009

Design methodology for differentiating Rogowski Step 1: Estimate the di/dt in the circuit. di 2   I pk dt T

Step 2: Fix the max. limit for the induced voltage (Vcoil). Step 3: Use the basic equation: Vcoil

0 di  NA   2R dt

A  ab

Step 4: Choose optimum values for – a,b, R and N.

John Anderson, RSI 42,7,1971

International Workshop on Plasma Diagnostics and Applications, Singapore

July 2 – 3, 2009

Current Monitors

- are similar to self integrating Rogwski Coils in response but utilize high permeability magnetic core for coil winding. - the presence of high permeability core is important for the extension of flat response to low frequency. - Usage: CT’s – Universal / Rogowski Coil - Customized. International Workshop on Plasma Diagnostics and Applications, Singapore

July 2 – 3, 2009

Thank you