time domain analysis of current transducer responses using

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/LEMCPA.2020.3031986, IEEELetters on Electromagnetic Compatibility Practice and Applications

Time Domain Analysis of Current TransducerResponses using Impulsive Signals

Bas ten Have, Student Member, IEEE, Niek Moonen, Member, IEEE, Frank Leferink, Fellow, IEEE

Abstract—For the measurement of impulsive currents, whichmight occur in cases of electromagnetic interference, for examplecurrents generated by the non-linear behavior of electronicappliances, a wide-band large dynamic range current transduceris needed. The electrical response of such a transducer is deter-mined using conventional techniques, that use frequency sweepsof sinusoidal continuous wave signals. For non-linear and/or timeinvariant systems the superposition of continuous wave signals ofmultiple frequencies might not be equal to an impulsive current,which is representative for the actual measured signals, and istherefore of interest. In this paper the electrical response ofcurrent transducers is determined using impulsive signals, andcompared to continuous wave tests. Time domain parameterssuch as rise time and peak amplitude are extracted, and thefrequency response is analyzed using a Fourier transform. Theexperiments show that the impulsive test is in agreement with thecontinuous wave method and provides a good alternative method.A combination of impulses could cover a large bandwidth, andis a fast and cost effective approach.

Index Terms—Current transducer, Impulsive signals, Non-linear behavior, Time domain parameters, Wide-band

I. INTRODUCTION

Electronic appliances that behave non-linear are increas-ingly used in low voltage (LV) distribution networks. This canresult in conducted electromagnetic interference (EMI) issues,of which many problematic cases are described in [1].

As an example, static energy meters used for billingpurposes in residential situations are largely affected bythe non-linearities of such appliances. Problems werereported caused by: photovoltaic (PV) installations andpower drive systems [2], PV installations in Germany [3],[4], and high interference levels generated by active in-feedconverters [5]. These observations, possibly combined witha higher number of complaints and failures, resulted infaster publication of the TR50579 [6] technical reportand IEC 61000-4-19 standard [7]. In more recent studiesmisreadings due to dimmed lighting equipment of lightemitting diode (LED) and compact fluorescent lighting(CFL) technology [8], or a speed controlled water pump[9] have been reported. In [10] an analysis of waveforms

Manuscript received May 28, 2020; revised August 27, 2020; acceptedOctober 11, 2020. Date of publication Month XX, 20XX. ”This project hasreceived funding from the EMPIR programme co-financed by the ParticipatingStates and from the European Union’s Horizon 2020 research and innovationprogramme. The results found reflect the author’s view only. EURAMET isnot responsible for any use that may be made of the information it contains.”

Bas ten Have and Niek Moonen are with the University ofTwente, Enschede, The Netherlands (e-mail: [email protected],[email protected]).

Frank Leferink is with the University of Twente, Enschede, The Nether-lands, and also with THALES Nederland B.V., Hengelo, The Netherlands(e-mail: [email protected]).

Visual Summary:

CTs under test

Time domain response

TD signal parameters

Frequency response

Impulsive currents

0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11

Time (ms)

-2

0

2

4

6

8

10

Cu

rre

nt

(A)

RefCT1CT2CT3

I100

Ipk

trise

tfall

twidth

Q

-20

0

20

40

Err

or

wrt

refe

rence (

%)

CT1

CT2

CT3

7.1 A 7.6 A 1.1 µs 1.5 µs 49 µs 358µ C

101 102 103 104 105 106

Frequency (Hz)

-8

-6

-4

-2

0

2

4

Gain

(dB

)

CW test

fr = 50Hz

fr = 10kHz

known to cause problems showed narrow pulses in the mil-lisecond range. Critical rise times in the range between 2 µsand 150 µs, and current slopes higher than 0.1 A/µs werefound. More comparable electronic appliances and their re-lationship with metering errors were shown to exist [11].

In order to measure such impulsive currents in the timedomain, in laboratory or on-site situations, accurate currenttransducer (CT) elements are needed. Because of the fastrise times, these CTs should have a very wide instantaneousfrequency range without any phase shifts.

Conventional techniques to determine the electrical responseof CTs are performed in the frequency domain, such as theIEEE Std C57.13 [12]. And use sinusoidal continuous wave(CW) currents which are swept in frequency and amplitude.This determines the operating ranges of the CTs, but withoutmeasuring the phase the effect of wide-band signals canbe overlooked. Instead [13] addresses the necessity of timedomain testing, because systems behave non-linear and/ortime invariant. Therefore, the superposition of CW currentsof multiple frequencies is not equal to an impulsive current,and time domain testing is needed.

The use of time domain characterization methods is not anew idea, as [14] already proposed to use wide-band pulsesto characterize responses in linear systems. From this timedomain response also the frequency domain response of the

Take-Home Messages:• Impulsive testing provides a good alternative to

continuous wave testing.• The frequency response is within 1 dB accuracy.• Impulses test multiple frequencies at once, whereas

CW testing requires a combination of signals.• The half bridge is cost effective, as no wide-band

amplifier is required to cover a large bandwidth.



system can be determined using a Fourier transform. Thecharacterization of CTs in the presence of harmonic distortionis discussed in [15], where it is proposed to excite theCTs by a fundamental and harmonic frequency, because thistest is closer to the actual working conditions of the CTs.Experimental results using this method show differences withthe traditional frequency response tests [16], but these occuronly when the air gap of the core is also changed. In [17]research on time domain calibration of CTs is discussed, usinga Rogowski coil intended to be the used with pulsed currents.However, the resulting response is not quantified using timedomain parameters. Other time domain analysis measurementsare shown in [18], in which the time domain response of CTsthat use a current transformer, Rogowski coil, Hall element,and shunt resistor is investigated. Differences in the timedomain response of the tested CTs are observed.

The purpose of this paper is to analyze the electrical re-sponse of CTs using impulsive currents that are representativeto the currents found in household situations, and comparewith CW testing. Time domain parameters are extracted toverify if the low rise times and steep inclining slopes ofpulsed currents can be measured correctly by the CTs in time-domain. Furthermore, the frequency domain response of theseimpulsive signals is determined using fast Fourier transform(FFT), and is compared to conventional methods that use CWsignals.

II. TIME DOMAIN ANALYSIS OF SIGNALS

A set of time domain parameters is presented for theanalysis of impulsive signals. This time domain analysis isan extension of the parameters that were already introducedin [10].

A visualization of the time domain parameters is shown inFig. 1, these parameters are explained one-by-one hereafter:

• 100% value (I100): the steady state value of the signal.• Peak (Ipk): the peak value of the signal, which could be

higher than the 100% value of the signal due to overshoot.• Signal edge (dI): the difference between the 10% and

90% value of the signal.• Rise time (dtrise): the time the signal needs to rise from

10% to 90% of the steady state value.• Rising slope (dI/dtrise): the ratio between the signal edge

(dI) and rise time (dtrise).• Fall time (dtfall): the time the signal needs to fall from

90% to 10% of the steady state value.• Falling slope (dI/dtfall): the ratio between the signal edge

(dI) and fall time (dtfall).• Pulse width (twidth): the time the signal needs in-between

its rise to 50% and its fall to 50% of the signal value.• Charge (Q): is determined using (1), where N is the total

number of samples (and should at least cover one cycle),i is the current, and Δt is the time between two samples.When comparing two signals the ratio between N and Δtof both signals should be equal.

Q [C] =N∑

n=1

i(n) · ∆t (1)

dI

Current

dtrise dtfall

100%

90%

10%

Ipk

I100

Peak

50%

twidth

Q

Time

Fig. 1: Visualization of the time domain signal parameters.

III. METHOD

Two methods to test the response of CTs are described.The first method uses impulsive signals, and the second is aconventional test method that uses CW signals.

A. Response using impulsive signals

The impulsive signals are supplied using a gallium-nitride(GaN) half bridge that generates a pulse width modulation(PWM) signal. The half bridge consists of a GS665EVBMBmotherboard and a GS66508/16T daughter board. The halfbridge is operated via a schmitt trigger which is controlledusing a function generator model 3314A from HP. The carrierfrequency and dc-offset of the function generator controls therepetition frequency, f r, and duty-cycle (so the pulse width)of the generated impulse. The motherboard is powered by avoltage of 5 V, supplied by a dc power supply model 72-2720manufactured by TENMA. The half bridge is connected to adc power supply model E36234A manufactured by Keysight,generating Vsupply, on the supply side, and to a 2.4Ω 300 Wpower resistive load on the load side. This value of the resistoris verified from 10 Hz up to 200 kHz using a LCR bridgemodel HM8118 manufactured by Hameg. On the load sideline inductance can be added, using additional cable length,to increase the rise and fall time of the PWM pulse. Dependingon the load a current, Isupply, will flow through the conductorwhich is then measured by the CTs under test. Three differentcommercially available CTs are used: model TA189 from PicoTechnology, model SEN-11005 from SparkFun Electronics,and model AM 503 from Tektronix. These are referred to as:CT1, CT2, and CT3. These transducers measure the currentnon-invasive, using the current transformer method, and havea similar functioning and measurement ranges according tothe manufacturer specifications. The CTs are placed in acalibration fixture, which is shown in Fig. 2. A differentialvoltage probe model TA043 manufactured by Pico Technologymeasures the voltage over the resistor, acting as a shuntresistor used as reference. The CTs under test and referenceare connected to a 5444B Picoscope digitizer manufacturedby Pico Technology, this is a pc-based oscilloscope. Thedigitizer captures ten cycles of the response of the CTs andreference at frequency f r using a sampling rate of 40 MHz.



Some setup elements are from the same manufacturer, howeverall are calibrated independently. Table I shows the bandwidthlimitations of the used setup elements. The schematic of thetest setup is shown in Fig. 3.

Fig. 2: Calibration fixture to which the CTs under test aremounted.

V

Half

Bridge

Driver

Voltage supply Half Bridge Load

Line inductance

Reference:

TA043

Differential

Voltage

Probe

1 2 3Transducers

under test

Vsupply

Fig. 3: Schematic of the test setup generating impulsivesignals.

TABLE I: Bandwidth limitations of the setup elements.

Setup element BandwidthHalf bridge 0-10 MHzLoad: 2.4Ω 10-200 kHzDigitizer: 5444B Picoscope 0-200 MHzReference: TA043 0-100 MHzCT1: TA189 0-100 kHzCT2: SEN-11005 0-75 kHzCT3: AM 503 0-200 kHz

The generated PWM signal, Fig. 4, is varied throughoutthe experiments to verify the response of the CTs in dif-ferent realistic scenarios. The tested CTs are intended tomeasure non-linear currents that occur in LV distributionnetworks at mains frequency. The non-linear current wave-forms of interest have critical rise times between 2 µs and150 µs, this corresponds to frequencies between 1 kHz and500 kHz [10]. Therefore, repetition frequencies, f r, of 50 Hz,mains frequency, and 10 kHz, with lower harmonics aroundthe critical rise times, are used. The current amplitude, Isupply,is varied between 2 A to 10 A, by varying Vsupply between5 V to 20 V. The current slope is varied by inserting smallinductance values by means of additional wire length, whichis referred to as line inductance in Fig. 3. This is done toresemble the waveforms of interest in [10], which shows a

correlation between the inclining slope and EMI issues. Thegenerated impulsive signals corresponds to the range in whichthe majority electronic appliances operate.

Fig. 4: Normalized 10 kHz PWM signal, with duty-cycle of50%.

The results obtained using this method are further processed.The time domain parameters as introduced in Section II aredetermined, and the frequency domain behavior is determinedusing FFT. For the frequency domain, the gain of the CTs isdetermined with respect to the reference. Frequency compo-nents other than the harmonics of the fundamental frequencyare removed. Harmonics with an amplitude lower than the CTsresolution are considered as noise and are filtered out. Bothresponses are then compared with the reference.

B. Response using CW signals

To compare the results to conventional test methods, acharacterization using CW signals is also performed. This isdone by using a CW signal with an amplitude of 1 A, ofwhich the frequency is swept from 10 Hz to 1 MHz, using100 steps per decade. The signal is generated using a 5444BPicoscope digitizer manufactured by Pico Technology. Thisgenerated signal is then amplified by an audio amplifier model6552-1A manufactured by Solar Electronics for frequenciesfrom 10 Hz to 100 kHz, and a wideband RF amplifier model110C manufactured by Kalmus for frequencies from 100 kHzto 1 MHz. The generated CW signal is applied to the 2.4Ωresistor. The CTs, reference, and digitizer are connected inthe same manner as before.

IV. TIME DOMAIN RESULTS

A. Initial setup settings: fr=10 kHz and Isupply=7 A

The time domain responses of the CTs using the impulsivetest are shown in Fig. 5, and in Fig. 6 the time domainparameters of each CT can be seen with the relative errors withrespect to the reference, also the absolute value of the referenceis shown. There is a slight difference in the 100% current forall CTs compared to the reference. The peak current of CT1 ishigher than the reference, resulting from overshoot before thecurrent falls towards zero. Also the other CTs have a differencein peak current. For CT2 a slower rising slope compared tothe reference is observed, i.e. have a smaller frequency bandspan than the reference, which is good. Also the other CTsexperience a difference in the fall time. The width and chargeare nearly identical.



0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11

Time (ms)

-2

0

2

4

6

8

10

Cu

rre

nt

(A)

RefCT1CT2CT3

Fig. 5: Time domain response of CTs and reference (Ref),when using an impulsive signal.

I100

Ipk

trise

tfall

twidth

Q

-20

0

20

40

Err

or

wrt

re

fere

nce

(%

)

CT1

CT2

CT3

7.1 A 7.6 A 1.1 µs 1.5 µs 49 µs 358 µC

Fig. 6: Time domain parameters of the CTs with respect tothe reference, for: f r=10 kHz and Isupply=7 A.

B. Varying setup settings

Changes in the setup settings are made and the effect ofthis on the CTs is tested. Fig. 7a shows the effect of loweringthe current amplitude. In this case the effect is shown on CT1,because it has the largest error in peak current based on theinitial settings. It shows that the deviation of the peak valueincreases when lowering the amplitude, although the absolutedeviation remains nearly identical. This is remarkable as theabsolute overshoot is expected to be lower at lower amplitudes.When increasing the rise time by inserting a small inductance,it is clear from Fig. 7b that a lower rise time will result inhigher deviations for CT2. A similar effect can be seen for thefall time. When decreasing the strength of the signal higherfrequency components are not excited. This results in a higherrise time which corresponds to a smaller frequency bandwidththus the frequency limit of the CT is excited less, and thusthe differences are less. Changing the repetition frequencyfrom 10 kHz to 50 Hz does not have a big influence on thetime domain parameters, as Fig. 7c shows the effect on CT2.The deviation of the rise time is slightly lower, but the totalrise time increased, so this is logical based on the previousvariation.

V. FREQUENCY DOMAIN RESULTS

The frequency domain responses of the CTs with respect tothe reference can be seen in Fig. 8, it shows the results of theCW test and the FFT of the impulsive test. The results obtainedusing CW signals show a flat response in the bandwidth ofthe CT and are in accordance with the specifications of themanufacturers. The orange and yellow dots obtained via theFFT of the impulsive test indicate the response with respect

I100

Ipk

trise

tfall

twidth

Q

-20

0

20

40

Err

or

wrt

re

fere

nce

(%

)

CT1 7A

CT1 5.5A

CT1 4A

CT1 2A

1.1 µs1.2 µs1.7 µs1.1 µs

1.5 µs1.5 µs1.5 µs1.3 µs

49 µs49 µs49 µs49 µs

358 µC271 µC182 µC 92 µC

7.6 A5.7 A3.8 A2.1 A

7.1 A5.4 A3.8 A1.9 A

(a) Varying the amplitude; Isupply is 7 A, 5.5 A, 4 A, and 2 A.

I100

Ipk

trise

tfall

twidth

Q

-20

0

20

40

Err

or

wrt

re

fere

nce

(%

)

CT2 1.1us

CT2 1.4us

CT2 1.8us

1.5 µs2.0 µs2.3 µs

49 µs49 µs49 µs

358 µC354 µC351 µC

1.1 µs1.4 µs1.8 µs

7.6 A7.5 A7.4 A

7.1 A7.0 A7.0 A

(b) Varying the rise time; trise is 1.1 µs, 1.4 µs, and 1.8 µs.

I100

Ipk

trise

tfall

twidth

Q

-20

0

20

40

Err

or

wrt

refe

rence (

%)

CT2 fr=10kHz

CT2 fr=50Hz

1.5 µs1.5 µs

49 µs 3 ms

358 µC 22 mC

1.1 µs1.3 µs

7.6 A7.4 A

7.1 A7.3 A

(c) Varying the repetition frequency; f r is 10 kHz, and 50 Hz.

Fig. 7: Time domain parameters of the CTs with respect tothe reference, when varying different setup settings.

to the reference at the fundamental and harmonic frequenciesof the impulse. The responses from both tests are comparable,and the points obtained using impulsive test are within therated 1 dB accuracy in the manufacturers specifications.

VI. DISCUSSION

The time domain response of the impulsive tests suggestedinitially errors, but from the frequency domain it is clear thatthese errors occur because the corresponding frequencies areoutside the bandwidth of the CTs. These can thus also befiltered out of the time domain response data.

The repetition frequencies used try to resemble currents atmains frequency (50 Hz), and at critical frequencies based onprevious research (10 kHz), however the combination of bothgenerate 35% measurement points less compared to the CWtest in the bandwidth up to 1 MHz. Further, the repetitionfrequency of the impulses should be optimized to avoidoverlap of the harmonics and to create a better spreading of thefrequency points, thus better coverage in this bandwidth. Stillthe impulses allow to test multiple frequency points at oncecompared to CW testing, which would require a combinationof signals that differ in frequency.

According to the manufactures specifications the GaN halfbridge allows to test up to 30 A with a bandwidth of 10 MHz.



101 102 103 104 105 106

Frequency (Hz)

-8

-6

-4

-2

0

2G

ain

(dB

)

CW test

fr = 50Hz

fr = 10kHz

(a) Frequency response of CT1.

101 102 103 104 105 106

Frequency (Hz)

-8

-6

-4

-2

0

2

Gain

(dB

)

CW test

fr = 50Hz

fr = 10kHz

(b) Frequency response of CT2.

101 102 103 104 105 106

Frequency (Hz)

-8

-6

-4

-2

0

2

Gain

(dB

)

CW test

fr = 50Hz

fr = 10kHz

(c) Frequency response of CT3.

Fig. 8: Frequency response of tested CTs, plot contains theCW test, and test using impulsive signal of 50 Hz and 10 kHz.

In comparison the CW test would require the use of a highpower wide-band amplifier to achieve these high currents in awide bandwidth, and is thus a more expensive solution.

VII. CONCLUSION

This paper has shown that the impulsive test method using ahalf bridge to calibrate wide-band current transducers providesa good alternative to conventional CW testing. The impulsivetest results in CT verification which is within the rated1 dB accuracy of the manufactures specification. However,the repetition frequencies of 50 Hz and 10 kHz combined donot provide sufficient measurement points in the frequencydomain in the bandwidth until 1 MHz. The impulses allowto test multiple frequency points at once compared to CWtesting, which would require a combination of signals witha different frequency. Furthermore, the half bridge allows totest up to 30 A with a bandwidth of 10 MHz according to themanufactures specifications without the use of a high powerwide-band amplifier, and is thus a low cost solution.

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time domain analysis of current transducer responses using

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