Sensor Design for a Current Measurement System with High Bandwidth and High Accuracy Based on the

St. Rietmann, J. Biela Power Electronic Systems Laboratory, ETH Zürich Physikstrasse 3, 8092 Zürich, Switzerland

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Sensor Design for a Current Measurement System with High Bandwidth and High RIETMANN Stefan Accuracy Based on the Faraday Effect

Sensor Design for a Current Measurement System with High Bandwidth and High Accuracy Based on the Faraday Effect

Stefan Rietman and Jurgen¨ Biela Laboratory for High Power Electronic Systems, ETH Zurich, Switzerland Keywords Current Sensor, Sensor, Transducer, Frequency-Domain Analysis Abstract This paper presents the design of the optical system of a current sensor with a wide bandwidth and a high accuracy. The principle is based on the Faraday effect, which describes the effect of magnetic fields on linearly polarized light in magneto-optical material. To identify suitable materials for the optical system the main requirements and specification are determined. A theoretical description of the optical system shows a maximal applicable magnetic field frequency due to the finite velocity of light inside the material. Hence, the theoretical characterisation of the system implies practical boundaries on the optical material and its specifications. Finally, two different magneto-optical crystals, Terbium Gallium and Cadmium Manganese Telluride, are investigated, assembled and put into an optical system prototype. 1 Introduction Highly accurate current measurement systems with high bandwidths are for example required for precise operation and control of power switches in injection and extraction kicker magnet systems. These sys- tems, as for example used in CERNs particle accelerators, require the measurement of fast rising currents with more than 150 kA/μs [1] to generate the required pulsed magnetic fields. The actual current rise times in such applications from 0.1 μs up to 1 μs [2, 3] lead to bandwidth requirements between some kHz and several MHz. Furthermore, high measurement accuracy in the range of several ppm is necessary to reliably control and operate these systems. Classical current measurement concepts, such as shunts, current transformers, Rogowski coils and Hall effect based systems are usually capable of measuring bandwidths from DC or a couple of Hz up to se- veral tens of MHz [4, 5, 6, 7, 8, 9]. The uncertainty of these systems is usually in the range of 0.1 % up to 5 % [6]. However, the accuracy of these systems decreases usually significantly at high frequencies. For instance, the uncertainty of a shunt at low frequencies can be in the ppm range but increases for higher frequencies up to several percent [9].

Laser diode system

Pf ,λ,T

Magnetic field Optical system, Optical to electrical Current-voltage Analog to digital Measurement generation faraday rotation conversion conversion (TIA) conversion (ADC) I Digital processing value I → B B → Θ Θ → I pd I pd → Vo Vo → x[n]

Optical system Sensor

Beamsplitter Optical to electrical diode system FOCPolariser PM FOC PM FOC Analyser +45° converter E Single mode Opto-magnetic material e1.1 λ = 660nm Ee0 PM FOC Analyser −45° Pf = 50mW Ee1.2

Fig. 1: The current measurement system is shown as the concatenation of transfer functions of multiple subsystems. The optical system is built using an intensity modulation scheme with two polarising stages and a magneto-optical crystal (sensor) in between. A single mode laser diode (λ = 660nm) is used as light source.

EPE'19 ECCE Europe ISBN: 978-9-0758-1531-3 - IEEE catalog number: CFP19850-ART P.1 Assigned jointly to the European Power Electronics and Drives Association & the Institute of Electrical and Electronics Engineers (IEEE) Sensor Design for a Current Measurement System with High Bandwidth and High RIETMANN Stefan Accuracy Based on the Faraday Effect

Table I: Current sensor requirements

Specification Current range 100A ... 10kA Frequency bandwidth DC... ≥ 10MHz Measurable pulse rise time (5% - 95%) < 30ns...ms Full bandwidth uncertainty (accuracy) < 0.1% Reproducibility error (precision) < 25ppm

A promising approach for measuring a current with high accuracy and high bandwidth is based on the Faraday effect. The Faraday effect describes the rotation of the plane of polarisation (PoP) of linearly polarized light inside a magneto-optical material. The rotation of the PoP is proportional to an externally applied magnetic field in the direction of the optical path. This magnetic field is generated by the current to be measured. Hence, a quasilinear relation can be expected between the rotation of the PoP and the current. In addition, Faraday effect based current measurement systems are insensitive to electromagne- tic interference (EMI) and they provide good isolation from the power rail. Over the years, different current measurement concepts utilising the Faraday effect have been investiga- ted targeting diverse specification and using different material, geometrical shapes and different signal processing schemes [10, 11, 12, 13, 14]. In contrast to the system approach of this paper, most of the investigated systems limit their scope to either high current amplitudes, highly accurate measurements or high bandwidths. Furthermore, the rotation of the PoP has usually been limited to 180◦, such that the initial current and magnetic field strength are explicitly reproducible. To achieve the requirements given in Tab. I, i.e. aiming at high accuracy and wide bandwidth, a concept using rotation angles larger than 180◦, as presented in [15], is investigated in this paper. In [15], the sensor is designed using a bismuth substituted RIG-film (ferrimagnetic) with a saturation rotation of around 150 ◦ mm−1. The authors use a total Faraday rotation of 3300◦ resulting in an comparably high accuracy of 4.9 ppm. The focus in [15] lies on the limitations caused by the analog signal processing. In contrast, this paper focuses on the characterization and modelling of the optical system to derive its transfer function (cf. Fig. 1). Even- tually, a complete analytical model of the current measurement system is pursued. Moreover, different magneto-optical materials are presented in this paper. In section 2 the optical system is explained including the basic concept of the measuring process, the identification of possible error sources and the choice of the magneto-optical material. In section 3 an approach chosen to model the optical system and derive the transfer function is introduced and applied to the actual chosen material. Eventually, the paper concludes in section 4. 2 Optical System The optical system, as schematically depicted in Fig. 1, denotes the physical measuring part of the current measurement system. It contains a laser diode emitting linearly polarised light, two (or more) polarisers for the intensity modulation and the magneto-optical material. The interface between the optical system and the subsequent optical-to-electrical conversion system is a photodiode. The optical system maps the physical measurand (current, magnetic field strength) to its optical and further to its electrical counterpart (intensity modulated polarised light, photodiode current). 2.1 Faraday Effect The effect allowing to map the magnetic field strength to the polarisation state of a light beam is the Faraday effect. The rotation angle of the PoP Θ (1) and the V (λ) (2) are described by this effect with  L e λ dnr Θ = V (λ) · μ0 · μr · H dl (1) V (λ)=− · · (2) 0 me 2c dλ where H is the magnetic field strength parallel to the optical path and L the optical path length exposed to the magnetic field. The Verdet constant characterises the material’s optical activity for an incident wave with wavelength λ. The wavelength dependency of the Verdet constant V (λ) is described in (2) [16], where e is the charge of an electron, me the mass of an electron, c the speed of light in vacuum and nr the materials refractive index.

EPE'19 ECCE Europe ISBN: 978-9-0758-1531-3 - IEEE catalog number: CFP19850-ART P.2 Assigned jointly to the European Power Electronics and Drives Association & the Institute of Electrical and Electronics Engineers (IEEE) Sensor Design for a Current Measurement System with High Bandwidth and High RIETMANN Stefan Accuracy Based on the Faraday Effect

Ee1,norm cos2(Θ) cos2(Θ − π ) 1 4 0.8 0.6 0.4 0.2 Θ 0 0 /2 3 /2 2

Fig. 2: Using a polariser after the magneto-optical material results in a sinusoidal intensity modulation of the signal. Imple- menting two or more analysers can provide more information about the state of the PoP [15].

2.2 Measurement Concept As depicted in Fig. 1, the rotation angle of the PoP is analysed by modulating the intensity of the light beam. After the PoP of a beam of linearly polarized light is rotated inside the magneto-optical material, a polariser (analyser) modulates it to represent the intensity as a sinusoidal signal. Applying Malus’s law, the intensity Ee1 at the output of the analyser is described as 2 Ee1 = α · Ee0 cos (Θi) (3) where Ee0 is the intensity of the beam before the initial polariser, α a factor for the transmission losses and Θi the angle between the analyser’s axis of polarisation and the angular direction of the PoP. Figure 2 represents the output of the optical system after using for example a polarising beamsplitter with two channels with an offset of 45◦. 2.2.1 Multiple Rotation Concept (Θ > 180◦) The measurement resolution can be improved by relatively increasing the rotation angle of the PoP to the current to be measured. From this point of view, it is beneficial if the rotation angle is as large as possible which poses a critical restriction to the chosen magneto-optical material (cf subsection 2.3). This includes specifically that the rotation of the PoP exceeds 180◦. As shown in Fig. 2, after the rotation angle of the PoP exceeds 180◦ the output at the analyser becomes ambiguous even if multiple channels are observed. Hence, a counting mechanism needs to be introduced to distinguish between the different rotation intervals. Considering (1) and (2), the rotation of the PoP can be affected in multiple ways: • Choice of magneto-optical material: The choice of the material determines the Verdet constant and hence the primary influence on the rotation. • Choice of center wavelength: The Verdet constant of a certain material is wavelength dependent. Therefore, decreasing or increasing the wavelength results in more or less rotation per unit mag- netic field strength, respectively. • Length of the optical path: The length of the optical path through the magneto-optical material increases the final rotation due to the relation stated in (1). On the other hand, optical transmission through longer optical pathes damps the intensity due to absorption and scattering. • Magnetic field strength: The maximal magnetic field strength determines the maximum angle of rotation. By improving, for example, the conductor geometry the maximal magnetic field strength could be increased. A further advantage of having a rotation angle larger than 180◦ is the degression of the relative measu- rement error due to imprecision in the determination of the rotation. For simplifying the analysis one needs to consider the measurement of the rotation angle and the mechanism to detect the crossing of 180◦ to be two independent events. Hence, measuring the angle of the part of the rotation which exceeds multiples of 180◦ is a single event bound to a certain accuracy. This event and its accuracy do not differ from the measurement of a PoP which does not exceeded 180◦, meaning that the measurement error only applies to the last interval of 180◦. Therefore, the ratio between the absolute measurement error and the absolute angle of rotation decreases if the total rotation is increased. Assuming a percentaged measurement error em, the ratio between the absolute error er and the total rotation Θi can be expressed as e e · (Θ mod 180◦) r = m i (4) Θi Θi

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Source System Parameters System Performance

Total Optical Setup Transmission Accuracy + + - + Measurement - Bandwidth + + + Light Source Optical Measurement Wavelength Path Length + Accuracy + + Rotation of the + Plane of + + Polarisation Θ

- + Verdet + Value increases Constant - Value decreases

Fig. 3: The evaluation of suitable magneto-optical material entails a set of optimisation parameters. Optimal optical material shows a high Verdet constant to increase the Faraday rotation and allows for high total transmission of the given input light intensity. Changing the wavelength of the light source or the length of the optical path influences those parameters. Eventually the system performance is determined by the trade-off found for the system parameters.

The ration between the absolute error and the total rotation is divided in half for every additional 180◦ of rotation. If the measurement error is static (e.g. polariser misalignment) by representing an offset of ΔΘ, the additional rotation is decreasing this ratio even further resulting in er/Θi = ΔΘ/Θi. Since more rotation leads to a better resolution of the measurement, the error per magnetic field measured decreases and the overall system performance improves. A potential restriction to more optical rotation is the urge for a faster analog-to-digital (ADC), comparator circuit and transimpedance circuitry. Since the current to measure ramps at with the same di/dt but the angular velocity of the optical rotation increases, the time interval in which at least one measurement has to be captured shortens. Hence, designing an accurate and fast signal processing stage is crucial to benefit from the concept of multiple turns. 2.2.2 Optical System Error Sources Deviations from the ideal measurement response can occur due to tolerances and imperfections in the above mentioned system parameters which influence the rotation of the PoP. For the parameter depen- dencies, as shown in Fig. 3, and the optical system setup three error classes have been identified. 1. Polariser misalignment: If the polariser and analyser are misaligned by a static angle β, the reference for the intensity modulation is wrong. Hence, the interpretation of the signal is set of against the expected result. Observing the analysers output with a total rotation Θi, this error adapts (3) to 2 Ee1(t)=α · Ee0 cos (Θi(t)+β) (5) 2. Rotation angle error: Manufacturing tolerances and environmental drifts in the magneto-optical material and in the light pulse characteristics affect the total rotation angle of the PoP. Examples for this effect are tolerances in the length of the crystal, drifts in the light’s wavelength due to temperature changes, and additional rotation in the light guiding material (fibre optical cables). Since the total rotation depends on the Verdet constant, the length of the magneto-optical material and the magnetic field strength, the dependency of the error can be written as

Θ(t)=Θi(t)+ΘΔ(t)=B(t) · eopt · (V + Verr) · (L + Lerr) (6)

ΘΔ(t)=B(t) · eopt · (V Lerr + VerrL + VerrLerr) (7)

where the subscript err denotes the error term of the Verdet constant and the length and eopt is the unit vector in direction of the optical path. Hence, the time-dependent output characteristic at the analyser from (3) changes to  2 Ee1(t)=α · Ee0 cos (Θi + ΘΔ)(t) (8)

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Note, that this error source exhibits the same effect as the polariser misalignment for the DC case with a constant magnetic field. 3. Transmission rate error: Due to tolerances and drifts in the length of the magneto-optical mate- rial and the light’s wavelength, the transmission through the optical crystal is also affected. Those tolerances affect the amplitude of the intensity with a scaling factor α introduced in (3). The trans- mission rate of the crystal is wavelength dependent and longer crystals have higher losses due to scattering and absorption. The wavelength dependent parameter α is described by the Beer- Lambert law according to

α = a(λ) · exp(−b(λ) · dL) (9)

where a and b depend on the material and dL is the length of the material passed by the light. Assu- ming tolerances in the material length and the wavelength the output characteristic at the analyser is   2 Ee1 = a(λ + Δλ) · exp − b(λ + Δλ) · (dL + ΔdL) · Ee0 cos (Θi(t)) (10)

Summarizing the three error sources, the time-dependent output at the analyser can be described as Ee1 = a(λ + Δλ) · exp − b(λ + Δλ) · (dL + ΔdL) · Ee0   (11) 2 · cos Θi(t)+B(t) · eopt · (V Lerr + VerrL + VerrLerr)+β Reducing the impact of these error sources is addressed in different parts of the complete current measu- rement system design. The polariser misalignment error source is a matter of calibration. Hence, when setting up the system, the actual output of the analyser needs to be adjusted to fit with the expected output. Tolerances issuing rotational errors must be avoided by using accurate measures to define the respective materials and a stable light source. Likewise, drifts in runtime parameters (e.g. temperature drifts which lead to wavelength shifts) need to be addressed either by implementing suitable control loops (e.g. TEC drivers, laserdiode power monitoring) or sufficient stabilisation of the parameters (e.g. passive cooling). A concept to make the output independent of the input intensity Ee0 and reduce the impact of potential drifts in the transmission has to be applied. Since the intensity modulation relies entirely on the input intensity getting rid of this dependency has to be pursued in the data processing stage. For this project, the sum over difference principle, as used in [15], is applied. 2.3 Magneto-optical Material 2.3.1 Material Evaluation Process The magneto-optical material is a key component of the optical system. It defines the performance of the measurement system and introduces limitations and requirements to the preceding and subsequent stages. In general, the material used for the sensing element needs to comply with the following list of requirements. 1. Large Verdet constant: A large Verdet constant sets the basis for a large rotation of the PoP. 2. High optical transmission: The longer the optical path, the less transmission can be expected at the output. On the other hand, a long optical path results in a larger rotation of the PoP. A trade-off between optical path length and suitable transmission rate needs to be found. 3. Bandwidth: The complete setup needs to provide a large bandwidth to support low (Hz range) and high (MHz range) magnetic field frequencies. 4. Linearity: For the reproduction of the initial magnetic field, the material needs to behave linearly in the measured range. For the reproducibility of the measurement saturation and hysteresis effects need to be minimised. Those requirements pose optimisation goals for the design of the optical system. The optical rotation, the total transmission and the measurement bandwidth are the design specifications of the optical systems performance. The relation between those specifications is depicted in Fig. 3. In general, a large Verdet constant is the primary requirement since it directly increases the rotation of the PoP. On the other hand, the Verdet constant is a material dependent value and can only be adapted in a very limited range by ad- justing the center wavelength of the light source. Contrariwise, increasing the light sources wavelength

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Sensor housing CAD (polycarbonat) GRIN lense Crystal 2.3mm (CdMnTe, TGG) 2.3mm Prototype PM fibre 71 mm

6.6mm 2.2mm 2.3mm 5.3mm

2.3mm 5.3mm

Sensor housing with glued crystal (a) Cd57Mn43Te crystal (b) Sensor setup assembly (CAD & Photo)

Fig. 4: (a) Crystal (CdMnTe, TGG). (b) Full assembly. The sensing element is attached to two optical fibers with GRIN lenses. The optical fibers are polarisation maintaining to prevent polarisation shifts due to mechanical stress or other environmental influences. The crystal is glued into the housing to prevent the setup from becoming misaligned. will decrease the total transmission. Obviously, a longer optical path decreases the transmission since there is more material in which the beam can be scattered and absorbed. It is worth to note, that coupling losses (Fresnel losses) account for a substantial portion of the complete transmission loss (> 4% per surface) using graded-index (GRIN) lenses. While it is possible to detect very low intensities with pho- todiodes, a subsequent transimpedance amplifier would need to convert a very small current drawn from the photodiode into a voltage. In general, higher photodiode currents lead to higher possible bandwidths of the transimpedance amplifier and noise considerations are simplified. The necessary measurement bandwidth is defined by the angular velocity of the rotation of the PoP and further limited by the optical path length as described in section 3. 2.3.2 Magneto-Optical Material Decision Two paramagnetic crystals, namely (TGG) and cadmium manganese telluride (CdMnTe) are presented in this section. These two magneto-optical materials are characterised along the requirements introduced in the previous section. Both materials are tested in two different lengths in order to prove the presented theory. The relevant specifications are listed in Tab. II. Furthermore, the Verdet constant of examples for ferrimagnetic and diamagnetic materials is given for comparison. Paramagnetic materials do not show saturation effects even if they are exposed to high magnetic field amplitudes. Due to the inherent saturation effects of diamagnetic and ferrimagnetic materials, the optical current measurement sensor needs to be designed such that B < Bsat. The magnetic field strength inside the optical path is subject to the actual location of the magneto- optical sensor with respect to the current carrying conductor, hence it is a design parameter. On the other hand, this means that a ferrimagnetic and diamagnetic material needs to tradeoff the maximal field with a larger Verdet constant and a long optical path. Examples for ferrimagnetic material are (YIG) or gallium yttrium iron garnet (Ga:YIG) which show saturation effects at 0.178 T and 0.04 T [17], respectively. On the other hand, the Verdet constant (VYIG ≈ 126deg/(T · mm) [18], VGa:YIG ≈ 353deg/(T · mm) [17]) of these material is comparable with CdMnTe and the trans- mission for small (< 5mm) sample lengths is reported to be high (> 95%) in the infrared region be- tween 1100 nm and 1400 nm. Taking the saturation into account, the maximal rotation per length is VYIG ≈ 21.4deg/mm and VGa:YIG max ≈ 14.5deg/mm which makes large sensor designs necessary to achieve the same performance as with the paramagnetic materials. Diamagnetic material shows sig- nificantly lower Verdet constants than TGG or CdMnTe. Examples for those materials are yittrium aluminium garnet (YAG) (VYAG = 0.336deg/(T · mm)), BK-7 glass (VBK-7 = 0.246deg/(T · mm)) and Dynasil 1001 (VDynasil1001 = 0.199deg/(T · mm)) [18]. Note, that these values are given for a center wavelength of λ = 632.8nm. Designs with these materials would require very long sensors and conse- quently a high transmission which makes a design, given the requirements from Tab. I, unfeasible. TGG is a widely used material for optical Faraday rotators. Due to its popularity in other designs and, as a consequence, the broad documentation, it also serves as a reference value for the evaluation of the

EPE'19 ECCE Europe ISBN: 978-9-0758-1531-3 - IEEE catalog number: CFP19850-ART P.6 Assigned jointly to the European Power Electronics and Drives Association & the Institute of Electrical and Electronics Engineers (IEEE) Sensor Design for a Current Measurement System with High Bandwidth and High RIETMANN Stefan Accuracy Based on the Faraday Effect

H(t)

τlight

ΔH3 Θ ΔH2 1 Θ2 H(t) ΔH1 Θ3 vlight,λ,Θ V (λ),nr, μr t t0 t0 +2Ts t1 t1 +2Ts t0 + Ts t1 + Ts Θ(t) 0dMagneto-optical crystal

Θ3 Θ2 Θ1 ΔΘ3 ΔΘ2 ΔΘ1

t t0 t0 +2Ts t1 t1 +2Ts t0 +Ts t1 +Ts

Fig. 5: During the entry of light (t0) into the magneto-optical material and its exit (t1), the magnetic field H(t) changes by a factor ΔHi. Hence, the rotation angle represents the integration over the complete period the light remains inside the crystal. By observing the rotation angle for multiple points in time a moving average can be identified. optical system performance. TGG features a high transmission rate and a moderate Verdet constant in the visible and infrared (∼ 600nm − 700nm) spectrum. It can be doped with different rare earth ions (e.g. (Nd), dysprosium (Dy) or praseodymium (Pr)). Doping TGG can increase the Verdet constant by 30% to 40% [18] which linearly affects the total Faraday rotation. Due to the high absolute transmission TGG is suitable for long sensor designs (> 20mm). This also results in a higher rotation of the PoP despite the limitations imposed by the comparably low Verdet constant. Note, that long sensor designs decrease the possible measurement bandwidth as explained in section 3 and shown in Fig. 3. The expected total Faraday rotation is noted in Tab. II. CdMnTe has been intensively investigated in the past decades [19, 20, 21, 22] as well as modification of it such as for example Cadmium Manganese Mercury Telluride (CdMnHgTe) [23]. It is available in polycrystalline and crystalline form [24]. Since the polycrystalline form suffers from significantly higher light-scattering, the pure crystalline form has been chosen for this sensor design. In general, CdMnTe offers a considerably higher Verdet constant compared to TGG. The composition of (Cd1−xMnxTe) can be altered to achieve different transmission and Verdet constant values for specific wavelengths. Since the absorption of light in CdMnTe is very high it is necessary to adapt the wavelength specifically to the chosen composition and to very careful choose the physical dimension of the crystal (optical path). Counteracting the high transmission loss with higher light input power will eventually lead to higher thermal losses in the material itself. Hence, samples with over 20mm length are hardly suitable and will need special care in terms of external cooling of the magneto-optical material. 3 Sensor Transfer Function As depicted in Fig. 1, the optical system including the sensor is modeled with a transfer function and as a part of a larger system. The final aim is to fully determine the transfer function of all parts of the sy- stem which enables to comprehensively optimise the sensor. The main input to the optical system is the magnetic field H(t)=1/(μ0μr) · B(t). The measurable output of the systems is the intensity of the laser Table II: Magneto-optical crystal specification: The optical and wavelength dependent values are given for a incident laser wavelength of 660 nm.

Specification Cd57Mn43Te Cd57Mn43Te TGG TGG Units Optical path length 2.2 6.6 2.2 10.0 mm

Material Verdet constant Vmat 150 150 6.6 6.6 deg/(T · mm) Absolute Verdet constant Vabs 330 990 14.52 66 deg/T Absolute transmission rate 54 45 >99 >99 % Refractive index 2.9 2.9 1.98 1.98 - Magnetic Material Class Paramagnetic

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beam modulated by a polariser setup. The modulated intensity indicates the angle of rotation caused by the magneto-optical material. In previous publications [12, 25], the frequency dependency of the Faraday rotation to an applied magne- tic field has been analysed. In [12], the time-bandwidth product (TBP) for gaussian shaped laser pulses is used to determine the measurement bandwidth of the sensor. The TBP (12) describes the relation between the cutoff frequency f3dB (13) of the optical system and the laser pulse length τlight = . · 1 = . · c TBP = τlight · f3dB (12) f3dB 0 44 0 44 (13) τlight L · nr where nr is the refractive index of the material, L the length of the optical path and c the speed of light in vacuum. For a gaussian shaped laser pulse the TBP is ≈ 0.44 [12, 26]. For a long optical path L inside magneto-optical materials this approach limits the measurement bandwidth. A different effect has been investigated in [25], focusing on the frequency dependency of Cd1−xMnxTe due to magnetisation effects inside the material. For different compositions a different frequency be- haviour can be expected, whereas the Faraday rotation increases with an increasing amount of manga- nese (x). This cutoff frequency has been reported to be around 2 GHz for the Cd55Mn45Te composition and 0.2 GHz for Cd90Mn10Te, irrespective of the sample length. 3.1 Analysis of the Filter Model In the sensor, a time-variant magnetic field H(t) is integrated over the length of the magneto-optical crystal, as described in (1). The sensor frequency response can been modeled and analyzed as a finite impulse response (FIR) filter implementing a moving average, as shown in Fig. 5. Every Θ(t) at the output of the system represents the sum of all fractions of the rotation over the complete transmission time (history). The model is predicated on the fact that the speed of the light passing the sensor is finite and needs to be taken into account. The speed vlight at which light travels inside a material with the refractive index nr and the transmission time τlight are calculated according to · = c L n vlight (14) τlight = (15) nr c

The applied magnetic field, and hence the resulting Faraday rotation, change during τlight by the value ΔH and ΔΘ, respectively. Assuming that one could measure every distinguishable package of protons independently, a moving average for the total rotation of the PoP results, as depicted in Fig. 5. For each light sample, the averaging window with size τlight moves one sample step Ts to the right. For this model the sample time Ts has been set to a fraction m of τlight inside the magneto-optical material approximating the continuity of light to discrete values. The system and its transfer function can be described by: m m m−i m 1 1 z 1 − h[n]= ∑ b · δ[n − i] (16) H(z)= ∑ b · = ∑ b · z i (17) + i + i m + i m 1 i=0 m 1 i=0 z m 1 i=0 with bi = V · L = const ∀i. The applied magnetic field as the input parameter x[n] to the above described system and the respective transformation can be described as μ I μ0I zsin(ω¯ ) x[n]= 0 sin(ω¯ · n) (18) X(z)) = (19) 2πr 2πr z2 − 2zcos(ω¯ )+1 ω = 2πk with ¯ N . Eventually, the convolution of the input signal with the system transfer function describes the Faraday rotation Θ(z) as μ IV L 1 m zsin(ω¯ ) Θ(z)=H(z)X(z)= 0 ∑ Θ[n]=h[n] ∗ x[n] (20) π + 2+i − 1+i (ω)+ i (21) 2 r m 1 i=0 z 2z cos ¯ z The transfer function eventually describes the sensor material’s time-dependent behaviour analytically. Applying this relation to actual magneto-optical material allows the identification of suitable material with respect to its material dependent and geometrical parameters. 3.2 Transfer Function Results For the identified sensor materials, CdMnTe and TGG, the analysis of the sensor transfer function is performed. Figure 6 shows the calculated cutoff frequencies for the filter model for different crystals and

EPE'19 ECCE Europe ISBN: 978-9-0758-1531-3 - IEEE catalog number: CFP19850-ART P.8 Assigned jointly to the European Power Electronics and Drives Association & the Institute of Electrical and Electronics Engineers (IEEE) Sensor Design for a Current Measurement System with High Bandwidth and High RIETMANN Stefan Accuracy Based on the Faraday Effect

0 0

-1 -1

100mm 80mm 60mm 40mm 20mm 10mm 6.6mm 2.2mm -2 -2 100mm 80mm 60mm 40mm 20mm 10mm 6.6mm 2.2mm Magnitude (dB) Magnitude (dB) -3 -3

-4 -4 10 8 10 9 10 10 10 8 10 9 10 10 Frequency (Hz) Frequency (Hz) (a) Cutoff Frequency for CdMnTe (b) Cutoff Frequency for TGG

Fig. 6: Filter model for the cutoff frequency: The calculated cutoff frequency of the two investigated materials, CdMnTe and TGG is shown. The sample length chosen for the experimental setup described in section 2 are denoted in bold. In [25], a cutoff frequency for CdMnTe due to magnetisation effects is proposed to be at 2 GHz (red line). For samples longer than 40 mm the cutoff frequency of the magnetisation effect is dominated by the transmission delay of the light. their respective lengths. Inserting the length of the TGG crystal from Tab. II to the limiting TBP formula, the cutoff frequency is expected to be at ≈ 32GHz for the 2.2mm and ≈ 7.5GHz for the 10mm crystal. For the CdMnTe crystals, the cutoff frequency (TBP approach) is expected to be at ≈ 20GHz for the 2.2mm and ≈ 8GHz for the 6.6mm crystal. The calculated values match with the results received from the TBP approach and the model from [26]. For bulk material with short (mm range) to medium (< 100mm) optical path length the low-pass behavi- our of the magneto-optical material poses no crucial limitation. For CdMnTe the cutoff frequency due to magnetisation effects, as explained at the beginning of section 3 and [25], has been added for comparison (red line). For samples longer than 40mm the transmission delay limits the design’s maximal bandwidth, for shorter samples the magnetisation effect is dominant and prevents higher bandwidths. Finally, the analysis shows the tradeoff between the crystal length, the applicable bandwidth, the max- imal rotation and hence the accuracy. Longer crystals lead to more rotation and hence a better ratio of applied current to received rotation. On the other hand, the maximal possible bandwidth decreases with a longer optical path. Consequently, both materials are suitable for long sensor designs allowing a larger absolute rotation of the PoP. Considering Fig. 3, a trade-off between the maximal frequency and the optical path length can be disregarded for the current specifications given in Tab. I. The length of the crystal is defined by the required rotation angle of the PoP and the transmission. 4 Conclusion This paper presents the design of an optical system of a highly accurate and wide bandwidth current measurement system. The performance of the magneto-optical material is characterised by its length, the materials Verdet constant (optical activity) and the total transmission of the applied optical input power. Eventually, the combination of all requirements and the specifications from the material lead to an optimisation process for the material choice. Given the requirements for the system, two magneto-optical material have been chosen. Both materials are paramagnetic to prevent the occurrence of saturation effects and achieve high linearity in a large range of possible magnetic field amplitudes. Terbium Gallium Garnet (TGG) has been chosen to provide a reference for the optical system and make it comparable to other systems since the material is widely used an documented. It provides a large transmission rate even with very long samples trading-off the rather low Verdet constant. Cadmium Manganese Telluride (CdMnTe) provides a very large Verdet constant but it shows large absorption and scattering effects reducing the actual transmission of the input power. Moreover, this paper presents a simple model to describe the frequency behaviour of the magneto-optical material. The model presents a further tool to evaluate the suitability of the magneto-optical material for the complete system. The sensing element has been depicted as high order FIR filter implementing a moving average over the light pulse transmission time window. Using this model, TGG shows a cutoff

EPE'19 ECCE Europe ISBN: 978-9-0758-1531-3 - IEEE catalog number: CFP19850-ART P.9 Assigned jointly to the European Power Electronics and Drives Association & the Institute of Electrical and Electronics Engineers (IEEE) Sensor Design for a Current Measurement System with High Bandwidth and High RIETMANN Stefan Accuracy Based on the Faraday Effect

frequency of 32 GHz and 7.5 GHz for the 2.2 mm and the 10 mm samples, respectively. In contrast, CdMnTe shows lower possible frequencies with 20 GHz and 8 GHz for the 2.2 mm and the 6.6mm samples, respectively. For the specification given in this design, the cutoff frequencies pose no further limitation on the magneto-optical material and the analysis shows that a trade-off between the absolute transmission and the optical path length regarding the current measurement bandwidth is not necessary. The length of the magneto-optical material is defined by the necessary rotation angle of the PoP and the transmission rate. Acknowledgement The authors would like to thank CERN for funding the project under contract KE3928/TE. In addition, we would like to thank Dr. M. Barnes and Mr. M.C. Bastos for their valuable scientific input. References [1] M. Barnes, L. Ducimetire, T. Fowler, V. Senaj, and L. Sermeus, “Injection and extraction magnets: kicker magnets,” CERN-2010-004, 2011. [2] L. Ducimetire, N. Garrel, M. J. Barnes, and G. D. Wait, “The LHC injection kicker magnet,” in Proc. Particle Accelerator Conf., 2003, pp. 1162–1164. [3] T. Kramer, T. Stadlbauer, B. Goddard, W. Bartmann, D. Woog, L. Ducimetire, D. Barna, V. Senaj, F. Burkart, and M. J. Barnes, “Considerations for the injection and extraction kicker systems of a 100 TeV centre-of- mass FCC-hh collider,” in Proc. IPAC, 2016, pp. 3901–3904. [4] F. Costa, E. Labour, F. Forest, and C. Gautier, “Wide bandwidth, large AC current probe for power electronics and EMI measurements,” IEEE Trans. on Ind. Electron., vol. 44, no. 4, pp. 502–511, 1997. [5] W. Ray and C. Hewson, “High performance Rogowski current transducers,” in Conf. Rec. of the IEEE Ind. Appl. Conf., vol. 5, 2000, pp. 3083–3090. [6] S. Ziegler, R. C. Woodward, H. H.-C. Iu, and L. Borle, “Current sensing techniques: A Review,” IEEE Sensors J., vol. 9, no. 4, pp. 354–376, 2009. [7] M. Hartmann, J. Biela, H. Ertl, and J. W. Kolar, “Wideband current transducer for measuring AC signals with limited DC offset,” IEEE Trans. on Power Electron., vol. 24, no. 7, pp. 1776–1787, 2009. [8] P. Ripka, “Electric Current Sensors: a Review,” Measurement Science and Technology, vol. 21, no. 11, 2010. [9] M. C. Bastos, “High Precision Current Measurement for Power Converters,” Proc. of the CAS-CERN Acce- lerator School: Power Converters, 2016. [10] T. Cease and P. Johnston, “A Magneto-Optic Current Transducer,” IEEE Trans. on Power Delivery, vol. 5, no. 2, pp. 548–555, 1990. [11] H. B. Sohlstrom¨ and K. G. Svantesson, “Waveguide-based fiber optic magnetic field sensor with directional sensitivity,” in Proc. SPIE, vol. 1511. Fibre Optic Sensors: Eng. and Appl., 1991, pp. 142–149. [12] H. Sohlstrom,¨ “Fibre Optic Sensors Utilizing Iron Garnet Materials,” PhD Thesis, Royal Institute of Technology Stockholm, 1993. [13] A. Cruden, Z. Richardson, J. McDonald, and I. Andonovic, “Optical Crystal Based Devices for Current and Voltage Measurement,” IEEE Trans. on Power Delivery, vol. 10, no. 3, pp. 1217–1223, 1995. [14] K. Bohnert and P. Guggenbach, “A Revolution in High DC Current Measurement,” ABB Review, vol. 1, pp. 6–10, 2005. [15] D. Gerber and J. Biela, “High-dynamic and high-precise optical current measurement system based on the Faraday effect,” IEEE Trans. on Plasma Sci., vol. 43, no. 10, pp. 3550–3554, 2015. [16] D. Meschede, Gerthsen Physik, 25th ed. Springer Berlin Heidelberg, 2015. [17] Deltronic Crystal Industries, Inc. Yttrium Iron Garnet. Accessed: 05-31-2019. [Online]. Available: http://deltroniccrystalindustries.com/deltronic crystal products/yttrium iron garnet [18] S. Kumari and S. Chakraborty, “Study of different magneto-optic materials for current sensing applications,” Journal of Sensors and Sensor Systems, vol. 7, no. 1, pp. 421–431, 2018. [19] N. Kullendorff and B. Hk, “Temperature Independent Faraday Rotation Near the Band gap in Cd1−xMnxTe,” Appl. Phys. Lett., vol. 46, no. 11, pp. 1016–1018, 1985. [20] D. Aksionov, V. Konov, P. Nikitin, A. Prokhorov, A. Savchuk, A. Savitski, and K. Ulyanitski, “New Aspect of Giant Exciton Faraday Rotation in Cd1−xMnxTe Semimagnetic Compound: Fundamentals and Applicati- ons,” Sensors and Actuators, vol. 23, no. 1-3, pp. 875–878, 1990. [21] N. Mikami, C. Nagao, T. Sawada, H. Takahashi, Y. Furukawa, and E. Aikawa, “Temperature Dependence of Magnetic Field Sensors Using (Cd1−xMnx)Te and a LightEmittingDiode Light Source,” J. of Appl. Phys., vol. 69, no. 1, pp. 433–438, 1991. [22] Y. Hwang, S.-s. Chung, and Y. Um, “Giant Faraday Rotation in Cd1−xMnxTe (0 < x < 0.82) Crystals,” Phys. Stat. Sol., vol. 4, no. 12, pp. 4453–4456, 2007. [23] Y. Hwang, H. Kim, S. Cho, Y. Um, H. Park, and G. Jeen, “Magneto-Optical Properties for Bulk Cd0.63−yMn0.37HgyTe Single Crystals,” J. Appl. Phys., vol. 100, no. 6, p. 063509, 2006. [24] H. Guerrero, J. L. Escudero, and E. Bernabeu, “Polycrystalline materials for magneto-optical devices,” Opt. Lett., vol. 17, no. 10, pp. 760–762, 1992. [25] M. Butler, S. Martin, and R. Baughman, “FrequencyDependent Faraday Rotation in CdMnTe,” Appl. Phys. Lett. 49, vol. 49, no. 17, pp. 1053–1055, 1986. [26] A. Kersey, F. Bucholtz, and A. Dandridge, “Sensitivity-bandwidth limitations in opticalfiber Faraday-rotation current sensors,” Int. J. of Optoelectronics, vol. 3, no. 4, pp. 323–332, 1988.

EPE'19 ECCE Europe ISBN: 978-9-0758-1531-3 - IEEE catalog number: CFP19850-ART P.10 Assigned jointly to the European Power Electronics and Drives Association & the Institute of Electrical and Electronics Engineers (IEEE)