The investigation of choking-coils characteristics in a wide range of current and frequency

THE INVESTIGATION OF CHOKING-COILS

CHARACTERISTICS IN A WIDE RANGE

OF CURRENT AND FREQUENCY

Kalina Detka, Krzysztof Górecki

Gdynia Maritime University

Faculty of Marine Electrical Engineering Poland

ABSTRACT

In the paper the problem of measuring choking-coils characteristics in a wide range of a dc component of current and frequency is considered. Disadvantages of classical bridge methods are discussed and the manner of measurements of dependences of the module and the phase of the choking-coil impedance on a dc component of the current on inductance and frequency is described. The accuracy of this manner is discussed. Some results of measurements of the considered characteristics of choking-coils containing ferromagnetic cores made of different materials are shown. On the basis of the obtained results of investigations the ranges of current and frequency, in which each of the considered choking-coils has the best exploitive properties, are shown.

INTRODUCTION

The choking-coils are necessary components of many switching-mode power converters [1, 2]. The properties of these electronic elements depend strongly on the properties of both the winding and the applied ferromagnetic cores [2, 3, 4]. In order to miniaturize the dimensions of electronic

equipment it is also indispensable to miniaturize power supplies. For switching-mode power supplies, a natural way to limit their dimensions is an increase of the switching frequency, which allows the use of choking-coils of smaller inductance and smaller sizes [1, 2]. One of the factors limiting an increase of the operating

frequency of switch-mode power supplies are properties of magnetic elements. The choking-coils are typically modelled with the use of the equivalent network shown in Fig. 1 [5, 6].

R

C L

Fig. 1. The equivalent network of a choking-coil

The network consists of serially connected: an inductor L and a resistor R and parallelly connected capacitor C. In the literature [7] a lot of methods of measuring inductance, resistance and capacitance using, among others, an impedance bridge are described. Unfortunately, these methods are dedicated to measure the values of the mentioned quantities at the zero-value of the dc component of the current or the voltage of the examined element [6, 7, 8].

As it appears from the literature [2, 3] and the authors’ measurements [9, 10], the basic choking-coil parameters like inductance L and series resistance R depend on a dc component of the choking-coil current and the material used to build a core. The dependences L(i) for many choking-coils are non-linear functions [5, 9, 10, 11]. In the authors’ previous papers an essential influence of the choking-coil current on inductance and series resistance was shown [10], but the research was limited to the frequency not exceeding 100 kHz. It was also demonstrated that non-linearity of the choking-coil characteristic has a significant influence on the characteristics of non-isolated dc-dc converters [9, 11, 12, 13].

In this paper, which is an extended version of the paper [14], the limitations of the bridge method of measuring the RLC parameters of choking-coils are discussed. The oscilloscopic method of measuring parameters of the choking-coil over a wide range of changes of the current of this element and frequency is proposed. The measuring error is analyzed and some results of measurements of the characteristics of the selected choking-coils are presented.

1. LIMITATIONS OF THE BRIDGE METHOD

The impedance bridges have been known for many years [7, 8] and they allow measuring RLC elements at the zero-value of a dc component of their current and voltage. The measurement method of nonlinear capacitance of electronic elements is described in [10, 15]. This method requires the use of, apart from measurement bridge, the circuit which biases the measured element and capacitors which make impossible the flow of a dc component of the current through the measuring bridge. Using the analogous conception, the circuit for bridge measurements of series resistance and inductance of the choking-coil is proposed in the paper [17]. This circuit is shown in Fig. 2.

In Fig. 2, the measured choking–coil L2 is biased by the dc current from the voltage

source EZ. The value of this current is measured by the ammeter, the resistor R

limit the value of the choking–coil current. The inductance measurement is realized

using an automatic RLC bridge. The capacitors C1 and C2 determine the

short-circuit for the variable component of the measuring signal from the bridge and protect all the bridge’s components against the flow of the biased current of the

choking–coil. On the other hand, the choking-coil L1 absorbs the variable

The disadvantage of the circuit shown in Fig. 2 is the influence of the elements of

the biased network (the choking-coil L1, the resistor R, the ammeter, and the

voltage source EZ), connected parallelly to the choking-coil L2, on the indicated by

the RLC bridge values of inductance and series resistance of the examined choking-coil. Thus, in order to achieve reliable measurement results in the considered circuit, it is necessary to provide the relation L1>>L2. However, due to

non-linearity of the magnetization characteristics of the ferromagnetic core [3, 18], the required relation between the inductance of the choking-coils L1 and L2 can be

achieved only in a limited range of values of the chocking-coil current. Therefore in the considered circuit for changes of the value of the chocking-coil current in a wide range, there could occur a problem of understating the values of the choking-coil inductance. L2 C1 RLC bridge L1 C2 R EZ

A

Fig. 2. The circuit for measuring inductance of an inductor

Additionally, this circuit makes possible the realization of the measurement of the mentioned parameters only for the frequency at which the applied bridge operates, and the small value of the amplitude of the signal stimulating the examined choking-coil limits the accuracy of measurements of the series resistance value.

2. MEASURING CIRCUIT

In order to measure the parameters of the chocking-coil over a wide range of frequency and current the measuring circuit shown in Fig. 3 was used.

In the presented circuit the voltage source EZ stimulates the dc current measured by

the ammeter. In turn, the generator EG produces a sinusoidal signal excited by the

examined choking-coil L2. The current probe allows measuring the time course of

the choking-coil current. The courses of this current and the voltage on the choking-coil are measured by the oscilloscope. On the basis of these measurements, the values of the impedance module of the examined choking-coil are calculated as a quotient of the current and the voltage amplitudes, whereas the phase shift between the current and the voltage is equal to the phase of the impedance. Assuming that the choking-coil can be modelled by a series connection

of an ideal coil with inductance L and by a resistor with resistance R [5, 9] for frequency lower than the resonant frequency frez, the values of these components

are calculated by the measured results of the module and the phase of impedance. On the other hand, the choking-coil capacitance value C is estimated on the basis of the measurement of the resonant frequency of the choking-coil using the following formula: L R L f C rez⋅ ⋅+ _⋅ ⋅ ⋅ = 4 4 1 2 2 2 π (1) L2 C1 L1 R EZ

A

Fig. 3. The circuit for measuring inductance and series resistance of the choking-coil

3. ESTIMATION OF THE MEASUREMENT ERROR

The presented measuring method was elaborated to measure the module and the phase of the choking-coil impedance. The sources of the measurement error are inaccuracies in the measurement of the peak-to-peak values of the current Ipp and

the voltage Upp, the period T and the time delay τ between voltage and current

waveforms of the choking-coil. The values of these errors result mostly from the resolution of the applied oscilloscope and can be calculated using the method of the complete differential.

From simple transformation it results that the relative error of the measurement of the impedance module is equal to the sum of the relative error of the measurement of the peak-to-peak values of the voltage and the current of the choking-coil. The value of the error is determined by the applied oscilloscope resolution. In a typical digital oscilloscope with 8-bit resolution in the Y-axis direction [19], assuming that the image of the measured waveform is at half of the screen, the relative error of the measurement of the module and the phase of impedance does not exceed 1%. Of course, in order to obtain high accuracy of the measurement, it is necessary to use cursors or the function of the automatic readout of the value of the measured peak-to-peak signal value.

On the other hand, the relative error of the measurement of the phase of impedance is the sum of two components. The first is the error of the measurement of a signal period and the second is the error of the measurement of a delay of the course of the current waveform in relation to the course of the voltage. To minimize the value of this error, it is necessary to read the time value during the waveforms of the current and the voltage, which cross zero on the decreasing part of these signals. The typical oscilloscope resolution in horizontal axis direction is equal to 10 bits [19]. Assuming that the image of one period of the measured signal is at least half of the oscilloscope screen, the relative error of the phase of impedance of the choking-coil can be estimated by the formula

(

)

where ΔT and Δτ denote the absolute errors of the period T and the delay τ

measurements.

As it is visible, for the phase shift ϕ = 90o _{the measurement error is equal to 3.5%}

and it increases to infinity for ϕ→0. Thus, the measurement error of the phase shift and the impedance module is on an acceptable level when the imaginary component of impedance is higher than the real component. So, the measurement should be made at high frequency. On the other hand, this frequency must be less than the choking-coil resonant frequency. Based on the measured value of the impedance module and the phase, inductance and resistance of the choking-coil can easily be calculated. The relative errors of the measurements of the induction δL

and the resistance δR of the choking–coil are described by the formulas ϕ ϕ δ δL=± Z +Δ ⋅ctg (3) ϕ ϕ δ δR =± Z +Δ ⋅tg (4)

where δZ denotes the relative error of the measurement of the impedance module,

Δϕ − the absolute error of the measurement of the phase shift of impedance. In Fig. 4 the calculated dependences of the errors δϕ, δL, δR on the phase shift of

impedance are shown. In the calculations it was assumed that the relative measurement error of the impedance module equals δZ = 1%.

As it is visible, the relative measurement error of induction has the value of 1% less than the measurement error of the phase. This error goes to infinity while the phase goes to zero. This is due to the fact that the phase shift between the inductor current waveforms and the voltage is very small and close to the resolution of the oscilloscope in the direction of the horizontal axis. The inductance measurement error is small in the range, in which the impedance of the choking-coil has an inductive character. On the other hand, the resistance measurement error is the smallest in the range of small values of the phase shift of impedance, when the impedance of the choking-coil has a resistive character.

0 10 20 30 40 50 60 70 80 90 100 -90 -60 -30 0 30 60 90 ϕ [o ] δϕ , δL , δR [%] δR δϕ _δ L

Fig. 4. The calculated dependences of the relative errors of the measurements of the phase shift, inductance and resistance of the choking-coil on the phase shift of impedance

4.

RESULTS

Using the measuring circuit shown in Fig. 3, the characteristics of choking-coils with toroidal cores made of different ferromagnetic materials with the diameter equal to about 25 mm and the height equal to about 10 mm were measured. For all the cores 50 turns of copper wire in the enamel of the diameter equal to 0.8 mm were wound.

In Fig. 5 the measured dependences of inductance of the considered choking-coils on a dc component of their current are shown. The measurements were performed at the frequency equal to 100 kHz. The symbols shown in Fig. 5 mean: RTN – nanocrystalline core, RTF – ferrite core of F867 material, RTMSS – powder core including the alloy of iron, silicon and aluminium, HF – core made of nickel, iron and molybdenum alloy powder material, RTP 106-26 and RTP 106-2 are cores made of powdered iron which has different values of permeability. The properties of the used magnetic materials are described in the paper [20] and their basic parameters are given in the paper [9].

As it is visible in Fig. 5 the characteristics L(i) strongly depend on the selection of the magnetic material used to build the core of the choking-coil. As a result the value of inductance for the fixed value of the current is different for each choking-coil and the inductance values can change even 50 times. As it is visible, the choking-coil with the nanocrystalline core achieves the highest value of inductance and the lowest – the choking-coil with the powdered iron core RTP 106–2. The differences between the values of inductance of the considered choking-coils arise from different values of the initial magnetic permeability of these cores. It can also be seen that inductance of the choking-coil is a decreasing function of the current. The steepness of the fall of the dependence L(i) is the highest for the choking-coil with nanocrystalline and ferrite cores, and the smallest for choking-coil with the

powdered iron core. For example, the inductance of the choking-coil with the nanocrystalline core decreased 250 times for a specific range of changes of the current, while the inductance for the choking-coil with the powdered iron core decreased only just about 45% in the same range of changes of the current.

1 10 100 1000 10000 0 1 2 3 4 5 i [A] L [ μH] Ta = 23oC RTMSS RTF RTN RTP 106-2 RTP T106-26 HF

Fig. 5. The measured dependences of inductance of choking-coils with cores made of different materials on a dc component of the current

For RTP, HF and RTMSS cores a horizontal section is visible on the considered characteristics, which results from occurrence of an air gap in the considered cores. The air gap allows maintaining a constant value of the choking-coil inductance in a wide range of changes of the current, which is very important in dc-dc converters [1, 2].

As it is known, the impedance of the choking-coil can change its own character with regard to frequency, because in the equivalent circuit of this element there exist [5, 18]: the inductor, the capacitor and the resistor. Therefore, on the course of the impedance of the choking-coil there appears a resonance at some frequency. From the users’ point of view it is important that the resonance frequency occurred over an operating frequency of the circuit containing this choking-coil.

In Figs. 6–11 the measured dependences of the module and the phase of impedance of the considered choking-coil on frequency are shown. The measurements were performed for the selected values of a dc component of the current.

In Fig. 6 the characteristics of the choking-coil with the core HF made of the powdered alloy of nickel and iron are shown.

As can be observed, the resonant frequency of the considered choking-coil assumes values from 3 to 4 MHz. The phase characteristics of the considered choking-coil have an inductive character of impedance for the frequency not higher than 2 MHz. The constant value of a slope of the dependence Z(f) in this frequency range indicates the constant value of inductance of the choking-coil in a wide range of the current, which is convergent with the results shown in Fig. 5. The oscillations, visible on the phase characteristic, result from an inaccuracy of the applied measuring method.

0 2000 4000 6000 8000 10000 12000 0 1000 2000 3000 4000 5000 f [kHz] Z [ Ω ] IDC=0 A IDC=0,5 A IDC=1 A IDC=2 A IDC=5 A HF -40 -20 0 20 40 60 80 100 120 0 1000 2000 3000 4000 5000 f [kHz] ar g Z [d eg ] IDC=0 A IDC=0,5 A IDC=1 A IDC=2 A IDC=5 A HF

Fig. 6. The measured dependences of the module and the phase of impedance on frequency for the choking-coil with the HF core

The frequency characteristics of impedance of the choking-coil with the core made of the powdered iron are shown in Figs. 7 and 8. The character of the obtained dependences of the module and the phase of impedance on frequency is different and the observed differences are connected with the dependencies L(i) presented previously.

For the choking-coil with the RTP 106-26 core, the resonant frequency is situated within the range from 1 to 2 MHz. From the phase characteristics it is visible, that the inductive character of impedance of this choking-coil is kept within the frequency smaller than 1 MHz. A strong influence of the choking-coil current on its inductance (determining the slope of the characteristic Z(f)) for small values of frequency can be also seen.

In turn, the choking-coil with the core RTP T106-2 does not show resonance in the investigated frequency range, and the frequency characteristic corresponds to inductive character of the choking-coil impedance. It is worth noticing that the obtained characteristic of the considered choking-coil predestines this element to use in dc-dc converters controlled by the signal of frequency not higher than several MHz.

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 0 1000 2000 3000 4000 5000 f [kHz] |Z | [ Ω ] IDC=0 A IDC=0,5 A IDC=1 A IDC=2 A IDC=5 A RTP T106-26 -60 -40 -20 0 20 40 60 80 100 0 1000 2000 3000 4000 5000 f [kHz] arg Z [d eg] IDC=0 A IDC=0,5 A IDC=1 A IDC=2 A IDC=5 A RTP T106-26

Fig. 7. The measured dependences of the module and the phase of impedance on frequency for the choking-coil with the RTP T106-26 core

0 500 1000 1500 2000 2500 3000 3500 4000 0 1000 2000 3000 4000 5000 f [kHz] |Z| [ Ω ] IDC=0 A IDC=0,5 A IDC=1 A IDC=2 A IDC=5 A RTP T106-2 0 10 20 30 40 50 60 70 80 90 100 0 1000 2000 3000 4000 5000 f [kHz] ar g Z [ de g] IDC=0 A IDC=0,5 A IDC=1 A IDC=2 A IDC=5 A RTP T106-2

Fig. 8. The measured dependences of the module and the phase of impedance on frequency for the choking-coil with the RTP T106-2 core

The choking-coil characteristics with ferrite and nanocrystalline cores shown in Figs. 9 and 10 have a strong influence of the choking-coil current on the impedance of the module and the phase of this element. At the zero-value of a dc component of the chokin-coil current the resonance frequency achieves the value only just several hundred kHz and it rapidly increases with an increase of the choking-coil current. The observed character of the dependence Z(f) results from the strongly decreasing dependence L(i) for the considered choking-coils (Fig. 5). Due to the constant value of winding turns of the considered choking–coils and the constant distance between them, capacitance of the choking-coil winding is constant, too. Its value can be estimated on the basis of the obtained value of the resonance frequency and the previously measured value of inductance for the considered choking-coil. In this way the value of the choking–coil capacitance equal to 62.5 pF is obtained.

For the choking-coil with the nanocrystalline core operating at the current higher than 0.5 A and the ferrite core operating at the current higher than 2 A the resonance is not observed. The obtained results testify to the fact that the considered choking-coil can be used in switch-mode power supplies, if the direct current is sufficiently high.

0 5000 10000 15000 20000 25000 0 1000 2000 3000 4000 5000 f [kHz] |Z| [ Ω ] _{IDC=0 A} IDC=0,5 A IDC=1 A IDC=2 A IDC=5 A RTF -100 -80 -60 -40 -20 0 20 40 60 80 100 0 1000 2000 3000 4000 5000 f [kHz] ar g Z [d eg ] IDC=0 A IDC=0,5 A IDC=1 A IDC=2 A IDC=5 A RTF

Fig. 9. The measured dependences of the module and the phase of impedance on frequency for the choking–coil with the RTF core

0 1000 2000 3000 4000 5000 6000 7000 8000 0 1000 2000 3000 4000 5000 f [kHz] |Z| [ Ω ] IDC=0 A IDC=0,5 A IDC=1 A IDC=2 A IDC=5 A RTN -80 -60 -40 -20 0 20 40 60 80 100 0 1000 2000 3000 4000 5000 f [kHz] ar g Z [ d eg ] IDC=0 A IDC=0,5 A IDC=1 A IDC=2 A IDC=5 A RTN

Fig. 10. The measured dependences of the module and the phase of impedance on frequency for the choking-coil with the RTN core

The last figure (Fig. 11) refers the choking-coil with the RTMSS core made of the powdered alloy of iron, silicon and aluminium. For the considered material in whole pointed current range the resonance frequency from 1.7 to 2.2 MHz is obtained. The value of this frequency depends on the value of the choking-coil current. The high value of the module of the choking-coil impedance in the resonance provides low series resistance of this element, which is useful from the point of view of the designer of the switch-mode power supplies.

In the paper [21] the choking-coil model for SPICE software is described and it is shown that with the use of this model a good agreement between the simulated and measured characteristics of the considered core is obtained. It proves the correctness of the used measuring method and its usefulness in the investigations of choking-coils.

0 5000 10000 15000 20000 25000 30000 0 500 1000 1500 2000 2500 3000 3500 f [kHz] |Z| [ Ω ] IDC=0 A IDC=0,5 A IDC=1 A IDC=2 A IDC=5 A RTMSS -100 -80 -60 -40 -20 0 20 40 60 80 100 0 500 1000 1500 2000 2500 3000 3500 f [kHz] ar g Z [ de g] IDC=0 A IDC=0,5 A IDC=1 A IDC=2 A IDC=5 A RTMSS

Fig. 11. The measured dependences of the module and the phase of impedance on frequency for the choking-coil with the RTMSS core

6. CONCLUSIONS

In the paper the problem of measuring choking-coil parameters in a wide range of a dc component of the current and frequency is discussed. In particular disadvantages of the bridge method are pointed out and the simple circuit to measure inductance, resistance and capacitance of the choking-coil is described. The analysis of the measurement error in the considered circuit is performed. This analysis shows that in the typical range of the choking-coil at frequency much lower than the resonant frequency, the measurement error does not exceed a few percent.

Using the proposed measurement circuit the properties of the choking-coils with ferromagnetic cores made of different ferromagnetic materials were examined. The measurements were performed in a wide range of current and frequency changes. The obtained results show that the choking-coil with nanocrystalline or ferrite core can achieve high value of inductance, but this value strongly depends on the current and it is a decreasing function of this current. On the other hand, the cores

made of powdered iron or powdered iron’s alloys have the constant value of inductance in a wide range of current values, but the achieved value is smaller than for the choking-coils with ferrite or nanocrystalline cores.

During the measurements of the choking-coil impedance in the function of frequency one can observe that the higher value of the resonance frequency characterizes choking-coils of the smaller inductance value. In particular, for the choking-coils with ferrite or nanocrystalline cores the big impact of the current on the resonant frequency of this element is observed. Therefore, the investigated cores should not be used in dc-dc converters operating at high switching frequency exceeding several hundreds kHz. Within the range of so high frequency it is necessary to use an air gap in ferrite and nanocrystalline cores resulting in a decrease of permeability and in extension of the current range, in which inductance of the choking-coil is constant.

From the point of view of a possibility of using the investigated choking-coils to construct switch-mode power supplies operating at high switching frequencies, it is preferred to use cores made of powdered iron or its alloys. Such cores should have a low value of magnetic permeability, which determines the low value of the choking-coil inductance and simultaneously guarantees a small influence of the choking-coil current on inductance and a wide range of operating frequency. Of course, an increase in frequency results in an increase of losses in the choking-coil [20], which should also be taken into account, when selecting magnetic material for the core of the choking-coil.

7. ACKNOWLEDGEMENTS

This project is financed from the funds of National Science Centre which were awarded on the basis of the decision number DEC-2011/01/B/ST7/06738.

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