https://doi.org/10.6113/JPE.2018.18.3.902

ISSN(Print): 1598-2092 / ISSN(Online): 2093-4718

Investigation of Rise Time and Overshoot in Pulse Transformers with Different Topologies for Electromagnetic Trigger of SCRs

Gang Lv^*, Dihui Zeng^†, and Tong Zhou^*

^†,*School of Electrical Engineering, Beijing Jiaotong University, Beijing, China

Abstract

This study investigates the influences of different core parameters on the dynamic performances, such as rise time and overshoot, in pulse transformers for the triggering circuit of SCRs. First, a simplified transformer equivalent circuit, which emerges from a standard transformer equivalent circuit, is developed to analyze the step response. Second, the relations between the dynamic performances and the parasitic parameters are calculated by the simplified equivalent circuit. Third, the variations of rise time and overshoot, which are vital to the stability of triggering SCRs, with different core parameters, such as mechanic dimensions and topologies, are comprehensively investigated by analyzing the parasitic parameters. Finally, prototype transformers are fabricated to experimentally validate the analysis. The presented method can practically instruct the design of a pulse transformer for triggering SCRs.

Key words: Dynamic performance, Pulse transformer, Rectifier, Topology, Trigger circuit

Manuscript received Oct. 30, 2017; accepted Jan. 25, 2018

Recommended for publication by Associate Editor Yijie Wang.

^†Corresponding Author: zengdh@bjtu.edu.cn Tel: +86-105168-4100, Fax: +86-1051684100, Beijing Jiaotong Univ.

School of Electrical Engineering, Beijing Jiaotong University, China

Ⅰ. INTRODUCTION

Pulse transformers are widely utilized in many fields, such as industrial high-power system and nuclear physics engineering. In the application of an industrial high-power converter, the isolation component, which is used to transmit the control signal to the high voltage side, is either the photoelectric or electromagnetic method. The photoelectric method is extensively applied in many apparatus; however, it is more complicated compared with the electromagnetic method [1]-[4] since the independent power supply must be set in each SCR block. Currently, the electromagnetic method is an optimal solution for this issue because of its cost, maintainability, and miniaturization.

The scheme of the electromagnetic method is shown in Fig. 1. The secondary side (high-voltage side) of the pulse transformer is connected to the gate of an SCR, and a pulse source, which is controlled by the logic circuit in the low-voltage side, is connected to the primary side of the transformer [5]. Then, the isolated triggering signal is transferred to the gate of the SCR through the transformer without any extra power supply.

Fig. 1. Scheme of the electromagnetic trigger.

The analyses of hysteresis and the accuracy of the current transformer, which is used to measure the component of the power system, are presented in [6]-[9]. Although the current transformer is more similar to the pulse transformer, these analyses are difficult to apply in analyzing the pulse transformer since they mainly focus on output accuracy and magnetic saturation. In [10]-[12], the secondary loads in the analysis are high-power klystrons or magnetrons. In these papers, the pulse transformers are mostly microsecond transformers, which apparently do not satisfy the requirement of the triggering SCR that needs a nanosecond one. Therefore, an analysis on the pulse transformer used in the electromagnetic trigger of SCRs is practically significant.

Since the dynamic performances of the pulse transformer are the key factors to SCR triggering, the present study first analyzes the requirements of a prototype SCR and its triggering pulse waveform. On the basis of the characteristics of stability in triggering SCRs [13], [14], the key parameters of the pulse transformer are determined from the requirements. A simplified equivalent circuit based on the standard equivalent circuit of the pulse transformer is analyzed. Then, an analytical method for predicting the parasitic parameters, which determine the dynamic performances, with various core parameters and topologies is proposed. Thus, this paper comprehensively discusses the influences of the core parameters and topologies on the dynamic performances, and relevant measurements are presented to validate the analysis.

Ⅱ. PULSE SHAPE AND EQUIVALENT CIRCUITS

In the applications of triggering SCR, the SCR turn-on depends on the amount of energy that can be safely dissipated in the region where switching is initiated, and a quasirectangular current pulse is demanded by the structural characteristics. A typical gate current pulse [15], [16] is shown in Fig. 2, and the gate current specifications for 5STP04D4200 are shown in Table I. According to the table, rise time and overshoot (peak current) are the crucial factors for triggering SCRs; specifically, dependable triggering means pulse energy is safely dissipated in a certain region. The experimental results presented by relevant papers indicate that only the overshoot (peak current) affects the magnitude of the anode current, di/dt. Although the rise time of the triggering pulse is insignificant for controlling anode current di/dt, it can lower the switching losses and improve the robustness of triggering.

Fig. 2. Typical waveform of gating current pulse.

TABLE I SPECIFICATIONS OF GATING CURRENT FOR 5STP04D4200

Quantity	Value
Peak forward gate current (IFGM)	10 A
Continuous pulse current (IGon)	≤ 400 mA
Rate of gate current (dig/dt)	≥ 2 A/μs
Width of gate pulse current (tp)	5–20 μs

In practice, obtaining an equivalent circuit for pulse transformers is a practical method for designing a prototype transformer. The waveform of the output current needs a quasi-rectangular curve. However, it contains a wide frequency spectrum. To transfer the current pulse with a minimum pulse distortion, especially during the rising stage, a maximum bandwidth is achieved, which means that the parasitic parameters should be minimized [17], [18].

The IEEE standardized equivalent circuit of the pulse transformer is shown in Fig. 3(a) [19]. To simplify the analysis on the transient behavior with a quasi-rectangular current pulse, the standardized equivalent circuit can be simplified, as shown in Fig. 3(b). This simplified equivalent circuit can only be used for transient analysis during the rising edge if n>>1 [20]. Consequently, all impedances and the input source are transferred to the secondary, and the standardized transformer model can be ignored. In the following, all measured impedances are referred to the secondary if nothing mentioned. Since the pulse rise time is within 100 ns and no excitation of the core occurs due to the small current-time-product, the influence of the core material (i.e. and ) can be ignored during the rise time. Even if the core resistance is considered, it is connected in parallel to the load resistance, which is = 10 Ω in this case if it refers to the secondary or = 1 mΩ if it refers to the primary and the turns ratio is set to 100. Similarly, the load resistance is smaller than the resistance of the core material, which is ≈ 0.5 Ω on the primary.

Fig. 3. Equivalent circuit of pulse CT. (a) IEEE standardized equivalent circuit. (b) Simplified equivalent circuit.

(a)

(b)

According to the simplified circuit, rise time and overshoot are mainly affected by the leakage inductance and the equivalent capacitance . During the rising stage, the transfer function of the simplified circuit is described as

   (1)

Assuming an ideal step current signal in the primary, the secondary output current can be calculated with the inverse Laplace transform as follows:

    (2)

with ,

where the damping coefficient σ, which is extracted from (2), is defined as

          (3)

As (3) describes, damping coefficient σ mainly depends on the internal resistance of the pulse source and the transformer characteristics. Even though a specific damping coefficient σ can be calculated by (3), its practicability is extremely limited when only the relation between the output pulse shape and the transformer characteristics is considered. Thus, the assumption is that the damping coefficient σ considers only the influence of the pulse transformer (the internal resistance of the pulse source is neglected), and (3) can be simplified to

    (4)

The normalized output current curves for the step transient response is shown in Fig. 4 at . The decreasing damping coefficient σ leads to faster rise time . Starting from σ < 1, an overshoot is emerged. Therefore, to achieve a minimum rise time , the damping coefficient σ should be minimal, while the resulting overshoot should be below the maximum gate current of the SCR. The overshoot may be calculated by

           (5)

Fig. 4. Normalized rise time for step response.

As (3) and (4) describe, the damping coefficient σ is determined by the parameters, such as leakage inductance , equivalent capacitance , source internal resistance , and load resistance , which is a fixed value for a certain type of SCR. Furthermore, the rated anode current directly determines the magnitude of the current pulse. In addition to the overshoot, the rise time can be calculated by

       (6)

On the basis of (3) and (6), a small internal resistance and a high load resistance can achieve a fast rise time, a phenomenon that leads to an increase in rise time. Load resistance is normally a fixed value that cannot be adjusted. Thus, internal resistance, which is substantially related to the rise time with a fixed -product, should be fully considered.

Ⅲ. ANALYSIS

The dynamic performances of the transformer can be varied by its parasitic parameters. According to [20], the mechanical dimensions of a transformer directly determines the ratio of leakage inductance and equivalent capacitance , which are the height and length of the winding, respectively. Moreover, the product of and is defined by the transformer topology. In practice, it demands both the smallest -product and the appropriate -ratio to achieve the optimal dynamic performance of pulse transformation.

In the following, the three possible topologies for SCR triggering are comprehensively investigated, and the -product of the three topologies is analyzed by electromagnetic energy theory, which can calculate leakage inductance and equivalent capacitance with the energy stored in the electromagnetic field. They are described by (6) and (7), respectively [21–23].

    (6)

   (7)

where μ is the permeability of the magnetic core, ε is the permittivity of the gap between the bobbins, is the primary winding’s current, is the primary winding’s voltage, and dV is the volume element in the magnetic core. To simplify the comparison, only the energies between the windings are considered.

A. Toroidal Winding Type I

Toroidal winding topology (type I) is widely used in the triggering circuit of high-voltage apparatus in which the series SCR is needed due to its special construction Fig. 5(a) whose primary winding crosses the center of the transformer.

Fig. 5. Toroidal winding type I. (a) Real product. (b) Analysis model. (c) Stretched analysis model.

(a)

(b)

(c)

The leakage inductance and the equivalent capacitance are defined by the mechanical dimensions of the transformer. For this topology [Fig. 5(b) and (c)], and are analyzed as follows.

On the basis of Ampere’s law and assuming an ideal magnetic core material (μ = ∞), the magnetic field strength can be described by (8):

      (8)

where N_pri is the turns of the primary winding, and is the magnetic path radius of the core.

In [22], [23], the arithmetic average value is used as the equivalent value for magnetic field strength to simplify the calculation of inference. Magnetic field strength in the border of the core is described as

      (9)

with

The top and bottom of the stretched core are closed as shown in Fig. 5(c). Therefore, the integration path of magnetic strength is also closed. Assuming the current density and the magnetic field strength in the ribbons, then, the magnetomotive force is given by

      (10)

with

With Equations (10) and (6), the leakage inductance can be calculated by

     (11)

According to the structure of the transformer bobbins, a linear voltage distribution is assumed across the windings. The distribution is defined by

       (12)

where is the reference angle.

Therefore, the voltage difference between the primary and secondary winding depends on the angular position , i.e., . The electric field depends on the -position, that is,

       (13)

With Equations (13) and (7), the relation between the equivalent capacitance and electric field energy is defined by

          (14)

where n is the ratio of , and is the cross radius for the primary conductor.

Then, the equivalent capacitance is calculated by

    (15)

B. Toroidal Winding Type II

Given that the primary winding is limited to only one turn, the magnetic field strength excited by the primary cannot be improved with a limited primary current. Thus, this topology is no longer suitable for triggering the high anode current SCR. The type II topology, as shown in Fig. 6(a), obviously satisfies SCR needs. However, the primary winding of this topology is difficult to install due to the primary wounds on the bobbins, which are the same as those of the secondary winding. Therefore, this topology is used in the triggering circuit of a high-power apparatus.

Fig. 6. Toroidal winding type II. (a) Real product. (b) Analysis model.

(a)

(b)

In the following, the equivalent capacitance of this topology is mainly analyzed, as shown in Fig. 6 (b), because the analysis of the leakage inductance is the same as that of the toroidal winding type I. Then, a linear voltage distribution, the electric field , and the stored electric energy are described in (16) to (18), respectively.

        (16)

   (17)

   (18)

The equivalent capacitance and the -product of the transformer are then expressed as follows:

           (19)

C. Parallel Winding

Another classical parallel winding topology that is widely used in many fields should also be considered. The primary and secondary winding are wound on two parallel bobbins, whose clearances are defined by their need for electrical insulation. For this topology Fig. 7(a), and are analyzed as follows [21].

Fig. 7. Parallel winding. (a) Real product. (b) Analysis model.

(a)

(b)

According to Ampere’s law and assuming an ideal magnetic core material (μ = ∞), the magnetic field strength can be described by (20).

        (20)

where is the turns of the primary winding, and is the magnetic path radius of the core.

With (20) and (6), the stored magnetic energy between the windings can be approximately calculated by (21), and is the depth of the transformer core.

     (21)

The leakage inductance is

     (22)

According to the bobbin structure of the transformer, a linear voltage distribution is assumed across the windings. The distribution is defined by

           (23)

where is the reference height.

Therefore, the voltage difference between the primary and secondary winding depends on the angular position , i.e., . The electric field depends on the -position, that is,

         (24)

With Equations (24) and (7), the relation between the equivalent capacitance and the electric field energy is defined by

      (25)

Then, the equivalent capacitance, , is calculated by

           (26)

D. Efficiency

The efficiency of the pulse transformer generally exceeds 95%. The losses in the transformer are negligible if only one transformer exists in the triggering circuit. However, the triggering circuit is equipped with several transformers (the specific number is dependent of the series of the SCRs). Therefore, the losses cannot be ignored in the analysis.

In this paper, the cross-section of the core is circular, while the primary and secondary winding resistances R_cu1 and R_cu2 are defined by

         (27)

where ρ is the winding coil resistivity, S is the cross-section area of the winding coil, and N_1,2 is the turns of the primary or secondary winding.

Based on the handbook of the transformer, the equivalent resistance of the iron loss R_fe is given by

   (28)

where C_fe is the coefficient to the core material, which can be obtained from the handbook; f is the supply frequency; G is the core weight; I_m is the magnetizing current; μ₁ is the core permeability; and l is the average length of the magnetic circuit.

In (27) and (28), the key component parameters in the equivalent circuit are proposed, and the total loss and efficiency in the transformer may be obtained.

E. Design Criteria

To calculate accurately, the parameters of the source and load should be considered. In practical applications, the pulse generator is connected to the primary side, and the load is connected to the secondary winding. Thereafter, a certain inductance or capacitance occur and should be considered during the rise time and overshoot. In this design, the typical values of SCR are in the range of = 100–1000 pF. Hence, Equation (4) should be extended to

          (29)

Ⅳ. SIMULATIONS AND VALIDATIONS

The prototype transformers are fabricated, and each winding topology is used with various physical dimensions to test the object in the validation. The experimental circuit, as shown in Fig. 8, consists of a Schottky diode , a 5STP04D4200 SCR , and an ultra-low inductance resistor . In the measurement, the voltage magnitude of , which can be transferred to the current magnitude, is observed with an oscilloscope. The specifications of the instruments are presented in Table II.

Fig. 8. Experimental circuit.

The analytically predicted rise time, overshoot, and efficiency are provided in Figs. 9 to 12, and the main parameters of the prototype transformers are listed in Table III. The comparisons of the different values of the core cross-section radius or winding height are presented in these figures, which show the tendency of the dynamic performance with the variation of the core dimension or winding height.

TABLE II LIST OF EXPERIMENTAL EQUIPMENT

Item	Type
Oscilloscope	GWINSTEK GDS-2102E
Signal generator	SUIN TFG1920B
DC supply	HUAWEI HD4825-2
Voltage probe	Tektronix TPP0201
Resistor	DALE 0.05R/5W
Oscilloscope	GWINSTEK GDS-2102E

TABLE III MAIN PARAMETERS OF PROTOTYPE TRANSFORMERS

Symbol	Quantity	Toroidal I	Toroidal II	Parallel	Unit
N	Turns ratio	200	200	200
Npri	Turns of primary	1	5	10
Nsec	Turns of secondary	200	1000	2000
r0	Radius of core cross-section	15, 24, 28	22, 28	--	mm
dw	Gap length between the primary and secondary winding	--	1.5, 3	5, 7, 10	mm
Rm	Radius of toroidal core	35, 45, 55	35, 45, 55	--	mm
hw	Height of parallel winding core	--	--	32, 60, 87	mm
	Core materials	Si-Fe	Si-Fe	Si-Fe
I1	Rated pulse current	400	400	400	A
f	Rated pulse frequency	20	20	20	kHz

In Fig. 9(a), the curves, which represent the different values of the core cross-section radius, rapidly decrease with the increasing core radius. This outcome basically conforms with the analytical results, since the reduction of the leakage inductance and the increase of the equivalent capacitance are augmented, while the core radius of the transformer increases. This phenomenon leads to a relatively shorter rise time. In Fig. 9(b), the curve trend is reversed since a short rise time causes a high overshoot, a trend that is consistent with Fig. 4. In Figs. 10 and 11, the curve trends are basically the same as in Fig. 9, and these analytical results are verified by measurements. In Fig. 12, the efficiency increases with the magnetic path length because the larger length will lower the flux density R_fe.

Fig. 9. Toroidal winding Type I. (a) Rise time. (b) Overshoot.

(a)

(b)

Fig. 10. Toroidal winding Type II. (a) Rise time. (b) Overshoot.

(a)

(b)

Fig. 11. Parallel winding. (a) Rise time. (b) Overshoot.

(a)

(b)

Fig. 12. Efficiency. (a) Toroidal winding I and II. (b) Parallel winding.

(a)

(b)

Ⅴ. CONCLUSIONS

This paper briefly introduces the application of the triggering circuits of SCRs and the specifications of the triggering current pulse. According to this application, a simplified equivalent circuit is presented by extracting the standard equivalent circuit of the pulse transformer, which ignores the influence of some passive components that only affect the steady-state performance. The relation between dynamic performance, such as rise time and overshoot, and parasitic parameters is discussed by the analytical method. Furthermore, this investigation can aid in the design of the pulse transformer, improve the performance for triggering SCRs, and lower manufacturing cost.

ACKNOWLEDGMENT

This work was fully supported by the National Natural Science Foundation of China through Project Nos. 51377009 and 51777009.

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Gang Lv received his Ph.D. degree in Electric Machine and Driven from Beijing Jiaotong University, Beijing, China, in 2007. From 2007 to 2009, he was a postdoctoral research fellow with the Technology Center, CRRC Qingdao Sifang Locomotive and Rolling Stock Co., Ltd., Qingdao, China. In 2007, he joined the School of Electrical Engineering, Beijing Jiaotong University, where he is currently an associate professor. His research interests include the application, control, and design of linear machines and drives and the analysis and control of ac traction machines.

Dihui Zeng received his M.Eng. degree in Mechatronic Engineering from China University of Mining and Technology, Beijing, China, in 2013. From 2013 to 2015, he was a Hardware Engineer with CRRC Zhuzhou Locomotive Institute Co., Ltd., Zhuzhou, China. He is currently working toward his Ph.D. degree in Electric Machine and Driven in Beijing Jiaotong University, China, where he has been engaged in linear motors.

Tong Zhou received his B.Eng. degree in Electrical Engineering from Qingdao University, Shandong, China, in 2013. He is currently working toward his Ph.D. degree in Electric Machine and Driven in Beijing Jiaotong University, China, where he has been engaged in the design and analysis of linear machines.