Output Characteristics of a Kind of High-Voltage Pulse

IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 38, NO. 4, APRIL 2010

1019

Output Characteristics of a Kind of High-Voltage Pulse Transformer With Closed Magnetic Core Yu Zhang, Jinliang Liu, Xinbing Cheng, Hongbo Zhang, and Guoqiang Bai

Abstract—A new kind of miniature high-voltage pulse transformer based on closed magnetic core is developed, and its output characteristics are analyzed in this paper. The amplitude of the output high-voltage pulse of the transformer is 210 kV, the step-up ratio is 1:105, and the effective coupling coefficient is 0.984. The time-domain and frequency responses of the transformer have also been analyzed in detail by circuit theory. The experimental results show that the pulse transformer can respond well to square voltage pulse with a pulsewidth ranging from 5 to 100 μs and a frequency band ranging from 100 Hz to 500 kHz. With these characteristics, the small pulse transformer with very low cost can be used for applications of dielectric barrier discharge and high-voltage nanosecond-pulse generator. Index Terms—Closed magnetic core, frequency band, highvoltage pulse transformer, output characteristics, response, square-pulse amplifier, step-up ratio.

I. I NTRODUCTION

H

Many applications need pulse waveforms with high quality. However, the distributed parameters and geometric structure of transformer windings have great impacts on the output characteristics of a pulse transformer [14]–[17]. In view of the fact that the responsive pulse signal of a transformer varies according to the source pulse signal with different frequencies, pulsewidths, and rise times, analyses of the frequency response and time-domain response of a pulse transformer are very important and essential [14]–[21]. Redondo et al. employed auxiliary windings to improve the pulse shape of a core-type high-voltage pulse transformer [16], [17]. Ruthrofft designed broadband transformers with a bandwidth ratio of 20000:1 for applications of wideband amplifiers and oscilloscopes [18]. Pleite et al. established a frequency response model for a transformer with several cells [21]. However, pulse response analyses of transformers at several hundred kilovolts are done in a very few papers. In this paper, a small-sized high-voltage pulse transformer based on closed magnetic core is developed, with a coupling coefficient of 0.984 and a step-up ratio of 1:105. According to its structure, circuit simulations were carried out, and the characteristics of the transformer’s pulse response have been analyzed in both time and frequency domains. By solving the equivalent circuit equation of the transformer, a responsive voltage signal is presented, and the impacts on the transformer’s time-domain response of square pulse are analyzed. The experimental results show that the pulse transformer produce highvoltage pulses with an amplitude of 210 kV. The transformer responded well to square pulse with a rise time of 500 ns and a pulsewidth ranging from 5 to 100 μs. By using this pulse transformer, a miniature high-voltage square-pulse amplifier system is designed for dielectric barrier discharge (DBD) applications. At present, this kind of transformer is also used in the high-voltage nanosecond-pulse generator system in our laboratory.

IGH-VOLTAGE pulse transformers are of great importance in the fields of high-voltage engineering and pulsed-power technology [1]–[7]. Usually, high-voltage pulse transformers are used to charge the pulse-forming line of a high-voltage pulse generator for high-power microwave applications [1]–[5]. In addition, they have also been employed in many other fields such as amplifiers, high-voltage isolation [6], synchronous triggering [6], [7], reversed transformation of phase [8], [9], and the field of subnanosecond pulses [10]. There are mainly three kinds of high-voltage pulse transformers, namely, air-core transformer, transformer with open magnetic core, and transformer with closed magnetic core. Kim et al. designed an air-core pulse transformer with an output of 500 kV [11]. However, the transformer with large volume had a small coupling coefficient and a low step-up ratio of 1:10. The Tesla transformer with open magnetic core designed by Russian scientists has a much bigger coupling coefficient (> 0.9) and a high step-up ratio [12], [13]. However, this technology is more complicated, and the costs usually become intolerable, which limit its common use. The pulse transformer with closed magnetic core becomes one of the most important devices to boost voltage due to its highest coupling coefficient, high step-up ratio, small size, and lowest cost.

A. Development of Pulse Transformer

Manuscript received October 25, 2009; revised December 3, 2009. First published March 8, 2010; current version published April 9, 2010. This work was supported by the National Natural Science Foundation of China under Grant 10675168. The authors are with the College of Opto-electronic Science and Engineering, National University of Defense Technology, Changsha 410073, China (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPS.2010.2041368

At present, there are very few papers that have researched on small-sized transformers with closed magnetic core at the 200-kV range. In order to develop a miniature pulse transformer that has the characteristics of high effective coupling coefficient, high transfer ratio, and low charge voltage, an ironbased amorphous alloy was used to make the closed magnetic core of the transformer. Due to this superior material, the saturated magnetic inductive intensity (Bs ) is as large as 1.56 T,

II. D EVELOPMENT OF P ULSE T RANSFORMER W ITH C LOSED M AGNETIC C ORE

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TABLE I E LECTROMAGNETIC PARAMETERS OF THE T RANSFORMER

Fig. 1. Miniature high-voltage pulse transformer. 1. Primary winding. 2. Secondary winding. 3. Insulated support. 4. Insulated films.

Fig. 3.

Schematics of the test experiment on the pulse transformer.

Fig. 4.

Charging voltage waveform of load capacitor C2 .

Fig. 2. Cross section of the pulse transformer. 1. Magnetic core. 2. Insulated support. 3. Windings.

and the residual magnetic inductive intensity is relatively so small that it can be ignored in estimation. The initial relative permeability of the material (μr ) is about 2500. The magnetic core is fixed into a bigger hollow insulated cylinder to enable good endurance to high voltage. The primary and secondary windings of the transformer are separately wound around the walls of the insulated cylinder without overlapping, and an essential distance between the two windings is needed to keep insulation. At last, the insulated cylinder and the magnetic core are enclosed in the windings completely. The pulse transformer is shown in Fig. 1, and the structure of its cross section is shown in Fig. 2. The outer radius of the transformer is 170 mm, and the length is 100 mm. In order to get a high turns ratio, the primary winding of the transformer contains only one turn, while the secondary winding has 110 turns. There are some features of the transformer. To resist a high pulse current in the 10-kA range, the one-turn primary winding consists of three wires in parallel. The secondary winding consists of two layers of wires, as shown in Fig. 1. One turn of wire at the outer layer is wound after its former turn at the inner layer, and then, another turn at the inner layer is wound so that the voltage between adjacent turns is lowest and the distributed capacitance of the secondary winding becomes smaller (177 pF). This winding structure is useful to improve the characteristics of insulation and the pulse response of the transformer. Some of the transformer’s electromagnetic parameters are defined as follows. For the primary winding, the self-inductance is Lp , and the leakage inductance is Lps . For the

secondary winding, the self-inductance is Ls , and the leakage inductance is Lss . The mutual inductance of the windings is M , and the effective coupling coefficient is keﬀ . The important electromagnetic parameters of the transformer were measured by accurate meter “HP4284A,” and the results are shown in Table I. B. Output Test Experiment A test experiment on the transformer was carried out, and the schematics of the experiment are shown in Fig. 3. The pulse transformer was used to charge a 0.32-nF high-voltage load capacitor (C2 ). C1 was the primary energy-storage capacitor with 5-μF capacitance. R1 and L1 were the stray resistance and inductance of the primary circuit, respectively. R2 and R3 formed the resistant divider that was used to detect the charging voltage of C2 . The experimental result is shown in Fig. 4. When the initial charging voltage U0 of C1 was 2 kV, the highest charging voltage of C2 was obtained as high as 210 kV, and the step-up ratio was 1: 105. The voltage peak time was about 5 μs, and the charging period was on the order of 12 μs. III. A NALYSIS OF F REQUENCY R ESPONSE The equivalent charge circuit of an ideal pulse transformer is shown in Fig. 5(a) [21], [22]. In the primary circuit, Rp represents the stray resistance, Llp stands for the sum of the stray

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ZHANG et al.: OUTPUT CHARACTERISTICS OF A KIND OF PULSE TRANSFORMER WITH CLOSED MAGNETIC CORE

Fig. 5.

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Equivalent charge circuit of the pulse transformer. (a) Charge circuit of an ideal pulse transformer model. (b) Equivalent circuit of transformation.

inductance of the primary circuit and the leakage inductance of the primary winding of the transformer, Rc is the loss resistance of the magnetic core, and CDp is the distributed capacitance of the primary winding. Lμ stands for the magnetization inductance of the transformer. In the secondary circuit, CDs is the distributed capacitance of the secondary winding, Lls stands for the sum of the stray inductance and the leakage inductance of the secondary winding, Rs is the stray resistance, and RL is the load resistance. Cw is the distributed capacitance of the two windings of the transformer. U1 represents the square-pulse source in the primary circuit. The distance between the primary and secondary windings is long enough so that Cw can be ignored. If we transform the secondary circuit into the primary circuit, the equivalent circuit of this transformation is shown in Fig. 5(b). CDs , Lls , Rs , and RL in Fig. 5(a) orderly correspond to CDs0 , Lls0 , Rs0 , and RL0 in Fig. 5(b). The principle of this transformation is like this ⎧ ⎨ Lls0 = Lls Lp , CDs0 = CDs Ls Ls Lp (1) ⎩ Rs0 = Rs Lp , RL0 = RL Lp . Ls Ls A. Analyses of Low- Frequency Response Under the condition of low frequency (in the kilohertz range), Fig. 5 can be simplified. In Fig. 5(b), CDp and CDs0 are in parallel, and their sum is at the 100-pF range. The capacitive reactance of the circuit branch of CDs0 and CDp is about 10 MΩ. Thus, the impacts of CDs0 and CDp can be ignored. According to Table I, Lls is about 11.6 mH, but Lls0 is 1 μH after calculation from (1). The inductive reactance of the Lls0 branch is less than 1 mΩ so that Lls0 can also be ignored, so does leakage inductance Llp . Because Rs0 RL0 and Rc RL0 , a simplified circuit of low-frequency response is shown in Fig. 6(a). R0 is the sum of Rs0 and RL0 , and R0 ∼ = RL0 . Because the load resistance RL in Fig. 5 is 50 Ω, R0 is 4 mΩ from (1). The measurement result shows that Lμ is 11.9 μH and that Rp is 0.09 Ω. In Fig. 6(a), Lμ and R0 are in parallel. If the angular frequency of the square-pulse source is ω0 , the reactance of the Lμ branch increases when ω0 increases. When ω0 is big enough (ω0 Lμ R0 ), the Lμ branch is open, R0 is series-wound with Rp , and the voltage of the load resistor is like this U2 = R0 U1 /(Rp + R0 ).

(2)

On the contrary, if ω0 Lμ R0 , no current flows through R0 so that the transformer can no longer respond to square-pulse source U1 . It can be concluded that the characteristics of the lowfrequency response of the pulse transformer is mainly determined by magnetization inductance Lμ . The capability of low-frequency response can be improved by increasing Lμ . Excellent magnetic core materials contribute much for higher μr and Lμ . PSpice analysis is used to simulate the simplified circuit of low-frequency response, and the result is shown in Fig. 6(b). The amplitude of U1 is set as 1 V, and the voltage of the load resistor varies at different frequencies. The pulse transformer responds stably when frequency is higher than 100 Hz. The lower cutoff frequency is close to 1 Hz. B. Analyses of High-Frequency Response Under the condition of high frequency (105 −106 Hz), because ω0 Lμ R0 and ω0 Lμ Rp , the branch of Lμ can be ignored. If Llp and Lls0 are incorporated as Ll and CDs0 and CDp are incorporated as CD , the circuit in Fig. 5(b) can be simplified as it’s shown in Fig. 7(a). In the simplified circuit of high-frequency response, when ω0 increases, inductive reactance ω0 Ll also increases, and the capacitive reactance 1/(ω0 CD ) of the CD branch decreases. If ω0 is large enough so that ω0 Ll R0 and 1/(ω0 CD ) R0 , there will be no signal in the branch of load resistor R0 . If 1/(ω0 CD ) ≥ R0 , CD and R0 are in parallel, but load resistor R0 is dominant. Leakage inductance Ll has great impacts on the current of the circuit, which can influence the output signal of the R0 branch. It can be concluded that the pulse transformer’s capability of high-frequency response can be improved by decreasing distributed capacitance CD and leakage inductance Ll . From the schematics in Fig. 7(a), the result of PSpice simulation is shown in Fig. 7(b). The amplitude of U1 is also set as 1 V. When the frequency of the square-pulse source is lower than 500 kHz, the transformer can respond stably. The higher cutoff frequency is about 30 MHz. From Figs. 6 and 7, the pulse transformer with closed magnetic core has a stable responsive frequency band, which ranges from 100 Hz to 500 kHz. IV. A NALYSES OF T IME -D OMAIN P ULSE R ESPONSE The distributed parameters of the pulse transformer have great impacts on the waveform of the output voltage signal.


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Fig. 6. Low-frequency response of the pulse transformer. (a) Simplified circuit of low-frequency response. (b) Circuit simulation results of low-frequency response.

Fig. 7. High-frequency response of the pulse transformer. (a) Simplified circuit of high-frequency response. (b) Circuit simulation results of high-frequency response.

of the CD branch is Uc (t). The circuit equations of Fig. 8 are listed as ⎧ ⎨ U1 (t) = i(t)Rp + Llp di(t)/dt + Lls0 di1 (t)/dt + i1 (t)R0 Lls0 di1 (t)/dt + i1 (t)R0 = i2 (t)dt/CD ⎩ i(t) = i1 (t) + i2 (t). (3)

Fig. 8. Equivalent circuit of time-domain response.

Analyses of the time-domain response of the transformer are essential to explore those covered characteristics. In Fig. 5(b), CDp and CDs0 can be incorporated as CD , and Rs0 and RL0 are also incorporated as R0 . Moreover, Rc is too large so that it can be ignored. According to these reasonable precepts, the schematics in Fig. 5 can be simplified as Fig. 8. U1 stands for the square-pulse source, i(t) is the source current, and U2 represents the voltage signal of the load resistor. The currents flowing through R0 , Lμ , and CD are i1 , i3 , and i2 in order. A. Response to the Front Edge of Square Pulse Because magnetization inductance Lμ is as large as 11.9 μH, the rise time of the pulse signal are both in the 100-ns range, and the inductive reactance of the Lμ branch is much larger than R0 at the time when the front edge of pulse comes. In the situation of ωLμ R0 , the Lμ branch can be ignored when we only pay attention to the response to the front edge. The voltage

The initial conditions are like this: i(0) = 0, i1 (0) = 0, and Uc (0) = 0. If p is the factor of Laplace transformation, U1 (t) and i1 (t) orderly correspond to U1 (p) and I1 (p) after Laplace transformation. The constants for simplification, such as α, β, γ, and λ, are defined as R L CD +R0 Llp CD R R C +L +L α = p ls0 , β = 0 pLlpDLls0 ClpD ls0 Llp Lls0 CD (4) Rp +R0 γ = Llp L , λ = Llp L1ls0 CD . ls0 CD By Laplace transformation, (3) can be simplified as I1 (p) =

p3

λU1 (p) . + αp2 + βp + γ

(5)

In equation p3 + αp2 + βp + γ = 0, the forms of its three roots are a, b + jω, and b − jω. Furthermore, “j” is the unit of imaginary number, while a, b, ω, and ξ are real numbers. The relation of (a, b, ω) and (α, β, γ) is shown as ⎧ Δ 3 3 2 β2 3 β +α γ γ2 3γ−αβ ⎪ − α108 − αβγ − α27 ⎪ξ = 27 6 + 4 − 6 ⎪ ⎪ −1 1 ⎨ a = ξ 3 − ξ 3 (3β − α2 )/9 − α/3 (6) −1 1 ⎪ − α2 )/18 − α/3 − ξ 3 /2 b = ξ 3 (3β ⎪ ⎪ √ ⎪ −1 1 ⎩ 2. ω = 3 (3β − α2 )ξ 3 9 + ξ 3



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Thus, (5) can fall into three parts like this A1 A2 (p − b) + I1 (p) = λU1 (p) p − a (p − b)2 + ω 2

ω A2 b + A3 + . (7) ω (p − b)2 + ω 2

In (7), constants A1 , A2 , and A3 are defined as A1 =

1 (a − b)2 + ω 2

A2 =

−1 (a − b)2 + ω 2

A3 =

2b − a . (a − b)2 + ω 2

Fig. 9. signal.

(8)

If Us is the amplitude of U1 (t) and T0 is the pulsewidth, the form of U1 (t) is 0, t < 0 & t ≥ T0 U1 (t) = (9) Us , 0 ≤ t < T0 . By inverse Laplace transformation and convolution, (7) is figured out as (10), shown at the bottom of the page. Because U2 = i1 (t)R0 , responsive voltage signal U2 has the same characteristics as i1 (t). When t > 0, U2 consists of an attenuated exponential part and an attenuated resonant part. The attenuated resonant part has great contribution to the harmful parasitic fluctuations at the front and back edges of U2 . Constant a is the attenuation factor of the flat top, b is attenuation factor of the attenuated resonant part, and ω is the resonant frequency. U0 is used to take the place of “λR0 Us A1 ” for short. According to (10), the theoretical waveform of U2 is shown as curve 1 in Fig. 9 when T0 is 5 μs. From (10), the attenuated resonant part can be separated as function f1 (t), and the pure resonant part without attenuation is defined as f2 (t) [see (11) and (12) at the bottom of the page]. f1 (t) and f2 (t) are shown as curves 2 and 3 in Fig. 9, respectively. Obviously, U2 , f1 (t), and f2 (t) have parasitic resonances of the same frequency. Therefore, the rise time of

Theoretical waveform of the front edge of the responsive voltage

responsive pulse signal U2 is half of the resonant period t1 = π/ω.

(13)

t1 is the rise time of U2 , and resonant angular frequency ω is presented in (6). From curve 1, t1 is about 496 ns. Thus, it can be concluded that parasitic resonant frequency increases when distributed capacitance CD , leakage inductance Llp , and Lls0 all decrease. A larger resonant frequency leads to a shorter rise time and a shorter fall time of responsive pulse signal. Distributed capacitance and leakage inductance must be minimized so that the pulse transformer’s time-domain response can be improved. B. Response to the Flat Top of Square Pulse When the voltage-rising process of responsive pulse comes to an end, Uc (t) and the currents that flow through Llp and Lls0 become stable so that the impacts of CD , Llp , and Lls0 can be ignored. However, magnetization inductance Lμ has a great impact on the flat top of the responsive pulse signal. The equivalent circuit is the same as Fig. 6(a). The circuit equation is listed as ⎧ ⎨ U1 (t) = i(t)Rp + i1 (t)R0 (14) U (t) = i1 (t)R0 = Lμ di2 (t)/dt ⎩ 2 i(t) = i1 (t) + i2 (t).

⎧ 0, t≤0 ⎪ ⎨ λU {A exp(at)+[A cos(ωt)+(A b+A ) sin(ωt)/ω] exp(bt)} , 0 < t ≤ T0 s 1 2 2 3 i1 (t) = λU {A exp(at)+[A cos(ωt)+(A b+A ) sin(ωt)/ω] exp(bt)} ⎪ s 1 2 2 3 ⎩ −λUs {A1 exp [a(t−T0 )]+[A2 cos ω(t−T0 )+(A2 b+A3 ) sin ω(t−T0 )/ω] exp [b(t−T0 )]} , t > T0

⎧ 0, ⎪ ⎨ U [A cos(ωt) + (A b + A ) sin(ωt)/ω] exp(bt)}, 0 2 2 3 f1 (t) = U [A cos(ωt) + (A b + A ⎪ 0 2 2 3 ) sin(ωt)/ω] exp(bt)} ⎩ −U0 [A2 cos ω(t − T0 ) + (A2 b + A3 ) sin ω(t − T0 )/ω] exp [b(t − T0 )]},

t≤0 0 < t ≤ T0

(10)

(11)

t > T0

f2 (t) = U0 [A2 cos(ωt) + (A2 b + A3 ) sin(ωt)/ω] Authorized licensed use limited to: National Univ of Defense Tech. Downloaded on April 21,2010 at 00:57:40 UTC from IEEE Xplore. Restrictions apply.

(12)

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Fig. 10. Theoretical waveform of the flat top of the responsive voltage signal.

If the constants are defined as follows for short, (16) can be solved easily by Laplace transformation, and the output voltage signal U2 (t) of the load is figured out as (20) R0 R0 1 0 +R α1 = L Ll , β1 = Ll CD , γ1 = Ll Lμ CD μ (17) α2 = R0 [i(0) − i2 (0)] , β2 = RL0 Ul 0 , γ2 = − RL0liC2 (0) . D ⎧

3 3 Δ β1 +α1 γ1 α21 β12 γ2 α3 ⎪ 1 β1 ⎪ ξ = − 108 − α1 β61 γ1 + 41 − 3γ1 −α − 271 , ⎪ 1 27 6 ⎪ ⎪ 1 ⎪ ⎨ ω = √3 3β − α2 ξ −1 3 9 + ξ3 2 s

1

1

1

1

−1 1 ⎪ ⎪ ⎪ a1 = ξ13 − ξ1 3 3β1 − α12 /9 − α1 /3, ⎪ ⎪ −1 1 ⎪ ⎩ b1 = ξ1 3 3β1 − α12 /18 − α1 /3 − ξ13 /2

(18)

Fig. 11. Equivalent circuit of back-edge response.

The initial conditions are like this: i2 (0) = 0 and U2 (0) = R0 U1 (0)/(R0 + Rp ). Responsive voltage pulse U2 is figured out as R0 U1 (t) t U2 (t) = exp − , Rp + R0 τ Lμ (Rp + R0 ) , 0 < t < T0 . (15) τ= Rp R0 In (15), τ is the time constant of the flat top. τ increases when Lμ increases so that the flat top of U2 attenuates more slowly. If U20 takes the place of R0 Us /(Rp + R0 ) for short, the responsive curve of the flat top is shown as Fig. 10. If T0 is in the microsecond range, the amplitude of the flat top keeps the same when time varies. However, if T0 is in the millisecond range, time constant τ has great impacts on the amplitude of the flat top. In Fig. 10, the waveform of U2 likes a sawtooth pulse when T0 is 10 ms. The conclusion is that a larger Lμ can improve the transformer’s response to the flat top of the square pulse by increasing time constant τ . The Lμ value of the transformer in this paper is 11.9 μH, which is much larger than that in [1]–[5] and [11]–[13], and the longest responsive range of the flat top is 125 μs with an amplitude descent that is less than 5%.

α2 a21 + β2 a1 + γ2 B1 = (a1 − b1 )2 + ωs2 α2 a21 + β2 a1 + γ2 B2 = α2 − (a1 − b1 )2 + ωs2 2 α2 a1 + β2 a1 + γ2 b21 + ωs2 γ2 − B3 = a1 [(a1 − b1 )2 + ωs2 ] a1 ⎧ U2 (t) = B1 exp(a1 t) + exp(b1 t)

⎪ ⎪ ⎪ ⎨ × B2 cos(ωs t) + B2 bω1 s+B3 sin(ωs t) f3 (t) = B1 exp(a1 t), ⎪ ⎪ ⎪ ⎩ f (t) = exp(b t) B cos(ω t) + 4 1 2 s

B2 b1 +B3 ωs

sin(ωs t) .

(19)

(20)

If B1 + B2 = U0 , according to (20), U2 (t) still consists of an exponential attenuated part f3 (t) and an attenuated resonant part f4 (t). U2 (t), f3 (t), and f4 (t) are shown in order as curves 1, 2, and 3 in Fig. 12(a). If the time of the back edge of the pulse is t2 and the angular frequency of resonance is ωs , t2 = ωs /π. When magnetization inductance Lμ changes from 1 μH to 1 mH while other distributed parameters keep the same, the responsive voltage curves of the back edge are shown as Fig. 12(b). In view of the fact that the voltage curves are nearly in superposition, Lμ is not the main factor that impacts backedge response. From Fig. 12(c) and (d), it can be concluded that the time of the back edge of the pulse increases obviously when leakage inductance Ll and distributed capacitance CD increase.

C. Response to the Back Edge of Square Pulse

D. Experiments of Time-Domain Response of Pulse Transformer

When the time of the flat top is over (defined as t = 0), there is no longer any pulse-generating source, while all the reactance components in Fig. 8 have stored electromagnetic energy. However, the electromagnetic energy must be delivered to the load in complicated resonant processes, which lead to fierce resonances at the back edge of the output voltage pulse. The equivalent circuit is shown in Fig. 11. Ll represents the leakage inductances of the windings. The initial voltage of CD and the initial currents of Ll and Lμ are U0 , as well as i(0) and i2 (0) in order, respectively, which are all decided by the flat top of the pulse. The circuit equation is like this U0 − i(t)dt/CD = Ll di(t)/dt+i1 (t)R0 (16) U2 (t) = i1 (t)R0 = Lμ di2 (t)/dt, i(t) = i1 (t)+i2 (t).

The miniature pulse transformer with closed magnetic core has been used to respond square pulses with different pulsewidths, which vary from the microsecond to the millisecond range. Square voltage pulses (−10 mV) were sent to the primary winding of the transformer, and the responsive voltage signal was exported from the secondary winding to the oscilloscope. The terminal of the oscilloscope is a 50-Ω resistor, which was also used as a load resistor. The amplitude of the source square pulse was set as −10 mV. When T0 was 2 μs, 5 μs, 50 μs, and 10 ms, responsive voltage waveforms are shown in Fig. 13. When T0 was 2 μs, the waveform in Fig. 13(a) was similar to curve 1 in Figs. 9 and 12(a). Parasitic resonant fluctuations



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Fig. 12. Theoretical waveforms of back-edge analyses. (a) Theoretical waveform of the back edge of the responsive voltage signal. (b) Impacts of Lμ on back-edge response. (c) Impacts of Ll on back-edge response. (d) Impacts of CD on back-edge response.

Fig. 13. Responsive voltage waveforms of the pulse transformer. (a) Responsive voltage waveform when T0 was 2 μs. (b) Responsive voltage waveform when T0 was 5 μs. (c) Responsive voltage waveform when T0 was 50 μs. (d) Responsive voltage waveform when T0 was 10 ms.

appeared at the front and back edges of the responsive voltage pulse. The flat top was so short that the resonances had great impacts on the pulse waveform. When T0 was 5 μs, the adverse impacts of resonances on the flat top were less obvious, and the waveform was better than the situation of shorter pulses. When T0 increased to 50 μs, the responsive voltage waveform

was nearly a square pulse except for the resonances at front and back edges. The amplitude of the flat top was 1 V, and the step-up ratio was 1:100. However, if T0 > 100 μs, the inclining deformation of the flat top became obvious with an amplitude descent that is more than 5%. When T0 was changed to 10 ms, the flat top of the responsive waveform became a


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Fig. 16. Fig. 14. High-voltage nanosecond-pulse generator system.

High-voltage square-pulse amplifier system for DBD applications.

voltage pulse with an amplitude of 165 kV, a rise time of 6.5 ns, and an FWHM of 68 ns. B. High-Voltage Square Pulse Amplifier

Fig. 15. Output waveform of the pulse generator.

descending slope, and the voltage signal was a sawtooth pulse, which corresponded to Fig. 10. From the perspective of good flat top, that experimental results showed that the pulse transformer developed in this paper can respond well to square voltage pulses with a pulsewidth ranging from 5 to 100 μs. The transformer can also respond voltage pulses with a pulsewidth ranging from 100 μs to 10 ms, but the descent distortion of the flat top was obvious. A useful method of eliminating harmful resonance is to add damped resistors in parallel with the load resistor, and its detailed principle will be analyzed in successive papers.

The experimental results in Figs. 4 and 13 show that the pulse transformer can respond to not only sinusoidal pulses (Section II) but also to square pulses (Sections III and IV) with a step-up ratio of 1:105 and a frequency band ranging from 100 Hz to 500 kHz. Because the pulse transformer with closed magnetic core has the advantages of small-sized volume, high step-up ratio, high-voltage outputs, wide responsive frequency band, low cost, and good stability, it is valuable for DBD applications [23]–[25]. The structure of the DBD system is shown in Fig. 16. The system consists of a square-pulse source, a square-pulse transformer, DBD electrodes, and an ICCD camera. The lowvoltage square-pulse source delivers 1-kV-range pulses to the transformer with a pulsewidth in the microsecond range. Resistor R and diode D1 protect the pulse source. The pulse transformer with a step-up ratio of 1:105 can produce a highvoltage square pulse for DBD electrodes with a pulse amplitude of 100 kV and a rise time of 500 ns. At the same time, the ICCD camera controlled by the controller takes photographs on the discharge process between the electrodes. If the low-voltage square-pulse source can deliver pulses at different frequencies, DBD electrodes can work at repetitive mode. Because no pulseforming lines and spark gaps are used in the system, the system can be minimized to be a portable device.

V. A PPLICATIONS A. High-Voltage Nanosecond Pulse Generator In view of the fact that the amplitude of the output voltage pulse of the small pulse transformer can reach as high as 210 kV, the pulse transformer was used to construct a smallsized high-voltage nanosecond-pulse generator, according to the experimental analysis in Section II. The generator system is shown in Fig. 14. It consists of this kind of pulse transformer with closed magnetic core, curled parallel strip pulse-forming line, spark gap, and load resistor. The output voltage and current waveforms of the matched load of the generator are shown in Fig. 15. The amplitude of the output voltage pulse was 84 kV, the rise time was 5.1 ns, and the full-width at half-maximum (FWHM) was 9 ns. When load resistance was changed to 50 Ω, the load resistor can deliver a

VI. C ONCLUSION A miniature pulse transformer with closed magnetic core has been developed in this paper. The output characteristics of the transformer, including the frequency response and the time-domain response, are analyzed by theoretical calculations, circuit simulations, and experiments. The distributed capacitances, leakage inductances, and magnetization inductance of the transformer have great impacts on the responsive pulse shape. Through special winding structures, the responsive characteristics have been improved. The experimental results show that the transformer can produce a high-voltage pulse with an amplitude of 210 kV. The transformer responds well to square pulses with 500-ns rise time. The responsive frequency band ranges from 100 Hz to 500 kHz, and the responsive pulsewidth



ranges from 5 to 100 μs with an amplitude descent that is less than 5%. By using this pulse transformer, a small-sized repetitive high-voltage pulse amplifier has been designed for DBD applications. At present, this kind of transformer is also used for the application of the high-voltage nanosecond pulse generator in our laboratory.

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Yu Zhang was born in Chongqing, China, in 1984. He received the B.S. and M.S. degrees in physical electronics from the National University of Defense Technology, Changsha, China, in 2007 and 2009, respectively, where he is currently working toward the Ph.D. degree in the College of Opto-electronic Science and Engineering. His research interests include pulsed-power and measurement systems.

Jinliang Liu was born in Hunan, China, in 1964. He received the B.S. degree from Hunan University, Changsha, China, in 1990, the M.S. degree from the University of Electronic Science and Technology of China, Chengdu, China, in 1995, and the Ph.D. degree from Tsinghua University, Beijing, China, in 2008. As a Professor with the College of Opto-electronic Science and Engineering, National University of Defense Technology, Changsha, his research works focus on pulsed-power systems and microwave radiation.

Xinbing Cheng was born in Sichuan, China, in 1983. He received the B.S. degree in applied physics from Huazhong University of Science and Technology, Wuhan, China, in 2006 and the M.S. degree from the National University of Defense Technology, Changsha, China, in 2008, where he is currently working toward the Ph.D. degree in the College of Opto-electronic Science and Engineering. His research works are mainly focused on pulsedpower systems.

Hongbo Zhang received the B.S. degree from the National University of Defense Technology, Changsha, China, in 2008, where he is currently working toward the M.S. degree in the College of Opto-electronic Science and Engineering. His research work is focused on pulse transformers.

Guoqiang Bai was born in Hebei, China, in 1981. He is currently working toward the M.S. degree in engineering in the College of Opto-electronic Science and Engineering, National University of Defense Technology, Changsha, China. His research work is mainly focused on pulsedpower technology.
