Abstract: With the increasing demand for high-frequency operation, the influence of transformer distributed parameters has become increasingly significant. Starting from the equivalent circuit of high-frequency operation, this paper conducts a detailed theoretical analysis and simulation verification of the influence of distributed parameters on switching transformers. Several measures to reduce distributed parameters in the design and winding of transformers are proposed. The simulation results show the specific implementation of a high-frequency soft-switching circuit that uses distributed parameters as part of the resonant element. Keywords: high-frequency transformer; distributed parameters; equivalent circuit 1. Introduction Traveling wave tube amplifiers (TWTAs) have advantages such as wide bandwidth, high gain, and high efficiency, and are widely used in microwave communication, radar, and electronic countermeasures. TWTAs consist of a space traveling wave tube (TWT) and an electronic power regulator (EPC). EPC[1,2] is a complex and special electronic device composed of a large number of electronic components and high-voltage components. It consists of functional modules such as command circuits, telemetry circuits, converters, and protection circuits. Theoretical analysis and practical experience show that the volume and weight of transformers, inductors, and capacitors in electrical products are inversely proportional to the square root of the power supply frequency. Therefore, the most direct way to achieve circuit miniaturization and weight reduction is to increase the switching frequency. Due to the limited carrying capacity of rockets, strict restrictions are imposed on the volume and weight of spaceborne EPCs. Therefore, it is necessary to increase the frequency to meet the requirements of small volume and light weight. High-frequency transformers can also be called pulse transformers or switching transformers. The differences between them and ordinary transformers are roughly as follows: (1) The power supply voltage is not a sine wave, but an AC square wave, and the current in the primary winding is non-sine wave; (2) The operating frequency of the transformer is relatively high, usually in the tens of kilohertz, or even as high as hundreds of thousands of hertz. When determining the core material and losses, it is necessary to consider the need to meet the high-frequency operation and the influence of high-order harmonics in the core. 2. Equivalent circuit of transformer In general theoretical analysis, in order to simplify the analysis process, the magnetizing inductance and leakage inductance of the power transformer are usually ignored in order to obtain the basic principle and basic characteristics of the circuit operation. In fact, parasitic parameters exist objectively, and the influence of distributed parameters becomes more serious as the switching frequency increases. (1) Magnetizing inductance Since the permeability is finite, there is an excitation current in the primary winding. This increased current can be represented by adding a magnetizing inductance Lm in parallel with the primary coil in the equivalent circuit. The magnetizing inductance energy represents the energy stored in the core with finite permeability and the air gap at the junction of the two halves of the core. The stored energy is related to the volts per turn applied to the coil and is independent of the load current. (2) Leakage inductance In a real transformer, if the magnetic flux between the primary and secondary, between turns, and between layers is not fully coupled, leakage inductance will occur. The leakage inductance energy represents the energy stored in the space through which the uncoupled magnetic flux between the coils passes. In the equivalent circuit, the leakage inductance is connected in series with the excitation coil of the ideal transformer, and its stored energy is proportional to the square of the excitation coil current. (3) Distributed capacitance There is distributed capacitance in the windings of a real transformer, especially between the coil conductors and the transformer core and between the windings. The size of the capacitance depends on the geometry of the winding, the dielectric constant of the core material, and its encapsulation material. In the equivalent circuit, a concentrated capacitor is connected in parallel across each ideal coil. Taking all the above factors into account, the general equivalent circuit of the transformer can be derived, as shown in Figure 1. Where Rp and Rs represent the winding resistances of the primary and secondary sides, Llp and Lls represent the leakage inductances of the primary and secondary sides, Lm represents the magnetizing inductance, Cdp and Cds represent the distributed capacitances of the primary and secondary sides, and Rc represents the core loss, including hysteresis loss and eddy current loss. The secondary leakage inductance, secondary winding resistance, and secondary distributed capacitance are respectively referred to the primary side, and the primary and secondary leakage inductances, winding resistances, and distributed capacitances are grouped into a single term, resulting in the simplified equivalent circuit shown in Figure 2. Let the number of turns on the primary side of the transformer be N1, the number of turns on the secondary side be N2, and the turns ratio be n (n=N2/N1), then R=Rp+ Rs/n², Cd=Cdp+ n²Cds, Ll=Llp+ Lls/n². [align=center] Figure 1 General equivalent circuits of transformer Figure 2 Simplified equivalent circuits of transformer[/align] 3. Theoretical analysis of the influence of distributed parameters of transformer Since the input of high frequency transformer is AC square wave, the following will explain the pulse leading edge, pulse top, and pulse trailing edge[3]. (1) Pulse leading edge At the pulse leading edge, time changes very quickly, so strong current and voltage changes are generated on the leakage inductance and distributed capacitance. For the instantaneously changing input voltage, the impedance of the open circuit inductor on it tends to infinity and can be ignored. Assume that the winding resistance and core loss resistance are ignored. Thus, the rising edge equivalent circuit shown in Figure 3 is obtained. Calculate the current at node X and obtain the second-order differential equation by taking the reciprocal of its equation. [align=center] Figure 3 Equivalent circuits of ascending edge[/align] (2) At the pulse top, the voltage and current remain basically unchanged during the pulse duration. Therefore, the leakage inductance and distributed capacitance do not play a major role, and the magnetizing inductance plays an important role. Thus, the equivalent circuit of the pulse flat top shown in Figure 4 is obtained. Calculate the current at node X and obtain the first-order differential equation: The solution to this equation is: [align=center] Figure 4 Equivalent circuits of flat part[/align] (3) The leakage inductance at the pulse trailing edge is usually much smaller than the magnetizing inductance and can be ignored. At the pulse trailing edge, the magnetic energy stored in the magnetizing inductance and the electrical energy in the distributed capacitance are released. Therefore, the magnetizing inductance and distributed capacitance play a major role. Thus, the equivalent circuit of the pulse falling edge shown in Figure 5 is obtained. Calculate the current at node X to obtain the second-order differential equation: [align=center] Figure 5 Equivalent circuits of descending edge[/align] 4. Simulation Analysis of the Influence of Transformer Distributed Parameters Based on the above analysis, simulation was performed using PSPICE software. The parameters used are shown in Figure 6, and the simulation waveform is shown in Figure 7. [align=center] Figure 6 Schematic diagram of the simulation Figure 7 The waveform computed by PSPICE[/align] As can be seen from the simulation waveform in Figure 7, due to the existence of distributed parameters, there is an overshoot at the rising edge and an undershoot at the falling edge. Mutual inductance and leakage inductance energy cause voltage spikes during switching, resulting in increased losses and, in severe cases, damage to the switching transistor. It is also a major source of EMI, so it must be controlled. 5. Suppression and Utilization of Transformer Distributed Parameters 5.1 Suppression of Transformer Distributed Parameters Based on the causes of leakage inductance and distributed capacitance, the following measures can be taken to suppress them. (1) Methods to reduce leakage inductance: ① Reduce the number of turns of the winding and select magnetic materials with high saturation magnetic induction intensity and low loss; ② Reduce the thickness of the winding and increase the height of the winding; ③ Minimize the insulation thickness between the windings as much as possible; ④ The primary and secondary windings are layered and cross-wound; ⑤ The primary and secondary windings should be double-wired. (2) Methods to reduce distributed capacitance: ① Windings are segmented; ② The polarity of the windings is correctly arranged to reduce the potential difference between them; ③ Electrostatic shielding measures are adopted. 5.2 Utilization of distributed parameters of transformers In order to meet the miniaturization requirements and overcome the influence of distributed parameters, so that the switching converter can operate efficiently at high frequency, since the 1970s, high-frequency soft-switching technology has been continuously researched and developed at home and abroad [4]. Soft-switching technology makes good use of the distributed parameters in the circuit, and uses parasitic inductance and capacitance as part of the resonant element to eliminate the voltage spikes caused by distributed parameters. The resonant converter circuit shown in Figure 8 and the corresponding simulation waveforms given in Figure 9 illustrate the effect achieved by soft switching using distributed parameters in a more vivid way. [align=center] Figure 9 The waveform computed by PSPICE Figure 8 The resonant converter circuit[/align] 6. Conclusion When transformers operate at higher frequencies, many problems arise, such as increased iron and copper losses, and enhanced skin and proximity effects. Therefore, for different applications, transformers should be rationally designed according to different operating requirements to minimize leakage inductance and distributed capacitance, and increase magnetizing inductance, so that the transformer performance approaches ideal conditions. The author's innovation lies in: addressing the distributed parameter problem of high-frequency transformers through simulation analysis and proposing several measures to reduce distributed parameters during transformer design and winding. References: [1] Jerzy Dora, Jan Pyzik, Janusz Sobanski. TWTA power supply unit. Microwaves, Radar and Wireless Communications, 2002. MIKON-2002. 14th International Conference on Volume 2, 20-22 May 2002 Page(s): 693 – 696. [2] Neil Fraser. High Power Radar Transmitter Power Supplies for 500W to 1500W Transmitters. Power Electronics for Demanding Applications (Ref. No. 1999/059). [3] Shen Jian. The Influence of Parasitic Parameters and Magnetizing Inductance of Pulse Transformer on Pulse Waveform, Nanjing Fourteenth Research Institute [4] Chang Wenping, Fan Zheng, Wang Xiaomin. Online Monitoring System for Transformer Faults and Its Application, Microcomputer Information 2005(12): 125～127.