Abstract: Soft-switching series resonant capacitor topologies are used for charging high-voltage capacitors due to their constant average charging current and strong short-circuit withstand capability over a wide voltage range. However, the constant current characteristic of a series resonant charging power supply with a fixed switching frequency is not constant due to fluctuations in the DC bus voltage and the distributed capacitance of the high-voltage transformer and rectifier unit. This paper analyzes the charging current characteristics of ideal and practical series resonant charging power supplies. A graphical method for parameter design and debugging of series resonant power supplies is proposed, overcoming the blind spots in the design and debugging of previous high-voltage pulse power supplies, and possessing significant engineering practical value. Keywords: Power engineering, series-parallel resonant parasitic parameters, constant current capacitor charging power supply (CCPS) Introduction With the development of pulse power technology, the demand for high-voltage pulse power supplies is becoming increasingly widespread and numerous. Under a fixed switching frequency, the ideal series resonant charging topology is widely used for charging high-voltage capacitors due to its constant average charging current over a wide voltage range and strong load short-circuit withstand capability. However, the series resonant charging current in actual devices is not constant, mainly due to: ① changes in the DC bus voltage during charging; ② distributed capacitance in the transformer; and ③ inter-electrode capacitance in the high-voltage rectifier. This presents challenges for parameter design and equipment debugging. Currently, debugging is typically achieved by continuously changing the resonant parameters until a suitable resonant parameter is found, resulting in a long debugging cycle and unnecessary waste of manpower and resources. There are very few reports on the influence of distributed capacitance both domestically and internationally. Literature mentions that the charging current decreases as the output voltage increases due to the influence of distributed capacitance, but this has not been studied in depth. The literature (Bowles EE, Chapelle S. A high power density, high voltage powersupply for pulsed rada system[C]. The 21st International Power Modulator Symposium, 1994: 170-173.) implemented a series-parallel resonant CCPS, but did not conduct a detailed study of the circuit's operating characteristics. This paper studies the current characteristics of an ideal series resonant capacitor charging power supply and a practical series resonant capacitor charging power supply. It analyzes the influence of parasitic parameters of the high-voltage transformer and high-voltage rectifier diodes in the charging system. An equivalent circuit is used to describe the complex parasitic capacitances in the transformer and diodes, which can be measured experimentally. The paper points out that due to the presence of parasitic capacitances in the transformer and diodes, the designed high-voltage series resonant charging power supply becomes a high-voltage series-parallel resonant charging power supply, and its charging current is not constant. The paper systematically analyzes the soft-switching series-parallel resonant CCPS, deriving some of its inherent important characteristics. A valuable chart is also provided, enabling rapid design of resonant parameters, replacing the previous method of repeatedly changing resonant parameters and conducting continuous experiments to design and debug high-voltage charging power supplies. A 25kW high-voltage pulse power supply system is used as an example to verify the effectiveness of the chart method. Operating Characteristics of an Ideal Series Resonant CCPS The main circuit topology of the high-voltage capacitor charging power supply is shown in Figure 1. The transformer turns ratio is n, L is the resonant inductance, C1 is the resonant capacitance, TS is the switching period, T1 is the resonant period, fS is the switching frequency, TS>2T1, and the switching transistor operates in a soft-switching state. In all series resonant CCPS, let Co and Vco be the charging capacitance and charging voltage, respectively, and n2Co>>C1 holds true. The average charging current is given by equation (1). It can be seen that when Vin, L, C1, and fS are constant, the average charging current is constant, and the capacitor voltage rises linearly. However, in actual devices, since the transformer and high-voltage rectifier diode are not ideal devices, the transformer has distributed capacitance, and the high-voltage rectifier diode also has inter-electrode capacitance. Therefore, the average charging current of the open-loop controlled series resonant CCPS is not constant, and the voltage rise curve is not linear. The distributed capacitance of the actual series resonant CCPS high-frequency step-up transformer and high-voltage rectifier diode has a significant impact on the operating state of the charging current and cannot be ignored. The distributed capacitance of the transformer is quite complex. In high-frequency high-voltage step-up transformers, to reduce transformer size and leakage inductance, a core with high permeability, such as microcrystalline alloy material, is usually used, and the number of turns on the primary side of the transformer is small. To reduce the coupling between the primary and secondary sides of the transformer, a shielded winding is usually provided; thus, the influence of the primary side distributed capacitance and the primary and secondary side distributed capacitance can be ignored. The excitation reactance of the transformer is relatively large, and its influence can also be ignored. Therefore, the actual series resonant capacitor charging circuit can be equivalent to the circuit shown in Figure 2. It can be seen that the actual circuit becomes a series-parallel resonant charging circuit. Unlike series resonant CCPS, the resonance process of series-parallel resonant CCPS is related to the input voltage, charging capacitor voltage, series resonant inductance, series resonant capacitor, and parallel resonant capacitor. Therefore, there are multiple operating conditions in half a switching cycle, and different operating modes exist under each operating condition. The resonant frequencies of each operating mode are also different, and its operating process is much more complex than that of an ideal series resonant CCPS. Because the resonant frequency and switching frequency are relatively high, the voltage change of the charging capacitor is very small during one resonant cycle. Therefore, the series-parallel resonant charging during one resonant cycle can be equivalent to series-parallel resonant charging with a constant output voltage. Let Vo be the equivalent voltage of the charging capacitor to the primary side of the transformer. Based on the presence or absence of the charging current during one resonant cycle, there are three cases. Before analysis, the following variables are defined: Case 1: The charging current exists in both positive and negative resonant cycles, resulting in the following three operating modes. Mode 1: Q1 and Q3 are turned on, v2(t0) = Vo, rectifier diodes D5 and D7 are turned on, resonant current i > 0, charging current io = i. The equivalent circuit of this mode is shown in Figure 3(a). The voltage and current equations are: When the series resonant current is 0 (i.e., at time t1), this mode ends, and the following expression can be obtained: Mode 2: When i(t1) = 0, the resonant current starts to reverse i < 0 and passes through diodes D1 and D3. In freewheeling mode, all rectifier diodes are in the off state, and the charging current i_o = 0. Its equivalent circuit is shown in Figure 3(b). The voltage and current equations are: When v₂(t₂) = -V_o, this mode ends, and the following expression can be obtained: Mode 3: From v₂(t₂) = -V_o, the resonant current i_o < 0, and the freewheeling diodes D₁ and D₃ are still in the freewheeling conduction state. In this stage, v₂(t₂) = -V_o, and the rectifier diodes D₆ and D₈ are conducting, and the charging current i_o = -i, its equivalent circuit is shown in Figure 3(c), the current and voltage equations are: when i(t3) = 0, this mode ends, and the following expression formula is given. The critical condition for the circuit to work in this case should satisfy equations (22) and (23). Therefore, the condition for satisfying case 1 is V[sub]o[/sub] 0, charging current i[sub]o[/sub]=0, the equivalent circuit is shown in Figure 4(a). Mode 2: When v[sub]2[/sub](t[sub]1[/sub])=V[sub]o[/sub], rectifier diodes D[sub]5[/sub] and D[sub]7[/sub] are turned on, i[sub]o[/sub]=i, its equivalent circuit is shown in Figure 4(b). Mode 3: When the resonant current i(t[sub]2[/sub])<0, freewheeling diodes D[sub]1[/sub] and D[sub]3[/sub] are turned on, rectifier diodes are turned off, i[sub]o[/sub]=0, the equivalent circuit is shown in Figure 4(a). Following the analysis of case 1, the following conclusions can be drawn: (1) The condition for working in this case is V[sub]in[/sub]/(k+1). 2V_in/(k+1), the charging current is zero. Based on the analysis of the above three cases, the series-parallel resonant CCPS has the following properties: (1) When k is constant, the relationship with the change of V_o/V_in is the same; (2) The charging voltage can reach up to 2V_in/(k+1). Based on the above properties, the curves of the change of V_o/V_in under different k values ​​can be obtained through simulation, as shown in Figure 6. This figure can be used for resonant parameter design and debugging. The k values ​​of the curve from top to bottom are: 0; 0.02; 0.05; 0.1; 0.2; 0.3; 0.4; 0.5; 0.6; 0.7; 0.8; 0.9; 1.0; 2.0; 3.0; 4.0; 6.0; 8.0; 19.0. From Figure 6, the following conclusions can be drawn: (1) For open-loop controlled series-parallel resonant CCPS, the charging current decreases as the output voltage increases, and the average charging current is not constant; (2) When V_o/V_in is the same, as k increases, the value of k decreases. To increase the charging current at high voltage, it is necessary to decrease the value of k; (3) When k is the same, V_o/V_in decreases as V_o/V_in increases; (4) The highest output voltage is 2V_in/(k+1). When k>1, the output voltage cannot reach the input voltage. Design Examples and Experiments Based on Figure 6, the resonant parameters can be easily designed and the equipment can be debugged. Design requirements: 2560µF charging capacitor, input voltage 380V±10%, adjustable charging voltage from 0 to 25kV, constant charging current 1A. Based on the input and output voltages, a transformer ratio of n=60 is selected. To ensure a constant average charging current throughout the charging process, maintaining 1A even at 25kV, closed-loop control is necessary. The principle of the closed-loop design is: at the highest permissible switching frequency, the average charging current should still reach the required constant charging current value at the highest output voltage. The equivalent distributed capacitance of the transformer and rectifier diodes referred to the primary side was measured to be 0.155µF, the leakage inductance of the transformer was 3µH, the maximum switching period was set to 60µs, the frequency modulation range was 11.8kHz～16.7kHz, and the design steps of the resonant parameters were as follows: (1) Design the resonant capacitance required for T[sub]S[/sub]=2T[sub]1[/sub] under the ideal series resonance CCPS using equation (1), and obtain C[sub]1[/sub]=0.9µF. (2) Calculate the charging current at the maximum V[sub]o[/sub]/V[sub]in[/sub], V[sub]o[/sub]/ Vin =0.9, k=0.17, and from Figure 6, we can obtain that the charging current is 0.44A at this time. (3) Adjust the resonant capacitor, select C1 = 1.55µF, then k = 0.1, and the maximum charging current under Vo/Vin is calculated to be 1.09A, which meets the requirements. From this, the resonant inductance L = 14.7µH can be calculated. Considering the line voltage drop and ensuring that the circuit works in soft switching mode, the resonant inductance is appropriately reduced, and L = 13.2µH (including transformer leakage inductance) is selected. An experiment was conducted based on the resonant parameters designed above, and the experimental waveform is shown in Figure 7. It can be seen that in order to keep the charging current constant, the switching frequency increases with the increase of the output voltage. The converter efficiency is 92.7% when the measured charging voltage is 23kV. The experiment shows that the designed resonant parameters fully meet the design requirements, and the device has been used in the Shenguang III energy system. Conclusion The effects of transformer distributed capacitance and high-voltage rectifier diode inter-electrode capacitance in a series resonant capacitor charging power supply were analyzed. It was concluded that when the ratio of distributed capacitance to resonant capacitance is the same, the charging current characteristics are identical. A graphical method for designing and adjusting resonant parameters was proposed, and the graphical method was provided. The results were verified through example design and experiments.