Abstract: The theory and testing of intrinsically safe circuits are closely related to electrical discharge. Since the output of a switching power supply has a large capacitance, it significantly affects the intrinsically safe output of the power supply. Therefore, it is necessary to further study the discharge characteristics of capacitive circuits. Keywords: Electrical discharge; Discharge characteristics; I-V characteristics. The theory and testing of intrinsically safe circuits are closely related to electrical discharge. Electrical discharge is considered a potential source of danger, such as short circuits, open circuits, or grounding. If the energy generated by the discharge during the opening and closing of the electrodes in a spark test device exceeds the ignition energy of the gas mixture, it will cause an explosion. Therefore, electrical discharge should be studied first, and the forms and laws of discharge should be analyzed. Since the output of a switching power supply has a large capacitance, it significantly affects the intrinsically safe output of the power supply. Therefore, it is necessary to further study the discharge characteristics of capacitive circuits. Furthermore, with the increase in operating frequency, the inductors used in switching power supplies are becoming smaller, usually less than 1mH (intrinsically safe theory considers circuits with an inductance of less than 1mH to be resistive circuits). The filter capacitor at the output of the switching power supply has a significant impact on the intrinsically safe output of the power supply. From the load side, the switching power supply is a capacitive circuit. Therefore, it is necessary to study the intrinsically safe performance of switching power supplies. First, it is necessary to understand the discharge process of a capacitor and analyze its discharge patterns. [b]I. Intrinsically Safe Forms of Electrical Discharge[/b] Circuit theory and testing are closely related to electrical discharge. When points considered to be potentially dangerous, such as short circuits, open circuits, or grounding, are opened or closed at the electrodes of a spark test device, the energy generated by the discharge, if exceeding the ignition energy of the gas mixture, will cause an explosion. Therefore, electrical discharge should be studied first, and the forms and patterns of discharge should be analyzed. According to gas discharge theory, there are three basic forms of discharge during circuit switching: spark discharge, arc discharge, glow discharge, and a mixed discharge composed of these three forms. Spark discharge generally occurs when connecting and disconnecting intrinsically safe circuits with capacitors, due to the breakdown of the discharge gap. The spark discharge process can be divided into three main stages: The first stage is the spark formation stage, which begins when an external voltage is applied and ends when the gap is broken down. During this stage, the current in the spark band is small, and the voltage applied to the discharge gap is relatively stable. The duration is short, about 10 seconds. At the end of the spark formation stage, a conductive band is formed. The second stage begins when all the charge on the capacitor flows along the formed spark band, heating it to 10,000–20,000°C. The voltage on the gap drops rapidly to a very small value, while the current can reach a maximum value of 10²–10⁴ amps. From the end of this stage, the capacitor continues to discharge, and the resistance of the discharge gap drops from its maximum initial value to a very small final value. The third stage (the reduction stage) is when the spark band is destroyed. This is caused by the thermal radiation of the high-temperature spark band being absorbed by the surrounding gas layer, causing the spark band to widen. These three processes are completed in a very short time of about 10⁻⁶ to 10⁻⁸ seconds. The energy released by spark discharge mainly consists of two parts: the energy lost in the discharge electron beam and the energy conducted to the electrode surface. The size of the latter determines whether the discharge can ignite an explosive gas mixture. Clearly, sparks with low energy conduction on the electrode surface but high energy loss in the discharge electron beam are more easily ignited. Arc discharge is a frequently studied form of discharge in intrinsically safe theory. When switching between low-current, low-voltage intrinsically safe circuits, arc discharge occurs due to the breaking of the liquid metal bridge. The formation of the liquid metal bridge is as follows: at the instant the contacts break, the contact pressure drops sharply, the electrode contact area decreases, and the transition resistance increases. When the current and voltage on the electrodes reach values ​​corresponding to the melting of the contact point, a liquid metal droplet forms between the electrodes. As the electrodes continue to separate, the liquid metal droplet is stretched into a bridge connecting the two electrodes. As the voltage on the bridge increases, the metal boils, causing the bridge to break explosively. Metals with low melting points easily form liquid bridges, and their boiling temperature is also low, resulting in a smaller current required to break the bridge compared to refractory metals. Cadmium, with its relatively low melting point, is used in the spark test apparatus and easily forms an arc. Glow discharge can occur when the voltage is very high and the current is relatively small. A characteristic of glow discharge is that its cathode voltage drop is higher than that of arc discharge, reaching 100–400 volts. Therefore, the discharge energy is essentially dissipated at the electrodes, rather than being used to ignite the hazardous mixture. Furthermore, glow discharge is very rare in practical safety circuits, so this situation is generally not considered. Analysis of the three types of discharge shows that in intrinsically safe circuits, spark discharge and arc discharge require much less energy to ignite a flammable mixture than glow discharge. Therefore, spark discharge and arc discharge are the main forms of discharge in intrinsically safe circuits and are the main factors igniting flammable mixtures. [b]II. Characteristics of Capacitive Discharge[/b] Capacitors have the characteristic that the voltage across their terminals cannot change abruptly, unlike inductive and resistive circuits. Spark discharge in capacitive circuits occurs when the electrode contacts are closed, and does not occur when the contacts are open. 1. Analysis of the Discharge Process in Capacitive Circuits Capacitors are energy storage elements that can store the energy of a power source in the form of electric field energy. When the circuit is closed, both the power supply discharges to the electrode gap and the capacitor discharges stored energy, primarily in the form of sparks and arcs. Since the charging resistance R0 is very large, the influence of the power supply on the capacitor discharge can be ignored. At the instant the capacitor discharges, the discharge current is extremely large, and the discharge is extremely rapid (the discharge time constant i=RC is very small), resulting in highly concentrated energy and a high degree of danger. The discharge process of a capacitive circuit can be artificially divided into three stages: the first stage is the spark discharge stage. Initially, the electrode contacts are in an open state. When the electrodes close (t=t0), the voltage between the contacts breaks down the discharge gap, generating a spark. The gas along the light-emitting channel is broken down and becomes a good conductor, the current rises rapidly, and the voltage between the electrodes drops rapidly from the open-circuit voltage, exhibiting a significant negative impedance characteristic. At this time, a popping sound can be heard, caused by the rapid rise in temperature and the outward expansion of the increased pressure in the discharge channel. After the discharge current reaches its maximum value, it begins to decrease, and the discharge voltage drops according to a certain pattern. When it drops to the discharge sustaining voltage, the second stage begins, namely the discharge sustaining stage. In this stage, the discharge channel expands to configurational equilibrium, the internal pressure is balanced by the self-generated magnetic field constraint force, and the voltage between the electrodes remains almost constant. Its magnitude is related to the electrode material (e.g., 15V for tungsten, 11V for cadmium, generally referred to as the discharge sustaining voltage). The duration of this stage depends on the closing speed of the electrodes. The third stage is the end of the inter-electrode discharge and the complete closure of the electrodes. The electrodes are closed by external force, and the inter-electrode voltage drops from the discharge sustaining voltage to zero. Due to the release of residual energy in the capacitor, the current peaks, but the electrodes are already closed, and the energy is mainly absorbed by the resistance in the circuit. 2. Spark Discharge Power and Energy in Capacitive Circuits When an electric spark ignites a flammable gas mixture, in addition to the discharge energy parameter, the instantaneous discharge power must be considered. The discharge must have both appropriate energy and appropriate power to ignite the gas mixture. Strictly speaking, only when the discharge power is quite large and an appropriate amount of energy is released will the flammable gas mixture be ignited. If the spark power of the discharge is quite small, it is difficult to ignite even though the discharge duration is long. This paper examines the energy and power waveforms of spark discharge. Based on the spark discharge current and voltage, the spark discharge energy and power curves are obtained. The spark discharge power waveform is quite similar to the discharge current waveform. After the discharge gap is broken down, the instantaneous power of the discharge reaches its maximum value almost simultaneously with the discharge current. During the discharge process of the capacitor circuit, the energy released in the discharge maintenance stage and the discharge end stage is very small. The first stage of the discharge—spark discharge—is the main energy source for igniting flammable hazardous mixtures. It can also be seen that the closed discharge of the capacitive circuit has the characteristics of rapid voltage change, short duration, large current change, and concentrated discharge energy. Therefore, this type of discharge is relatively easy to ignite mixed gases. 3. I-V Characteristics of Spark Discharge in Capacitive Circuits To analyze the discharge characteristics of the intrinsically safe DC capacitive circuit, we first analyze its I-V characteristics. Through experiments, a large number of spark discharge voltage and current waveforms under various circuit parameters are measured, and then the corresponding spark discharge I-V characteristic curves are plotted based on the voltage and current data. These current-voltage characteristic curves have the same characteristics: during the process of the current rising to the peak value of the corresponding spark discharge, the current increases rapidly and the voltage drops due to the breakdown of the discharge gap at this time, and the circuit shows a significant negative impedance state; the process of the spark current decreasing from the peak value to zero and the voltage decreasing to the discharge sustaining voltage shows the current-voltage characteristics of ordinary resistors. And both processes can be approximated as straight lines. In the current rising stage, the spark voltage decreases as the spark current increases; in the current falling stage, the spark voltage also gradually decreases as the spark current decreases. The spark discharge gap resistance in the spark discharge stage can be obtained from the spark discharge voltage and current waveforms. The spark discharge gap resistance in the spark discharge stage is like a concave curve. The resistance is relatively large in the reduction stage when the discharge gap just breaks down and the spark band is destroyed during discharge, and the resistance value is small and relatively constant in the stage when the spark discharge forms the conduction band. When the spark current rises to the maximum peak value, the spark discharge resistance drops to the minimum value. It has been experimentally measured that this value is very small, generally only a few tenths of an ohm. References: [1] Jia Xiangzhi. Current Status and Development Trend of DC Regulated Power Supply in Coal Mines [J1, Coal Mine Design, 1998(9): 34-36. [2] Zhang Yanmei, Li Weijian. Intrinsically Safe Circuit Design [M]. Beijing: Coal Industry Press, 1992. [3] B. C. Zarafchink, translated by Zhang Bingjun. Safe Spark Circuits [M]. Beijing: Coal Industry Press, 1981. Click to download: Research on Discharge Characteristics of Capacitive Circuit of Intrinsically Safe Power Supply.