*3.2. Static Self-Breakdown Characteristics*

The three-electrode planar spark gap high-voltage switch based on copper foil, like other high-voltage switches, needs to have a specific operating voltage range; that is, the gap between the main electrode and the trigger electrode of the switch can withstand a certain high voltage without self-breakdown. Therefore, the self-breakdown voltage *USB* of the switch is also the maximum working voltage of the switch. The high voltage capacitor (0.2 μF) is slowly charged at a rate of about 20 V/s from the high voltage DC power supply, until the air in the gap between the two electrodes occurs self-breakdown. A high-voltage probe and Rogowski coil were used to record the self-breakdown voltage *USB* and loop current I changes. When the width *a* of the trigger electrode is 0.6 mm and the width *b* of the gap between the two main electrodes is 1.2 mm, the test waveform of the self-breakdown characteristic of the switch is shown in Figure 6a. The maximum operating voltage *USB* is 2361 V, and the maximum output current peak value is 2892 A. The *USB* test curves of different parameters of the plane spark gap switch by the orthogonal method are shown in Figure 6b.

**Figure 6.** Waveform and curve of self-breakdown characteristic of three-electrode planar switch. (**a**) Self-breakdown characteristic waveform (C = 0.2 μF) Figure. (**b**) Self-breakdown characteristic curve.

It can be seen from Figure 6.b that as the main electrode gap increases from 0.8 mm to 2.6 mm, the self-breakdown voltage of the planar spark gap switch gradually increases, and the operating voltage also increases. When the main electrode gap is a maximum of 2.6 mm, the self-breakdown voltage of the switch can reach 3480 V, which indicates that the maximum operating voltage of the switch is 3480 V. According to Thomson's theory and Baschen's law [24,25] of uniform electric field self-discharge under low pressure, the breakdown voltage USB of the air gap is related to the air pressure *p* and the main electrode gap *b*, and under the condition of a fixed gas atmosphere, the maximum operating voltage *USB* is positively correlated with b. By carrying out a large number of self-breakdown characteristic tests, it is shown that the self-breakdown voltage fluctuates greatly (the

range is about 180 V), and the larger the gap, the greater the fluctuation. According to the principle of electrostatic discharge, this is because the trigger electrode is right-angled, and tip discharge is prone to occur during the conduction process, which makes the field strength here larger, resulting in an increase in the unevenness of the electric field.

#### *3.3. Dynamic Operating Characteristics*

#### 3.3.1. Dynamic Minimum Trigger Voltage

In order to determine the conduction condition of the three-electrode planar spark gap high voltage switch with seven kinds of main electrode gaps, the three-electrode planar spark gap high voltage switch with main electrode gaps of 0.8 mm, 1.0 mm, 1.2 mm, 1.8 mm, 2.0 mm, 2.2 mm, and 2.6 mm are designed, and the trigger electrode widths are 0.6 mm and 0.8 mm, respectively. With the charging voltage of 2.0 kV, the minimum trigger voltage curves of various switch parameters are shown in Figure 7.

**Figure 7.** The curves of minimum trigger voltage varying with gap.

As shown in Figure 7, under the condition of charging voltage of 2.0 kV, as the main electrode gap increases from 0.8 mm to 2.6 mm, the minimum trigger voltage value of the planar spark gap switch increases from 677 V to 1783 V (*a* = 0.6 mm), 685 V rises to 1766 V (*a* = 0.8 mm). This shows that with the continuous increase of the main electrode gap, the minimum trigger voltage of the switch increases. With the same gap, the width of the trigger electrode is wider, the minimum trigger voltage becomes lower, for the reason that the conduction principle of the three-electrode planar spark gap high voltage switch is to apply pulse trigger voltage to the trigger electrode. Herein, the gap electric field is distorted and the air breakdown effect occurs between the gaps, making the two poles of the switch conduct. When the three-electrode planar spark gap high voltage switch is in the triggering state, the average electric field strength between the two poles is calculated as follows [26,27]:

$$E = \frac{\mathcal{U}\_{SB}}{b - a} \tag{1}$$

*E*: Average electric field, V/m;

*USB*: Working voltage, V;

*b*: Gap, mm;

*a*: Trigger electrode width.

As shown in Formula (2), under the condition of the same trigger electrode width, when the applied voltage *USB* between the two poles is constant, the average electric field strength *E* increases with the decrease of gap *b*, meaning that the smaller the gap between the two poles of the switch is, the greater the average electric field strength becomes, and the easier the air gas breakdown effect occurs, so the energy required for the trigger electrode is lower. On the contrary, the average electric field strength between the two poles of the switch is stronger and the energy required for the trigger is higher, when the switch is on. As shown in Formula (2), under the condition of the same gap, when the applied voltage *USB* between the two poles is fixed, the width of the trigger electrode is increased, the average electric field strength increases, and the air breakdown effect occurs easily, resulting in the lower energy required for the trigger electrode.

The matching test between the working voltage and the trigger voltage was carried out. The test results show that the relationship between the trigger voltage and the working voltage is inversely proportional. When the working voltage was high, the switch turned on easily, and the minimum trigger voltage was reduced. That is because when a relatively high voltage is applied between the two poles of the switch, the average electric field strength increases, and it is easier for breakdown effect to take place between the two poles of the switches, the trigger pole and air interface. Therefore, the required trigger energy will become low. The fitting curve of the relationship between the working voltage of the switch and the trigger voltage was shown in Figure 8.

**Figure 8.** Relation curves between trigger voltage and working voltage.

3.3.2. Switch Dynamic Conduction Performance

The time *ton* is the conduction time of the three-electrode planar spark gap high voltage switch. This is measured from the time when applying the trigger pulse voltage for the trigger electrode to the time when completely connection of the two poles of the switch and the oscillation current occurred in the discharge circuit. When the trigger electrodes are 0.6 mm and 0.8 mm, the trigger voltage is 1.8 kV, and the working voltage is 2.0 kV, the switch on-time *ton* test results of different gaps are 16 ns, 22 ns, 28 ns, 48 ns, 64 ns, 77 ns, and 93 ns (*a* = 0.6 mm) and 26 ns, 34 ns, 51 ns, 67 ns, 81 ns, and 102 ns (*a* = 0.8 mm). The test waveforms are shown in Figure 9.

**Figure 9.** The tested waveform of switch conduction performance (**a**) b = 0.8 mm, (**b**) b = 1.0 mm, (**c**) b = 1.2 mm, (**d**) b = 1.8 mm, (**e**) b = 2.0 mm, (**f**) b = 2.2 mm, (**g**) b = 2.6 mm.

In Figure 9, the tested waveform of the on-off performance of the switches can be seen. With the increasing gap, the on-off time of the switch becomes gradually longer, and the peak current of the discharge circuit is reduced. When the switch is on, the breakdown effect starts between the pulse trigger voltage and the strong electric field with the air interface, resulting in the electric field distortion between the two poles of the switches. A certain number of ions or electrons are generated instantaneously and move with a high speed under the electric field of the two poles of the switch. When the working voltage, trigger voltage, and the width of trigger electrode are fixed, with the increase of the switch gap, the average electric field strength between the two poles of the switch decreases, which

leads to the decrease of the velocity of ions or electrons generated when the switch is on, so that the on-time of the switch becomes longer. On the contrary, when the switch gap is low, with the increase of the average electric field, the average electric field strength between the two poles of the switch decreases, the velocity of ions or electrons increases and the on-time decreases. In addition, with the increase of the gap between the two poles of the switch, the average electric field strength between the two poles of the switch decreases. When the breakdown effect occurs between the trigger pole and the air interface, the energy loss is large, leading to a decrease in the peak current in the circuit. The regular curves between the trigger voltage and operating voltage of the switch and the on-time of the switch are shown in Figure 10.

**Figure 10.** Curve of factors affecting the conduction time of the three-electrode plane spark gap high-voltage switch. (**a**) Trigger voltage and on-time relationship curve. (**b**) Working voltage and on-time relationship curve.

## 3.3.3. Switch Dynamic Impedance and Inductive Reactance Characteristics

In order to realize the function of switching and disconnecting the narrow pulse current in the exploding foil initiation circuit, the high voltage switch not only has a higher turn-off impedance to reduce the power consumption of the exploding foil initiation system, but also has a lower conductive impedance and inductive reactance to improve the narrow pulse current output characteristics of the high-voltage pulse capacitor.

In principle, the initiation circuit of exploding foil can be equivalent to a RLC series circuit [28–30]. The parasitic resistance and inductance of the three-electrode planar spark gap high voltage switch can be calculated by measuring the waveform parameters of discharge oscillation current of the circuit with oscilloscope.

The formula of parasitic inductance is as follows.

$$L\_0 = L - l \tag{2}$$

$$L = \frac{\overline{T}^2}{4\pi^2 \overline{C}}\tag{3}$$

The formula of parasitic resistance is as follows.

$$R\_0 = R - r \tag{4}$$

$$R = \frac{2L}{\overline{T}} \ln \mathfrak{J}, \text{ among them, } \mathfrak{J} = \frac{\sum\_{j=1}^{n} \lambda\_j}{n}, \lambda\_j = \frac{I\_j}{I\_{j+1}} \tag{5}$$

*L*: Total inductance of discharge circuit, nH;

*l*: Load inductance, nH;

*R*: Total resistance of discharge circuit, mΩ;

*r*: Load resistance, mΩ;

*T*: The average period of oscillation, μs;

*Ij+*1, *Ij*: The value of forward oscillation current, kA;

*ξ*: The average coefficient of current attenuation;

*C*: High voltage pulse capacitance, μF;

According to the test and calculation results, the corresponding data of the relationship between the gaps of two main electrodes, the width of trigger electrode, the dynamic impedance, and inductive reactance of the switch are shown in Tables 2 and 3, and the corresponding curves are shown in Figure 11.

**Table 2.** The conductive impedance data of the switch.


**Table 3.** The inductive reactance data of conductive switch.


**Figure 11.** Corresponding curves of switch parameters with dynamic impedance and inductive reactance of the switch.

As shown in Figure 11 and Tables 2 and 3, with the increase of the gap between the two main electrodes of the switches, the dynamic impedance and inductive reactance of the switches is increased, but they will decrease with the increase of the width of the trigger electrode. The increase range of impedance relativity is larger than that of the inductive reactance. With the increase of the gap between the two main electrodes of the switch, the average electric field strength between the two main electrodes had been reduced and the concentration of ions or electrons had been decreased, resulting in the decrease of electric current density passing through. Therefore, the impedance and inductive reactance will increase. As the width of trigger electrode increased, the gap between the two main

electrodes becomes smaller and the average electric field strength between two main electrodes increases, resulting in lower impedance and inductive reactance.
