Reliability Analysis of Transient Voltage Suppression Diodes Under Direct Current Switching Surge Stress

Abstract

This study examined the dependability of Transient Voltage Suppression (TVS) diodes under direct current (DC) switching surge stress from several manufacturers with identical electrical requirements. To prevent thermal damage, we applied a standard 3 ms DC switching surge and increased the surge voltage in increments of 0.1 V with intervals between surges. The breakdown voltage (V_BR) was measured after each DC switching surge to verify functionality. To find the maximum surge current and power level that each device could withstand before failing to clamp surge voltage at a defined V_BR level, three separate manufacturers’ TVS diode (V_BR = 6.8 V) samples were examined. There were significant variations in the computed maximum average surge current and power level between manufacturers’ samples determined by statistical analysis. Prior to failure, the average surge power was 202 W, 321 W, and 357 W, while the maximum average surge current was 29.0 A, 46.9 A, and 51.8 A, respectively. Computed 95% confidence interval ranges between manufacturers of TVS diodes revealed significant population reliability differences under DC switching surge stress. Therefore, an efficient TVS diode reliability metric for DC switching surge stress is the maximum average surge current and power immediately before device failure.

1. Introduction

The switch in a direct current (DC) system can be a solid-state power switch, DC contactor, mechanical circuit breaker, or any combination of these [1,2,3]. Large DC systems offer significant potential due to lower line losses and the absence of synchronous issues [3]. Unlike alternating current (AC) systems that benefit from the natural current zero crossings for switching, DC systems lack this advantage and are subjected to switching under load conditions [2]. Therefore, when the contacts of a DC switch start to open, dissipation of any stored line inductance energy should occur, which leads to voltage spikes or arcing that can severely damage either a solid-state or a mechanical switch [1,2,3]. An overload DC circuit breaker switch also opens automatically during short circuits, to interrupt high currents [2]. Therefore, rapidly decreasing stored inductance energy during switch opening will result in hazardous overvoltage transients because of the charge buildup on one side of the switch. This results in voltage spikes or arcing across the DC switch as stored inductance energy tries to maintain current flow. To overcome this problem, the DC circuit line inductance to divert built-up charge away from the DC switch is typically connected in parallel with a freewheeling diode.

However, this approach can be impractical for large-scale DC systems, and therefore, alternatively, a transient voltage suppression (TVS) diode can be locally connected in parallel with the DC switch. The TVS diode will divert switching surge currents away when the device breakdown voltage (V_BR) is exceeded, by shunting built-up charge around the DC switch as seen in Figure 1.

According to the authors, reliability analyses of TVS diodes subjected to increasing DC switching surge voltage levels are lacking. Only peak pulse power capability with a 10/1000 µs waveform is specified by manufacturer TVS diode datasheets. However, according to IEEE standard C62.11, a DC switching surge current is a rectangular waveform with a roughly constant current level throughout [4,5]. An appropriate energy rating window between 2 ms and 3.2 ms is specified by C62.11, which is based on industry understanding about failure risk within a finite time frame [4]. As a result, this kind of surge pulse more accurately simulates the stress that a TVS diode would encounter in a real-world DC switching surge event. Additionally, this type of surge stress has been shown to be a reliable method of investigating Metal Oxide Varistor (MOV) durability performance [6].

Focus and Outline of This Study

In this study, a novel experimental approach is used to determine how reliable TVS diodes from various manufacturers are under normal DC switching surge stress with identical electrical specifications. The suggested method is increasing the surge voltage in increments of 0.1 V while subjecting TVS diodes to a standard 3 ms DC switching surge with internal cool-down periods to prevent thermal degradation. In this manner, DC switching surge reliability can be determined using a TVS diode’s voltage–current characteristics rather than just comparing it to other reliability performance techniques that have been published. The authors claim that the novelty of this work is that, when conducting measurements at room temperature, a single method is utilised to characterise TVS diodes while simultaneously considering several real-world parameters.

The TVS diode conducts during a DC switching surge, bringing the voltage close to its V_BR down to a level that is safe for the DC switch. The highest average DC switching surge current or power level that a TVS diode can withstand before failing to successfully clamp at its V_BR level is focused upon in this work. For DC switching surge stress, this maximum average surge current or power can be used as a reliability parameter for TVS diodes. This study analyses the proposed reliability metric, in order to ascertain how TVS diodes chosen from three distinct manufacturers with identical electrical specifications compare under DC switching surge stress with a steadily rising surge voltage level. Because DC switching surges usually happen at random, the TVS diode will have adequate time to release any energy that has been absorbed as heat. To prevent any thermal device degradation, the study will incorporate a cool-down period between surges that has been experimentally determined. In the Introduction section, the identified problem is discussed, and the literature study includes the relevant papers. The Methodology section includes a description of the experimental setup. Following that, the analysis and the recorded measurement results are shown. This paper concludes with the Conclusion and a list of references.

2. Literature Study

TVS diodes have gained significant attention from researchers [7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]. The TVS diode serves as an important protection device for several applications such as a novel DC circuit breaker [8], RF and Microwave applications [12], cryogenic power electronics [14], solid-state circuit breakers for aircrafts [17], electrostatic discharge devices in high-speed input/output interfaces [19], and hybrid electric vehicles [22]. Therefore, it is essential to understand the behaviour of TVS diodes not only as a singular device but also when used in an application. In the work of [7], the authors studied the effects that high-power microwave pulses have on TVS diodes where five topologies were investigated. The typical operating mechanism of a TVS diode occurs when the applied voltage level is higher than the device V_BR. The TVS diode is triggered when avalanche breakdown occurs and it starts to absorb energy [9]. However, since the TVS diode contains doped semiconductor material, constantly operating it above its intended use will be detrimental and may cause degradation. The Zener diode, which can be seen as the precursor to the TVS diode, does in fact break down when subjected to DC switching surge stress [23]. A conventional TVS diode structure is comprised of a reverse-biased PN junction where the N region is typically larger than the P region. Five other types of TVS diodes have been developed and are listed below [8].

• A TVS diode with a graded P-N junction (G-TVSD);
• A TVS diode with a shorted P-N junction in the cathode region (PG TVSD);
• A TVS diode with trench P+ doping connected in the cathode region (TG-TVSD);
• A TVSD with a local Schottky contact (STG-TVSD);
• A TVSD with a lightly doped N-Drift at the cathode (LSTG-TVSD).

A popular configuration is to use a metal oxide varistor in conjunction with a TVS diode where several benefits have been studied and documented in the literature [8,11,16,17,18]. The TVS diode exhibits lower voltage ratings when compared to an MOV [8], although device degradation is much more likely to occur in MOVs when compared to TVS diodes. Some typical characteristics of TVS diodes are listed below [8]:

• TVS diodes are used for electrostatic discharge applications;
• The voltage level when the TVS diode starts to clamp is the V_BR or V_C;
• V_C should be lower than the maximum expected surge voltage to ensure protection;
• TVS exhibits a lower V_C compared to MOVs; therefore, it can be used together with semiconductors that have lower breakdown collector–emitter voltages;
• When the biasing voltage level is above V_BR, usually defined at I_R = 1 mA or I_R = 10 mA, the TVS enters avalanche mode. I_R will then increase exponentially;
• They offer low electromagnetic interference (EMI) due to intrinsic capacitance values;
• In the work of [4], the Cassie–Mayr black box model has been developed to analyse switching transients in low-voltage circuits during current interruptions. The switching overvoltage that is produced above the peak voltage during current interruption is limited by TVS diodes.

The EMTP-ATP model developed in [10] uses AC sources where in our study we use a DC source. TVS diodes were employed in the work of [11] to provide the current return channel for the gate capacitor discharge of the top devices and to control the power devices’ turn-off voltage. It must be noted that in the application, the TVS diode does not replace the MOV but simply aids in the turn-off process. An LTSpice simulation model for this TVS-MOV combination was developed and provided in [11]. The TVS diodes are described as system level elements of protection for high-frequency applications in [12]. A parasitic cancellation method was used to eliminate the parasitic capacitances that created low impedance leakage paths for RF signals that can degrade the RF specifications.

In the work of [14], the performances of snubber capacitors and TVS diodes for Cryogenic applications were jointly investigated. A 14% reduction in the breakdown voltage was reported with the use of liquid nitrogen when compared to room temperature. This shows that temperature does have an effect and should be considered, as illustrated in Figure 2.

It is for this reason (as discussed in Section 3) that a cool-down period (experimentally determined) between surges is implemented internally to ensure temperature does not have an effect since the focus of our work is to analyse TVS diode reliability based on the typical DC switching surge voltage level increase. In the work of [15], it was reported that the breakdown voltage can be reduced by raising the doping concentration of both sides of the TVS diode junction, which is a different method then the one used in this work. The authors of [16] tested pulse shapes that used damped sinusoidal oscillations or double-exponential functions, but these shapes are rarely mentioned in datasheets. This omission confirms that there is a research gap, and this study addresses typical DC switching surge stress effects on TVS diodes. The energy coordination is important for understanding the behaviour of TVS diodes and MOV devices [18]. The foldback characteristic of high-power TVS diodes partially explains the devices’ behaviour, as shown in Figure 3 [17]. The TVS diodes exhibit the behaviour illustrated in Figure 3 due to a reduced clamping voltage resulting in limited power dissipation which can reduce thermal runaway. The collapse generally occurs after the initial peak, which is generally seen in power TVS diodes. In this work, low-power TVS diodes were used, and thus, the peak was not as prominent.

The important aspect of Figure 3 to note is the characteristic of high-power TVS diodes. The point where the diode starts to clamp full bias voltage results in an increased current flow and gradual decrease in voltage developed across the device. The developed voltage then saturates at the average clamping voltage whereby current flow is restricted.

System-Efficient Electrostatic Discharged (SEED) design models of both a diode and TVS diode were developed in the work of [19], to study their transient response in high-speed input/output (IO) interfaces. External TVS diodes can be especially helpful in integrated circuit (IC) applications to clamp the voltage during an ESD event and can significantly reduce the current flow into the IO interfaces [19]. In the work of [24], a different TVS diode model is proposed which can be used to analyse the effects at the inputs of Low-Noise Amplifiers (LNAs). It was demonstrated that the TVS diode’s dynamic resistance is frequency dependent and exceeds the value in the ESD regime.

The protective device needs to be tested using a high-power tester capable of surging high inrush current in order for the TVS diode to function as intended [21]. The advantage of this method is that the actual characteristics can be determined, and the disadvantage is the cost of using this approach including possible breakdowns. Therefore, out-of-circuit testing methods are preferred where the benefits outweigh the method of testing in circuit. One issue with out-of-circuit testing is the number of units that can be tested per hour. The testing time in our work is significantly reduced using an automated testing method. In the work of [21], the Design for Six Sigma (DFSS) methodology was used to develop the interface test adapted to use the process of Define, Measure, Analyse, Design, and Verify (DMADV). The DMADV process approach was extensively used in this study.

3. Methodology

Three commercially available TVS diodes from different manufacturers that share the same electrical specifications were selected for this study. The TVS diodes were assigned to the following manufacturer group identification codes: AB, CD, and EF. The common TVS diode electrical characteristics of all three selected manufacturers are shown in

Table 1. Selected TVS diode manufacturer equivalent electrical specifications.

Parameter	Specification
Peak Pulse Power Dissipation by 10/1000 μs waveform (Pppm)	600 W
Peak Forward Surge Current by 8.3 ms single sine-wave (IFSM)	100 A
Steady State Power Dissipation (PD)	5 W
Breakdown Voltage (VBR)	6.8 V

.

The nominal V_BR of these TVS diodes, which are part of the standardised P6KE6.8A series, is 6.8 V, with a tolerance range of 6.45 V to 7.14 V. For each of the three selected manufacturers, thirty random TVS diodes from the same production batch were tested to obtain the required measurements for statistical analysis. The implemented algorithm flowchart for the novel experimental approach to determine the TVS diodes’ maximum average surge current and power level is illustrated in Figure 4.

Since the reliability of the three chosen TVS diode manufacturers under DC switching surge stress was compared using the same experimental setup, consistency in the V_BR and DC switching surge current measurements is more significant than absolute precision. In order to ascertain the maximum surge current and power level that each tested TVS diode can tolerate when exposed to an increasing DC switching surge voltage level, the algorithm flowchart in Figure 4 describes the sequential processes that must be followed. The TVS diode maximum average and standard deviation of the surge current and power level reached for each manufacturer’s sample group without any outliners was then calculated.

The applied surge voltage level was controlled by a digital-to-analogue converter (DAC) 12-bit device that remotely controls a laboratory grade 32 VDC, 30 A switch mode power supply (SMPS) explained in Section 3.1. The minimum V_BR of the three selected TVS diode manufacturers is 6.45 V, and therefore, at startup, the SMPS output is initially set to 6.4 V. The surge counter initially reset to zero is used to track the applied DC switching surge stress pulses. The produced voltage across the TVS diode under test is then measured using a specifically designed V_BR measurement circuit when a continuous current of 10 mA, as defined by the manufacturer, passes through the device at room temperature. A cool-down period of one second is allowed before the TVS diode is transferred by relay contacts to a DC switching surge and current measurement circuit. The applied SMPS surge voltage level is then accurately incremented by a 0.1 V step. The TVS diode being tested is then subjected to a typical DC switching surge period of 3 ms, and the average surge current level flowing through the device is recorded. The TVS diode is then allowed a two-second cool-down experimentally determined period where any absorbed surge energy is dissipated as heat. Both the one- and two-second cool-down periods allow sufficient time for the TVS diode to thermally recover, as experimentally verified by using an infrared thermometer to measure device temperature. After cool-down, the surge counter is incremented and the count value, measured TVS diode V_BR, set surge voltage level, and average measured surge current level are then recorded by serially transmitting to Microsoft Excel’s Data Streamer software tool available in Microsoft Office 365 package.

By trial and error it was determined that all three selected TVS diode batches will fail to clamp at V_BR within 90 applied DC switching surge events of 3 ms each when the surge voltage level starts at 6.4 V and increases in steps of 0.1 V. Thus, the TVS diode being tested is subsequently transferred back to the voltage breakdown measurement circuit if 90 applied surges have not yet been reached. The V_BR across the TVS diode is then measured again while the 10 mA current remains constant. For the next DC switching surge event, the SMPS surge voltage level is accurately increased by 0.1 V. This process is repeated until 90 DC switching surges have been applied. The recorded data captured in Microsoft Excel with the Data Streamer software tool were analysed to experimentally determine the maximum surge current level just before failure. The maximum power level is calculated by multiplying the maximum surge current with the associated V_BR level reached for each TVS diode. To achieve statistically significant results, at least 30 random TVS diodes selected from each of the three manufacturers excluding any outliers were tested. This allows calculation of the average including the standard deviation of the maximum surge current and power level reached just before failure at the specified V_BR level.

3.1. Surge Voltage Level Adjustment

A laboratory grade SMPS was used to supply the surge voltage to the TVS diode. The SMPS was remotely controlled via a 0 to 5 V adjustment input interface. Using a serial port interface (SPI), the microcontroller controlled a 12-bit DAC device to adjust the 0 to 5 V remote SMPS input interface. The algorithm to adjust the surge voltage in precise steps of 0.1 V incremented the 12-bit DAC output voltage step and then allowed a 500 ms delay for the SMPS to stabilize. The TVS diode surge voltage level was also measured using a voltage divider network to scale down the voltage to a microcontroller analogue-to-digital converter (ADC). If the 0.1 V incremented surge voltage level was not reached, the 12-bit DAC output voltage level was incremented again until a precise step increment of 0.1 V was achieved. Both a 5.1 kΩ and 1 kΩ resistor, each with a 1% tolerance range, were used to divide the 30 V of the adjustable SMPS setting down to the microcontroller 5 V maximum ADC input level.

A ten-bit resolution ADC with ±2 least significant bit (LSB) was used. Therefore, the maximum 5 V input divided by 2¹⁰ is 4.88 mV per bit and a 2 bit LSB error would be 9.76 mV. The maximum surge voltage level was reached after 90 incremental steps of 0.1 V from 6.4 V to 15.4 V. Therefore, the maximum potential error would be 0.06%. Additionally, a 6 and 1/2-digit precision multi-meter was used to manually adjust the required multiplication factor used in code to determine the real surge voltage level setting from the ADC result. By using voltage divider resistors of 1% tolerance and a code calibrated multiplication factor, the SMPS surge voltage level error will not be more than 0.1%. Thus, this is considered accurate for the purposes of this work. An ADC with fifty equally spaced sampled voltages at 100 µs intervals was used to further increase consistency. By averaging fifty voltage readings, the average surge voltage level applied to the TVS diode was determined. This provided the microprocessor with accurate feedback to ascertain whether the voltage level had increased by 0.1 V.

3.2. TVS Diode Breakdown Voltage Measurement

As shown in Figure 5, a V_BR measurement circuit was created to gauge the voltage that develops across the TVS diode when a constant current of 10 mA passes through the device. After each DC switching surge application, the TVS diode was automatically transferred using double throw double pole relay contacts to this V_BR measurement circuit. Here, the V_BR developed across the TVS diode when a constant current of 10 mA flows was measured. With this measurement, the TVS diode’s ability to regulate at the specified V_BR level of 6.8 V is evaluated. The TVS diode is allowed to reach full conduction before measuring the V_BR by applying a steady 10 mA current for 100 ms. This ensures precise measurement of the TVS diode’s V_BR regulation capacity. This procedure complies with IEEE standard C62.33. In this standard, it is recommended to supply a constant current source (CCS) between 20 and 100 ms prior to measuring an MOV’s reference voltage [25].

A fast-switching solid-state MOSFET that operates in less than 50 ns was used to switch a separate 30 V linear DC power supply across the TVS diode under testing. This was connected in series with a calibrated 10 mA CCS circuit. By using a precision 6 and 1/2-digit multi-meter, a potentiometer was used to calibrate an adjustable precision shunt device regulator to implement a 10 mA CCS.

A buffer circuit was used to eliminate circuit loading. The average voltage developed across the CCS circuit was measured by the implemented ADC. The average V_BR formed across the TVS diode under test was determined by subtracting the precise applied 30 V linear DC power supply from the average measured voltage. As shown in Figure 6, ten ADC voltage measured samples uniformly spaced by 10 ms intervals were used to calculate the average device V_BR level in order to increase measurement consistency after 10 mA constant current flows through the TVS diode for 100 ms.

3.3. DC Switching Surge Current Measurement

The TVS diode under testing was connected to the SMPS output adjusted surge voltage level for a certain amount of time in order to produce a DC switching surge current. A 12-bit DAC device was used for incremental adjustment of the SMPS’s output voltage to allow for a gradual increase in the applied surge voltage level in steps of 0.1 V. For a predetermined period of three milliseconds, a fast-switching solid-state MOSFET linked the TVS diode being tested to the adjusted surge voltage level. During the 3 ms surge application, the current passing through the TVS diode was sampled 10 times using an accurate ACS758 Hall-effect current sensor. The ACS758 Hall-effect current sensor has a sensitivity of 40 mV/A and an inaccuracy of ±2%. It can measure linear current up to 60 A. The average surge current level flow through the TVS diode was determined using ten measured current samples. Figure 7 shows a block diagram of the circuit configuration for measuring DC switching surge current.

During the 3 ms DC switching surge application, the Hall-effect current sensor sampled the surge current ten times at uniformly spaced intervals of 300 μs in order to increase measurement consistency. As shown in Figure 8, the average surge current was determined by summing the 10 samples and dividing by ten.

Figure 9 depicts a picture of the novel experimental test setup to analyse TVS diode reliability against DC switching surge stress.

The experimental test setup photograph shows a TVS diode (P6KE6.8A) connected under testing. The test setup operation used in this work was automated with the use of a microcontroller code to measure at least 90 applied surges. The measurements were recorded by serially transmitting results to Microsoft Excel’s Data Streamer software tool available in Microsoft Office 365. A push-button input was used to start the automated measurement procedure, and the recorded experimentally measured data for the TVS diode tested were analysed in Microsoft Excel.

4. Results and Discussion

A gradually increasing surge voltage (V_Surge) level in increments of 0.1 V was supplied during 90 DC switching surges in order to determine the maximum surge current (I_Surge) that a TVS diode can tolerate before failing to clamp at the V_BR level. This approach allows for precise detection of the maximum ${\mathrm{I}}_{\mathrm{Surge}}$ level just before the TVS diode can no longer maintain the V_BR (6.8 V) level. The TVS diode V_BR response to a gradually increasing ${\mathrm{V}}_{\mathrm{Surge}}$ level is shown graphically in Figure 10.

As seen in Figure 10, eventually, the TVS diode V_BR fails to clamp at 6.8 V and drops to approximately 1.0 V. The corresponding TVS diode ${\mathrm{I}}_{\mathrm{Surge}}$ response to a gradual increasing ${\mathrm{V}}_{\mathrm{Surge}}$ level is shown graphically in Figure 11. The ${\mathrm{I}}_{\mathrm{Surge}}$ through the TVS diode linearly increases as the applied ${\mathrm{V}}_{\mathrm{Surge}}$ level is increased in steps of 0.1 V. Eventually, the TVS diode fails to clamp at the V_BR level of 6.8 V and the ${\mathrm{I}}_{\mathrm{Surge}}$ through the device jumps to a maximum of 61 A that the SMPS can provide during a 3 ms DC switching surge.

Figure 10 and Figure 11 show the response of the TVS diode subjected to a gradually increasing ${\mathrm{V}}_{\mathrm{Surge}}$ level during 90 DC switching surge events. The overall TVS diode V-I characteristic curve is shown graphically in Figure 12.

Initially, the linearity between the gradually increasing DC switching ${\mathrm{V}}_{\mathrm{Surge}}$ and ${\mathrm{I}}_{\mathrm{Surge}}$ level can clearly be observed in Figure 12. For this device, at an approximate ${\mathrm{V}}_{\mathrm{Surge}}$ of 13.5 V, the TVS diode fails to clamp at V_BR (6.8 V) and ${\mathrm{I}}_{\mathrm{Surge}}$, then jumps to a maximum of 61 A that the SMPS can provide during a 3 ms DC switching surge. As the applied ${\mathrm{V}}_{\mathrm{Surge}}$ level reaches 13.5 V, the TVS diode average V_BR significantly drops from 6.8 V to 1.0 V. This demonstrates that at higher applied DC switching ${\mathrm{V}}_{\mathrm{Surge}}$ values, the TVS diode’s capacity to control voltage fails. In addition, it can be seen that as the ${\mathrm{I}}_{\mathrm{Surge}}$ through the TVS diode exceeds an approximate level of 44 A, it fails to clamp at the V_BR level of 6.8 V. After this failure, the TVS diode then conducts the maximum 61 A that the SMPS can provide. For the 30 TVS diodes of each selected manufacturer sample, the recorded ${\mathrm{I}}_{\mathrm{Surge}}$ levels of the 90 applied DC switching surge events were analysed to obtain the maximum ${\mathrm{I}}_{\mathrm{Surge}}$ level reached just before the device fails to maintain the V_BR clamp level.

To calculate the average maximum ${\mathrm{I}}_{\mathrm{Surge}}$ level of 30 TVS diodes selected from each manufacturer, the following equation was used:

$$\overline{{\mathrm{I}}_{\mathrm{Surge}}}={\displaystyle \frac{\sum {\mathrm{I}}_{\mathrm{Surge}}}{\mathrm{n}}}$$

(1)

where ${\mathrm{I}}_{\mathrm{Surge}}$ is the highest surge current attained just before V_BR clamp level failure and $\overline{{\mathrm{I}}_{\mathrm{Surge}}}$ is the average maximum surge current of a sample n (equal to 30), excluding any outlier measured data points. The following sample standard deviation equation can then be used to estimate the population standard deviation for each manufacturer sample:

$$\mathrm{S}=\sqrt{{\displaystyle \frac{\sum {\left({\mathrm{I}}_{\mathrm{Surge}}-\overline{{\mathrm{I}}_{\mathrm{Surge}}}\right)}^2}{\mathrm{n} - 1}}}$$

(2)

where $\mathrm{S}$ represents the range of measured maximum ${\mathrm{I}}_{\mathrm{Surge}}$ levels from the calculated average maximum surge current. A smaller $\mathrm{S}$ indicates that the 30 maximum ${\mathrm{I}}_{\mathrm{Surge}}$ measurements are closer to the calculated average, while a larger $\mathrm{S}$ suggests a wider spread. A measured outlier maximum ${\mathrm{I}}_{\mathrm{Surge}}$ will be significantly outside the typical accepted range of other measurements and can distort the calculated $\overline{{\mathrm{I}}_{\mathrm{Surge}}}$ and $\mathrm{S}$. Consequently, this makes it less representative of the sample. The calculated $\overline{{\mathrm{I}}_{\mathrm{Surge}}}$ and $\mathrm{S}$ are valid estimates when the distribution has no outliers and, therefore, will allow for reliable population statistical inferences.

4.1. TVS Diode Measured Sample Data Summary

A five-number summary and related boxplot graph are suitable methods to depict the measured TVS diode sample data distribution. The measured ordered sample data are divided into four equal 25% groups, or quartiles, using a five-number summary. The boxplot graph then graphically depicts this ordered sample data [26]. Boxplots allow for a comparison between the average and median, help to identify outliers that are outside of the plot’s whiskers, and can reveal skewness in the sample data. When comparing the measured sample data obtained from the different TVS diode manufacturers, boxplots allow for rapid visual analysis and comparison of statistical characteristics like centre and spread. Another helpful statistic derived from the five-number summary is the interquartile range (IQR), which can be calculated as follows:

$$\mathrm{IQR}=(\mathrm{Q}3 - \mathrm{Q}1)$$

(3)

where Q3 is the third quartile, Q1 the first quartile, and IQR the spread of the measured middle 50% of ordered sample data. Using the IQR, the presence of outliers can be mathematically determined by calculating upper and lower limits. Because they differ greatly from the bulk of the other sample data, sample data that fall outside of these limits can be regarded as outliers. Consequently, if measured data exceed the bounds of the following equation, they are regarded as outliers [26]:

$$\mathrm{Q}1 - (\mathrm{IQR} \times 1.5) \le \mathrm{Measured} \mathrm{Data} \le \mathrm{Q}3+(\mathrm{IQR} \times 1.5)$$

(4)

The average and related standard deviation for the five-number summary, computed IQR, and outlier limits for the measured V_BR, maximum surge current (${\mathrm{I}}_{\mathrm{Surge}}$) level reached, and the maximum surge power (${\mathrm{P}}_{\mathrm{Surge}}$) level reached of the three selected manufacturer samples of 30 TVS diodes each are shown in

Table 2. Measured TVS diode sample data summary for three different TVS diode manufacturers.

Manufacturer:	AB			CD			EF
Measured:	${\mathbf{V}}_{\mathbf{BR}}\left(\mathbf{V}\right)$	${\mathbf{I}}_{\mathbf{Surge}}\left(\mathbf{A}\right)$	${\mathbf{P}}_{\mathbf{Surge}}\left(\mathbf{W}\right)$	${\mathbf{V}}_{\mathbf{BR}}\left(\mathbf{V}\right)$	${\mathbf{I}}_{\mathbf{Surge}}\left(\mathbf{A}\right)$	${\mathbf{P}}_{\mathbf{Surge}}\left(\mathbf{W}\right)$	${\mathbf{V}}_{\mathbf{BR}}\left(\mathbf{V}\right)$	${\mathbf{I}}_{\mathbf{Surge}}\left(\mathbf{A}\right)$	${\mathbf{P}}_{\mathbf{Surge}}\left(\mathbf{W}\right)$
Minimum	6.90	25.7	178	6.76	43.6	297	6.84	47.7	327
Quartile Q1	6.93	27.9	194	6.83	45.9	315	6.87	50.3	347
Median Q2	6.93	28.7	199	6.84	47.2	323	6.90	51.6	355
Quartile Q3	6.96	29.7	207	6.87	48.1	329	6.92	53.6	368
Maximum	6.99	32.4	220	6.90	50.2	343	6.96	56.1	384
IQR = (Q3 − Q1)	0.03	1.8	13	0.04	2.2	14	0.05	3.3	21
Q1 − (IQR × 1.5)	6.89	25.1	175	6.76	42.6	293	6.79	45.4	316
Q3 + (IQR × 1.5)	7.01	32.5	225	6.94	51.4	351	7.00	58.5	400
Average	6.94	29.0	202	6.85	46.9	321	6.89	51.8	357
StDev (S)	0.02	1.9	14	0.03	1.9	12	0.03	2.2	15

. Although the quartiles (Q1, Q3, and IQR) provide an overview of the distribution, only certain dataset points are considered. The standard deviation includes all measured data values to provide a representative statistic of the spread of measured sample data.

In Table 2, it is shown that the measured minimum and maximum sample data values for ${\mathrm{V}}_{\mathrm{BR}}$, ${\mathrm{I}}_{\mathrm{Surge}}$, and ${\mathrm{P}}_{\mathrm{Surge}}$ of all three manufacturer samples do not exceed outlier calculated associated limits. This indicates that there are no extreme outlier measurements that can significantly distort the average and standard deviation calculations. Therefore, all the average and standard deviation calculations of the samples’ data shown in Table 2 can be considered reliable estimates for the respective TVS diode populations of each selected manufacturer. The tolerance range of the standard P6KE6.8A series with a V_BR nominal value of 6.8 V is between 6.45 V and 7.14 V. The measured average V_BR values for manufacturers AB, CD, and EF are 6.94 V, 6.85 V, and 6.89 V, respectively, and the standard deviations are only 0.02 V, 0.03 V, and 0.03 V, respectively. This validates the TVS diode V_BR circuit measurements, and the lower standard deviation values indicate that the measured V_BR data are clustered closer to the calculated average. Additionally, for each manufacturer, the minimum and maximum measured V_BR values are within the data sheet specified range. A visual comparison of the maximum surge current measured data distribution of manufacturers AB, CD, and EF is shown in side-by-side boxplots in Figure 13.

All 30 observed TVS diode maximum ${\mathrm{I}}_{\mathrm{S}\mathrm{u}\mathrm{r}\mathrm{g}\mathrm{e}}$ values attained right before the device fails to maintain the 6.8 V V_BR level are represented by the samples indicated by circles on each boxplot. The box with the centre line indicating the median of the maximum ${\mathrm{I}}_{\mathrm{S}\mathrm{u}\mathrm{r}\mathrm{g}\mathrm{e}}$ sample data represents the middle 50% of the ordered sample maximum ${\mathrm{I}}_{\mathrm{S}\mathrm{u}\mathrm{r}\mathrm{g}\mathrm{e}}$ data distribution (also known as IQR). All the maximum ${\mathrm{I}}_{\mathrm{Surge}}$ data values of all three samples do not exceed the boxplot whiskers and, therefore, do not exceed outlier limits. The average maximum ${\mathrm{I}}_{\mathrm{Surge}}$ data values marked by “X” for all three manufacturers are not within each other’s ordered middle 50% sample data range. This highlights distinct significant variation in the ability of 3 ms DC switching to handle surge currents for all three TVS diodes, thereby warranting further investigation of the population. It can also be seen that the average as well as the median values of each sample are almost equivalent, and therefore, there is a relative symmetrical distribution with almost no significant skewness. The side-by-side boxplots presented in Figure 14 provide a visual comparison of the maximum surge power (${\mathrm{P}}_{\mathrm{Surge}}$) sample data distribution for each of the three chosen TVS manufacturer samples (AB, CD, and EF).

The measured V_BR and maximum surge current level attained for each TVS diode in a manufacturer’s sample data are multiplied to obtain the maximum surge power. The maximum surge power (${\mathrm{P}}_{\mathrm{Surge}}$) level attained by each of the three manufacturers’ TVS diode samples that were chosen is also displayed in Table 2, together with the five-number summary, computed IQR, and outlier limits, including the average and related standard deviation. Again, the average maximum ${\mathrm{P}}_{\mathrm{Surge}}$ values marked by “X” for all the three manufacturers are not within each other’s ordered middle 50% sample data range. This again highlights the distinct significant variation in the 3 ms DC switching surge power handling capability of all three TVS diodes, thereby warranting further investigation of the population.

In addition, all three selected TVS diode manufacturer datasheets specify the peak pulse power dissipation with a 10/1000 μs lighting waveform. The determined average maximum ${\mathrm{P}}_{\mathrm{Surge}}$ values reached for manufacturers AB, CD, and EF are 202 W, 321 W, and 357 W, respectively. Therefore, TVS diode manufacturer datasheets could also specify the peak pulse power dissipation for a 3 ms DC switching surge square waveform by using these determined values. Alternatively, since the average maximum ${\mathrm{I}}_{\mathrm{Surge}}$ values reached for manufacturers AB, CD, and EF are 29.0 A, 46.9 A, and 51.8 A, respectively, it could also be specified as the peak pulse surge current for a 3 ms DC switching surge square waveform in datasheets.

4.2. TVS Diode Calculated Confidence Intervals

Calculated sample averages serve as an estimate of the actual TVS diode population average. A sample, however, is merely a subset of the population and does not accurately represent the whole population. As a result, different averages can be computed from samples taken from the same population because of random selected sampling variation [26]. To illustrate the uncertainty of the computed average estimate and take into consideration this inherent variability, a confidence interval can be utilised. The confidence interval will represent a range of possible averages that likely will contain the true population average parameter. A 95% level of confidence (LOC) is generally used when selecting a confidence interval range that will cover 95% of all possible averages that can be determined from multiple samples of a population. Level of significance (LOS) selection, sample size, and population variance affect the calculated confidence interval range width. Therefore, confidence interval range bounds for the population average can be computed by applying the central limit theorem to a single sample of thirty, including the computation of the average and standard deviation without outliers as a possible approximation [27]. The confidence interval range limits can then be found using the central limit theorem equation:

$${\mathrm{C}}_{\mathrm{I}}=\overline{X} \pm \mathrm{t}{\displaystyle \frac{\mathrm{S}}{\sqrt{\mathrm{n}}}}$$

(5)

${\mathrm{C}}_{\mathrm{I}}$ is the confidence interval where 95% of the time the true population average is within this range, $\overline{X}$ and $\mathrm{S}$ are the estimated average and standard deviation, while $\mathrm{n}$ is the sample size. The t-distribution was used to determine the confidence interval range when the actual population variance is not known and is instead estimated from a sample [27]. The t-distribution more closely approximates a normal distribution for a sample size of “n” = 30. The sample size and desired LOC can be used to derive the “t” value from a t-distribution table [27]. Alternatively, the “t” value can be calculated using the T.INV function with sample size and selected LOS using Microsoft Excel as shown in the following equation:

$$\mathrm{t}=\mathrm{T}.\mathrm{INV}\left(\mathrm{LOS}/2,\mathrm{n}-1\right)=\mathrm{T}.\mathrm{INV}\left(0.05/2, 30-1\right)=-2.045$$

(6)

By using Equation (5) with the sample average and standard deviation estimates, the confidence interval range limits of the maximum average surge current can be calculated for all three selected TVS diode sample batches, as shown in

Table 3. All selected manufacturer TVS diode average ${\mathrm{I}}_{\mathrm{Surge}}$ confidence interval limits.

Manufacturer	$\mathbf{Average} {\mathbf{I}}_{\mathbf{S}\mathbf{u}\mathbf{r}\mathbf{g}\mathbf{e}}$	${\mathbf{C}}_{\mathbf{I}}$ Lower Limit	${\mathbf{C}}_{\mathbf{I}}$ Upper Limit
AB	29.0 A	28.3 A	29.8 A
CD	46.9 A	46.2 A	47.6 A
EF	50.9 A	50.9 A	52.6 A

.

The calculated ${\mathrm{C}}_{\mathrm{I}}$ to compare the $\overline{{\mathrm{I}}_{\mathrm{Surge}}}$ population estimation ranges for TVS diode manufacturers AB, CD, and EF samples stressed by 3 ms DC switching surges is graphically displayed in the forest plot in Figure 15. This makes it possible to visually analyse any potential variations in the three manufacturers’ population DC switching surge current handling capacities. According to 95% of computed sample averages, each ${\mathrm{C}}_{\mathrm{I}}$ denotes the estimated range that a manufacturer’s true population maximum $\overline{{\mathrm{I}}_{\mathrm{Surge}}}$ is expected to be within.

As can be seen, the 95% ${\mathrm{C}}_{\mathrm{I}}$ ranges of the various manufacturer samples do not overlap. Thus, for all three of the chosen TVS diode manufacturers, the population maximum $\overline{{\mathrm{I}}_{\mathrm{Surge}}}$ is statistically significantly affected differently by the standard 3 ms DC switching surge stress treatment. According to this, there is a 95% likelihood that different device manufacturers with identical electrical parameters will have significantly varying TVS diode reliability in withstanding 3 ms DC switching surge stress. Additionally, using Equation (5) with sample average and standard deviation estimates, the confidence interval range extremes of maximum average surge power can also be calculated for all three selected TVS diode manufacturer samples, as shown in

Table 4. All selected manufacturer TVS diode average ${\mathrm{P}}_{\mathrm{Surge}}$ confidence interval limits.

Manufacturer	$\mathbf{Average} {\mathbf{P}}_{\mathbf{S}\mathbf{u}\mathbf{r}\mathbf{g}\mathbf{e}}$	${\mathbf{C}}_{\mathbf{I}}$ Lower Limit	${\mathbf{C}}_{\mathbf{I}}$ Upper Limit
AB	202 W	197 W	207 W
CD	321 W	316 W	326 W
EF	357 W	351 W	362 W

.

For TVS diode manufacturers AB, CD, and EF samples stressed by 3 ms DC switching surges, the forest plot in Figure 16 illustrates the calculated ${\mathrm{C}}_{\mathrm{I}}$ to analyse and compare the $\overline{{\mathrm{P}}_{\mathrm{Surge}}}$ population estimation ranges. This makes it possible to visually evaluate any potential variations in the population DC switching surge power handling abilities among the manufacturers of TVS diodes that were chosen.

As seen in Figure 16, there is no overlap between the 95% ${\mathrm{C}}_{\mathrm{I}}$ ranges of the various manufacturer samples. Thus, this shows that, among different device manufacturers with identical electrical parameters, there is a 95% possibility of a large potential variation in the reliability of TVS diodes to withstand 3 ms DC switching surge stress.

5. Conclusions

In this study, the reliability of 6.8 V breakdown voltage TVS diodes to withstand a typical DC switching surge of 3 ms with increasing surge voltage was investigated. Three TVS diodes selected from different manufacturers with the same electrical specifications were comparatively analysed. The novel experimental setup used was calibrated and then automated to apply and measure the V_BR, DC switching surge current, and calculated power level that a TVS diode can withstand before failure. The recorded measurement results were examined to obtain the maximum surge current and power level reached by each TVS diode in a sample, just before failure to clamp at a specified V_BR level. The maximum $\overline{{\mathrm{I}}_{\mathrm{Surge}}}$ and power level with outliers excluded, tolerated by 30 random TVS diodes, was obtained for each selected manufacturer sample.

The analysis of the three TVS diode manufacturer samples reveals a distinct maximum average surge current capability of 29.0 A, 46.9 A, and 50.9 A, respectively. Additionally, the samples reveal a distinct maximum average surge power capability of 202 W, 321 W, and 357 W, respectively. A boxplot comparison of the three-manufacturer measured TVS diode maximum surge current and power sample data distributions has also indicated a distinct capability difference in reliance.

The population maximum $\overline{{\mathrm{I}}_{\mathrm{Surge}}}$ and power level estimation ranges were statistically compared using the calculated 95% confidence intervals. On a forest plot, the compared 95% confidence interval ranges for maximum average surge current and power did not overlap for all three selected manufacturer TVS diodes samples. This showed that the population differences for maximum ${\mathrm{I}}_{\mathrm{Surge}}$ and power handling reliability between samples from TVS diode manufacturers were likewise statistically significant.

A useful indicator for assessing the ability of TVS diodes to tolerate DC switching surge stress is the statistical maximum $\overline{{\mathrm{I}}_{\mathrm{Surge}}}$ and power level just before device failure. These results show that TVS diodes from various manufacturers with identical electrical specifications varied in their capacity to handle DC switching surges. Manufacturer datasheets claim that their TVS diodes are designed to protect against voltage transients induced by lighting and inductive load switching. However, only the lighting capability specification is provided, but no inductive load maximum switching surge current or power capability specifications are provided. Therefore, the authors believe that the TVS diode manufacturers should provide either a maximum average surge current or power handling capability specification for typical DC switching surge inductive load stress.

The differences seen in this study could be attributed to manufacturing defects such as doping concentration mismatches, especially in the heavily doped region, and possible differences in packing. Additionally, the purity of the materials could have an impact. This is left for future research work.