Comparative Study for DC-DC Converter Output Bank’s Reliability Evaluation Using Prediction Standards MIL-HDBK-217F vs. Telcordia SR-332

Abstract

In the last decade, a higher level of reliability has become a compulsory demand when it comes to modern DC-DC converters. This work addresses the main reliability metrics: in many studies, the failure rate λ and MTBF of an output capacitor bank used within a high-current low-voltage buck converter have shown that the output capacitor bank is the most critical component within the converter. Many authors dealt with this issue by performing reliability predictions. The majority of studies use only one specific standard prediction to solve the problem. Herein, the calculation was performed using both the older standard, MIL-HDBK-217, and the latest one, Telcordia SR-332, providing a benchmark comparison between the two, which is a helpful tool for output capacitor selection in early-stage design. The military standard was well accepted for decades in reliability prediction, even in industrial electronics, and is still used today in a critical manner because there have been no more updates after the latest version, MIL-HDBK-217F—Notice 2, was released in 1995. Since then, newer prediction standards have appeared in the electronics reliability market. Over time, this standard was mostly used, but it does not accurately model the reliability because of a lack of taking account of the mission profile. The above-mentioned newer standard—i.e., Telcordia SR-332—also tries to compensate for the lack of the newest component technology in the older standard (which is the first standard released on the market), supplying useful design data for design engineers who use the so-called “design with reliability in mind” concept. This provides the designer of DC-DC converters with a comparison between the reliability values when the two mentioned standards are used. This paper establishes the environmental condition for the passive components by means of a point of load (PoL) buck converter that is used for both calculation methods. The influence of temperature and several specific concepts, like reference conditions, operating conditions, ripple, and internal self-heating, were taken into account in order to display the results. The temperature for the capacitor’s capsule needed in π_T stress factor calculation was derived using PSPICE simulation. High-fidelity and dedicated SPICE models provided by the manufacturer were used for MOSFETs, polymer electrolytic, and MLCC capacitors that comprise the converter.

1. Introduction

When taking into account current concepts, like decarbonization, Industry 4.0, sustainable energy, and green transition, which are very visible today [1], we must think more and more seriously about reliability. They can be guaranteed by good reliability, especially those aimed at power supply sources. The reliability of the electronic circuits that make up any computing, telecommunications, and automotive equipment requires a revision of the design mindset. In the last decade, the so-called concept of “designing with reliability in mind” has appeared more and more often. An increased reliability of electronic equipment leads to a correct realization of the above-mentioned concepts. Also, high reliability is a way to compensate for an unwanted but real phenomenon (which ruins the realization of any new project or any maintenance operation) that appeared after the pandemic period—such as a shortage of component supply.

On the other hand, more and more companies producing electronic components and devices (especially those in the power electronics subdomain) are starting to introduce a reliability chapter in the data sheet for the product in question in response to the increasing demand from designers and end users of electronic parts for data about the reliability of the purchased product [2,3].

But how can one create a satisfactory picture about the reliability of a product in the shortest possible time that is also “reliable”? It would seem that the most accessible and unanimously accepted method is the use of reliability prediction standards [4,5,6].

The calculation of the DC-DC converter’s prediction reliability remains crucial for several reasons:

• Mission-critical systems: DC-DC converters are integral to critical applications such as aerospace, medical devices, and telecommunications. Ensuring their reliability is essential to prevent system failures that could have severe consequences.
• Efficiency and cost optimization: reliable converters minimize downtime and maintenance costs. The calculation of the predicted reliability helps to optimize component selection, leading finally to efficient designs.
• Long service life: many systems require converters to function reliably for extended periods of time.
• Harsh environments: converters operate in different conditions, like elevated temperatures, humidity, and vibration.
• Safety and compliance: compliance with safety standards, e.g., IEC 60601 [7] or ISO 26262 [8], necessitates reliability analysis and investigations.

2. Brief Math Presentation of the Reliability Concept

A very well-accepted definition of reliability looks like this: the ability of an item like a part, device, or component to perform a specific function under given conditions but over a specific period of time. Often, this period of time is expressed by correlation with the failure rate λ:

$$R(t)=e^{-\lambda t}$$

(1)

The frequency of the component’s failures is represented by the symbol λ (Greek letter lambda), named the failure rate.

$$\lambda ={\displaystyle \frac{\mathit{number}\mathit{of}\mathit{component}\text{’}s\mathit{failures}}{\left[\mathit{number}\mathit{of}\mathit{components}\right]\times \left[\mathit{operating}\mathit{hours}\right]}}$$

(2)

More and more frequently, a more practical and commercial way to express reliability is the mean time between failure (MTBF) or the mean time to failure (MTTF) for non-repairable systems. Thus, MTBF, for example, specifies how often a unit (part, component, or device) fails as a statistical average, or the average length of time before the first failure appears after it starts to work, where the item is no longer able to continue functioning in normal operation.

This situation is mathematically expressed using the below integral:

$$\mathit{MTBF}={\int }_0^{+\infty }R\left(t\right)dt$$

(3)

Or, we could write a more straightforward form, like:

$$\mathit{MTBF}=1/\lambda$$

(4)

We could choose the specific moment of time t = 1/λ, such that

R = 1/e = 0.367

(5)

So we could say that the mathematical mean of R(t) represents the amount of time that should elapse until the first failure occurs. Or, in other words, only 37% of the items within a large group will last as long as the MTBF number.

Or we could see this as the device will work properly for as long as its MTBF figure, with a 36.7% confidence level [4,5,6,9].

Failure rate λ means the intrinsic failure rate, i.e., excluding early failures and wear-out failures. It is assumed as a constant value during the lifetime (useful life or service lifetime) period as we can see in the so-called bathtub curve [10] (Figure 1) in which we can distinguish three regions over time:

• Early life failures—characterized by a relatively higher initial failure rate, which reduces rapidly. Early life failures are primarily caused by manufacturing defects that are not effectively screened. Defects will always occur.
• Useful (normal) life failures—the region of the bathtub curve where the failure rate is relatively low and constant. This failure rate is quantified in units of failures in time (FIT) which is an estimate of the number of failures that could occur in a billion (i.e., 10⁹) cumulative hours of the product’s operation.
• Intrinsic wear-out—a period of the product’s lifecycle when intrinsic wear-out dominates and failures increase exponentially. The end of a product’s useful lifetime is specified as the time of onset of wear-out. These types of failures are caused by well-known factors such as channel-hot-carrier effects, electromigration, time-dependent dielectric breakdown and negative bias temperature instability [11]. Usually there are two units of measure for its expression:

  ○

  [F/10⁶ h], which stands for failures per one million component-hours.

  ○

  [FIT], which stands for failures in time (*) (that is, one failure per one billion component-hours).

(*) The latter is mainly used by component manufacturers and they use it in catalogs, application notes, etc.

The useful life period represents the segment of time during which failures occur randomly (this leads to λ = constant). Therefore, all the reliability prediction standards must provide a constant failure rate for the system’s components during the lifetime.

In practice, specifications are preferred in MTBF because the failure rate λ is given as 1 failure/hour (one failure per hour) which is a smaller value (as is the ‘‘failures in time’’ specification: 1 FIT = 1 failures/10⁹ h), whereas the MTBF uses the unit of hours [10,12,13,14,15].

A matter of nuance must be clarified from the start, that there is no direct connection (or correlation) between the notion of useful life and the notion of MTBF. For non-specialist engineers, these notions are very often confounded or mixed. The truth is that the concepts are different but both are compulsory to describe the reliability as a well-presented whole. But the thing they have in common and which makes them both to decrease is the temperature.

3. Reliability Investigation—Experimental Part

In order to determine the capacitor’s temperature (which will be required for the π_T stress factor calculation) several methods are used by engineers. In this paper, the PSPICE simulation-based method is chosen.

A buck synchronous circuit with parameters synthetized in Table 1 was elected for the reliability calculation of the DC-DC converter’s output capacitor bank.

The choice of a buck converter depends on efficiency, voltage accuracy, transient response, and load requirements. So, for this investigation I choose the parameters from the table because this converter is used in the following applications:

• Point of load voltage regulation, such as distributed power systems where the individual components (GPUs, FPGAs, CPUs) require precise and low-voltage power supplies (e.g., Vout = 1.2 V).
• Battery-powered devices, such as portable electronic devices which often operate at low voltages (buck converters efficiently step-down battery voltage to power these devices).
• Also, the 1.2 V output is suitable for powering digital circuits, sensors, and display panels.
• Automotive applications. Buck converters are used in automotive electronics for various purposes. Here, a 1.2 V output can be useful for specific sensors or low-power components.
• LED drivers. LEDs require precise current control which is suitable with buck converters which maintain constant current and efficiency.
• Telecommunications equipment. In networking devices, routers, and switches buck converters regulate voltage for various components, such as ASICs and memory. Also, they can power specific integrated circuits in this field.

Usually, reliability investigations are carried out involving both theoretical analysis and practical validation. If we combine technical knowledge, theoretical insights, and experimental results, we can comprehensively study the buck converter’s reliability. Using such a converter as a study circuit in a reliability investigation needs to consider several aspects:

Technical aspects:

• Topology—the buck converter is a very popular choice due to its simplicity, reliability and low cost. It is suitable for most DC-DC applications.
• Operating conditions—it is necessary to ensure that the converter operates within its specified voltage and current limits. It is compulsory to consider input voltage range, load conditions, and switching frequency.
• Component selection—choosing cutting edge high-quality components especially for capacitors and MOSFETs to ensure reliable operation.
• Efficiency—it needs to be evaluated (as it impacts reliability) knowing that all converters generate less heat and experience less stress when they are more efficient.

Theoretical aspects:

• Output impedance—needs to be investigated to understand load regulation and transient behavior.

Experimental conditions:

• Simulation—using tools like SPICE to simulate the buck converter behavior and evaluate thermal regime and performances.
• Real-time testing—conduct real-time experiments to verify the converter’s behavior under various load conditions.
• Comparison—compare different reliability prediction approaches.

In order to focus on the latest technologies for the component parts of the converter, two MOSFET transistors in silicon technology were chosen—IRF6617 [16] was chosen as the drive transistor and IRF6691 [17] Infineon as the sync transistor. These transistors are RoHS compliant, lead-free (qualified up to 260 °C reflow), and very suitable for application in DC-DC converters and have low conduction losses, high dv/dt immunity, and low profile (<0.7 mm). Construction is dual-sided cooling compatible with existing surface mount techniques.

Table 1. Elected parameters for the converter under study.

Convertor’s Parameters	Value
Rated output active power, Po	Max. 0.06 Ω × (25 A)2 = 37.5 W
Load current	Iout = max. 25 A, (5A @ transition step)
Input voltage, Vin	12 V DC with 5% tolerance
Output voltage, Vout	1.2 V DC ± 50 mV
Switching frequency, fsw	500 kHz @ Duty cycle = 7.65%
Output capacitor bank, C	Polymer electrolytic [18]: 2 pcs. × 470 μF MLCCs [19]: 4 pcs. × 100 μF HF through hole ceramic: 1 pcs. × 100 nF
Inductor, L	250 nH, 0.75 Ω, flat 1335, superflux
Switching transistors (MOSFETs)	IRF6617 (drive) and IRF6691 (sync) [16,18]
Transient load step	Current range variation: Idown = 5 A, Iup = 25 A

Table 1. Elected parameters for the converter under study.

Convertor’s Parameters	Value
Rated output active power, Po	Max. 0.06 Ω × (25 A)2 = 37.5 W
Load current	Iout = max. 25 A, (5A @ transition step)
Input voltage, Vin	12 V DC with 5% tolerance
Output voltage, Vout	1.2 V DC ± 50 mV
Switching frequency, fsw	500 kHz @ Duty cycle = 7.65%
Output capacitor bank, C	Polymer electrolytic [18]: 2 pcs. × 470 μF MLCCs [19]: 4 pcs. × 100 μF HF through hole ceramic: 1 pcs. × 100 nF
Inductor, L	250 nH, 0.75 Ω, flat 1335, superflux
Switching transistors (MOSFETs)	IRF6617 (drive) and IRF6691 (sync) [16,18]
Transient load step	Current range variation: Idown = 5 A, Iup = 25 A

The capacitor bank was composed of capacitors in currently used technologies—polymer aluminum can-type vertical: PCF0J471MCL6GS—manufacturer Nichicon [18]. Capacitance was 470 uF at voltage rating: 6.3 Volts, DC, tolerance: 20%, ESR: 18 mΩ—multilayer ceramic capacitor (MLCC) GRM32ER60J107ME20, SMD—Class II—X5R (EIA)—1210-inch package code (3225 mm), capacity of 100μF at voltage rating: 6.3 Volts, DC [17].

MLCCs have the biggest ESR of all capacitors and behave very well with frequency. Polymer capacitors have greater volumetric efficiency. Conductive polymers are used in aluminum capacitors to replace the wet electrolyte. These capacitors have much lower ESR and do not dry out over time. In order to meet the high frequency (HF) work requirements, a 100 nF through hole ceramic capacitor was added in parallel to this bank. All converter’s components are automotive qualified. The complete diagram of the buck converter used in the PSPICE simulation is shown in Figure 2.

The output capacitor bank made with three types of capacitors is presented. DC-DC converters typically use a combination of capacitors in the output stage to achieve stable performance and efficient power delivery. These capacitors serve as an output filter in conjunction with the coil (inductor). They ensure smooth charging and discharging linked to the output ripple voltage centered around the desired output voltage. Ceramic multilayer capacitors provide low ESR and equivalent series inductance (ESL) and fast transient response due to their high switching frequency capability. Polymer capacitors have the role of the bulk capacitor or “hold-up” capacitor to provide energy storage to bridge short interruptions in the input voltage, for example, during load transients or input voltage drops. Usually they are aluminum electrolytic capacitors, but in this experiment the modern (and optimal) approach was chosen which is the usage of polymer capacitors. Also, this type of capacitor helps to prevent voltage drop during sudden load changes. The HF ceramic THD capacitor acts only at high frequencies. So, the combination of different capacitors optimizes the performance, stability, and efficiency of the converter. Each type plays a specific role in managing the output characteristics.

4. PSPICE Simulation for Determining the Capacitor’s Temperature

For the simulation, precise, dedicated models, provided by the manufacturer, were used for MOSFETs and for polymer electrolytic capacitors and MLCCs [16,17,18,19]. This gives a better and more realistic approach for results on the temperature of the capacitors and increaseas precision. To simulate the step-load effect (which generates overshoots and undershoots in the form of a wave at the output of the converter), switches from the SPICE library are used.

As is well known, the ripple current is defined as the RMS value of the current which is flowing into the capacitor and out of the capacitor each time the switch state turns ON and OFF.

We start from the fact that the current ripple flows through the so-called equivalent series resistance (ESR) within the capacitor, which will dissipate power as given by the well-known formula for power, i.e.,

$$P_{diss}=I_{RMS}^2·ESR$$

(6)

Some combinations of n = 1 ÷ 3 aluminum polymer can-type SMD electrolytic and m = 1 ÷ 6 MLCC-SMD type capacitors are considered in [20]. Each capacitor’s current ripple was measured with PSPICE at a maximum load current where the ripple yields the highest value. The results show that if using more than four ceramic capacitors, the number of electrolytic capacitors does not influence the current ripple.

Among various choices, the optimized and specific calculation refers to an optimal combination of two electrolytic and four ceramic capacitors; one piece of HF ceramic capacitor THD (through hole mounting) was added in parallel for a better behavior at high frequencies. It must be said that ESR could be dependent on temperature but also on switching frequency but that will be the subject of a future study. From [21] the simulation of the circuit gives a 2A intensity of the ripple current; so, the temperature change of the GRM32ER60J107ME20 ceramic MLCCs packaged in SMD 1210 style is (for ambient temperature T_amb = 27 °C):

$$P_{dissipate}={\displaystyle \frac{\mathsf{\Delta }T}{R_{thermic}}}$$

(7)

R_thermic represents the thermal resistance in °C per Watt and ΔT is the allowable temperature rise of the capacitor under test, i.e., the temperature difference between the capacitor and ambient environment.

$$\begin{gathered} {\mathsf{\Delta }T}_{MLCC}=R_{thermic-MLCC}‧P=R_{thermic}‧I_{RMS}^2‧{ESR}_{MLCC}=157{\displaystyle \frac{°C}{w}}‧2^2‧8\mathrm{m}\mathsf{\Omega }=5.024°\mathrm{C} \\ \mathrm{i}.\mathrm{e}.,MLCCtemperature=T_{amb}+{\mathsf{\Delta }T}_{MLCC}~32°\mathrm{C} \end{gathered}$$

(8)

and the temperature change for the PCF0J472MCL6G aluminum polymer can-type SMD capacitors packaged in SMD V style with 6A intensity of the current ripple is (for ambient temperature T_amb = 27 °C):

$$\begin{gathered} {\mathsf{\Delta }T}_{polymer\_cap}=R_{thermic-polymercap}‧P=R_{thermic}‧I_{RMS}^2‧{ESR}_{polymer\_cap}=50{\displaystyle \frac{°\mathrm{C}}{w}}‧6^2‧18\mathrm{m}\mathsf{\Omega }=32.4°\mathrm{C} \\ \mathrm{i}.\mathrm{e}.,Polymer\_captemperature=T_{amb}+{\mathsf{\Delta }T}_{polymer\_cap}~59°\mathrm{C} \end{gathered}$$

(9)

5. MIL-HDBK-217F Prediction Standard—Brief Presentation, Discussion, and Reliability Calculation according to It

The United States Navy’s failure rate prediction of electronic components standard—Military Handbook 217 [22]—was published 1965 and was widely accepted as the “bible” of engineers involved in electronics reliability prediction. It has good international acknowledgement among specialists. It is still used today in a critical manner because no more updates after its latest version MIL-HDBK-217F—Notice 2 released in 1991 have been made (see Figure 3). Several experienced well-known manufacturers have shown concern about the values for failure rates of this standard, which are considered too conservative versus the ones within the Telcordia SR-332 standard [23]. The latter are based on values from a wide range of industrial experience and are close to reality. This is the reason for using its latest release from 2016 which was used for calculation and to make a comparison with the military standard.

5.1. How MIL-HDBK-217 Standard Describes the Reliability Calculation

Usually, the reliability of a DC-DC converter is predicted by considering the reliability of the sum of its components. This method is often named the “parts count” reliability prediction [20]. Then, when the power electronic product has been designed and component stresses can be measured or calculated a more precise “parts stress reliability prediction” can be well established. The failure rate data should ideally be obtained from the field. Despite being used for decades this standard does not accurately model the reliability because of a lack of taking account of the mission profile [20,21]. In this paper the reliability calculus within [20,21] is considered for comparison which is focused on the output capacitor bank’s failure rate calculation according to MIL-HDBK-217 rev.2 cap.10.1. So, we will use the schematic for the converter from the above-mentioned papers where PSPICE simulation was described for a multiple-constraint choice of capacitor bank (see Figure 2) with the same parameters (see Table 1).

Failure rate prediction uses the reference conditions (parts count). The relationship for the failure rate of electrolytic and ceramic capacitors is stated within the standard as follows:

λ_{capacitor-MIL-HDBK-217} = λ_base × π_T × π_Q × π_V × π_SR × π_E × π_C

(10)

and the failure rate for equipment under reference conditions is calculated as follows:

$${{\mathsf{\lambda }}_{system}}_i={\sum }_{i=1}^n{\left({\mathsf{\lambda }}_{ref}\right)}_i$$

(11)

where λ_ref is the failure rate under reference conditions and n is the number of components. The reference conditions adopted need to be typical for the majority of applications of components in the convertor and they include:

• operating phase;
• failure criterion;
• mode of operation (continuous or intermittent);
• mechanical stresses;
• electrical stresses;
• climatic stresses.

It is assumed that the failure rate used under reference conditions is specific to the component, which means it includes the effects of:

• technology of packaging;
• different manufacturers;
• manufacturing process;
• complexity.

Data sources used should be the latest available that are applicable to the power electronic product and its specific conditions for use.

5.2. Reliability Calculation for the Converter under Test

The DC-DC converter under test in this paper consists of a buck converter having a series structure from a reliability calculation point of view, so, the parts count method is used. Thus, the overall system failure rate is the sum of all components’ failure rates:

$${\mathsf{\lambda }}_{system}={\sum }_{i=1}^N{\mathsf{\lambda }}_i$$

(12)

Equation (9) illustrates the total failure rate [20] with n = total number of components and λ_i = the failure rate for the ith component.

According to parameters of the converter from Table 1 and taking into account the three technology types for capacitors used in the converter under test, the calculation shown in [21] has delivered the following results:

λ _{[polymer electrolytic capacitor V-SMD -MIL-HDBK-217]} = 0.007667 [F/10⁶ h] or 7.667 [FIT]
(for 2 parts in parallel we have 0.015334 or 15.334 [FIT])

(13)

λ _{[MLCC capacitor MLCC SMD1210 package -MIL-HDBK-217]} = 0.131475 [F/10⁶ h] or 131.47 [FIT]
(for 4 parts in parallel we have 0.5259 [F/10⁶ h] or 525.9 [FIT])

(14)

λ _{[ceramic HF capacitor TH-MIL-HDBK-217]} = 0.007666 [F/10⁶ h] or 7.666 [FIT]
(for only 1 part)

(15)

and for the entire bank:

λ _{[entire capacitor bank -MIL-HDBK-217]} = (10) + (11) + (12) = 0.5489 [F/10⁶ h]
or 548.9 [FIT], (2 × polymer-SMD + 4 × MLCC-SMD + one ceramic HF)

(16)

MTBF_{[entire capacitor bank -MIL-HDBK-217]} = 1,821,826 [hours]

(17)

If we take this latter result at a glance, it might seem to be very big (i.e., 1,821,826 h). But, do not forget that MTBF is a statistical number and, importantly, it is not equal to useful life (the latter being usually 10 to 15 years, depending of the manufacturer’s declaration).

6. Telcordia SR-332 Prediction Standard—Brief Presentation and Reliability Calculation according to It

Telcordia SR-332 is a reliability prediction standard that uses so called black-box technique (also called parts count method—according to subchapter 3.1 from the standards [23,24]) in order to establish a reliability calculation. In this paper we consider that one part is one capacitor. The process for prediction of the steady-state failure rate for an investigated device is based on a generic steady-state failure rate for any type of device. This process provides methods for estimating the failure rates of electronic equipment rather for the early life and steady-state periods of the equipment lifecycle. The methods do not cover the wear-out period of the lifecycle; it is assumed that the equipment has not entered the wear-out phase of its lifecycle—for details please see the content of the reliability standard. Then, the generic value is modified for:

• quality;
• stress;
• temperature.

The result is the mean black-box steady-state failure rate, as follows:

λ_BBi = λ_Gi× π_Qi × π_Si × π_Ti

(18)

and for the standard deviation of the black-box steady-state failure rate:

σ_BBi = σ_Gi × π_Qi × π_Si × π_Ti

(19)

where:

• the term λ_Gi represents the generic steady-state failure rate for the device i (according to Section 8 within the standard);
• the term σ_Gi represents the standard deviation of the generic steady-state failure rate for device i (according to Section 8 within the standard);
• the term π_Qi represents the quality factor for device i (according to Section 9.3 within the standard);
• the term π_Si represents the electrical stress factor for device i (according to Section 9.2 within the standard) and is based on the percentage of electrical stress. If stress is unknown, we use 1, which assumes 50% electrical stress;
• the term π_Ti represents the temperature factor that corresponds to device i (according to Section 9.1 within the standard) and is based on normal operating temperature during the steady state.

If there are no laboratory data or field data for the device under test, then, the mean deviation and standard deviation of the device steady-state failure rate λ_SSi and σ_SSi both equaling the mean deviation and standard deviation of the black-box steady state failure rate [22], Refs. [4,10,25,26,27] are used:

• λ_SSi = λ_BBi;
• σ_SSi = σ_BBi.

The reliability calculation for the output capacitor bank using the Telcordia SR-332 standard is performed as follows:

• Electrical stress percentage for capacitors in this standard is based on voltage, i.e., electrical stress (%) = (applied DC voltage + AC peak voltage)/rated voltage. So, we have for both MLCCs and for polymer: (1.2 + 0.2 V)/6.3 V = 22.2%, and for ceramic TH mounted capacitor: (1.2 + 0.2 V)/25 V = 5.6%.
• The π_S factor for capacitor stress is taken from Table 9-2 (from the standard) and for polymer capacitors π_S = 0.32 (using curve 3), for MLCCs π_S = 0.52 (using curve 7), and for ceramic TH capacitors π_S = 0.2.
• From the standard’s Table 8-1: λ_G-polymer = 0.19, λ_G-MLCC = 1, σ _G-polymer = 0.13, σ _G-MLCC = 4.4, and the temperature factors: π_T-polymer = 1.48, π_T-MLCC = 0.7, π_{T-ceramic TH} = 0.9.

The results of the calculation for the investigated PoL converter failure rates are as follows (according to the parameters and converter’s specs within Table 1 if using the calculated temperatures of the converter component’s capsule according to (8) and (9)):

λ_{[BB-polymer electrolytic capacitor SMD V-package Telcordia SR-332]} = 0.19 × 0.9 × 1.4 × 0.32 = 0.076608 [F/10⁶ h] = 76.608 [FIT], (153.216 [FIT] for two pieces)

(20)

σ_{[BB-polymer electrolytic capacitor SMD V-package Telcordia SR-332]} = 0.13 × 0.9 × 1.4 × 0.32 = 0.052416[F/10⁶ h] =
52.416 [FIT]

(21)

λ_{[BB-MLCC capacitor SMD 1210 package Telcordia SR-332]} = 0.41 × 0.6 × 0.7 × 0.53 = 0.091266 [F/10⁶ h] = 91.266 [FIT], (365.064 FIT for 4 pieces)

(22)

σ_{[BB-MLCC capacitor SMD 1210 package Telcordia SR-332]} = 0.19 × 0.6 × 0.7 × 0.53 = 0.042294 [F/10⁶ h] =
42.294 [FIT]

(23)

λ_{[BB ceramic HF capacitor Telcordia SR-332]} = 0.1 × 1 × 0.9 × 0.2 = 0.018 [F/10⁶ h] = 18 [FIT] (one pcs.)

(24)

σ_{[BB ceramic HF capacitor Telcordia SR-332]} = 0.01 × 1 × 0.9 × 0.2 = 0.0018 [F/10⁶ h] = 1.8 [FIT]

(25)

λ_{[BB-entire capacitor bank Telcordia SR-332]} = 0.15321 + 0.365,064 + 0.018 =
0.53628 [F/10⁶ h] = 536.28 [FIT]

(26)

for 2 × polymer electrolytic capacitor V SMD, 4 × MLCC-SMD 1210 package, and 1 × HF ceramic capacitor TH mounting.

And finally:

MTBF_{[capacitor bank Telcordia SR-332]} = 1,864,697 [h]

(27)

If, at a glance, these values seem to be a very long period of time it should be taken into account that the MTBF is a statistical concept so we deal with a probability and not with analogue quantities. The result of 1,864,697 h is the period of time in which a failure could happen for one converter or a lot of N converters. In

Table 2. Resulting values for λ and MTBF.

Capacitor’s Technology	Failure Rate [FIT] and MTBF [h] (Values Calculated for 27 °C Ambient Temperature)
	λ MIL-HDBK-217 MTBF MIL-HDBK-217	λ Telcordia SR-332 MTBF Telcordia SR-332
Two polymer electrolytic capacitors (SMD); each capacitor has T = 59 °C	15.3 [FIT] 65,359,477 h	153.216 [FIT] 6,526,733 h
Four MLCCs (SMD); each capacitor has T = 32 °C	525.8 [FIT] 1,901,863 h	365.064 [FIT] 2,739,245 h
One HF ceramic capacitor (through hole); T = 28 °C (due to small amount of current through it)	7.6 [FIT] 131,578,947 h	18 [FIT] 55,555,555 h
Entire capacitor bank	548.9 [FIT] 1,821,825 h	536.28 [FIT] 1,864,697 h

are synthetized the failure rate and MTBF values from both calculations used.

7. Comparative Results

Below is the comparison of the values for failure rate and MTBF summarized in Table 2 and in Figure 4 according to the temperatures of the three types of capacitors obtained by SPICE simulation and considering a 27 °C ambient temperature for the tests. The test considered no ventilation, only natural convection. Also, no radiators are attached to the transistors. Mission profile is ground benign (see the standard). In the table, the failure rate is measured in FIT and the MTBF is measured in hours (for the entire capacitor bank, the value in years is also shown).

8. Conclusions

The novelty provided by the work presented consists of the calculation of reliability using both the standard that appeared first on the market, MIL-HDBK-217F, and the newest one, Telcordia SR-332 (which is mostly used by engineers in the telecommunications industry) applied to a synchronous buck converter in a PoL configuration built with the newest components and using dedicated SPICE models offered by the manufacturers for simulation. MIL-HDBK-217 is more conservative and comprehensive, while Telcordia SR-332 is simpler and often yields lower failure rate predictions. The choice between them depends on the specific context and requirements of the project. SPICE simulation used for finding the component’s case temperature was used in the calculation of the thermal stress factors necessary to evaluate the MTBF. Experimental results showed that calculation with the MIL-HDBK-217 standard gives an enhanced value of failure rate for MLCCs and an extremely low value for polymer capacitors. Using Telcordia standard prediction we found more balanced values. For the entire capacitor bank, the failure rate had quasi-similar values. A more functional value for the ceramic TH capacitor results from the Telcordia calculation. Thus, the numbers offered by the Telcordia standard seem to be more realistic.