3.1. Derating

Derating is conducted according to rules that preserve a “safety margin” (robustness) in terms of the maximum values of components guaranteed by manufacturers, in the case of operational constraints (electric overloads, disruptions, overheating, etc.) or in the case of errors or accidents while in use.

From a theoretical viewpoint, derating is defined by the following equation:

[3.1]

Let us illustrate this by considering the example of a capacitor whose manufacturer guarantees a maximum voltage of 50 V. If, in the application concerned, a voltage of 20 V is applied, the derating will be 20/50 = 40%. In order to check if this derating is acceptable, the derating rules must be clarified.

Derating has a positive impact on the reliability of components. Consider the three types of failures mentioned in Chapter 1. It is clear that derating has little to no influence on youth failures because they are generally the result of manufacturing errors.

However, derating has some influence on catastrophic failures. It is important to recall that the latter are normally the result of accidental overloads, for example, overvoltage. If we return to the example of the capacitor mentioned above, we see that, in certain cases, derating may prevent a failure from occurring if the value of the overvoltage remains below the guaranteed maximum voltage. Similarly, a slightly undersized component can lead to premature aging. The derating applied may then push this aging beyond the point when the product integrating the component is in operation.

There are several data sources that indicate the derating rules to be applied. Some of them are listed below:

• – Certain rules indicated by the manufacturers of components are detailed in section 3.2.
• – Rules outlined in derating standards are listed in section 3.3.

To our knowledge, there is no justification for the rules proposed in the standards and fairly often these rules continue to be applied from one generation of products to the next, while component technology continues to evolve. Furthermore, these rules do not seem to be established according to physical laws of failures that model the component failure mechanisms. Finally, these rules are sometimes different from one standard to another, most likely due to the domain of the product application (aeronautics, rail, space, automotive, etc.).

On the basis of these findings, section 3.3 proposes a method for minimizing these defects and, above all, provides justification for the derating rules under consideration.

3.2. Rules provided by the manufacturers of components

3.2.1. CMS resistors

For this type of component, there are three parameters for which the maximum value guaranteed by the manufacturer must not be exceeded.

3.2.1.1. Dissipated power

3.2.1.1.1. Steady state

The maximum dissipated power depends on the type of enclosure and on the ambient temperature. It is generally provided in the datasheet for an ambient temperature between -55°C and +70°C. Taking the example of Vishay resistors (Vishay 2018), this power decreases linearly above +70°C until it becomes zero at a temperature around 155°C, as illustrated in the figure below (Vishay 2018).

For example, a 1210 resistor can dissipate a maximum power of 500 mW, up to an ambient temperature of 70°C. The table below indicates the maximum power by the type of CMS resistor.

Resistor type	Maximum direct power (mW)
0402	63
0603	100
0805	125
1206	250
1210	500
1218	1,000
2010	500
2512	1,000

The temperature derating curve can be modeled as follows:

[3.2]

For example, for a 0805 enclosure and an ambient temperature of 85°C, the following data are obtained:

or Pr(85°C)~103 mW

3.2.1.1.2. Transient state

For transient power dissipations, the maximum power depends on the duration of this transient state (Vishay 2018).

For repetitive pulses, Figure 3.3 is obtained (Vishay 2018).

For example, a 1206 resistor can dissipate a maximum power of 300 mW for 1 s.

3.2.1.2. Applied voltage

3.2.1.2.1. Steady state

Under a steady state, the voltage across resistors must not exceed the maximum value guaranteed by the manufacturer. These values are given in the following table.

Type of resistors	Maximum voltage (V)
0402	50
0603	75
0805	150
1206	200
1210	200
1218	200
2010	400
2512	500

3.2.1.2.2. Transient state

In a transient state, the voltage applied may be higher than in a continuous state.

For example, for a 1206 resistor, a maximum voltage of ~500 V can be applied for 10 ms.

3.2.2. Capacitors

In this section, we will discuss ceramic capacitors (types I and II), solid tantalum capacitors and electrolytic capacitors.

3.2.2.1. Ceramic capacitors

The parameter of which the maximum value should not be exceeded is the voltage across the capacitor. This voltage depends on the type of enclosure. Generally, there is no derating mentioned as a function of temperature.

However, certain manufacturers specify (but do not always guarantee) a lifetime under specific conditions (derating), as illustrated below (Murata 2020).

NOTE.– For this manufacturer, lifetime is defined by the time elapsed until 1% of the components fail;

• – since the three lines are parallel, the activation energy is the same for the three classes of temperature.

3.2.2.2. Tantalum capacitors

For this type of component, there are three parameters for which the maximum value guaranteed by the manufacturer should not be exceeded.

3.2.2.2.1. Direct voltage

Direct voltage is the voltage across the capacitor. It should not exceed the maximum value UR guaranteed by the manufacturer. A temperature derating is provided by the manufacturer (Firadec 2015).

This temperature derating curve can be modeled as follows:

[3.3]

with Tmax = 125°C and T85 = 85°C.

3.2.2.2.2. Dissipated power

This is presented in Figure 3.7 (Firadec 2015).

This temperature derating can be modeled as follows:

[3.4]

with a = 1.1279; b = 0.086395; c = 0.018611.

3.2.2.3. Electrolytic capacitors

Four stresses should be considered for electrolytic capacitors:

• – The direct voltage applied, equal to the continuous voltage plus the positive peak voltage due to the equivalent series resistance (ESR) of the capacitor.
• – Overvoltage for short periods, which should not exceed 1.15 times the rated voltage guaranteed by the manufacturer.
• – The reverse voltage applied that must be below or equal to 1 V.
• – Storage duration. There is no variation in electrical characteristics when stored for long periods of time, but leakage current may increase. This is due to chemical reactions between the alumina dielectric and the electrolyte. These reactions are reversible when the capacitor is under voltage. The manufacturer normally guarantees storage duration without reformation under well-defined temperature conditions and durations, for example, up to temperatures of 50°C under the following conditions:
  • - Voltage below 100 V ➔ 5 years.
  • - Between 100 V and 360 V ➔ 3 years.
  • - Between 360 V and 500 V ➔ 1 year.
  • - Above 500 V ➔ 6 months.

Similar to with tantalum capacitors, it is recommended to have voltage derating depending on the operating temperature. A 60% derating is often recommended.

NOTE.– This type of capacitor is mainly used as an energy reserve (compensating for the power supply microcuts). Due to their large overall external dimensions, a 60% derating rate, as mentioned in the “derating summary” table (Table 3.6), is not achievable at the industrial scale. Moreover, a more significant derating is often considered as going up to 90%.

3.2.10. Tranzorb diodes

The main stresses are:

• – maximum pulse power Pppm;
• – maximum operating temperature;
• – steady-state power.

3.2.10.1. Maximum pulse power

Maximum pulse power is derated depending on pulse duration. The curve below, derived from the manufacturer data, is defined for a non-repetitive bi-exponential wave. This is generally how lightning pulses are described in the specifications of the product concerned.

3.2.10.2. Steady-state power

Generally, the manufacturer provides a temperature derating of the steady-state dissipated power, as illustrated below.

3.2.10.3. Pulse power

Generally, the manufacturer provides a temperature derating of the steady-state dissipated power, as illustrated below.

There is no derating for the junction temperature.

3.2.14. High power MOSFET transistors

The main stresses are:

• – drain source voltage Vds;
• – grid source voltage Vgs;
• – grid drain voltage Vgd;
• – steady-state direct current ID;
• – pulsed state direct current ID;
• – junction temperature;
• – steady-state dissipated power.

There is generally a derating of the dissipated power depending on the case temperature Tc, as illustrated below.

3.3. Reference-based approach

There are no standards defining the maximum load rate per family of components; however, methodology guides do exist. Load rates often differ from one guide to another, and sometimes the stress parameters of a family of components are not all identical. Moreover, most of the time, these derating rules are not justified and therefore not readily applicable to a given application. Our first approach was to list all the derating values obtained and to thus draw a common basis, as shown by the following table.

NOTE.– The rates in the table are an average of the rates issued from the following guides:

• – MIL-HDBK-338B (1988);
• – NAV-SEA (1991);
• – MIL-STD-975 NASA (2003).

3.4. Creation of derating rules

The derating rules proposed in this book were established in order to provide a justification for the rules generally used in the design of electronic circuits. This analysis relies on the physics of the failure of components.

It therefore seems appropriate to take into account the reliability level of the component, depending on the physical contribution involved in these derating rules. More specifically, the focus will be on the sensitivity of component reliability with respect to the empirical acceleration law modeling the influence of the considered physical contribution.

As already noted, the derating rate is defined as the ratio of the value applied to the component and the maximum value guaranteed by the manufacturer of the component. It therefore ranges between 0 and 100%. It therefore seems relevant to consider that the maximum acceptable derating DR_Max is applicable to the family of components most sensitive to the physical contribution being considered.

Moreover, it is appropriate to take a minimal derating rate DR_Min to avoid needless overdesign. This derating rate will be assigned to the family of components least sensitive to the applied physical contribution. The value of this margin depends on the type of application (consumer products, aeronautics, automotive and aerospace industries, etc.).

The value of these derating rates is the result of a compromise between “overdesign” and a good level of reliability, as illustrated in the figure above.

This qualitative analysis must be followed by a quantitative approach to building these rules. This involves using the sensitivity of a function of a given parameter as the ratio between the relative variation of the function and the relative variation of the considered variable. The sensitivity of the function “f” with respect to the variable x is given by:

[3.5]

An equivalent form of the sensitivity of a function is generally expressed as:

[3.6]

For the derating, the function “f” is considered as the acceleration factor of the underlying physical law governing the failure. As for the parameter “xp”, the characteristic parameter of this law is considered (e.g. the activation energy for the temperature). The following derating rule “DR” is then proposed:

[3.7]

where “a” and “b” are two parameters to be calculated. The problem is that the parameter “p” can take various values depending on the type of component and therefore on the failure mechanism being considered. Therefore, two extreme cases must be considered, namely the minimum value p_min and the maximum value p_max. The previous qualitative rules lead to the following product of equations:

[3.8a]

[3.8b]

The values of DR_Max and DR_Min correspond, respectively, to the minimal and maximum values of the derating rules. The method proposed here is first illustrated in Figure 3.14.

A compromise between the robustness margin and overdesign can lead to the following rules:

• – DR_Max = 90%;
• – DR_Min = 50%.

The next step is then to determine the values of the parameters DR_Max and DR_Min. These values depend on the field of application and should therefore be estimated by those responsible for derating studies in the company concerned. For example, the MIL-HDBK-338B handbook (MIL 1998) provides similar information in the following table.

For certain applications, such as those in the aerospace sector, where the stakes of reliability, safety, etc. are very high, the following rules can be considered:

• – DR_Max = 80%;
• – DR_Min = 30%.

The next step is to calculate parameters a and b satisfying the previous product of equations, depending on the physical law of the failure. The result is then:

[3.9]

[3.10]

PROOF.–

The previous product of equations leads to:

The ratio of the two equations term by term leads to eliminating parameter a. Parameter b can then be calculated as follows:

The natural logarithm of the previous equation gives:

or finally

Inserting the value of b in the first equation, the value of parameter “a” is obtained.

or finally

End

The derating rules are then written for constant temperature as follows:

[3.11]

PROOF.–

As already noted: therefore:

Hence:

End

3.4.1. Rules for constant temperature

The failure mechanisms accelerated by temperature are generally governed by the Arrhenius law (Arrhenius 1889) whose acceleration factor is given by:

[3.12]

NOTE.– This is an acceleration with respect to the reference temperature θo.

• – Here, T designates the junction temperature θj for the active components and the hotspot temperature Th for the passive components.

Let us then study the sensitivity of this acceleration factor with respect to the activation energy Ea. This can be written as:

or

Consequently, parameters “a” and “b” are written as:

[3.13a]

[3.13b]

The derating rules can then be written for the constant temperature as:

[3.14]

PROOF.–

It is known that: and that

Combining these two equations leads to:

or finally:

End

Based on the FIDES guide for predictive reliability (FIDES 2009), the following table presents activation energy as a function of component type.

Types of components	Ea (eV)
Ceramic capacitors	0.1
Electrolytic capacitors	0.4
Tantalum capacitors	0.15
Plastic capacitors	0.25
CMS resistors	0.15
Fuses	0.15
Magnetic components	0.15
Diodes	0.7
Transistors	0.7
Integrated circuits	0.7
LED	0.6
Optocouplers	0.4
ASIC	0.7
Relay	0.25
Interrupters and switches	0.25
Connectors	0.1
Hybrid	0.7
RF and HF Circuits	1.5
LCL STN screen	0.6
LCD TFT screen	0.5
Lithium battery	0.4

Therefore, Ea_Min = 0.1 eV and Ea_Max = 0.7eV. Using the proposed derating rules, the following derating rates are obtained.

Types of components	Derating
Ceramic capacitors	50%
Connectors	50%
Tantalum capacitors	54.6%
CMS resistors	54.6%
Fuses	54.6%
Magnetic components	54.6%
Plastic capacitors	61%
Relay	61%
Interrupters and switches	61%
Electrolytic capacitors	67.6%
Optocouplers	67.6%
Lithium battery	67.6%
LCD TFT screen	70.9%
LED	73.8%
LCL STN screen	73.8%
Diodes	76.3%
Transistors	76.3%
Integrated circuits	76.3%
ASIC	76.3%
Hybrid	76.3%
RF and HF circuits	90.0%

This can be illustrated by Figure 3.15.

To illustrate the method, the acceleration factor can be calculated with respect to a maximum temperature of 125°C, and to the derated temperature, as illustrated in Figure 3.16.

It can be noted that the acceleration factors are relatively homogeneous.

3.4.2. Rule for voltage

Failure mechanisms accelerated by voltage are generally governed by a power law whose acceleration factor is given by:

[3.15]

Let us study the sensitivity of this acceleration factor with respect to parameter ∈. The following relation can be written:

or

This leads to:

[3.16]

PROOF.–

It is known that: and that

Combining these two equations leads to:

or

End

3.5. Summary

The proposed method for the estimation of derating rules relies on the physical laws of failure. Unfortunately, the parameters of a component that are guaranteed by the manufacturer cannot all be modeled by the laws of physics. Therefore, in order to have a summary of the various rules proposed (by the manufacturer, by standards and by the proposed method), only the parameters meeting this constraint are listed in the following table.