3.11. Annex B : Formulae concerning Capacitors

The formulae described in this annex conern Capacitors as described in Section 3.4.3.5.1.

3.11.1. Lambda physical formula

For ceramic and tantalum capacitors:

Equation

(3.11.1)\[\lambda_{\text{Physical}} = \lambda_{0_{\text{capacitor}}} \cdot \sum_{i}^{\text{Phases}}{\frac{\left( t_{\text{phase}} \right)_{i}}{t_{\text{total}}} \cdot \left( \Pi_{\text{Thermal}} + \Pi_{\text{TCy}} + \Pi_{\text{Mechanical}} \right)_{i}} \cdot \left( \Pi_{\text{induced}} \right)_{i}\]

With the following parameters:

Table 3.11.1 Details of parameters for ceramic capacitors

Parameter	Description
\(\lambda_{\text{phy}}\)	Physical stresses failure rate (overall term)
\(\lambda_{0_\text{capacitor}}\)	Base failure rate for one group of capacitor
\(\Pi_{\text{Thermo-electrical}}\)	Thermo-electrical factor
\(\Pi_{TCy}\)	Cycling factor
\(\Pi_{\text{mechanical}}\)	Mechanical factor
\(\Pi_{\text{induced}}\)	Induced factor

3.11.1.1. Physical stresses for capacitors (ceramic & tantalum)

The physical stresses modelled for capacitors are the thermal, thermal cycling and mechanical factors.

Equation

(3.11.2)\[\Pi_{\text{Thermal}} = \gamma_{\text{TH}_{\text{EL}}} \cdot \left( \frac{1}{S_{\text{reference}}} \cdot \frac{V_{\text{applied}}}{V_{\text{rated}}} \right)^{3} \cdot \exp\left\lbrack 11604 \cdot E_{a} \cdot \left( \frac{1}{293} - \frac{1}{{273 + T}_{\text{board}_{\text{ref}}} + \text{ΔT}} \right) \right\rbrack\]

(3.11.3)\[\Pi_{\text{Tcy}} = \gamma_{\text{TCy}} \cdot \left( \frac{{12 \cdot N}_{\text{cy}_{\text{phase}}}}{t_{\text{phase}}} \right) \cdot \left( \frac{\min\left( \theta_{\text{cy}},2 \right)}{2} \right)^{\frac{1}{3}} \cdot \left( \frac{\Delta T_{\text{cycling}}}{20} \right)^{1.9} \cdot \exp\left\lbrack 1414 \cdot \left( \frac{1}{313} - \frac{1}{{273 + T}_{\max_{\text{cycling}}}} \right) \right\rbrack\]

(3.11.4)\[\Pi_{\text{Mechanical}} = \gamma_{\text{Mech}} \cdot \left( \frac{G_{\text{rms}}}{0.5} \right)^{1.5}\]

Where, \(\lambda_{0_{\text{capacitor}}}\), \(E_{a}\), \(S_{\text{reference}}\), \(\gamma_{\text{TCy}}\), \(\gamma_{\text{Mech}}\), \(\gamma_{\text{TH}_{\text{EL}}}\) is explained in Annex A.3 to A.6 and presented in Table B.1-2 for ceramic capacitors and B.1-5 for tantalum capacitors.

Table 3.11.2 Details of parameters for ceramic capacitors

Description	Ref	\(\lambda_{0_{\text{capacitor}}}\)	\(E_{a}\)	\(S_{\text{reference}}\)	\(\gamma_{\text{TH}_{\text{EL}}}\)	\(\gamma_{\text{TCy}}\)	\(\gamma_{\text{Mech}}\)
Ceramic Capacitor Type I - Low CV	ECCC_01	0.03	0.1	0.3	0.7	0.28	0.02
Ceramic Capacitor Type I - Medium CV	ECCC_02	0.05	0.1	0.3	0.7	0.28	0.02
Ceramic Capacitor Type I - High CV	ECCC_03	0.40	0.1	0.3	0.69	0.26	0.05
Ceramic Capacitor Type II - Low CV	ECCC_04	0.08	0.1	0.3	0.7	0.28	0.02
Ceramic Capacitor Type II - Medium CV	ECCC_05	0.15	0.1	0.3	0.7	0.28	0.02
Ceramic Capacitor Type II - High CV	ECCC_06	1.20	0.1	0.3	0.44	0.51	0.05
Ceramic Capacitor Type II Polymer terminations - Low CV	ECCC_07	0.08	0.1	0.3	0.7	0.28	0.02
Ceramic Capacitor Type II Polymer terminations - High/Medium CV	ECCC_08	0.15	0.1	0.3	0.7	0.28	0.02

Table 3.11.3 Definition of CV product for ceramic capacitors for space applications

CV product Type I Type II Low CV product Less than 5.0x10-8V.F Less than 5.0x10-6V.F Medium CV product Between 5.0x10-8V.F and 1.0x10-6V.F or Higher than 1.0x10-6V.F and not in technological limit Between 5.0x10-6V.F and 1.0x10-4V.F or Higher than 1.0x10-4V.F and not in technological limit High CV product Higher than 1.0x10-6V.F and in technological limit Higher than 1.0x10-4V.F and in technological limit

Table 3.11.4 Groups of tantalum capacitors

Description Ref λ0_capacitor Ea (eV) Sreference \(\gamma\)TH_El \(\gamma\)TCy \(\gamma\)Mech Wet tantalum capacitor (ETCT_07) Wet tantalum capacitor silver case sealed by elastomer ECTC_01 0.77 0.15 0.6 0.87 0.01 0.12 Wet tantalum capacitor silver case sealed by glass beads ECTC_02 0.33 0.15 0.6 0.81 0.01 0.18 Wet tantalum capacitor beads tantalum case sealed by glass beads ECTC_03 0.05 0.15 0.6 0.88 0.04 0.08 Solid tantalum capacitor (ETCT_08) Solid tantalum capacitor drop packaging ECTC_04 1.09 0.15 0.4 0.86 0.12 0.02 Solid tantalum capacitor SMD packaging ECTC_05 0.54 0.15 0.4 0.84 0.14 0.02 Solid tantalum axial metal packaging ECTC_06 0.25 0.15 0.4 0.94 0.04 0.02

3.11.1.2. Physical stresses for plastic film capacitors

The generic formula for plastic film capacitors is a little different from the one presented above, as shown here:

General formula:`

Equation

(3.11.5)\[\lambda = \lambda_{\text{Physical}} \cdot \Pi_{\text{Film}} \cdot \Pi_{\text{PM}} \cdot \Pi_{\text{Process}}\]

With:

Equation

\[\lambda_{\text{Physical}} = \lambda_{0_{\text{capacitor}}} \cdot \sum_{i}^{\text{Phases}}{\frac{\left( t_{\text{phase}} \right)_{i}}{t_{\text{total}}} \cdot \left( \Pi_{\text{Thermal}} + \Pi_{\text{TCy}} + \Pi_{\text{Mechanical}} \right)_{i}} \cdot \left( \Pi_{\text{induced}} \right)_{i}\]

With the following parameters:

Table 3.11.5 Details of parameters for plastic film capacitors

Parameter Description \( \lambda_{\text{phy}} \) Physical stresses failure rate (overall term) \( \lambda_{0_\text{capacitor}} \) Base failure rate for one group of capacitor \( \Pi_{\text{Thermal}} \) Thermal factor \( \Pi_{TCy} \) Cycling factor \( \Pi_{\text{mechanical}} \) Mechanical factor \( \Pi_{RH} \) Humidity factor \( \Pi_{\text{induced}} \) Induced factor

Note

PFILM is defined in 8.3.3.9 and A.2.18.

The physical stresses modelled for plastic film capacitors are the thermal, thermal cycling, mechanical and humidity factors.

Equation

(3.11.6)\[\Pi_{\text{Thermal}} = 0.18 \cdot \left( \frac{1}{S_{\text{reference}}} \cdot \frac{V_{\text{applied}}}{V_{\text{rated}}} \right)^{6} \cdot exp\left\lbrack 11604 \cdot E_{a} \cdot \left( \frac{1}{293} - \frac{1}{{273 + T}_{board\_ ref} + \Delta T} \right) \right\rbrack\]

(3.11.7)\[\Pi_{\text{Tcy}} = 0.14 \cdot \left( \frac{{12 \cdot N}_{cy\_ phase}}{t_{\text{phase}}} \right) \cdot \left( \frac{min(\theta_{\text{cy}},2)}{2} \right)^{\frac{1}{3}} \cdot \left( \frac{\text{ΔT}_{\text{cycling}}}{20} \right)^{1.9} \cdot exp\left\lbrack 1414 \cdot \left( \frac{1}{313} - \frac{1}{{273 + T}_{max\_ cycling}} \right) \right\rbrack\]

(3.11.8)\[\Pi_{\text{Mechanical}} = 0.02 \cdot \left( \frac{G_{\text{rms}}}{0.5} \right)^{1.5}\]

(3.11.9)\[\Pi_{\text{RH}} = {0.66 \cdot \left( \frac{\text{RH}_{board\_ ref}}{70} \right)}^{4.4} \cdot \ exp\left\lbrack 11604 \cdot 0.9 \cdot \left( \frac{1}{293} - \frac{1}{{273 + T}_{board\_ ref} + \Delta T} \right) \right\rbrack\]

Where, \(\lambda_{0_{\text{capacitor}}}\), \(E_{a}\), \(S_{\text{reference}}\) explained in Annex A.3 to A.6 and presented in Table B.1-2 for ceramic capacitors and B.1-5 for tantalum capacitors.

Table 3.11.6 Parameters for physical stresses of plastic film capacitors.

Type of plastic film capacitors Ref λ0_capacitor Ea (eV) Sreference γTH El γTCy γMech γRH Polypropylene film capacitor PP 0.02 0.65 0.3 0.18 0.14 0.02 0.66 Polyethylene terephtalate film capacitor PET 0.06 0.48 0.3 0.18 0.14 0.02 0.66 Polyethylene naphtalate film capacitor PEN 0.03 0.55 0.3 0.18 0.14 0.02 0.66 Polyphenylene sulfide film capacitor PPS 0.02 0.55 0.3 0.18 0.14 0.02 0.66 Teflon film capacitor PTFE 0.03 0.55 0.3 0.18 0.14 0.02 0.66

Induced factor Πinduced

Csensitivity

Table 3.11.7 Coefficient of sensitivity for capacitors

Technologies	\(C_{\text{sensitivity}}\)
Ceramic capacitor with defined temperature coefficient (type I)	6.30
Ceramic capacitor with non-defined temperature coefficient (type II X5R)	6.48
Ceramic capacitor with non-defined temperature coefficient (type II X7R)	6.48
Ceramic capacitor with polymer terminations and non-defined temperature coefficient (type II X5R)	6.08
Ceramic capacitor with polymer terminations and non-defined temperature coefficient (type II X7R)	6.03
Tantalum capacitors	7.43
Plastic film capacitors	6.05

Pi Part-Manufacturing

Ceramic capacitors

Table 3.11.8 Recommendation for definition of parameter \(QA_{\text{component}}\) for ceramic capacitors

Ceramic capacitors: Component quality assurance level	Position relative to the state of the art	\(QA_{\text{component}}\)
Qualification according to one of the following standards: MIL-PRF-xxxx level T, MIL-PRF-xxxx level S, MIL-PRF-xxxx level R, ESCC 300x, NASDA-QTS-xxxx class I (JAXA-QTS-2040E)	Higher	3
Qualification according to one of the following standards: AEC Q200, MIL-PRF-xxx level P, NASDA-QTS-xxxx class II, with identification of manufacturing sites for these standards, qualification according to approved CECC standards.	Equivalent	2
Qualification according to one of the following MIL-PRF-xxxx level M, or qualification program internal to the manufacturer and unidentified manufacturing sites	Lower	1
No information	Much lower	0

Tantalum capacitors

Table 3.11.9 Recommendation for definition of parameter \(QA_{\text{component}}\) for tantalum capacitors

Tantalum capacitors: Component quality assurance level	Position relative to the state of the art	\(QA_{\text{component}}\)
Qualification according to one of the following standards: AEC Q200, MIL-PRF-xxxx level T, MIL-PRF-xxxx level B, ESCC 300x, NASDA-QTS-xxxx class I (JAXA-QTS-2040E)	Higher	3
Qualification according to one of the following standards: MIL-PRF-xxxx level C, NASDA-QTS-xxxx class II with identification of manufacturing sites for these standards, qualification according to approved CECC standards.	Equivalent	2
Qualification according to one of the following: MIL-PRF-xxxx level D, or qualification program internal to the manufacturer and unidentified manufacturing sites	Lower	1
No information	Much lower	0

Plastic film capacitors

Table 3.11.10 Recommendation for definition of parameter \(QA_{\text{component}}\) for plastic film capacitors

Plastic film capacitors: Component quality assurance level	Position relative to the state of the art	\(QA_{\text{component}}\)
Qualification according to one of the following standards: AEC Q200, MIL-PRF-xxxx level T, MIL-PRF-xxxx level S, MIL-PRF-xxxx level R, ESCC 400x, NASDA-QTS-xxxx class I (JAXA-QTS-2050D)	Higher	3
Qualification according to one of the following standards: MIL-PRF-xxx level P, NASDA-QTS-xxxx class II with identification of manufacturing sites for these standards, qualification according to approved CECC standards.	Equivalent	2
Qualification according to MIL-PRF-xxxx level M, or qualification program internal to the manufacturer and unidentified manufacturing sites	Lower	1
No information	Much lower	0