Use a consistent system of units for all input data. For an electromagnetic field analysis, see EMUNIT for information about appropriate settings for free-space permeability and permittivity.
For micro-electromechanical systems (MEMS), it is best to set up problems in more convenient units since components may only be a few microns in size. For convenience, the following tables list the conversion factors from standard MKS units to µMKSV and µMSVfA units.
Table 1.3: Mechanical Conversion Factors for MKS to μMKSV
| Mechanical Parameter | MKS Unit | Dimension | Multiply by This Number | To Obtain μMKSv Unit | Dimension |
|---|---|---|---|---|---|
| Length | m | m | 106 | µm | µm |
| Force | N | (kg)(m)/(s)2 | 106 | µN | (kg)(µm)/(s)2 |
| Time | s | s | 1 | s | s |
| Mass | kg | kg | 1 | kg | kg |
| Pressure | Pa | (kg)/(m)(s)2 | 10-6 | MPa | (kg)/(µm)(s)2 |
| Velocity | m/s | m/s | 106 | µm/s | µm/s |
| Acceleration | m/(s)2 | m/(s)2 | 106 | µm/(s)2 | µm/(s)2 |
| Density | kg/(m)3 | kg/(m)3 | 10-18 | kg/(µm)3 | kg/(µm)3 |
| Stress | Pa | kg/(m)(s)2 | 10-6 | MPa | kg/(µm)(s)2 |
| Young's Modulus | Pa | kg/(m)(s)2 | 10-6 | MPa | kg/(µm)(s)2 |
| Power | W | (kg)(m)2/(s)3 | 1012 | pW | (kg)(µm)2/(s)3 |
Table 1.4: Thermal Conversion Factors for MKS to μMKSV
| Thermal Parameter | MKS Unit | Dimension | Multiply by This Number | To Obtain µMKSv Unit | Dimension |
|---|---|---|---|---|---|
| Conductivity | W/(m)(°C) | (kg)(m)/(°C)(s)3 | 106 | pW/(µm)(°C) | (kg)(µm)/(°C)(s)3 |
| Heat Flux | W/(m)2 | kg/(s)3 | 1 | pW/(µm)2 | kg/(s)3 |
| Specific Heat | J/(kg)(°C) | (m)2/(°C)(s)2 | 1012 | pJ/(kg)(°C) | (µm)2/(°C)(s)2 |
| Heat Flow | W | (kg)(m)2/(s)3 | 1012 | pW | (kg)(µm)2/(s)3 |
| Heat Generation Per Volume | W/m3 | (kg)/(m)(s)3 | 10-6 | pW/(µm)3 | kg/(µm)(s)3 |
| Convection Coefficient | W/(m)2(°C) | kg/(s)3(°C) | 1 | pW/(µm)2(°C) | kg/(s)3(°C) |
| Dynamic Viscosity | kg/(m)(s) | kg/(m)(s) | 10-6 | kg/(µm)(s) | kg/(µm)(s) |
| Kinematic Viscosity | (m)2/s | (m)2/s | 1012 | (µm)2/s | (µm)2/s |
Table 1.5: Electrical Conversion Factors for MKS to μMKSV
| Electrical Parameter | MKS Unit | Dimension | Multiply by This Number | To Obtain µMKSv Unit | Dimension |
|---|---|---|---|---|---|
| Current | A | A | 1012 | pA | pA |
| Voltage | V | (kg)(m)2/(A)(s)3 | 1 | V | (kg)(µm)2/(pA)(s)3 |
| Charge | C | (A)(s) | 1012 | pC | (pA)(s) |
| Conductivity | S/m | (A)2(s)3/(kg)(m)3 | 106 | pS/µm | (pA)2(s)3/(kg)(µm)3 |
| Resistivity | Ωm | (kg)(m)3/(A)2(s)3 | 10-6 | T Ωµm | (kg)(µm)3/(pA)2(s)3 |
| Permittivity [a] | F/m | (A)2(s)4/(kg)(m)3 | 106 | pF/µm | (pA)2(s)4/(kg)(µm)3 |
| Energy | J | (kg)(m)2/(s)2 | 1012 | pJ | (kg)(µm)2/(s)2 |
| Capacitance | F | (A)2(s)4/(kg)(m)2 | 1012 | pF | (pA)2(s)4/(kg)(µm)2 |
| Electric Field | V/m | (kg)(m)/(s)3(A) | 10-6 | V/µm | (kg)(µm)/(s)3(pA) |
| Electric Flux Density | C/(m)2 | (A)(s)/(m)2 | 1 | pC/(µm)2 | (pA)(s)/(µm)2 |
[a] Free-space permittivity is equal to 8.854 x 10-6 pF/µm.
Table 1.6: Magnetic Conversion Factors for MKS to μMKSV
| Magnetic Parameter | MKS Unit | Dimension | Multiply by This Number | To Obtain µMKSv Unit | Dimension |
|---|---|---|---|---|---|
| Flux | weber | (kg)(m)2/(A)(s)2 | 1 | weber | (kg)(µm)2/(pA)(s)2 |
| Flux Density | tesla | kg/(A)(s)2 | 10-12 | tesla | kg/(pA)(s)2 |
| Field Intensity | A/m | A/m | 106 | pA/µm | pA/µm |
| Current | A | A | 1012 | pA | pA |
| Current Density | A/(m)2 | A/(m)2 | 1 | pA/(µm)2 | pA/(µm)2 |
| Permeability [a] | H/m | (kg)(m)/(A)2(s)2 | 10-18 | TH/µm | (kg)(µm)/(pA)2(s)2 |
| Inductance | H | (kg)(m)2/(A)2(s)2 | 10-12 | TH | (kg)(µm)2/(pA)2(s)2 |
[a] Free-space permeability is equal to 4 π x 10-25 TH/µm.
Note: Only constant permeability may be used with these units.
Table 1.7: Piezoelectric Conversion Factors for MKS to μMKSV
| Piezoelectric Matrix [a] | MKS Unit | Dimension | Multiply by This Number | To Obtain µMKSv Unit | Dimension |
|---|---|---|---|---|---|
| Stress Matrix [e] | C/(m)2 | (A)(s)/(m)2 | 1 | pC/(µm)2 | (pA)(s)/(µm)2 |
| Strain Matrix [d] | C/N | (A)(s)3/(kg)(m) | 106 | pC/(µN) | (pA)(s)3/(kg)(µm) |
[a] For information on piezoelectric matrices, see Piezoelectric Analysis.
Table 1.8: Piezoresistive Conversion Factors for MKS to μMKSV
| Piezoresistive Matrix [a] | MKS Unit | Dimension | Multiply by This Number | To Obtain µMKSv Unit | Dimension |
|---|---|---|---|---|---|
| Piezoresistive Stress Matrix [π] | Pa-1 | (m)(s)2/kg | 106 | (MPa)-1 | (µm)(s)2/kg |
[a] For information on piezoresistive matrices, see Piezoresistivity in the Material Reference.
Table 1.9: Thermoelectric Conversion Factors for MKS to μMKSV
| Thermoelectric Parameter | MKS Unit | Dimension | Multiply by This Number | To Obtain µMKSv Unit | Dimension |
|---|---|---|---|---|---|
| Seebeck Coefficient | V/°C | (kg)(m)2/(A)(s)3(°C) | 1 | V/°C | (kg)(µm)2/(pA)(s)3(°C) |
Table 1.10: Mechanical Conversion Factors for MKS to μMSVfA
| Mechanical Parameter | MKS Unit | Dimension | Multiply by This Number | To Obtain µMsvfa Unit | Dimension |
|---|---|---|---|---|---|
| Length | m | m | 106 | µm | µm |
| Force | N | (kg)(m)/(s)2 | 109 | nN | (g)(µm)/(s)2 |
| Time | s | s | 1 | s | s |
| Mass | kg | kg | 103 | g | g |
| Pressure | Pa | (kg)/(m)(s)2 | 10-3 | kPa | g/(µm)(s)2 |
| Velocity | m/s | m/s | 106 | µm/s | µm/s |
| Acceleration | m/(s)2 | m/(s)2 | 106 | m/(s)2 | µm/(s)2 |
| Density | kg/(m)3 | kg/(m)3 | 10-15 | g/(µm)3 | g/(µm)3 |
| Stress | Pa | kg/(m)(s)2 | 10-3 | kPa | g/(µm)(s)2 |
| Young's Modulus | Pa | kg/(m)(s)2 | 10-3 | kPa | g/(µm)(s)2 |
| Power | W | (kg)(m)2/(s)3 | 1015 | fW | (g)(µm)2/(s)3 |
Table 1.11: Thermal Conversion Factors for MKS to μMSVfA
| Thermal Parameter | MKS Unit | Dimension | Multiply by This Number | To Obtain µMsvfa Unit | Dimension |
|---|---|---|---|---|---|
| Conductivity | W/(m)(°C) | (kg)(m)/(°C)(s)3 | 109 | fW/(µm)(°C) | (g)(µm)/(°C)(s)3 |
| Heat Flux | W/(m)2 | kg/(s)3 | 103 | fW/(µm)2 | g/(s)3 |
| Specific Heat | J/(kg)(°C) | (m)2/(°C)(s)2 | 1012 | fJ/(g)(°C) | (µm)2/(°C)(s)2 |
| Heat Flow | W | (kg)(m)2/(s)3 | 1015 | fW | (g)(µm)2/(s)3 |
| Heat Generation Per Volume | W/m3 | (kg)/(m)(s)3 | 10-3 | fW/(µm)3 | g/(µm)(s)3 |
| Convection Coefficient | W/(m)2(°C) | kg/(s)3(°C) | 103 | fW/(µm)2(°C) | g/(s)3(°C) |
| Dynamic Viscosity | kg/(m)(s) | kg/(m)(s) | 10-3 | g/(µm)(s) | g/(µm)(s) |
| Kinematic Viscosity | (m)2/s | (m)2/s | 1012 | (µm)2/s | (µm)2/s |
Table 1.12: Electrical Conversion Factors for MKS to μMSVfA
| Electrical Parameter | MKS Unit | Dimension | Multiply by This Number | To Obtain µMsvfa Unit | Dimension |
|---|---|---|---|---|---|
| Current | A | A | 1015 | fA | fA |
| Voltage | V | (kg)(m)2/(A)(s)3 | 1 | V | (g)(µm)2/(fA)(s)3 |
| Charge | C | (A)(s) | 1015 | fC | (fA)(s) |
| Conductivity | S/m | (A)2(s)3/(kg)(m)3 | 109 | nS/µm | (fA)2(s)3/(g)(µm)3 |
| Resistivity | Ωm | (kg)(m)3/(A)2(s)3 | 10-9 | - | (g)(µm)3/(fA)2(s)3 |
| Permittivity [a] | F/m | (A)2(s)4/(kg)(m)3 | 109 | fF/µm | (fA)2(s)4/(g)(µm)3 |
| Energy | J | (kg)(m)2/(s)2 | 1015 | fJ | (g)(µm)2/(s)2 |
| Capacitance | F | (A)2(s)4/(kg)(m)2 | 1015 | fF | (fA)2(s)4/(g)(µm)2 |
| Electric Field | V/m | (kg)(m)/(s)3(A) | 10-6 | V/µm | (g)(µm)/(s)3(fA) |
| Electric Flux Density | C/(m)2 | (A)(s)/(m)2 | 103 | fC/(µm)2 | (fA)(s)/(µm)2 |
[a] Free-space permittivity is equal to 8.854 x 10-3 fF/µm.
Table 1.13: Magnetic Conversion Factors for MKS to μMKSVfA
| Magnetic Parameter | MKS Unit | Dimension | Multiply by This Number | To Obtain µMKSv Unit | Dimension |
|---|---|---|---|---|---|
| Flux | weber | (kg)(m)2/(A)(s)2 | 1 | weber | (g)(µm)2/(fA)(s)2 |
| Flux Density | tesla | kg/(A)(s)2 | 10-12 | - | g/(fA)(s)2 |
| Field Intensity | A/m | A/m | 109 | fA/µm | fA/µm |
| Current | A | A | 1015 | fA | fA |
| Current Density | A/(m)2 | A/(m)2 | 103 | fA/(µm)2 | fA/(µm)2 |
| Permeability [a] | H/m | (kg)(m)/(A)2(s)2 | 10-21 | - | (g)(µm)/(fA)2(s)2 |
| Inductance | H | (kg)(m)2/(A)2(s)2 | 10-15 | - | (g)(µm)2/(fA)2(s)2 |
[a] Free-space permeability is equal to 4 π x 10-28 (g)(µm)/(fA)2(s)2.
Note: Only constant permeability may be used with these units.
Table 1.14: Piezoelectric Conversion Factors for MKS to μMKSVfA
| Piezoelectric Matrix [a] | MKS Unit | Dimension | Multiply by This Number | To Obtain µMKSv Unit | Dimension |
|---|---|---|---|---|---|
| Piezoelectric Stress [e] | C/(m)2 | (A)(s)/(m)2 | 103 | fC/(µm)2 | (fA)(s)/(µm)2 |
| Piezoelectric Strain [d] | C/N | (A)(s)3/(kg)(m) | 106 | fC/(µN) | (fA)(s)3/(g)(µm) |
[a] For information on piezoelectric matrices, see Piezoelectric Analysis.
Table 1.15: Piezoresistive Conversion Factors for MKS to μMKSVfA
| Piezoresistive Matrix [a] | MKS Unit | Dimension | Multiply by This Number | To Obtain µMKSv Unit | Dimension |
|---|---|---|---|---|---|
| Piezoresistive Stress Matrix [π] | Pa-1 | (m)(s)2/kg | 103 | (kPa)-1 | (µm)(s)2/g |
[a] For information on piezoresistive matrices, see Piezoresistivity in the Material Reference.
Table 1.16: Thermoelectric Conversion Factors for MKS to μMKSVfA
| Thermoelectric Parameter | MKS Unit | Dimension | Multiply by This Number | To Obtain µMKSv Unit | Dimension |
|---|---|---|---|---|---|
| Seebeck Coefficient | V/°C | (kg)(m)2/(A)(s)3(°C) | 1 | V/°C | (g)(µm)2/(fA)(s)3(°C) |