Formulas of Electric Engineering and Electronic
|
Cross-section for single wires round
| q = |
D² x π |
or D² x 0.7854 |
| 4 |
Cross-section for bunched wires
| q = |
d² x π |
x n or d² x 0.7854 x n |
| 4 |
Diameter for single wires
| D = √ |
q x 4 |
or √q x 1.2732 |
| π |
Diameter for bunched wires
|
q = Cross-section in mm²
D = Conductor diameter in mm
d = Single wire diameter in mm
n = Number of wires |
Conductor resistance
| RCircuit = |
2 x l |
or |
2 x l x p |
| κ x q |
q |
|
| R |
= |
Electrical direct current resistance Ohm |
| RCircuit |
= |
Resistance of complete circuit |
| q |
= |
Cross-section in mm² |
| κ (Kappa) |
= |
Conductivity |
| ρ (Rho) |
= |
Specific resistance |
|
| l |
= |
Conductor length in m |
|
| Materials |
Conductivity
|
Spec. Resistance
|
| Copper |
58.00 |
0.01724 |
| Aluminum |
33.00 |
0.0303 |
| Silver |
62.00 |
0.1613 |
| Iron |
7.70 |
0.1299 |
| Constantan |
2.00 |
0.50 |
|
| Serial Connection |
| Resistance: |
R = R1 + R2 + R3 + ... + Rn |
| |
|
| Capacitance: |
| C = |
1 |
+ |
1 |
+ |
1 |
+ ... + |
1 |
| C1 |
C2 |
C3 |
Cn |
|
| |
|
| Inductance: |
L = L1 + L2 + L3 + ... + Ln |
| |
|
| Parallel connection |
| Resistance: |
| R = |
1 |
+ |
1 |
+ |
1 |
+ ... + |
1 |
| R1 |
R2 |
R3 |
Rn |
|
| |
|
| Capacitance: |
C = C1 + C2 + C3 + ... + Cn |
| |
|
| Inductance: |
| L = |
1 |
+ |
1 |
+ |
1 |
+ ... + |
1 |
| L1 |
L2 |
L3 |
Ln |
|
| |
|
| Equivalent resistance of 2 parallel connections |
| |
|
| |
|
| |
|
| Mutual capacity |
| Coaxial cable: |
| C = |
ξr x 10³ |
(nF/km) |
| 18 x ln |
Da |
| d |
|
| |
|
| Parallel conductor: |
| C = |
ξr x 10³ |
(nF/km) |
| 36 x ln |
Da |
| d |
|
| |
|
| Shielded twisted pair: |
| CB = |
ξr x 10³ |
(nF/km) |
| 36 ln |
2a x (Da²-a²) |
| d x (Da²-a²) |
|
| |
|
|
| Da |
= |
Outer diameter over insulation |
| Ds |
= |
Diameter over shield |
| d |
= |
Diameter of conductor |
| a |
= |
Distance - mid to mid of both conductors |
| ξ |
= |
dielectric constant |
|
Ohm's Law
The current intensity (I) is proportional to Voltage (U) and universaly proportional to Resistance (R)
| I = |
U |
|
I = |
U |
|
U = I x R |
| R |
|
R |
|
|
| I |
= |
Current intensity (in Ampere - A) |
| R |
= |
Electrical resistance (in Ohm - Ω) |
| U |
= |
Electrical Voltage (in V) |
|
Conductance
| G = |
1 |
|
S = |
1 |
|
1μS = |
1 |
| R |
|
1Ω |
|
1MΩ |
|
S (Siemens) = Reziprocal value of a resistance is used as conductance
S Siemens = 1/Ohm
G = Electrical conductance |
| Capacitance |
| Single conductor against ground |
| |
| CB = |
ξr x 10³ |
(nF/km or pF/m) |
| 18 x ln |
Di |
| d |
|
| |
|
| Unshielded symmetrical twisted pair |
| |
| CB = |
ξr x 10³ |
(nF/km or pF/m) |
| 36 x ln |
2a |
| d |
|
| |
|
| Coaxial pair |
| |
| CB = |
ξr x 10³ |
(nF/km or pF/m) |
| 18 x ln |
Di |
| d |
|
| |
|
| Shielded symmetrical twisted pair |
| |
| CB = |
ξr x 10³ |
(nF/km or pF/m) |
| 36 ln |
2a x (Da²-a²) |
| d x (Da²-a²) |
|
|
| Di |
= |
Outer diameter over single conductor |
| Da |
= |
Outer diameter of multi conductors (mm) |
| d |
= |
Diameter of conductor |
| a |
= |
Distance - mid to mid of both conductors |
|
Inductance of parallel conductors
at low frequencies
| L = 0.4 (In |
Da |
+ 0.25) mH/km |
| r |
at high frequencies
| L = 0.4 (In |
Da |
+ 0) mH/km |
| r |
Inductance of coaxial cable
at high frequencies
| L = 0.2 (In |
Da |
+ 0) mH/km |
| r |
|
| Da |
= |
Distance - mid to mid of both conductors |
| r |
= |
Radius of conductor |
| ξr |
= |
dielectric constant |
|
Impedance (Z)
for coaxial cable
for communication cable
at low frequencies
| Z = √ |
R |
(Ω) x tan φ = 1, φ = 45° |
| ωC |
at high frequencies
|
| |
|
|
| |
|
|
| D |
= |
Diameter over insulation |
| d |
= |
Conductor diameter |
| |
|
|
| |
|
|
| |
|
|
| R |
= |
Resistance (Ω/km) |
| L |
= |
Inductance (mH/km) |
| C |
= |
Capacitance (nF/km) |
| ω |
= |
2 π f |
|
Wave Length
Units of attenuation - Neper (Np), Decibel (dB) and Bel (B)
1 Np = 8.686 dB
1 dB - 0.1151 Np = 1/10 Bel
1 Bel = 10 dB = 1.1513 Np
|
| λ |
= |
Wave length |
| V |
= |
Propagation velocity |
| f |
= |
Frequency |
|
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