A list of some basic equations and constants I have found useful in my life as a chip and board designer.
| Rule | Value |
|---|---|
| Speed of light | c = 299,792,458 m/s (~3.00x10^8 m/s) |
| Vacuum permitivity | eps0 = 8.854187817 x 10-12 F/m |
| Vacuum permeability | u0 = 4pi x 10-7 H / m or (Vs/Am) |
| Time of Flight (air) | 3.35 ps/mm |
| Time of Flight (FR4-inner layer) | 7.09 ps/mm |
| Capacitance (parallel plate) | C = k * eps0 * Area / d |
| Inductance (wire/ground plan) | L = (u/2pi) * ln ( 4 * h / d) |
| Capacitor current | I = C * dV / dt |
| Inductor voltage | V = L * dI / dt |
| Resistor voltage | V = I * R |
| Charge on capacitor | Q = C * V |
| Power | P = I * V |
| Dynaminc power for capacitive load | P = Freq * Cap * VDD^2 |
| Energy | E = P * t |
| Rule | Value |
|---|---|
| Lumped system rule of thumb (mm) | length < 1/6*Rise_time/time_of_flight |
| Rule | Value |
|---|---|
| De Morgan's Law | ~(A & B) =~A or ~B, ~(A or B) =~A &~B |
| RC delay | (0.35) * res/um * cap/um * L(um)^2 |
| Relative permitivity (SiO2) | 3.9 |
| Relative permitivity (Si) | 11.68 |
| Line capacitance / mm (max density) | (highly variable!) |
| Line resistance / mm (fat layer) | (copper, highly variable!) |
| Rule | Value |
|---|---|
| Chip wire pitch | ~0.1um |
| 2.5D wire pitch | 4um |
| Wirebond pitch | 30um |
| 2.5D Bump pitch | 45um |
| Flip-chip pitch | 170um |
| BGA pitch (advanced) | 400um |
| BGA pitch (standard) | 1000um |
| Hobby "solderable" connector | 2540um |
| Ethernet connector | ~10,000um |