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formulas-pcbs

PCB Design CheatSheet

Fundamentals of PCB Design

Basic Concepts

Track Width (W) The minimum width of PCB tracks can be calculated using the formula:

Where:

  • = Current in amperes (A)
  • = Desired temperature rise in degrees Celsius (°C)

Track Area The area of the track can be calculated as:

Where:

  • = Length of the track
  • = Width of the track

Materials

Dielectric

The dielectric constant (ε) of a material can influence the capacitance of a PCB. For a parallel plate capacitor, the formula used is:

Where:

  • = Capacitance in farads (F)
  • = Permittivity of the material (ε = ε₀ * εr)
  • = Area of the capacitor plates
  • = Distance between the plates

Track and Trace Design

Track Design

Track Resistance (R) The resistance of a track can be calculated as:

Where:

  • = Resistivity of the material (ohm-meters, Ω·m)
  • = Length of the track
  • = Width of the track
  • = Thickness of the track

Track Capacitance

Capacitance Between Tracks For two parallel tracks, capacitance can be approximated as:

Where:

  • = Distance between the tracks
  • = Radius of the tracks

Impedance Calculation

Track Impedance

Characteristic Impedance (Z₀) For a microstrip or stripline track, the impedance is calculated using the formula:

Where:

  • = Height of the substrate
  • = Width of the track
  • = Relative permittivity of the material

Power Distribution

Voltage Drop

Voltage Drop Across Tracks The voltage drop across a track can be calculated as:

Where:

  • = Current flowing through the track
  • = Resistance of the track

Current Density

Current Density (J) Current density is defined as:

Where:

  • = Cross-sectional area of the track

Thermal Management

Temperature Calculation

Temperature Calculation in PCBs To estimate the temperature rise, the following can be used:

Where:

  • = Power dissipated in watts (W)
  • = Thermal resistance in °C/W
  • = Area of the PCB

Signal Analysis

Bandwidth

System Bandwidth To calculate the bandwidth of a system, use:

Where:

  • = Total resistance
  • = Total capacitance

Rise Time

Rise Time (T_r) Rise time can be estimated using:

Where:

  • = Load capacitance

Design Rules

Spacing Rule

Minimum Space Between Tracks The minimum space between tracks can be calculated using:

Where:

  • = Spacing factor according to the class of PCB (typically between 1.5 and 3).

Trace Length

Maximum Trace Length To minimize inductance, the following can be used:

Where:

  • = Maximum frequency of the system.

Simulation and Testing

Circuit Analysis

Superposition Theorem To analyze linear circuits, use:

Where:

  • = Output due to sourcein the circuit.

Impedance Testing

Impedance Test To verify the impedance of the track, a network analyzer can be used:

Where:

  • = Reference voltage
  • = Test current.