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 source in the circuit.
Impedance Testing
Impedance Test To verify the impedance of the track, a network analyzer can be used:
Where:
= Reference voltage = Test current.