Essential PCB Formulas

Variables

• Z₀—Characteristic impedance (Ω)
• εᵣ—Dielectric constant
• h—Dielectric height
• w—Trace width
• t—Trace thickness

Notes

Valid for w/h ratio between 0.1 and 3.0. For w/h < 1, accuracy ~2%.

Variables

• Z₀—Characteristic impedance (Ω)
• εᵣ—Dielectric constant
• b—Distance between ground planes
• w—Trace width
• t—Trace thickness

Notes

For centered stripline. Offset stripline requires more complex calculation.

Variables

• Zdiff—Differential impedance (Ω)
• Z₀—Single-ended impedance (Ω)
• s—Trace spacing
• h—Dielectric height

Notes

For loosely coupled pairs, Zdiff ≈ 2 × Z₀. Tight coupling reduces Zdiff.

Variables

• tpd—Propagation delay
• εᵣ(eff)—Effective dielectric constant
• c—Speed of light (983.6 × 10⁶ ft/s)

Notes

Microstrip εᵣ(eff) ≈ (εᵣ + 1)/2. Stripline εᵣ(eff) = εᵣ. Typical FR-4: ~6 in/ns.

Variables

• λ—Wavelength
• c—Speed of light
• f—Frequency
• εᵣ(eff)—Effective dielectric constant

Notes

Trace becomes transmission line when length > λ/10. At 5 GHz in FR-4, λ ≈ 1.2 inches.

Variables

• Lcrit—Critical length for transmission line effects
• tr—Signal rise time
• vp—Propagation velocity

Notes

If trace length > Lcrit, treat as transmission line. Rule of thumb: 1 inch for 1 ns rise time.

Variables

• Rdc—DC resistance (Ω)
• ρ—Resistivity (1.7 × 10⁻⁸ Ω·m for Cu)
• L—Trace length
• w—Trace width
• t—Trace thickness

Notes

1 oz copper = 1.4 mils (35 µm). 0.5 oz = 0.7 mils.

Variables

• δ—Skin depth
• ρ—Resistivity
• f—Frequency
• μ₀—Permeability of free space
• μᵣ—Relative permeability

Notes

At 1 GHz, copper skin depth ≈ 2.1 µm. Current concentrated in 3δ depth.

Variables

• αd—Dielectric attenuation (Np/m)
• f—Frequency
• εᵣ—Dielectric constant
• tan δ—Loss tangent (Df)
• c—Speed of light

Notes

Convert Np/m to dB/inch: multiply by 0.22. Dielectric loss dominates above ~1 GHz.

Variables

• NEXT—Near-end crosstalk coefficient
• Cm—Mutual capacitance
• Lm—Mutual inductance
• C—Self-capacitance
• L—Self-inductance
• Kb—Backward crosstalk coefficient

Notes

NEXT saturates after coupled length = rise time × velocity. Dominant in microstrip.

Variables

• FEXT—Far-end crosstalk coefficient
• Length—Coupled trace length
• tr—Rise time
• Z₀—Characteristic impedance

Notes

FEXT increases with coupled length. Zero in ideal stripline (homogeneous medium).

Variables

• Spacing—Edge-to-edge distance between traces
• Trace_Width—Width of signal trace

Notes

Reduces crosstalk to ~10%. For critical signals, use 5W spacing or shielding.

Variables

• Ztarget—Target PDN impedance (Ω)
• Vdd—Supply voltage
• Ripple%—Allowed voltage ripple (typically 5%)
• Imax—Maximum transient current

Notes

For 1.0V supply with 5% ripple and 10A transient: Ztarget = 5 mΩ.

Variables

• fres—Self-resonant frequency
• L—Equivalent series inductance (ESL)
• C—Capacitance

Notes

Above resonance, capacitor becomes inductive. Use multiple values to cover frequency range.

Variables

• L—Via inductance (nH)
• h—Via height (inches)
• d—Via diameter (inches)

Notes

Typical 10-mil via, 62-mil board: ~1 nH. Reduce with larger diameter or ground vias.

Variables

• Γ—Reflection coefficient
• ZL—Load impedance
• Z₀—Line impedance

Notes

Γ = 0 for matched load, Γ = 1 for open, Γ = -1 for short. |Γ| < 0.1 typically acceptable.

Variables

• RL—Return loss (dB)
• Γ—Reflection coefficient

Notes

RL > 20 dB means |Γ| < 0.1 (10% reflection). Higher RL is better.

Variables

• VSWR—Voltage Standing Wave Ratio
• Γ—Reflection coefficient

Notes

VSWR = 1 is perfect match. VSWR < 1.5 typically acceptable for digital signals.