Rise Time and Bandwidth

Rise Time and Bandwidth

Every digital signal has a rise time — the time to transition from 10% to 90% of the final voltage. Faster rise times mean higher signal bandwidth, which means more stringent PCB design requirements.

The relationship between rise time and bandwidth (using a Gaussian approximation):

BW = 0.35 / t_rise

Where:

• BW = bandwidth in Hz
• t_rise = 10-90% rise time in seconds

This bandwidth tells you the highest frequency content in the signal. Your PCB traces must support this bandwidth without excessive loss or reflection.

Critical Length Rule

A trace is considered electrically long (transmission line behavior must be modeled) when:

L_critical = t_rise × v / 6

Where:

• v = signal velocity ≈ c / √εr_eff (propagation velocity)
• For FR4 microstrip: v ≈ c / √2.6 ≈ 1.86 × 10⁸ m/s

Any trace longer than L_critical needs controlled impedance.

Your Task

Implement:

• signalBandwidth(t_rise_ps) returning bandwidth in GHz
• criticalLength(t_rise_ps, v_mmps) returning critical trace length in mm
  • v_mmps = signal velocity in mm/ps (default FR4: ~0.186 mm/ps)