Scope Bandwidth Calculator

The relationship BW × t_r ≈ 0.35 for a first-order RC system comes from Fourier analysis of a step response: the 10–90% rise time of a single-pole low-pass filter with cutoff BW is exactly ln(9) / (2π·BW) ≈ 0.35/BW. Harold Black, Hendrik Bode, and the Bell Labs school of the 1930s–40s established this relationship early as a fundamental trade-off between bandwidth and time-domain response.

Analog oscilloscopes of the 1950s–70s (Tektronix 7000 series, HP 180A) were specified directly in bandwidth, with rise time as a derived parameter. Modern digital sampling scopes (DSOs) split the specification: analog bandwidth of the front end plus sampling rate of the ADC, plus memory depth. The classic rule scope BW ≥ 3–5× signal BW for <3% measurement error persists across both analog and digital designs.

Modern scope designs have blurred bandwidth boundaries. Teledyne LeCroy\'s DSP-enhanced bandwidth uses digital correction to flatten the amplifier rolloff, effectively extending specified BW beyond the analog front-end cutoff. Probes matter too — a 1 GHz scope with a 200 MHz probe is a 200 MHz system. Always calculate the combined scope+probe rise time using RSS.

Enter the signal\'s rise time (10–90% transition time) and desired margin (3× or 5× the minimum scope BW). The tool computes the minimum scope bandwidth needed, the recommended scope bandwidth with margin, the corresponding scope rise time, and the measurement error at the selected margin.

For digital signals, a rule of thumb: the signal rise time is typically 0.35× the clock period for square waves, or from data-sheet AC timing specs for logic families. Probe tip capacitance (10 pF typical for 10× probes) + source impedance determines the probe\'s loading-induced rise time, which adds in RSS. Everything runs client-side.