📡 Rise Time to Bandwidth Calculator
Convert signal rise time to bandwidth (and vice versa) using Gaussian & step response models. Supports cascade, system budget, and margin analysis.
Enter rise times of individual system stages. System rise time: RTsys = √(RT¹² + RT²² + ... + RTn²)
| System / Standard | Data Rate / BW | Rise Time (Gaussian) | Rise Time (Step) |
|---|---|---|---|
| 10BASE-T Ethernet | 10 Mbps | 35 ns | 45 ns |
| 100BASE-TX Fast Ethernet | 100 Mbps | 3.5 ns | 4.5 ns |
| 1000BASE-T Gigabit | 1 Gbps | 350 ps | 450 ps |
| 10GBASE-R 10 Gigabit | 10 Gbps | 35 ps | 45 ps |
| 25GBASE-R 25 Gigabit | 25 Gbps | 14 ps | 18 ps |
| 100GBASE-R 100 Gigabit | 100 Gbps | 3.5 ps | 4.5 ps |
| USB 2.0 Hi-Speed | 480 Mbps | 729 ps | 938 ps |
| USB 3.0 SuperSpeed | 5 Gbps | 70 ps | 90 ps |
| PCIe Gen 3 | 8 GT/s | 43.75 ps | 56.25 ps |
| PCIe Gen 4 | 16 GT/s | 21.88 ps | 28.13 ps |
| HDTV (BT.709) | 22.7 MHz | 15.4 ns | 19.8 ns |
| OC-12 / STM-4 SONET | 622 Mbps | 563 ps | 724 ps |
| Unit | Symbol | Seconds | Equivalent |
|---|---|---|---|
| Millisecond | ms | 1 × 10⁻³ s | 1,000 μs |
| Microsecond | μs | 1 × 10⁻⁶ s | 1,000 ns |
| Nanosecond | ns | 1 × 10⁻⁹ s | 1,000 ps |
| Picosecond | ps | 1 × 10⁻¹² s | 1/1000 ns |
| Femtosecond | fs | 1 × 10⁻¹⁵ s | 1/1000 ps |
| Unit | Symbol | Hertz | Common Use |
|---|---|---|---|
| Hertz | Hz | 1 Hz | Audio low frequency |
| Kilohertz | kHz | 1,000 Hz | Audio / AM radio |
| Megahertz | MHz | 10⁶ Hz | RF / oscilloscope / WiFi |
| Gigahertz | GHz | 10⁹ Hz | Network / microwave |
| Terahertz | THz | 10¹² Hz | Optical / photonics |
| Scenario | Stage Rise Times | System RT (RMS) | System BW (Gaussian) |
|---|---|---|---|
| Scope + Probe (1 GHz) | 350 ps + 350 ps | 495 ps | ~707 MHz |
| Tx + Cable + Rx (10G) | 35 + 20 + 35 ps | 52 ps | ~6.7 GHz |
| Driver + Filter + Amp | 1 ns + 500 ps + 800 ps | 1.36 ns | ~257 MHz |
| 3-Stage Video Chain | 10 + 8 + 6 ns | 14.1 ns | ~24.8 MHz |
rise time and bandwidth are closely bound in electronics, if you mess up one, you will feel the results on the second. Here is the basic relation: take 0.35 and divide it by your bandwidth in Hz, and you will get the rise time in seconds. Assume that a signal wave has a rise time of around 350 picoseconds.
That means that it requires frequencies up to about 1 GHz to properly recreate that rise or fall. It helps for quickly counting numbers locally.
How Rise Time and Bandwidth Are Linked
What does the rise time genuinely measure? Digital signals exist in a binary world. Either 0 or 1, nothing else.
The rise time shows how much time the shift from bottom to upper level takes (or vice versa). If you push data too quickly, the signal does not manage to follow the changing needs, which causes corrupt data. Usually one defines the rise time as the duration that the signal requires to climb from its 10-percent level to 90 percent of the maximum value.
bandwidth, vice versa, points to which frequencies bear the biggest part of the energy in the signal. Engineers usually measure it at the spot of -3 dB in a filter. Here is where it gets interesting: rise time and bandwidth move opposite.
Shorten the rise time, and the bandwidth expands. Those extra frequencies mean that high frequencies are not so strongly filtared, which allows the signal to adjust more quickly. So designers commonly say that little bandwidth matches a slow circuit.
In practice even so it is not possible to create a perfect square wave with no rise time. Every device that makes a signal, or every cable that bears it… Always forces some limited bandwidth.
Those high frequency parts above the limit dull down. If you loose those parts, the square wave can not adjust instantly. Rather, it shows a clear rise time.
For an RC-circuit, the causes become mathematically sorted. The rise time from 10 to 90 percent matches around 2.2 times the time constant RC. The bandwidth of the same circuit is 1 divided by 2π times the time constant RC.
Those formulas bind everything nicely, and show how a simple filter changes the wave shape.
Historically, makers of oscilloscopes based their designs on this rule: bandwidth times rise time matches 0.35. That matched what one- or two-pole filters give. Modern high-end digital oscilloscopes sometimes differ a bit from that rule.
The number 0.35 works best with the standard rise time of 10 to 90 percent, which is the most used. Control theory is more strict even so, it measures the rise time differently, depending on whether you work with underdamped systems (0% to 100%) or critically damped (5% to 95%).
rise time alone can not describe the whole story about the transfer function. It always stays an imprecise guess. Want genuine accuracy?
Measure the complete answer to an impulse, and you will have the right transfer function. Two signals could have the same rise times, but entirely different rates of change. Also there is no perfect one-to-one relation between rise time and bandwidth, when rate limiting steps in, because that is genuinely a nonlinear filter.
If your design requires telling apart 1.3 GHz and 1.5 GHz, that simple thumbrule probably will not suffice.
