Transmission-Line Critical Length
lcrit = tr / (2 · tpd)
Quick answer
This calculator solves lcrit = tr / (2 × tpd) for Critical Length. With Rise Time 10 ns, Propagation Delay 6 ps/mm, the result is 0.8333 m. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
A PCB trace must be treated as a transmission line (with controlled impedance and termination) once its length exceeds the critical length, where the round-trip propagation delay becomes comparable to the signal rise time. Below this length the trace behaves as a lumped node and reflections settle within the edge; above it, reflections cause ringing and must be managed.
Variables
- lcrit — Critical (electrically-long) length (m)
- tr — Signal rise time (s)
- tpd — Propagation delay per unit length (s/m)
Practical Notes
A common rule uses tr/(2·tpd); some designers use tr/(6·tpd) for a stricter limit. FR-4 microstrip has tpd ≈ 6–7 ps/mm, so a 1 ns edge gives a critical length around 75 mm.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| lcrit | Critical Length | mm | mm, cm, m, km |
| tr | Rise Time | ns | ps, ns, µs, ms, s, min, h |
| tpd | Propagation Delay | ps/mm | ps/mm, ns/m |
Step by step
- 1. What you know: Rise Time 10 ns, Propagation Delay 6 ps/mm
- 2. The relation: lcrit = tr / (2 × tpd)
- 3. Substitute: tr = 10 ns, tpd = 6 ps/mm
- 4. Result: Critical Length = 0.8333 m
Worked examples
Minimum range
Given: Rise Time 100 ps, Propagation Delay 0.1 ps/mm
Result: Critical Length = 50 cm
Low range
Given: Rise Time 1 ns, Propagation Delay 1 ps/mm
Result: Critical Length = 50 cm
Typical
Given: Rise Time 10 ns, Propagation Delay 6 ps/mm
Result: Critical Length = 0.8333 m
High range
Given: Rise Time 100 ns, Propagation Delay 20 ps/mm
Result: Critical Length = 2.5 m
Maximum range
Given: Rise Time 1 µs, Propagation Delay 200 ps/mm
Result: Critical Length = 2.5 m
Solving for each variable
Solve for Critical Length
Rise Time 100 ps, Propagation Delay 0.1 ps/mm → 50 cm
Solve for Rise Time
Critical Length 0.1 mm, Propagation Delay 0.1 ps/mm → 0.02 ps
Solve for Propagation Delay
Critical Length 0.1 mm, Rise Time 100 ps → 500 ps/mm
How Critical Length changes with Rise Time
| Rise Time (input) | Critical Length (result) |
|---|---|
| 1 ns | 8.333 cm |
| 2.5 ns | 20.83 cm |
| 5 ns | 41.67 cm |
| 7.5 ns | 0.625 m |
| 10 ns | 0.8333 m |
| 15 ns | 1.25 m |
| 20 ns | 1.667 m |
| 40 ns | 3.333 m |
| 70 ns | 5.833 m |
| 100 ns | 8.333 m |
The same result in other units
| Unit | Value |
|---|---|
| mm | 833.3 |
| cm | 83.33 |
| m | 0.8333 |
| km | 0.0008333 |
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<p><a href="https://vbatpower.com/formulas/critical-length/">Transmission-Line Critical Length</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Transmission-Line Critical Length?
Use lcrit = tr / (2 × tpd). With Rise Time 10 ns, Propagation Delay 6 ps/mm, Critical Length works out to 0.8333 m.
How do you calculate pcb critical length?
Rearrange for Critical Length: with Rise Time 1 ns, Propagation Delay 1 ps/mm, Critical Length is 50 cm.
What is the formula for Transmission-Line Critical Length?
The formula is lcrit = tr / (2 × tpd). A PCB trace must be treated as a transmission line (with controlled impedance and termination) once its length exceeds the critical length, where the round-trip propagation delay becomes comparable to the signal rise time.
How do you find Rise Time when you know the other values?
Rearrange for Rise Time: with Critical Length 0.1 mm, Propagation Delay 0.1 ps/mm, Rise Time is 0.02 ps.
How do you find Propagation Delay when you know the other values?
Rearrange for Propagation Delay: with Critical Length 0.1 mm, Rise Time 100 ps, Propagation Delay is 500 ps/mm.
What units does Transmission-Line Critical Length use?
Critical Length is shown in mm, cm, m, km. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
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