Transmission Line Propagation Delay

td = length × √(LC)

Quick answer

This calculator solves td = length × √(L_per_unit × C_per_unit) for td. With Trace Length 10 cm, Inductance per Unit Length 5 nH/cm, Capacitance per Unit Length 1 pF/cm, the result is 7.07 × 10⁻¹⁰ s.

Calculator

Result
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Formula

td = length × √(L_per_unit × C_per_unit)

Description

The propagation delay of a signal through a PCB trace depends on the trace length and the per-unit-length inductance and capacitance of the transmission line structure. For FR-4 microstrip, the delay is approximately 6-7 ns per meter (60-70 ps per cm). For stripline, it is about 7-8 ns per meter because the signal is fully immersed in dielectric. This delay is critical for timing analysis in high-speed digital systems, determining when signals arrive at their destinations and whether setup and hold times are met at receiving flip-flops.

Variables

  • td — Propagation delay (s)
  • length — Trace length (m)
  • L_per_unit — Inductance per unit length (H/m)
  • C_per_unit — Capacitance per unit length (F/m)

Practical Notes

For FR-4 microstrip: approximately 6.4 ns/m (64 ps/cm). For FR-4 stripline: approximately 7.2 ns/m (72 ps/cm). Propagation velocity = 1/√(LC) = c/√εr_eff. For microstrip, εr_eff ≈ (εr+1)/2 because half the field is in air. Length matching for differential pairs and clock distribution typically requires matching to within 5-50 ps depending on the data rate.

Symbols and units

Symbol Meaning Default unit Accepted units
length Trace Length cm cm
Lpu Inductance per Unit Length nH/cm nH/cm
Cpu Capacitance per Unit Length pF/cm pF/cm

Step by step

  1. 1. What you know: Trace Length 10 cm, Inductance per Unit Length 5 nH/cm, Capacitance per Unit Length 1 pF/cm
  2. 2. The relation: td = length × √(L_per_unit × C_per_unit)
  3. 3. Substitute: length = 10 cm, Lpu = 5 nH/cm, Cpu = 1 pF/cm
  4. 4. Result: td = 7.07 × 10⁻¹⁰ s

Worked examples

Minimum range

Given: Trace Length 0.1 cm, Inductance per Unit Length 0.1 nH/cm, Capacitance per Unit Length 0.01 pF/cm

Result: td = 1 × 10⁻¹³ s

Low range

Given: Trace Length 1 cm, Inductance per Unit Length 1 nH/cm, Capacitance per Unit Length 0.1 pF/cm

Result: td = 1 × 10⁻¹¹ s

Typical

Given: Trace Length 10 cm, Inductance per Unit Length 5 nH/cm, Capacitance per Unit Length 1 pF/cm

Result: td = 7.07 × 10⁻¹⁰ s

High range

Given: Trace Length 100 cm, Inductance per Unit Length 20 nH/cm, Capacitance per Unit Length 10 pF/cm

Result: td = 4.47 × 10⁻⁸ s

Maximum range

Given: Trace Length 1000 cm, Inductance per Unit Length 200 nH/cm, Capacitance per Unit Length 100 pF/cm

Result: td = 4.47 × 10⁻⁶ s

How td changes with Trace Length

Trace Length (input) td (result)
1 cm 7.07 × 10⁻¹¹ s
2.5 cm 1.77 × 10⁻¹⁰ s
5 cm 3.54 × 10⁻¹⁰ s
7.5 cm 5.3 × 10⁻¹⁰ s
10 cm 7.07 × 10⁻¹⁰ s
15 cm 1.06 × 10⁻⁹ s
20 cm 1.41 × 10⁻⁹ s
40 cm 2.83 × 10⁻⁹ s
70 cm 4.95 × 10⁻⁹ s
100 cm 7.07 × 10⁻⁹ s

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Frequently asked questions

How do you calculate Transmission Line Propagation Delay?

Use td = length × √(L_per_unit × C_per_unit). With Trace Length 10 cm, Inductance per Unit Length 5 nH/cm, Capacitance per Unit Length 1 pF/cm, td works out to 7.07 × 10⁻¹⁰ s.

What is the formula for Transmission Line Propagation Delay?

The formula is td = length × √(L_per_unit × C_per_unit). The propagation delay of a signal through a PCB trace depends on the trace length and the per-unit-length inductance and capacitance of the transmission line structure.

Related Concepts

All PCB & Traces formulas →
Trace Current Capacity (IPC-2221) Trace Resistance Trace Voltage Drop Via Current Capacity (IPC-2221) Microstrip Impedance Stripline Impedance Differential Pair Impedance Transmission Line Propagation Delay

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