Transmission & Grid calculator
Transmission Line Calculator: RLGC, Delay & Reflections
Calculate distributed-line AC characteristic impedance and propagation constants, plus lossless travel time and the first two step-wave arrivals.
GridBasis: Distributed RLGC equations · analytical lossless step arrivals
Results
- Enter values to calculate
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How to use this calculator
A transmission line stores energy along its length. Distributed resistance, inductance, conductance and capacitance describe that behavior more faithfully than a single lumped impedance for wave propagation. This calculator gives AC characteristic impedance and propagation constants using all four RLGC parameters.
The step-wave outputs are a separate lossless approximation: reflections first reach the load after one travel time, and the next load increment arrives after three travel times. They help explain switching-wave timing but are not a numerical inverse-Laplace solver for a lossy, frequency-dependent, multiphase line.
Formula
∂v/∂x = −R′i − L′∂i/∂t; ∂i/∂x = −G′v − C′∂v/∂t
γ(jω) = √[(R′+jωL′)(G′+jωC′)]; Zc(jω) = √[(R′+jωL′)/(G′+jωC′)]
For the lossless approximation: Z0 = √(L′/C′); velocity = 1/√(L′C′); τ = length √(L′C′).
ΓL = (RL−Z0)/(RL+Z0); ΓS = (RS−Z0)/(RS+Z0); Vincident = Vs Z0/(RS+Z0)
ΔVload at τ = Vincident(1+ΓL); ΔVload at 3τ = Vincident(1+ΓL)ΓLΓS
AC γ is per km when R′, L′, G′ and C′ are all per km. Convert mH to H and µF to F. For zero initial conditions the Laplace-domain parameters replace jω by s; a full transient requires boundary conditions and numerical inversion.
Worked example
With L′ = 1 mH/km, C′ = 0.01 µF/km and length = 100 km, the lossless surge impedance is 316.23 Ω and one-way delay is 0.31623 ms. For a 500 Ω resistive load, ΓL = 0.22515. The reflected step depends on the source termination as well as the load.
Assumptions and standards
- Single uniform line mode; constant RLGC; positive L and C; real source/load resistances.
- AC propagation includes R and G. Step results deliberately neglect both losses.
- No conductor geometry extraction, mutual coupling or frequency-dependent parameter fitting.
Calculation model checked: November 4, 2026
Frequently asked questions
Is characteristic impedance the line series impedance?
No. Characteristic impedance relates a travelling wave voltage to its current. Series impedance is the accumulated R+jωL along the line.
Does this numerically invert Laplace transforms?
No. It gives distributed-line AC parameters and analytical lossless step arrivals. A full Laplace transient needs the complete boundary-conditioned transfer function and a validated inversion method.
Can I use these results for final design?
Use them for preliminary design and checking. Final designs must be verified by a qualified engineer against the code edition and standards adopted where the work is installed.
Is my data sent anywhere?
No. Every calculation runs in your browser. Nothing you type is uploaded or stored on our servers.
References and further reading
Power system calculations: formulas and model guide