Electrical tools
Distortionless Line Designer
Check the Heaviside condition (R/L = G/C), design Pupin loading coils, and compare attenuation and phase velocity across the voice band for original, loaded, and ideal distortionless transmission lines.
liveHeaviside 1887 · Pupin 1900
Line preset
Typical 0.4 mm copper twisted pair, pre-1900 telegraph/telephone line. Severe distortion.
Heaviside condition — R/L = G/C
Severe distortionImbalance: 100.0%
R/L
1.67e+5 s⁻¹
G/C
2.00e+1 s⁻¹
Pupin loading coil design(spacing = 1.8 km)
Inductance / coil
8998.92 mH
Number of coils
28
Cutoff frequency
354 Hz
Post-load imbalance
0.0%
Secondary constants at 1 kHz
| Parameter | Original | Loaded | Distortionless |
|---|---|---|---|
| α (Np/km) | 0.1232 | 0.1057 | 0.0100 |
| β (rad/km) | 0.1275 | 0.1488 | 3.1416 |
| v_p (km/s) | 49272 | 42238 | 2000 |
| |Z₀| (Ω) | 564.4 | 580.9 | 10000.0 |
| ∠Z₀ (°) | -43.8 | -35.2 | 0.0 |
| Atten. (dB) | 53.50 | 45.91 | 4.34 |
Dispersion metrics (100 Hz → 3.4 kHz voice band)
Original linesevere
v_p at 100 Hz16076 km/s
v_p at 3.4 kHz86752 km/s
Velocity variation439.6%
Delay spread2.53 ms
Loaded linesevere
v_p at 100 Hz15818 km/s
v_p at 3.4 kHz55697 km/s
Velocity variation252.1%
Delay spread2.26 ms