Simple RF Coil Designer
Designs a single-turn loop coil for MRI or NMR. Given the loop dimensions and Larmor frequency, calculates self-inductance using the Wheeler formula and the tuning capacitor required for resonance.
Equations & Parameters ▸
\(L = \mu_0\mu_r\!\left(\tfrac{D}{2}\right)\!\left[\ln\!\left(\tfrac{8D}{d}\right)-2\right] \qquad C = \dfrac{1}{4\pi^2 f^2 L}\)
| d | Wire diameter (mm). Thicker wire → lower resistance → higher Q. |
| D | Loop diameter (mm). Larger loop → more inductance, more signal sensitivity. |
| f | Larmor frequency — the resonant frequency of the nucleus in the static B₀ field. ¹H at 3T ≈ 128 MHz, at 7T ≈ 298 MHz. |
| L | Self-inductance (Rosa formula). |
| C | Required tuning capacitor for resonance at f. |
Physical constants used
| µ₀ | 4π×10⁻⁷ H/m |
| ¹H γ/2π | 42.577 MHz/T (Larmor frequency per Tesla) |
| ¹H at 1.5 T | 63.87 MHz |
| ¹H at 3 T | 127.74 MHz |
| ¹H at 7 T | 297.7 MHz |
| σ_muscle @ 128 MHz | ≈ 0.77 S/m |
| ε_muscle @ 128 MHz | ≈ 58 |
| IEC SAR limit (WB normal) | 2 W/kg (over 6 min) |
| IEC SAR limit (head) | 3.2 W/kg (over 10 min) |
Inputs
Loop geometry
mm
Conductor diameter, not radiusmm
Centre-to-centre of conductorField parameters
¹H at 3T ≈ 128 MHz
Results
Coil Parameters
Self-inductance, L—
Tuning capacitor, C—
Diagram