Magloop (Magnetic Loop) Antenna Calculator

Calculator for single-turn magnetic loop antennas (Small Transmitting Loop, STL) on HF. Enter the loop dimensions, the material and the operating frequency: the calculation runs in your browser and updates on every change.

Main loop diameter (cm)Conductor diameter (mm)Conductor materialCopperAluminumSilverSilver-plated copperOperating frequency (MHz)Transmit power (W)Extra loss (connections, CV) (Ω)CV minimum (pF, optional)CV maximum (pF, optional)Coupling loop (cm, optional)

Results at the operating frequency

Wavelength	21.19 m
Circumference / λ	0.1483
Inductance	2.508 µH
Inductive reactance	223.0 Ω
Resonant capacitance	50.4 pF
Radiation resistance (Rr)	0.0954 Ω
Ohmic (RF) resistance	0.0490 Ω
Total loss resistance	0.0490 Ω
Efficiency	66.1 %
Q	1544
Bandwidth (−3 dB)	9.2 kHz
Loop current	26.3 A
Capacitor voltage	5867 V

Coupling loop

• Standard (1/5): 20.0 cm
• Tight coupling (1/8): 12.5 cm

Chart

Operating frequency Band centers

Band comparison

Band	MHz	Eff. %	Rr (Ω)	Rloss (Ω)	C (pF)	CV	Q	BW (kHz)	Loop
160m	1.900	0.2	0.0000	0.0180	2797.8	-	1664	1.1	OK
80m	3.750	1.8	0.0005	0.0252	718.2	-	2299	1.6	OK
60m	5.369	6.1	0.0020	0.0302	350.4	-	2630	2.0	OK
40m	7.150	15.2	0.0062	0.0348	197.6	-	2744	2.6	OK
30m	10.125	37.6	0.0250	0.0415	98.5	-	2400	4.2	OK
20m	14.175	66.2	0.0961	0.0491	50.3	-	1539	9.2	OK
17m	18.118	82.2	0.2565	0.0555	30.8	-	915	19.8	OK
15m	21.225	88.9	0.4831	0.0600	22.4	-	616	34.5	OK
12m	24.940	93.4	0.9209	0.0651	16.2	-	399	62.6	OK
10m	28.850	95.9	1.6490	0.0700	12.1	-	264	109.1	OK

Equations

The formulas are the classic small-loop theory (electrically small loop, uniform current), cross-checked against the references at the end of the page.

Where $f$ is the frequency, $c$ the speed of light, $D$ the loop diameter, $d$ the conductor diameter, $C=\pi D$ the circumference, $N=1$ the number of turns, $\rho$ the conductor resistivity, $\mu_0 = 4\pi\cdot10^{-7}$ H/m, $\omega=2\pi f$ and $P$ the power.

1. Wavelength

$$\lambda = \frac{c}{f}$$

2. Loop inductance (Terman)

$$L = \mu_0 \cdot \frac{D}{2} \cdot \left[\ln\!\left(\frac{8D}{d}\right) - 2\right]$$

3. Radiation resistance (Kraus)

$$R_r = 20\pi^2 N^2 \left(\frac{C}{\lambda}\right)^{4}$$

4. Skin depth

$$\delta = \sqrt{\frac{\rho}{\pi f \mu_0}}$$

5. Ohmic (RF) resistance

$$R_{ohmic} = \frac{\rho \, C}{\pi \, d \, \delta}$$

6. Inductive reactance

$$X_L = 2\pi f L$$

7. Resonant capacitance

$$C_{tune} = \frac{1}{\omega^{2} L}$$

8. Efficiency

$$\eta = \frac{R_r}{R_r + R_{loss}}$$

9. Unloaded Q

$$Q = \frac{X_L}{R_r + R_{loss}}$$

10. Bandwidth (−3 dB)

$$BW = \frac{f}{Q}$$

11. Loop current

$$I = \sqrt{\frac{P}{R_r + R_{loss}}}$$

12. Capacitor voltage at resonance

$$V_C = I \cdot X_L$$

13. Coupling loop (empirical range)

$$\tfrac{1}{8}\,D \;\le\; D_{coupling} \;\le\; \tfrac{1}{5}\,D$$

Small-loop validity: the Rr formula assumes uniform current. In amateur practice it is accepted up to a circumference of about 1/3 λ (most accurate below 1/10 λ). Above that the table flags LARGE and results should be treated as approximate.

On Q and capacitor voltage: some calculators (for example AA5TB's) halve Q for the "loaded/matched" condition, which also reduces the capacitor voltage. Here current and voltage come directly from the power balance, the more conservative figure for choosing the capacitor voltage rating. Always add a safety margin.

Coupling loop

None of the references gives a closed-form equation for the coupling loop size; matching is empirical. According to N4SPP/K5IJB:

• Standard starting diameter: 1/5 of the main loop diameter.
• Tighter-coupling alternative: as small as 1/8.
• Placement: in the same plane as the main loop, opposite the tuning capacitor, as close to the conductor as practical (SWR rises roughly linearly with the spacing between the loops).
• Final match: rotate the coupling loop about its feed axis instead of calculating.

References

• The ARRL Antenna Book (small/loop antenna chapter) and The ARRL Handbook for Radio Communications.
• Antena Magnetic Loop (PY4ZBZ)
• Small Transmitting Loop Antenna (AA5TB)
• Small Transmitting Loop Antenna Calculator (66pacific)
• Coupling Loop Configurations for Small Magnetic Loop Antennas (N4SPP / K5IJB)
• Loop Antenna Characteristics (Hi-Q Antennas)
• Small Magnetic Loop FAQ (K5IJB)