Magnetic Loop Antenna Selfmade Tubby indoor HB9ISP

Info: Homebrew rectangular loop made of thick copper tubing with vacuum capacitors, 10 m to 160 m.
Conductor: Copper tube 100mm
Capacitor: Vacuum Capacitor
Environment: Placed in an upstairs room of a timber-frame house, 0.8 m above the floor.

Antenna Efficiency Overview

Band		160m	80m	60m	40m	30m	20m	17m	15m	12m	10m
Frequency f	MHz	1.840	3.573	5.358	7.075	10.135	14.077	18.098	21.075	24.922	28.070
Intrinsic bandwidth B_int	kHz	1.8	3.5	8.5	15.5	28.1	97.3	263.4	206.8	273.5	356.9
Source of B_int		S-Parameters
Loop diameter D	m	1.006
Conductor diameter d	m	0.100
Loop count n	1	1
Inductance L	H	1.51e-06
Capacitance C	pF	4953	1314	584	335	163	84.6	51.2	37.8	27	21.3
Unloaded Q₀	1	1005	1033	632	456	361	145	69	102	91	79
Damping resistance R_T	Ohm	0.0174	0.0328	0.0804	0.147	0.267	0.923	2.499	1.962	2.595	3.386
Radiation resistance R_R	Ohm	0.000028	0.000398	0.00201	0.00613	0.0259	0.0969	0.267	0.493	0.974	1.582
Loss resistance R_Loss	Ohm	0.0173	0.0324	0.0784	0.141	0.241	0.826	2.233	1.468	1.621	1.804
Power to antenna P_fwd	W	100	100	100	100	100	100	100	100	100	100
swr_min_ant	1	1.10	1.13	1.06	1.09	1.05	1.02	1.02	1.02	1.02	1.02
eta_{SWR_ant}	%	99.8	99.6	99.9	99.8	99.9	100.0	100.0	100.0	100.0	100.0
Power antenna load P_load	W	100	100	100	100	100	100	100	100	100	100
Antenna efficiency η	%	0.161	1.21	2.50	4.16	9.70	10.5	10.7	25.2	37.5	46.7
Loop current I rms	A	75.80	55.11	35.25	26.05	19.36	10.41	6.33	7.14	6.21	5.43
Loop voltage U_loop rms	V	1323	1868	1792	1748	1861	1390	1086	1428	1468	1447
Magnetic dipole moment m	A m²	60.283	43.829	28.036	20.716	15.395	8.279	5.031	5.678	4.936	4.322
Link to calculator		calculator	calculator	calculator	calculator	calculator	calculator	calculator	calculator	calculator	calculator

Environment

The antenna was suspended from the ceiling on the upper floor, about 0.8 m above the floor. Several indoor positions were tested; the position shown gave comparatively low damping. The house is built in timber-frame construction. Additional features include a green roof with moist soil, a nearby PV system, aluminum-coated underfloor heating, stainless steel canopies, and aluminum window frames. Together, these factors still make for a challenging indoor RF environment.

Upper-floor floor plan. Red: antenna positions.

Perspective view of the house. Antenna in the room below point M.

The values shown on this page are newer than those in the linked paper below. They were determined from S-parameter measurements.
The values in the paper were determined using the VSWR = 2.62 criterion.

A detailed description is available in this paper: https://arxiv.org/abs/2607.10828

VNA measurements

The antenna S11 parameters were measured with the NanoVNA SAA2.
The following values were derived from these measurements.
Details on the measurement method can be found here.

The calibration of the VNA was done at the antenna feed point: green line.

The cable attenuation alpha and the cable delay tau in the following table should therefore be small.

File	model f0 MHz	model Bint kHz	model alpha db	model_tau ns	SWR_min_vna	SWR_min_ant	eta SWR
20261027_0939_tubby_indoor_saa2_1p8MHz_VALUES.py	1.840	1.8	0.003	0.54	1.10	1.10	0.998
20261102_0907_tubby_indoor_saa2_3p6MHz_VALUES.py	3.573	3.5	0.000	2.05	1.13	1.13	0.996
20261102_0952_tubby_indoor_saa2_5p4MHz_VALUES.py	5.358	8.5	0.007	7.79	1.06	1.06	0.999
20261102_0958_tubby_indoor_saa2_7p1MHz_VALUES.py	7.075	15.5	0.032	7.92	1.09	1.09	0.998
20261102_1457_tubby_indoor_saa2_10p1MHz_VALUES.py	10.135	28.1	0.003	6.47	1.05	1.05	0.999
20261102_1503_tubby_indoor_saa2_14p1MHz_VALUES.py	14.077	97.3	0.000	8.10	1.02	1.02	1.000
20261102_1508_tubby_indoor_saa2_18p1MHz_VALUES.py	18.098	263.4	0.000	8.35	1.02	1.02	1.000
20261102_1517_tubby_indoor_saa2_21p1MHz_VALUES.py	21.075	206.8	0.229	6.88	1.02	1.02	1.000
20261102_1524_tubby_indoor_saa2_24p9MHz_VALUES.py	24.922	273.5	0.000	6.94	1.02	1.02	1.000
20261102_1530_tubby_indoor_saa2_28p1MHz_VALUES.py	28.070	356.9	0.000	6.54	1.02	1.02	1.000

The following diagrams: red points = measured values; green line = fitted model.

Smith

SWR

Values

20261027_0939_tubby_indoor_saa2_1p8MHz

model_f0	1.840	MHz
model_Bint	1.8	kHz
model_alpha	0.003	db
model_tau	0.54	ns
SWR_min_vna	1.10
SWR_min_ant	1.10
eta_SWR_ant	0.998

20261102_0907_tubby_indoor_saa2_3p6MHz

model_f0	3.573	MHz
model_Bint	3.5	kHz
model_alpha	0.000	db
model_tau	2.05	ns
SWR_min_vna	1.13
SWR_min_ant	1.13
eta_SWR_ant	0.996

20261102_0952_tubby_indoor_saa2_5p4MHz

model_f0	5.358	MHz
model_Bint	8.5	kHz
model_alpha	0.007	db
model_tau	7.79	ns
SWR_min_vna	1.06
SWR_min_ant	1.06
eta_SWR_ant	0.999

20261102_0958_tubby_indoor_saa2_7p1MHz

model_f0	7.075	MHz
model_Bint	15.5	kHz
model_alpha	0.032	db
model_tau	7.92	ns
SWR_min_vna	1.09
SWR_min_ant	1.09
eta_SWR_ant	0.998

20261102_1457_tubby_indoor_saa2_10p1MHz

model_f0	10.135	MHz
model_Bint	28.1	kHz
model_alpha	0.003	db
model_tau	6.47	ns
SWR_min_vna	1.05
SWR_min_ant	1.05
eta_SWR_ant	0.999

20261102_1503_tubby_indoor_saa2_14p1MHz

model_f0	14.077	MHz
model_Bint	97.3	kHz
model_alpha	0.000	db
model_tau	8.10	ns
SWR_min_vna	1.02
SWR_min_ant	1.02
eta_SWR_ant	1.000

20261102_1508_tubby_indoor_saa2_18p1MHz

model_f0	18.098	MHz
model_Bint	263.4	kHz
model_alpha	0.000	db
model_tau	8.35	ns
SWR_min_vna	1.02
SWR_min_ant	1.02
eta_SWR_ant	1.000

20261102_1517_tubby_indoor_saa2_21p1MHz

model_f0	21.075	MHz
model_Bint	206.8	kHz
model_alpha	0.229	db
model_tau	6.88	ns
SWR_min_vna	1.02
SWR_min_ant	1.02
eta_SWR_ant	1.000

20261102_1524_tubby_indoor_saa2_24p9MHz

model_f0	24.922	MHz
model_Bint	273.5	kHz
model_alpha	0.000	db
model_tau	6.94	ns
SWR_min_vna	1.02
SWR_min_ant	1.02
eta_SWR_ant	1.000

20261102_1530_tubby_indoor_saa2_28p1MHz

model_f0	28.070	MHz
model_Bint	356.9	kHz
model_alpha	0.000	db
model_tau	6.54	ns
SWR_min_vna	1.02
SWR_min_ant	1.02
eta_SWR_ant	1.000

Inductance

The main loop inductance is an important parameter because it directly affects the antenna efficiency calculation.
The inductance can be estimated from geometry (L). In general, an additional measurement is used as a cross-check, especially for non-circular loops where the geometric estimate is more difficult.

Inductance cross-check measurement

The resonance frequency of the LC circuit depends on L and C. Additional known capacitors are connected in parallel with the existing capacitor, and the new resonance frequency is measured.

Capacitor switching concept — Schematic of the switched capacitors

Inductivity picture: 20261102_132615995_cap_switch.jpg — The switched capacitor is visible in the picture above.

f_NIX	10.191552	MHz	Resonance frequency with no additional capacitors connected.
f_OFF	10.137040	MHz	Capacitors and switches are physically connected at the antenna capacitor. A small parasitic capacitance from wiring and switches lowers the resonance frequency.
f₁₀₀	7.924246	MHz	Resonance frequency with an additional 100 pF capacitor switched in.
f₅₆₀	4.604633	MHz	Resonance frequency with an additional 560 pF capacitor switched in.
C₁₀₀	100.0	pF	Additional capacitance used for the 100 pF branch.
C₅₆₀	579.0	pF	Additional capacitance used for the 560 pF branch.
L	1.51e-06	H	Calculated from geometry of the main loop.
L₁₀₀	1.569e-06	H	Derived from the resonance frequencies f_OFF and f₁₀₀ deviation +4% vs L
L₅₆₀	1.638e-06	H	Derived from the resonance frequencies f_OFF and f₅₆₀ deviation +8% vs L
C_NIX	1.676e-12	As/V	Derived from using L₁₀₀, f_OFF, and f_NIX estimated parasitic capacitance of switches and wiring; expected value 1 ... 5 pF

The maximum deviation between L and the capacitor-based L_1x values is +8%. This is considered a small deviation and is accepted. L is used for the calculations of the antenna efficiency.

Overview of all Antennas with filter/selection: compare page
Overview of all Antennas static: static compare page
2026 Peter Märki (HB9ISP). This project is created in my free time and has no commercial background. Provided without warranty of any kind. Feedback is welcome.