MAGNETIC MOMENTS, Number 10
A probe to measure RF magnetic fields
and the Magnetic Moment of a transmitting loop.
(originally printed in Speleonics 20, Feb. 1994, p8.)
By Ian Drummond
Before describing the magnetic field probe, some background material on measurement of AC voltages may be useful.
Most voltmeters have a setting to measure "AC Volts". When making a measurement the test leads connect the circuit to the meter, where a diode rectifier converts the AC voltage to DC, which is measured and displayed. This arrangement works well at low frequencies, such as 60 Hz household power frequencies, but becomes increasingly inaccurate as the frequency rises. By 100 kHz, most meters will have errors of at least 50% in the indicated voltage, but depending upon the meter significant errors may happen at frequencies as low as 1 kHz.
There are several sources of error, but two of the most important are loading the circuit under test, and signal pick-up by the test leads.
For accurate measurement the meter must not draw significant current from the test circuit. When measuring DC voltages this means using a high input resistance voltmeter, often 10 Meg Ohm. For AC voltages the input capacitance must also be small, otherwise significant AC currents can flow.
With AC voltages and currents, the test leads can act as small antennas and totally spurious signals can be coupled into the test circuit.
The solution to these problems is to move the rectifier diode to the circuit end of the test leads, and use shielded leads to connect the meter to the circuit. The meter is set to read "DC Volts" as it is measuring the rectified voltage. Such a device is called an "RF Probe". RF probes can be purchased for many voltmeters, or easily constructed. The American Radio Relay League (ARRL) Handbook for Radio Amateurs has construction details and states that the finished probe is accurate to +/- 10% over the frequency range of 50 kHz to 250 MHz with an input impedance of 6000 Ohms shunted by a capacitance of 1.8 pF. My Heathkit probe states that it is useful down to 1 kHz.
The RF magnetic field probe is built on the same principles as the RF voltage probes. The rectifier circuit is located at the test site, and a shielded cable carries a DC voltage back to the meter. The circuit diagram is shown here.
I wound 50 turns of 32 AWG (0.203 mm dia.) wire on to a plastic 35 mm film canister, and mounted the capacitor, resistor, and diode inside the canister. A length of 1/4" (6mm) wood dowel was inserted through the diameter of the canister to act as a wand, and the coaxial cable was run down the wand and connected inside the canister.
It is important that the DC voltmeter must have an input resistance of 10 M Ohm, as this resistance forms half of a voltage divider to indicate RMS voltage, and hence RMS magnetic field strength.
The intensity of the magnetic field is given by
- H (Amp/m) = 1.27 x 105 . V / f . A . n
| where: V = | measured DC voltage |
| f = | frequency (Hz) |
| A = | area of RF probe loop (m2) |
| n = | no. of turns on RF probe |
For the probe described above, 50 turns on a film can, this becomes
- H (Amp/metre) = 3.2 x 106 . V / f
The magnetic moment of a cave radio transmitting antenna can be calculated directly from the strength of the magnetic field at the centre of the loop. The magnetic moment of a transmitting antenna is a very important parameter in determining the range of a radio. Normally it has been estimated by calculation (see a computer program in Speleonics #2, Magnetic Moments #2, by Ian Drummond, 1985), or by a multi-step measurement procedure where the current in the transmitting loop is calculated from knowledge of the power, and AC resistance of the loop at the operating frequency (which is often several times higher than the DC resistance of the loop.
The magnetic field at the centre of a circular loop of n turns of wire carrying a current of I Amps is given by the following expression:
- H (A/m) = n . I / 2 a
- where a = radius of transmitting loop (m)
Since the magnetic moment of the transmitting loop equals n.I.A, we can derive that the magnetic moment is equal to :
- M (amp.turn.m2) = 2 . p . H . a3
Thus if the RF magnetic field probe is used to measure the magnetic field at the hub of a transmitting loop (the RF probe must be small in diameter compared to the transmitting loop), the magnetic moment of the transmitting loop can be directly estimated.
Example
Consider a 1 metre square, 3 turn loop antenna operating with 2 watts of power at 185 kHz.
The Direct Measurement Method.
The RF probe gave a reading of 105 mV at the hub of the loop.
The magnetic field at the hub is
- H (A/m) = 3.2 x 106 x 0.105 / 185,000 = 1.8 A/m
The effective radius (radius of a circle with the same area) of the 1 metre square loop is 0.564 m, so the magnetic moment of the antenna is given by:
- Magnetic moment (A.m2) = 2 p . (0.564)3 . 1.8 = 2.0 A.m2
The Calculation Method
To calculate the magnetic moment the following information is needed, either by measurement, or further calculation.
- L = 39.6 micro Henries
- Q = 43
- f = 185 kHz
- P = 2 watts
| AC Resistance = | R(AC) = 2 p . f .L / Q |
| = | 6.28 x 185,000 x 39.6 x 10-6 / 43 |
| = | 1.07 Ohms |
| The current in the windings = | I amps = sqrt(power/R(AC)) |
| = | sqrt( 2 / 1.07) |
| = | 1.37 A |
| The magnetic moment = | Turns x current x area |
| = | 3 x 1.37 x 1 Amp.m2 |
| = | 4.1 A.m2 |
The agreement between the two independent methods of estimating the magnetic moment is not particularly good. The RF probe opens the way to much easier and more accurate testing of antennas, of their efficiency at converting electrical power into magnetic moment.
Incidentally, the computer program from Speleonics 2, mentioned above also predicts a value of 4.1 A.m2 for the experimental antenna.
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