Project

# Magnetic Field Strength Meter and Calibrator

October 28, 2022 by John Woodgate

## This project will explain how to develop a system to measure magnetic field emissions at frequencies up to 150 kHz from high-current power cables without cutting or disturbing the cable.

Magnetic fields are present almost everywhere. However, convenient means of assessing the magnetic field strength over wide ranges of strength and frequency (20 Hz to 150 kHz) are not widely available. Despite the limitations, there are still many reasons why you may need these measurements. One example is tracking down the interference from an unshielded or poorly-shielded cable.

In this project, we will develop a method to evaluate magnetic field emissions at frequencies up to 150 kHz from high-current power cables without cutting or disturbing the cable.

• A hand-held magnetic field meter with a field sensor probe
• A calibration reference verifier source capable of producing a magnetic field strength of up to 1000 A/m (amps per meter) or 1.26 mT

Generally, high-accuracy measurements are unlikely to be practicable or useful. This is because many magnetic field strengths, particularly at high frequencies, can vary considerably even over short periods and distances. In addition, it's important to note that the verifier overcomes a requirement for the instrument to have high intrinsic accuracy, but its stability is normally more than adequate.

### A Hand-held Unit for Measuring Magnetic Field Strength

Let's dive into the development and components of the hand-held magnetic field strength unit. To begin with, let's look at a block diagram of the meter and verifier shown in Figure 1.

##### Figure 1. Block diagram of the magnetic field meter and verifier.

Note that the meter is powered by a single 9 V battery. From here, we'll break down the different necessary components.

#### Magnetic Field Probe and Preamp

The probe consists of a 1.6 μH inductor that is 8 mm long and 7.5 mm in diameter. It is wound on an insulating former and has about 22 turns. An electrostatic shield (a single overlapped, insulated turn of copper foil) is provided. Regarding frequency response, the inductance value is not critical, but the physical dimensions affect the sensitivity. The probe is connected to a coaxial cable with the electrostatic shield connected to the cable shield.

The probe is directional, and normally it is placed with its axis vertical (assuming a horizontal cable) and senses the vertical component of the magnetic field. Still, the user can set it horizontally to measure the horizontal component.

Overall, the total field strength at a point is the square root of the sum of the squares of the vertical field, Hv, and the two components of the horizontal field, Hx and Hy.

$$H_{total} = \sqrt{H^2_v + H^2_x + H^2_y}$$

The schematic of the probe and preamp is shown in Figure 2.

##### Figure 2. Probe and preamp schematic.

The preamp is physically integrated with the main amplifier and shares a common ground. The output, X, from the preamp connects to the input, X, of the main amplifier schematic shown below in Figure 3.

##### Figure 3. Main amplifier schematic.

The preamp consists of a transconductance amplifier with a very low input impedance. This technique produces a flat frequency response from a mutual-inductance source. However, it can be impractical to obtain a low enough input impedance compared with the reactance of 1.6 μH at 20 Hz. One way to overcome this is to increase the inductance by a series 1 mH toroidal inductor insensitive to external magnetic fields. The resistance of the coil and the added 15 Ω resistor is compensated by including a capacitor in series with the 1 kΩ feedback resistor.

This inductor consists of about 20 turns on a ferrite toroid, 9.6 mm outside diameter, 4.7 mm inside diameter, and 3.2 mm thick. The Digi-Key part number of the toroid is 240-2522-ND. Commercially available 1 mH inductors are physically large parts designed to carry large currents and are unsuitable here.

#### Main Amplifier

The amplifier has only a small gain and includes two filters. When driving a high-impedance load, the probe, preamp, and main amplifier provide a sensitivity of 1 mV for 1 A/m field strength at the probe. The SI unit A/m (amps per meter) is a ‘small’ unit, as opposed to the farad, for example, which is a ‘big’ unit, so we normally use parts whose capacitance is a very small fraction of a farad. How small? Well, 1 A/m produces a flux density of 1.26 μT (microtesla) in the air or a vacuum, whereas the magnet in an earbud produces around 1 T.

Previously in Figure 3, we showed the schematic for the main amplifier. In it, the first stage is a 3rd-order low-pass filter to eliminate noise above about 200 kHz.

The low-pass filter is followed by a 3rd-order high-pass filter, whose -3dB frequency can be switched between 8 Hz and 800 Hz using switches S1a, S1b, and S1c. The switches can be implemented using a single 3-pole 2-way (or on-off) switch.

In Figure 3, the switches in the second stage are shown configured to produce an -3 dB frequency of 8 Hz from the second stage filter. This 8 Hz response is best for attenuating flicker noise in this wideband response mode. In this configuration, the full main amplifier provides a broadband output with a substantially flat response from below 20 Hz to 100 kHz and a limited fall up to 150 kHz, as shown in Figure 4. Because of the effect of other coupling capacitors (C2, C7, C11, C18), the -3 dB frequency of the full main amplifier response is 11 Hz.

##### Figure 4. Main amplifier frequency response showing the 3rd-order low-pass filter configured for an 8 Hz response.

For the 800 Hz high-pass response, 1.5 kΩ resistors are connected in parallel with R8, R9, and R11 to attenuate power frequency and harmonic components below 2 kHz. The main amplifier frequency response with the 800 Hz high-pass filter configuration is shown in Figure 5.

##### Figure 5. Main amplifier frequency response showing the 3rd-order high-pass filter configured for an 800 Hz response.

The filters look like Sallen-Key equal-component value 3rd-order Butterworth filters, but not exactly. For true Butterworth responses, the first passive sections should be followed by buffers so that the second sections are fed from low impedances. But for our purposes in this project, this is not necessary.

The output from the second-stage high-pass filter is applied to the third-stage low-power amplifier that provides an output that will drive a 50 Ω (or higher) load.

### Magnetic Field Strength Verifier

A simple way of producing a large magnetic field strength is to use a solenoid. The field strength and inductance can be calculated accurately from the physical dimensions and the current. The measured value of the inductance acts as a check on the calculated field strength.

The solenoid is 50 mm long, 16 mm in diameter, and has 200 turns. It is wound on a cardboard former (which will not melt if touched by a soldering iron). The former bore needs to be large enough to accommodate the probe, of course. It can be fitted with a phono connector glued in at one end (hence the need for soldering), so that it can be connected by a shielded cable to the verifier amplifier.

The verifier amplifier is a low-power amplifier using an LM386 operating from a 15 V supply. It is configured as a current-source output to produce a substantially constant current at any frequency from 20 Hz to 100 kHz, with a limited reduction up to 150 kHz.

The verifier schematic is shown in Figure 6.

##### Figure 6. Schematic of the verifier and solenoid.

The probe and solenoid are shown in Figure 7.

##### Figure 7. Probe and solenoid.

The frequency response of the verifier current output is shown in Figure 8. The magnetic field in the solenoid is, of course, strictly proportional to the current because air has a constant magnetic permeability.

##### Figure 8. Frequency response of the verifier current output.

It would be too much to expect the LM386 audio amplifier to produce 250 mA at 150 kHz and 1000 A/m in the solenoid. It will produce 250 mA up to 15 kHz, 25 mA up to 100 kHz, and 12.5 mA up to 150 kHz. Strong magnetic fields at high frequencies are rarely encountered.

Due to the highly-inductive load, the device gets quite warm when producing 250 mA. A heat sink could be glued onto it if the current needs to be supplied for more than a minute or two, which is normally quite long enough to check the calibration.

#### Using the Verifier

The probe coil is inserted into the solenoid to lie approximately at the halfway point to use the verifier. Moving the probe in and out shows how uniform the magnetic field strength is inside the solenoid; it changes only when the probe is near the end.

Figure 9 shows the overall frequency response from the verifier to the main amplifier output, with the main amplifier in broadband (11 Hz to 150 kHz) mode.

### Example Use Cases for the Magnetic Field Strength Meter

With all that in mind, let's explore some example use cases for this magnetic field strength meter.

#### Magnetic field leakage from a mains transformer

Although mains transformers are being replaced by switch-mode technology, billions are still in use, and for some purposes, they can be preferred. However, they do produce an external magnetic field, and the current is often not sinusoidal because the transformer feeds a rectifier with a filter capacitor. The field thus includes components at harmonics of the power frequency up to at least 10 kHz. This can cause significant ‘spikey hum’ interference in nearby audio circuits. Spikey hum is not a low growl: the harmonic content is exaggerated by the magnetic coupling process, where the induced voltage is proportional to its frequency. It used to be called ‘griddy hum’ in the days of tubes/valves with grids instead of bases or gates.

#### The magnetic field of a single straight conductor

The magnetic field direction is circular, centered on the conductor, and its strength, H, is accurately given by the formula:

$$H = \frac{I}{2πr}$$

Where:

• I = the current in amps
• r = the radius at which the field strength is measured

#### Magnetic field leakage from a flat cable (like Romex)

At a distance from the cable, compared with the spacing of the two current-carrying conductors, the magnetic fields from the opposing currents nearly cancel, but close to the cable, they do not. The field strength can be accurately calculated. Figure 10 shows the result of a simplified calculation of the vertical component of the field produced by two conductors 1 cm apart, with the conductors assumed extremely thin. It can be seen that the field strength falls off very rapidly with distance but can be quite strong close to the cable.

### Measured Values of Field Strength

In the next sections, we'll cover this project's different field strength measurements.

Magnetic Field Leakage From a Mains Transformer

At a distance of 25 mm from the enclosure of the transformer, the field strength measured 50 A/m. The waveform was a distorted 50 Hz sine wave. This field strength is plenty large enough to induce an audible ‘spikey hum’ signal in a nearby circuit.

#### Single Straight Conductor

The results of a measurement of a long (1 m), straight horizontal conductor carrying 10 A at 50 Hz are given in Table 1.

##### Table 1. A table showing the magnetic field of a long straight conductor

Distance From the Center of the Conductor (mm)

Output Voltage of the Meter (mV)

Magnetic Field Strength (A/m)

10 133 133
20 66 66
30 44 44
40 33 33
50 26 26

#### Magnetic Field Outside a Two-conductor Cable

Emissions measured at various distances from a horizontal two-conductor cable, with conductors 6 mm apart, are shown in Table 2.

##### Table 2. External vertical field of a 2-conductor cable

Distance From the Center of the Nearer Conductor (mm)

Output Voltage of the Meter (mV)

Magnetic Field Strength (A/m)

5 8.0 8.0
10 4.0 4.0
15 2.4 2.4
20 1.5 1.5
25 1.1 1.1

The cable carried the current of a 400 W resistive load dimmed to half current. The result cannot be compared numerically with Figure 9 because the conductors' diameter (1.6 mm) is not small compared with their spacing. However, Table 2 shows how the field strength decreases with distance.

Figure 11 shows the spectrum of the field in terms of voltage with the 50 Hz component at 7 mV, corresponding to 7 A/m.

##### Figure 11. Vertical magnetic field outside a 2-conductor cable, linear scale.

Figure 12 shows the same response in dB (mV), decibels referred to as 1 mV, to highlight the strengths of the higher-frequency components much better. Here we can see that the 150 Hz component is 7 dB below the 50 Hz fundamental, a ratio of 0.45. The harmonics actually extend up to about 10 MHz, but the spectrum analyzer will not extend to such frequencies.

### Field Strength Meter Prototype Summary

The two complete prototypes have been built on a plugboard with higher strays than printed boards. The performance of printed boards would likely be a little better.

#### Schematics

Schematics have been produced using the free and very powerful simulator LTspice (www.analog.com), with which I have no connection beyond being a satisfied user. They are reproduced as graphics, which will not run for simulation. The results of simulations are based on somewhat idealized parts with exact values. Component tolerances can affect the mid-frequency gain a little and cause gain variations at the extremes of the frequency response. While these could be corrected by adding several preset components, the verifier makes this unnecessary.

#### Frequency Responses and Spectra

The frequency responses and spectra are actual measurements captured and plotted using an affordable add-on for a PC, the Instrustar USB Oscilloscope ISD205C (www.instrustar.com). Again, I am simply a satisfied user. The user interface does need a bit of learning.

1 Comment
• M
MisterBill2 November 04, 2022

What I see as interesting is the definition of a “large ” current, at the start of this article. And I am presuming that the conductor would pass through the center of that coil, but torroid coils are mostly self shielding, with very little external field, and thus not very sensitive to external fields.  Aside from that, magnetic fields reduce with the square of the separation distance, and so a simple means of reduction is via separation. So while this article is educational, the utility of the device for other than measuring current in conductors is unclear to me.
Avoiding magnetic pickup by sensitive circuitry is a fairly well understood process, with a great deal of information available.
But certainly the value of this article as a description of the design process is good.

Like.