Demonstrating the Barkhausen effect with high signal-to-noise ratio

The Barkhausen detector is intentionally sensitive to minute changes of the magnetic field inside the detector coil. Therefore, any electromagnetic radiation from external sources causes noise. In particular, electromagnetic radiation from transformers and rectifier diodes in the apparatus itself is detected, see figure 1. Therefore the coil must be kept at a distance from any line-driven electric apparatus, including the amplifier for the present setup.

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Keeping away from transformers is necessary, but not sufficient. A typical experimental teaching environment is polluted with electromagnetic stray radiation from various sources. A very similar problem has been solved for electric guitars: the pickup consists of a coil, which is not only sensitive to the varying field of the magnetised vibrating string, but also to any other electromagnetic signal. A second coil of opposite winding is connected in parallel, with a magnet of opposite polarity. The signal from the vibrating string is doubled, while the noise cancels. This scheme is called hum-bucking.

A modified form of hum-bucking is used for the Barkhausen coil. While it is impossible to create a signal of opposite sign, one can still add a second coil with opposite polarity, which cancels the noise, but subtracts little or nothing off the sample's signal. One can put two coils of the same kind spatially and electrically in parallel and then turn around one coil by 180°. Alternatively, one can use a single coil with a central contact. Then the sample is placed asymmetrically in the first part of the coil, while the second part is left empty, see figure 2. The outer contacts are earth potential, and the signal is at the centre. Hum-bucking only works in spatially homogeneous fields. Therefore keeping away from radiating sources still is good advice. Inhomogeneous modification of electromagnetic fields, for example from an iron frame under a tabletop, should be avoided.

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Barkhausen used a coil with 300 turns. Early quantitative research by Tyndall [4] was carried out with 10 000 turns. Fewer turns are easier to handle in terms of noise and bandwidth, but require a higher amplification. A small cross section yields low inductance, and little sensitivity to electromagnetic noise, but a larger coil is easier to see by the audience. The present work was done with a large coil with 30 mm square opening, 1800 + 1800 turns with a central contact and $L=0.150\,{\rm{H}}$ and $R=75\,{\rm{\Omega }}$ for each half of the coil.

The coil should be connected directly to earth in order to minimise the influence of external fields. However, in many practical cases, one or several components of the system are connected to earth potential through their mains supply. A second earth contact at the coil defines a loop, in which induction can occur. This so-called earth loop causes a periodic noise signal and therefore the number of earth contacts has to be limited to one. Some audio amplifiers are connected to earth through a resistor of the order of 10–100 Ω in order to avoid the problem of earth loops. In such a case one has to find the best earthing scheme by trial and error.

The Barkhausen signal is of the order of below 1 mV and hence too weak for being transmitted by a power amplifier and audio speaker directly. Therefore, a pre-amplifier with 1000-fold voltage gain (60 dB) is required.

Upon changing the external magnetic field, a voltage with DC and low frequency components is induced in the coil. This perturbing induction voltage depends on the rate of field change, but typically is much larger than the signal from the ferroelectric sample. It is amplified as well as the signal, because the operational amplifier works at DC and modern power amplifiers have a very low frequency cutoff below 10 Hz. The cone of the speaker is driven easily to its mechanical limit and in the best case, the speaker does not speak. In the worst case, the speaker is destroyed. The problem of low frequency induction could be controlled by very slowly changing the magnetic field with a function generator, as reported in reference [5]. However, the free hand approach of a permanent magnet makes the demonstration easier to recognise, and more similar to the historic experiment.

The low frequency components are blocked with a steep high pass filter. The cutoff frequency is set to 70 Hz. It is near the low frequency limit of the compact speaker used in the present setup. Since the Barkhausen noise is a superposition of short pulses, very low frequencies are secondary.

A low-pass filter at the high frequency limit of the audio range is also important, because the coil is very sensitive to electromagnetic background. Noise at inaudible frequencies above 20 kHz can be parasitic to the limited power of the amplifier, overheat the speaker, or cause oscillation of the whole circuit. The upper frequency limit of 17 kHz was carefully tried out by listening and the value was chosen, at which further increase of the limit did not improve the sound.

The effort it takes to build a preamplifier from scratch is most likely less than the effort to understand and modify an existing amplifier. The following circuit is a variation of a simple, non-inverting operational amplifier circuit from reference [6]. The circuit is shown in figure 3.

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The non-inverting amplifier scheme is compatible with a wide range of coil resistance and inductance, as opposed to the inverting setup, which requires careful matching. The input resistor R₁ is chosen as 47 kΩ according to the standardised value in audio preamplifiers. Together with the coil inductance $L,{R}_{1}$ forms a low-pass with cutoff frequency ${\omega }_{c}={R}_{1}/L$. The low-pass must not extend to the audible range. With ${R}_{1}=47$ k${\rm{\Omega }},L\lt 0.37\,{\rm{H}}$.

The 60 dB gain of the preamplifier could be accomplished with a single operational amplifier, but two gain stages make it easier to suppress the unwanted low frequency components. The first stage has a gain of $g=1+{R}_{2}/{R}_{3}$, i.e. 30 dB. The capacitor in parallel to R₂ reduces the gain for high frequencies, when the impedance of C₂ becomes smaller than R₂; this is a low-pass with cut-off at ${\omega }_{l}={R}_{2}{C}_{2}=2\pi \cdot 17\,\mathrm{kHz}$. The impedance of capacitor C₁ enhances R₃ for low frequencies and acts as a high-pass with the cut-off at 70 Hz. The gain of the operational amplifier is unity at DC, and therefore a second high-pass is essential.

The first gain stage is followed by a passive bandpass, which consists of the high pass with cut-off frequency 32 Hz and a low pass with cut-off frequency 17 kHz. After the second filter, the input signal for the second gain stage contains little low frequency components, and saturation of the operational amplifier is very unlikely. The second gain stage is the same as the first one for the sake of simplicity.

Both operational amplifiers add noise to the signal, but only the contribution of the first one is relevant. It is worthwhile to use a low-noise operational amplifier for the first gain stage, such as OP27 [7] Compared to an all-purpose LM741, the noise reduction is clearly audible, and the measurement yields an improvement of −5 dB.

The supply voltage is provided by a small laboratory power supply ±15 V or a pair of lead batteries ±12 V. A battery most certainly does not introduce any noise. A power supply connected to a socket must not to be placed near the coil or on the preamplifier's circuit board.

The output of the preamplifier is on the same voltage level as the output of a CD-player or a headphone plug. Therefore any audio amplifier and speaker can be used to present the Barkhausen signal to the audience. The choice of the actual audio system used depends on the size of the room. Since the Barkhausen signal contains lots of high frequency components, it is worthwhile to check by listening whether the available laboratory speaker is sufficient, or if a high fidelity speaker yields a better sound. The latter might be more efficient as well. For the present setup, a compact active speaker Abacus C-Box was used. Its mains connection has no earth contact.