# New Magnetstrictive Transducer Designs for Emerging Application Areas of NDE
## 6 MsTs with Special Functionality: Generation of Higher Order Harmonics
This is intuitive because, by biasing the sensor in this fashion, it allows for the largest possible strain change for a given dynamic field strength. Thus, reducing the static bias field strength to produce second harmonic waves is not a viable strategy, given the simultaneous reduction in sensor performance. It is important to maintain a conventional bias field strength so that the sensor can realistically act as a sensor for inspection. The only other change that is possible is to adjust the dynamic field in such a way to produce higher frequency components. For similar EMATs, the dynamic field strength is not large enough to cause the maximum possible strain. In other words, the dynamic field causes positive and negative strains in the material without hitting any theoretical strain limits. However, it stands to reason that if the dynamic field is large enough, it should be possible to achieve the maximum and minimum theoretical strains possible in the material. It is clear that the largest signal amplitudes should occur when the dynamic field is large enough to produce the maximum possible strain. However, if the dynamic field strength is increased beyond this level, there will be moments during transmission where the strain under the sensor achieves the maximum strain state, and remains there until the dynamic field level is reduced. More simply, the time-varying strain caused by the sensor is a clipped sinusoid instead of a pure  
Figure 4: Photograph of pipe and MsT probe used for harmonic generation experiments. Figure 5: Acquired signal (**a**) together with its FFT (**b**) for a 50-kHz excitation with a bias magnet liftoff of 4 mm. sinusoid. The significance of this difference is that the Fourier transform of a clipped sinusoid has a dominant frequency component at the same frequency as the unclipped sinusoid, as well as every odd harmonic. Figure 7 illustrates the effect of clipping a sinusoid on its frequency content. Thus, it should be possible to produce higher frequency waves using a sensor that is similar to the ones described in this paper if the dynamic field strength is increased. For all practical purposes, it is not realistic to use high enough currents to achieve the required dynamic field strengths with a conventional EMAT. However, an MsT uses a solenoidal winding that encircles the magnetostrictive strip. This improves the efficiency of generating the dynamic field for a given transmit signal current. To test this concept, an experiment was performed using  
Figure 6: Acquired signal (**a**) and its FFT (**b**) for a 50-kHz excitation frequency with no bias magnet liftoff. Figure 7: Illustration of the effect of clipping a sinusoid on its frequency content. The top two figures show a 300-kHz sinusoid with a Gaussian envelope applied (**a**), and its associated spectrum (**b**). The bottom two figures show the same sinusoid clipped to be within the range of \(-0.1\) to \(0.1\) (**c**), and its associated spectrum (**d**). Note how the unclipped spectrum has its energy concentrated near 300 kHz, whereas the clipped spectrum has energy at the odd harmonics of 300 kHz (i.e., 300 kHz, 900 kHz, 1.5 MHz, etc.). the same sensor that is shown in Figure 4. The biasing magnets were installed without liftoff to achieve the correct biasing state. The transmit signal current was then increased beyond that which is typically used with an MsT. Figure 8 shows the results of this experiment. At a normal transmit current (Figure 8a,b), the received signal looks slightly triangular, and the frequency content is almost exclusively near 50 kHz, which is the transmit signal frequency. Note that the first result shown is the same data that is shown in Figure 6, but replotted here to aid in visual comparison. The second and third results shown are with the transmit signal current doubled (Figure 8c,d) and quadrupled (Figure 8e,f), respectively. As can be seen, the received signal shaped is distorted at these increased currents.