# New Magnetstrictive Transducer Designs for Emerging Application Areas of NDE
## 6 MsTs with Special Functionality: Generation of Higher Order Harmonics  
An MsT functions based on the interaction of two magnetic fields--one dynamic and the other static--within the magnetostrictive strip. The dynamic magnetic field is typically much weaker than the static field; the static bias field strength is designed to provide the best performance in generating guided waves. However, it is possible to adjust the relative strength of the two magnetic fields to produce interesting and potentially useful operational characteristics. For example, one possible configuration change results in the capability to produce higher order harmonics for the input frequency signal. One scenario where this would be advantageous is when the transmitter circuitry does not have sufficient bandwidth to generate higher frequency signals for a given inspection application. To explain how this modification works, recall that a magnetic field applied to an unstressed/unbiased magnetostrictive material will strain in one direction regardless of the polarity of the applied magnetic field. In other words, reversing the magnetic field polarity will produce the same strain vector in the material. The effect of this is that applying a time-varying magnetic field in this unbiased configuration causes time-varying strains, but the frequency of the strains are twice that of the input magnetic field. One essential purpose of the static field bias in an MsT is to induce a baseline strain in the strip so that the dynamic field produces both positive and negative strains relative to the baseline strain state. Thus, the frequency of the guided waves that are generated using an MsT is the same as the input signal to the sensor. Based on this, it should be possible to reduce the magnetic bias field strength and produce second order harmonics. Testing has been conducted to confirm this result using an MsT transducer. For this experiment, an 89 mm outer diameter, 6.35-mm thick wall (T(0,1) cutoff \(>\) 350 kHz), 3.65-m long pipe was used, as shown in Figure 4. A 19-mm wide magnetostrictive strip with the dynamic field coil wrapped around the strip with a 3-mm pitch was bonded to the pipe (2.1 m from the far end). The strip was biased with a magnetic belt arranged to provide an axial field and placed on top of the strip with 4-mm liftoff; the amount of liftoff between the biasing magnets and the magnetostrictive strip significantly reduced the bias field strength compared to the normal static field configuration. The magnetic field introduced into the strip was measured to be approximately 3 kGauss, whereas a typical bias field strength is 7 kGauss. The experimental process was to examine the frequency content of a reflection from the far end of the pipe from a 50-kHz torsional guided wave. The acquired signal from the reflection from the end of the pipe and its fast Fourier transform (FFT) are shown in Figure 5.  
From Figure 5, a peak at the input center frequency of 50 kHz can be observed, along with an additional peak near 100 kHz. In other words, the second harmonic was generated using only a single frequency input signal. Unfortunately, the signal-to-noise ratio (SNR) of the data was very poor, for comparison, Figure 6 shows data collected using the same sensor setup where the liftoff between the magnets and the magnetostrictive strip was removed, but all of the other settings remained the same. The reason for the reduced performance of the MsT at the low bias field strength configuration is that the magnitude of the magnetostrictively-induced strain was not purely dependent on the magnitude of the dynamic field. In reality, the second major purpose of the static bias was to improve the amplitude of the generated guided wave signals. It can be shown that the performance of similar EMATs is improved by biasing the sensor to an operating point where the slope of the magnetostrictive strain versus the applied field curve is high.