# Reducing Harmonic Distortion in Vibration Calibration

## Minimize Measurement Uncertainty

In the field of calibration, we are constantly working to minimize or eliminate any phenomena that contribute to measurement uncertainty. There are simple things that can be directly managed, like sensor mounting and cabling techniques. There are other uncertainty contributors such as noise and harmonic distortion that are often beyond the control of the calibration technician. The Modal Shop has designed an algorithm to help minimize the amount of distortion present in the system. This article will explain how the algorithm works and the impact that it has on reducing the harmonic distortion in the sensor signal.

Calibrations are typically performed with the Digital to Analog Converter (DAC) outputting a pure sine wave at a single frequency to the shaker, then measuring the response of the sensor under test (SUT), and finally comparing that to a known value (laser, reference sensor, etc.). The same process is repeated for each individual frequency at which the SUT is being calibrated. State of the art calibration systems use a Discrete Fourier Transform (DFT) or Fast Fourier Transform (FFT) to strip away distortion components and look only at the energy being applied to the SUT. Portable and older legacy benchtop calibration systems typically use RMS to measure the signal coming from the SUT. RMS is a good measurement method as long as the energy being put into the system consists of a single frequency – a pure sine wave. When there is distortion present in the system, all of the combined energy of all of the distortion components is combined with the energy at the desired frequency and becomes part of the measurement. To minimize the amount of distortion present in the system, the precomp algorithm adjusts the DAC output signal from that of a pure sine wave to a waveform that has distortion-cancelling components.

The precomp is a multi-step process for each frequency. First, the DAC outputs a pure sine wave and the data acquisition measures the response of the system. As the SUT signal is being measured, the precomp algorithm performs a DFT and calculates the amplitude of the distortion components at each harmonic frequency. Once the distortion components are identified, the amplitude at each of the measured harmonic frequencies is inverted. By inverting the amplitude of the distortion components but leaving the amplitude at the fundamental frequency unchanged, the distortion components in the system will effectively be cancelled out. The precomp algorithm then performs an inverse DFT to acquire the new time domain signal, which is no longer a pure sine wave, but a distorted signal. The DAC then outputs the new signal through the system.

The precomp algorithm constantly monitors and adjusts its output signal to actively eliminate as much of the distortion as possible. While we can never completely eliminate distortion at all frequencies, the effect of the distortion pre-compensation drastically reduces the amount of distortion present in the system at most frequencies.