Design and implementation of a fast logarithmic stepped sine for a fixed rate digital network analyzer

A method is presented for measuring transfer function and harmonic distortion with a very accurate 12th-octave stepped-sine analysis between 20 Hz and 20 kHz using a digital fast-Fourier-transform (FFT)-based analyzer. One of the major concerns in developing the algorithm was to obtain maximum measurement speed while maintaining high accuracy. The interpolated FFT algorithm is used, making it possible to reduce the frequency error relative to the perfect 12th-octave frequency to less than 0.1% while keeping the needed amount of measured data, and thus the measurement time, quite low. Despite some small problems with the calibration of the channel, the transfer-function measurement accuracy is better than ±0.0004 linear error of the amplitude and 0.01 deg in phase in the band from 20 Hz to 10 kHz. In the 10-20 kHz band, the phase error rises to ±0.1 deg, while the amplitude error remains the same. The dynamic range of the harmonic distortion measurement is about 75 dB. It allows the visualization of each of the harmonics as well as the total harmonic distortion for the first five harmonics in the 20-kHz band