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Except for the sine wave, the common test signals do not allow full control over their spectral content. For example, the harmonic components of a square wave are fixed in frequency, phase, and amplitude relative to the fundamental. However, you can generate multitone signals with a specific amplitude and phase for each individual frequency component.

A multitone signal is the superposition of several sine waves or tones, each with a distinct amplitude, phase, and frequency. A multitone signal is typically created so that an integer number of cycles of each individual tone are contained in the signal. If an FFT of the entire multitone signal is computed, each of the tones falls exactly onto a single frequency bin, which means no spectral spread or leakage occurs.

Multitone signals are a part of many test specifications and allow the fast and efficient stimulus of a system across an arbitrary band of frequencies. Multitone test signals are used to determine the frequency response of a device and with appropriate selection of frequencies, also can be used to measure such quantities as intermodulation distortion.

Crest Factor

The relative phases of the constituent tones with respect to each other determine the crest factor of a multitone signal with specified amplitude. The crest factor is defined as the ratio of the peak magnitude to the RMS value of the signal. For example, a sine wave has a crest factor of 1.414:1.

For the same maximum amplitude, a multitone signal with a large crest factor contains less energy than one with a smaller crest factor. In other words, a large crest factor means that the amplitude of a given component sine tone is lower than the same sine tone in a multitone signal with a smaller crest factor. A higher crest factor results in individual sine tones with lower signal-to-noise ratios. Therefore, proper selection of phases is critical to generating a useful multitone signal.

To avoid clipping, the maximum value of the multitone signal should not exceed the maximum capability of the hardware that generates the signal, which means a limit is placed on the maximum amplitude of the signal. You can generate a multitone signal with a specific amplitude by using different combinations of the phase relationships and amplitudes of the constituent sine tones. A good approach to generating a signal is to choose amplitudes and phases that result in a lower crest factor.

Phase Generation

The following schemes are used to generate tone phases of multitone signals:

• Varying the phase difference between adjacent frequency tones linearly from 0 to 360 degrees
• Varying the tone phases randomly

Varying the phase difference between adjacent frequency tones linearly from 0 to 360 degrees allows the creation of multitone signals with very low crest factors. However, the resulting multitone signals have the following potentially negative characteristics:

• The multitone signal is very sensitive to phase distortion. If in the course of generating the multitone signal the hardware or signal path induces non-linear phase distortion, the crest factor might vary considerably.
• The multitone signal might display some repetitive time-domain characteristics, as shown in the multitone signal in the following figure.

The signal in the previous figure resembles a chirp signal in that its frequency appears to decrease from left to right. The apparent decrease in frequency from left to right is characteristic of multitone signals generated by linearly varying the phase difference between adjacent frequency tones. You might want a signal that is more noise-like than the signal in the previous figure.

Varying the tone phases randomly results in a multitone signal whose amplitudes are nearly Gaussian in distribution as the number of tones increases. The following figure illustrates a signal created by varying the tone phases randomly.

In addition to being more noise-like, the signal in the previous figure also is much less sensitive to phase distortion. Multitone signals with the sort of phase relationship shown in the previous figure generally achieve a crest factor between 10 dB and 11 dB.

Swept Sine versus Multitone

To characterize a system, you often must measure the response of the system at many different frequencies. You can use the following methods to measure the response of a system at many different frequencies:

• Swept sine continuously and smoothly changes the frequency of a sine wave across a range of frequencies.
• Stepped sine provides a single sine tone of fixed frequency as the stimulus for a certain time and then increments the frequency by a discrete amount. The process continues until all the frequencies of interest have been reached.
• Multitone provides a signal composed of multiple sine tones.

A multitone signal has significant advantages over the swept sine and stepped sine approaches. For a given range of frequencies, the multitone approach can be much faster than the equivalent swept sine measurement, due mainly to settling time issues. For each sine tone in a stepped sine measurement, you must wait for the settling time of the system to end before starting the measurement.

The settling time issue for a swept sine can be even more complex. If the system has low-frequency poles and/or zeros or high Q-resonances, the system might take a relatively long time to settle. For a multitone signal, you must wait only once for the settling time. A multitone signal containing one period of the lowest frequency—actually one period of the highest frequency resolution—is enough for the settling time. After the response to the multitone signal is acquired, the processing can be very fast. You can use a single fast Fourier transform (FFT) to measure many frequency points, amplitude and phase, simultaneously.

The swept sine approach is more appropriate than the multitone approach in certain situations. Each measured tone within a multitone signal is more sensitive to noise because the energy of each tone is lower than that in a single pure tone. For example, consider a single sine tone of amplitude 10 V peak and frequency 100 Hz. A multitone signal containing 10 tones, including the 100 Hz tone, might have a maximum amplitude of 10 V. However, the 100 Hz tone component has an amplitude somewhat less than 10 V. The lower amplitude of the 100 Hz tone component is due to the way that all the sine tones sum. Assuming the same level of noise, the signal-to-noise ratio (SNR) of the 100 Hz component is better for the case of the swept sine approach. In the multitone approach, you can mitigate the reduced SNR by adjusting the amplitudes and phases of the tones, applying higher energy where needed, and applying lower energy at less critical frequencies.

When viewing the response of a system to a multitone stimulus, any energy between FFT bins is due to noise or unit-under-test (UUT) induced distortion. The frequency resolution of the FFT is limited by the measurement time. If you want to measure a system at 1.000 kHz and 1.001 kHz, using two independent sine tones is the best approach. Using two independent sine tones, you can perform the measurement in a few milliseconds, while a multitone measurement requires at least one second. The difference in measurement speed is because you must wait long enough to obtain the required number of samples to achieve a frequency resolution of 1 Hz. Some applications, such as finding the resonant frequency of a crystal, combine a multitone measurement for coarse measurement and a narrow-range sweep for fine measurement.