DSP System Toolbox
This example shows how to perform measurements using the Spectrum Analyzer block. The example contains a typical setup to perform harmonic distortion measurements (THD, SNR, SINAD, SFDR), third-order intermodulation distortion measurements (TOI), adjacent channel power ratio measurements (ACPR), complementary cumulative distribution function (CCDF), and peak to average power ratio (PAPR). The example also shows how to view time-varying spectra by using a spectrogram and automatic peak detection.
Several measurements and their corresponding setups are contained in the example model.
Exploring the Example
The model consists of five simple models of an amplifier, each of which is set up to perform specific measurements.
Open an amplifier model by double-clicking on an Amplifier block. The first amplifier model is shown below:
The input is first combined with a Gaussian noise source and then run through a high-order polynomial to model non-linear distortion.
You can modify the amount of additive noise on the input by clicking on the Noise Source and modifying the variance of the Gaussian distribution.
You can modify the parameters of the amplifier by changing the polynomial coefficients. The coefficients are arranged from highest-to-lowest order. If you edit the last coefficient you change the DC voltage offset of the amplifier. If you change the next-to-last coefficient, you change the voltage gain of the amplifier. If you change other coefficients, you can change the higher-order harmonics of the amplifier.
You can measure harmonic distortion by stimulating the amplifier with a sinusoidal input and viewing the harmonics in a spectrum analyzer. The harmonic distortion measurements can be invoked from the Measurements option in the Tools menu, or by clicking its corresponding icon in the toolbar (shown depressed in the figure, below).
Viewing the results in the Distortion Measurement panel you see the amplitudes of the fundamental and the harmonics as well as their SNR, SINAD, THD and SFDR values, which are referenced with respect to the fundamental output power.
Third Order Intermodulation Distortion
Amplifiers typically have significant odd-order harmonics. If you stimulate the amplifier with two closely spaced sinusoids of equal amplitude, you can produce intermodulation products at the output. Typically the distortion products decay away from the fundamental tones, the largest of which correspond to the third-order sum and difference frequencies of the input waveform. You can measure output third-order intermodulation (TOI) distortion by selecting intermodulation distortion measurements from the drop-down menu in the distortion measurement panel.
Also in the Distortion Measurement panel you see the intermodulation products highlighted and the output TOI displayed. Adjust the polynomial coefficients in the amplifier to change the harmonics shown in the signal.
If you stimulate an amplifier that is broadcasting a communications channel, you may see spectral growth leaking into the bandwidth of neighboring channels due to intermodulation distortion. You can measure how much power leaks into these adjacent channels by measuring the adjacent channel power ratio (ACPR). You can see the measurements both before and after the amplifier by toggling the measurement input in the Trace Selection Dialog. ACPR measurements can be selected from the drop-down menu in the Channel Measurements dialog. This dialog can be invoked from the Measurements option in the Tools menu, or by clicking its corresponding icon in the toolbar (shown depressed in the figure, below).
Adjust the polynomial coefficients in the amplifier to obtain different amounts of spreading of the central power due to intermodulation distortion. You can observe the ACPR readings at the specified offset frequencies.
You can qualitatively verify how much dynamic range an output signal occupies by viewing its complementary cumulative distribution function (CCDF). The CCDF dialog can be invoked from the Measurements option in the Tools menu or by clicking its corresponding icon in the toolbar (shown depressed in the figure, below).
In the above example you can see approximately 0.5 dB of compression between the input source (blue trace) and the output of Amplifier4 (yellow trace). The peak-to-average power ratio (PAPR) for the input channel is 3.3 dB whereas the PAPR for the output channel is 2.8 dB. This loss of dynamic range suggests that there is too much input power applied to the amplifier.
You can view time-varying spectral information by using the Spectrogram Mode of the spectrum analyzer. If you stimulate the amplifier with a chirp waveform you can observe how the harmonics behave as time progresses. Select "Spectrogram" from the "Type" dropdown menu in the Spectrum Settings dialog, which is invoked from the Spectrum Settings dialog in the View menu (not shown).
You can use cursors to make measurements of the period of the chirp and to confirm that the other spectral components are harmonically related. The Cursor Measurements dialog can be invoked from the Measurements option in the Tools menu, or by clicking its corresponding icon in the toolbar (shown depressed in the figure, above).
You can track time-varying spectral components by using the Peak Finder measurement dialog. You can show and optionally label up to 100 peaks. The Peak Finder dialog can be invoked from the Measurements option in the Tools menu, or by clicking its corresponding icon in the toolbar (shown depressed in the figure, above).
IEEE Std. 1057-1994 IEEE Standard for Digitizing Waveform Recorders
Allan W. Scott, Rex Frobenius, RF Measurements for Cellular Phones and Wireless Data Systems, John Wiley & Sons, Inc. 2008