Notes from the Test Bench
By Bruce Hofer, Chairman & Co-Founder, Audio Precision
Now that everyone is back from AES, I’d like to share the latest “first” we introduced at the show: a 1 MHz FFT with 24-bit A/D resolution and less than 2.5 Hz bin width.
No one has been able to look at out-of-band noise with this level of clarity before. And it’s noisy out there. With more Class D amps than ever going into designs, I can’t think of a more useful addition to an audio engineer’s tool kit.
The customers I spoke with agreed, as did the press: we were honored to receive the PAR Excellence Award from Pro Audio Review for this work on FFT analysis.
It wasn’t all ultra-high bandwidth analysis though. The cake and champagne of our 25th Anniversary celebration earned some attention too.
New: Ultra-High Bandwidth Analysis with BW52 Option for APx525 Family
Out-of-band noise is a significant issue for designers of Class-D, converters and other modern audio devices. The new APx BW52 ultra-high bandwidth option provides unprecedented detail with full 1 MHz bandwidth, 24-bit A/D resolution, and less than 2.5 Hz bin width. This latest achievement marks AP’s 25th anniversary as the recognized standard in audio test.
Class D amplifiers, switching power supplies, and D/A converters all produce spurious signals well outside of the 100 kHz bandwidth limit of most audio analyzers. These out-of band switching spikes, along with their harmonics and intermodulation products, can wreak havoc on audio gear and adjacent equipment. Audio signals combined with this noise can cause even more problems.
Noise that is reflected into the audible range will directly degrade the sound. Noise that remains above the audible range can also degrade the sound by causing problems such as oscillation, overheating and damage to components, loss of headroom, and interference with connected or adjacent equipment.
The new BW52 Ultra-high Bandwidth option for the APx525 family extends the APx’s FFT capability all the way to 1 MHz, with 24-bit A/D resolution, making APx ideal for looking at out-of-band noise in Class-D amplifiers, sigma-delta converters, and other modern audio devices.
By comparison, other audio analyzers have a maximum high-resolution FFT bandwidth of 100 kHz or less, making them unsuitable for looking at switching frequencies that often center around 300–500 kHz. RF spectrum analyzers can have much wider bandwidth, but their low impedance, low resolution, and low tolerance to high input levels make them unsuitable for audio design.
Webpage describing the BW52 option:
AP Applied: Ultra-High Bandwidth Analysis
Sound Advice: AP Knowledge Base
FFT Scaling for Noise
While we’re on the subject of FFTs, it’s a good time to delve into an often misunderstood topic—how to properly read noise levels on the graph. AP’s Director of Technical Support, Joe Begin, discusses this topic, and includes a useful macro for the AP2700 Series instruments.
In Audio Precision analyzers, FFT spectra are scaled so that the amplitude axis gives the correct reading for discrete tones. This makes sense, because most often we are characterizing the performance of a DUT using sine waves. The amplitude axis, however, can not be used to indicate the level of a spectrally non-discrete signal, such as noise, without first applying a correction factor that depends on the FFT bin width and the window used.
The spectrum of a signal containing discrete tones combined with band-limited noise is shown in Figures 1 and 2. In Figure 1, the spectrum was measured without an FFT window (window = None). Note that the level of the band-limited noise is approximately equal to the level of the discrete tone at 1 kHz (0.0 dBr1).
In Figure 2, the same test signal has been measured with a Hann window. In this case, the discrete tone at 1 kHz is still at 0.0 dBr1, but the level of the band-limited noise has increased by about 1.7 dB. This apparent increase in the noise level is due to the scaling applied by the SYS-2722 to correct for the Hann window. As noted, AP analyzers scale FFT results such that the amplitude axis gives the correct reading for tones. If the FFT had been scaled to give the correct reading for noise, then the level of the discrete tone would be -1.7 dBr1 and the band-limited noise would be at 0.0 dBr1.
This effect of window scaling is also immediately apparent if you look at the spectrum of a noisy signal measured at two different FFT resolutions, as shown in Figure 3. In this case, the digital generator of a SYS-2722 has been connected via loopback to the digital input with the generator switched off, resulting in a signal containing only broadband noise due to dither. The cyan trace was plotted with an FFT length of 32 k (32,768), and the green trace with an FFT length of 256. If a horizontal line were drawn through the middle of each trace, one would be tempted to conclude that the apparent “noise floor” of the cyan trace is about -184 dBFS, and the green about -163 dBFS.
So how is it that the apparent noise level of the signal changes by as much as 21 dB, based on the FFT resolution alone? This difference is due to the fact that the measurement of noise depends on the bandwidth of the measurement. For a spectrum display that contains all of the bins in the underlying FFT, each bin represents the narrow band RMS level of the signal in that bin, equivalent to the level that would be measured by a bandpass filter with a bandwidth of Δf, the width of the FFT bin in Hz. Thus, the apparent noise floor of the spectrum depends on the bin width, or Δf, which in turn is a function of the number of FFT bins. Each time you double the number of FFT bins, the bin width is halved, reducing the “noise power” in each bin by a factor of 2. This equates to a 3 dB decrease in the RMS noise level. Therefore, in the example above, changing the FFT resolution from 256 to 32 k (a factor of 128, or 27) results in the RMS noise level in each bin being decreased by 3 dB x 7, or 21 dB.
Noise spectra are often displayed in a normalized format called power spectral density (PSD), or amplitude spectral density (ASD). This normalizes the data to the power spectrum (level squared) or amplitude spectrum that would be measured with a bin width of 1.0 Hz using a perfect bandpass filter centered at each point. In addition to compensating for the bin width (Δf), it corrects the spectrum for the scaling of the FFT window used. The spectrum from an AP analyzer can be converted to power spectral density using equation (1).
where Spectrum represents the FFT level spectrum, Δf is the bin width, and NoisePowerBandwidth is a correction factor for the FFT window used. The noise power bandwidth compensates for the fact that the FFT window spreads the energy from the signal component at any discrete frequency to adjacent bins. If the spectrum is in units of V, the PSD is in units of V2/Hz. In the digital domain, for a spectrum in units of FS, the PSD would be in units of FS2/Hz. Noise power bandwidths for windows commonly used in AP analyzers are listed in Table 1.
The amplitude spectral density is simply the square root of the power spectral density (equation 2). For a spectrum in units of V or FS, it has units of V/√Hz or FS/√Hz, respectively.
The RMS noise level in any given spectral bandwidth can be determined by integrating the power spectral density over that bandwidth. For the entire bandwidth from DC to one half the sample rate (fS/2), the noise level is calculated by summing all FFT bins, as shown in equation 3.
When equation 3 is applied to the spectra shown in Figure 3, the calculated noise level across the entire spectrum is -141.5 dBFS for both the 32k and the 256 point FFTs. This compares well with the level measured using the audio analyzer’s RMS meter measurement.
The associated AP2700 macro file FFT_scaling.apb contains several functions that are useful for performing calculations on FFT spectra, including FFT spectrum integration with window correction. There is also a subroutine that will convert a measured FFT spectrum to amplitude spectral density in dB relative to 1.0 V/√Hz, or FS/√Hz, and plot it on the graph. The AP2700 test used to generate the graphs and data for this article (FFT_Scaling.at27) is also included in the download.
Figure 4 shows the noise floor of a DAC measured with a SYS-2722 and plotted as an ASD plot using the subroutine in the macro. If you use this subroutine to plot the ASD, change the graph’s Y-axis label back afterwards to its default value by right-clicking on it and selecting Auto-Label.
Test Results: AP News & Events
AP will be attending the CEA HDMI Plugfest 13 in San Francisco, November 8th to 13th. If you wish to schedule a test session with AP, please contact Daniel Knighten, Director of Products, at firstname.lastname@example.org.
AP was presented with Pro Audio Review’s Excellence Award for the new BW52 Ultra-high Bandwidth option at the recent AES convention in New York.
©2009 Audio Precision Inc.