# Digital predistortion improves data-acquisition performance

A data acquisition system (DAS) converts analog signals to digital for analysis by a digital signal processor. Applications such as imaging, audio, and vibration analysis require a DAS with a high signal-to-noise ratio (SNR) and ultra-low THD (total harmonic distortion).

Developing a wide-dynamic-range DAS does, however, present design and test challenges. The main test challenge is the lack of signal source with a better THD and SNR than the DAS itself. Both the THD and SNR of a signal generator become critical concerns when the DAS is rated for 100 dB SNR and -120 dB THD.

**Why improve source distortion?**

To characterize the THD of a DAS, you should connect an ideal sinewave with no distortion to the system input. From that, you can measure the THD introduced by DAS nonlinearity.

To guarantee that the THD measured at the output derives from DAS nonlinearity, you need to use a generator with negligible distortion compared to that of the DAS under test. Most signal generators, however, aren’t always good enough to measure the ultra-low-distortion DAS with better than -120dB THD.

**DAS and measurement setup**

The DAS under test has been designed using low distortion and low-noise devices on the main signal path. We performed experiments using the MAX11905DIFEVKIT, a wide-dynamic-range and ultra-low-distortion DAS, which consists of three three major components. Table 1 highlights the specs of these devices.

- MAX44205: a fully differential amplifier, 180 MHz gain bandwidth product, 3 nVRMS noise
- MAX11905: a fully differential SAR ADC, 20-bit, 1.6 Msample/s, low power
- MAX6126: an ultra-high-precision, ultra-low-noise series voltage reference

**Table 1. Noise and distortion performance of the signal-chain.**

Figure 1 shows the test setup to evaluate the DAS dynamic performance. The low-distortion signal generator is the Audio Precision AP 2722.

**Figure 1. This test setup measures dynamic performance of the DAS **

We used the Audio Precision 2722 to generate a fully differential 10 kHz sinusoidal signal. We applied it to the MAX44205 driver configured with a gain = 1 V/V. The MAX11905 ADC is used in fully differential mode with V_{REF} = 3 V supplied from the MAX6126 voltage reference. The signal analyzer and ADC are synchronized with the same clock generator to implement coherent sampling measurement.

**DAS Performance using a traditional approach**

The results in Figure 2 show the dynamic performance of the DAS with the setup configured in Figure 1. The ADC is running at a sampling rate of 1.6 Msamples/s.

**Figure 2. The plot shows initial FFT and dynamic performance of the DAS system tested on the MAX11905DIFFEVKIT at 1.6 Msamples/s.**

The 97.3 dB SNR is relatively good, but the harmonics at the output are higher than the expected value for the DAS. As we will demonstrate later in the article, the THD measured is limited to -112dB by the distortion of the signal generator.

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**Distortion improvement with digital predistortion**

We implemented a digital correction technique known as DPD (digital predistortion) to improve the distortion or THD of the digital signal generator. The process of adding harmonics to the digital signal to eliminate or reduce the harmonics introduced by the digital-to-analog conversion is known as digital predistortion or digital linearization. Figure 3 is the block diagram showing main building blocks of a typical digital signal generator.

**Figure 3. Block diagram of the digital signal generator with digital predistortion on the input.
**

System operation is noted below:

- The digital waveform block stores the digital samples of the waveform .
- The DAC block converts the digital samples into the respective analog values.
- The buffer block provides the necessary power and the output impedance to stimulate the DUT.
- The digital predistortion block provides the predistorted waveform.

The test setup uses a sine wave to stimulate the DUT. The signal generator creates the sine wave from digital samples.

Equation 1 represents the sine wave digital samples that feed the DAC to generate the analog output signal.

Where:

yd in represents digital signal

A1 is the amplitude of the fundamental signal

ω1 = 2 × π × f1

f1 is the fundamental sine wave frequency

t is the sampling period

φ1 is the phase of the fundamental signal

Equation 2 represents the analog output of the signal generator. The red terms in Equation 2 model the second and third harmonics introduced by the DAC and buffer (labelled red in Figure 3).

Where:

A2 and A3 are amplitudes of second and third harmonics, respectively.

φ2and φ3 are phases of the second and third harmonics, respectively.

The digital predistortion block labelled in blue if Figure 3 adds equal and opposite harmonics to eliminate the harmonics at the generator’s output. Equation 3 represents digital predistorted waveform.

Where yd_DPD is the digital waveform with predistortion applied.

The signal generated in Equation 3 is applied to the DAC (see Figure 3). Therefore, the new generator output waveform is:

+A2 sin(2ω1t+φ2)+A3 sin(3ω1t+φ3) [Eq. 4]

Where ya_DPD is the analog output waveform with digital predistortion.

The equal-and-opposite terms of the second and third harmonics cancel each other out, resulting in Equation 5.

The process of selecting second and third harmonics for the digital predistorted waveform is an iterative method explained in detail below.

For the measurements shown in Figure 2, the signal generator provides a 10 kHz sine wave to evaluate DAS performance. To implement digital predistortion, we use the signal generator’s arbitrary waveform mode (see Figure 3). We used MATLAB to generate digital samples of a 10 kHz sine wave to a file in .wav format. Now, we can load those digital samples into the signal generator where they will be converted to a 10 kHz analog sine wave using the integrated DAC. The signal generator used in this test has an internal maximum buffer capacity to store 16,384 digital samples.

**Practical experiment showing digital predistortion**

A sine wave at 10 kHz was generated using an arbitrary waveform generator with the test setup in Figure 4. The spectrum analyzer measures the distortion of the signal generator. A 10 kHz notch filter attenuates the fundamental signal to reduce the distortion of the spectrum analyzer.

**Figure 4. Use this test setup to eliminate the harmonics.**

Figure 5 shows the spectrum of the generated sinewave after the notch filter and without the digital predistortion. The fundamental at 10 kHz is at -23 dBV; the second harmonic is at -112 dBV and the third harmonic at -117 dBV.

**Figure 5. Performance before correcting harmonics.
**

Figure 6 shows the test results after the notch filter and while digital predistortion is applied to the digital samples loaded into the internal buffer of the signal generator.

**Figure 6. Performance after digital correction, which reduces the second and third harmonics.
**

After digital predistortion, the second harmonic from -112 dBV is reduced down to -123 dBV and the third harmonic from -117 dBV to -124 dBV. This reduction in second and third harmonic levels helps to improve overall THD.

This digital predistortion method needs to be performed very carefully, reducing one harmonic at a time. All parameters related to the third harmonic are set as 0, while the second harmonic is reduced per Equation 3. From Figure 6, you can see the second harmonic on the FFT is at approximately -112 dB which is equivalent to 2.5 µV. Values between -2.5 µV and +2.5 µV are chosen in iteration for A2 to verify which magnitude helps to reduce the second harmonic. After a few iterations, A2 = -1.5 µV reduces the second harmonic. The φ2 is also used to further reduce the harmonic. Using A2 = -1.5 µV with a combination of φ2 = -45°, yields the best result to eliminate the second harmonic, as shown in Figure 7. Using the same iterative procedure, A3 = -0.5 µV with combination of φ3 = 45° yields the best results.

DAS Performance with DPD

Figure 7 shows DAS performance at 1.6 Mamples/s after the second and third harmonics were eliminated.

Figure 7. FFT spectrum with Arb Wfm(D/A) mode, reducing the second and third harmonics.

The dynamic performance of the MAX11905DIFFEVKIT using Arb Wfm(D/A) waveform mode with digital predistortion improved THD measured on the DAS by 8 dB, from -112 dB to -120 dB at 1.6 Msamples/s.

SNR Limited by Arbitrary-Waveform Mode

The harmonics using Arb Wfm(D/A) mode are eliminated using digital predistortion. However, SNR degradation has been observed using Arb Wfm(D/A) mode compared to using Sine(D/A) mode.

Figure 8 shows the performance of the DAS at 1.6 Msamples/s, using Sine(D/A) generator mode provided by the signal generator. The results show show an improvement of 2 dB in SNR using the signal generator in this mode compared to the arbitrary-waveform-mode.

**Figure 8. FFT spectrum with Sine(D/A) mode.
**

SNR degradation with Arb Wfm(D/A) mode versus the Sine(D/A) mode will be a topic for further study in another article.

**Conclusion**

This article shows that the THD of a digital signal generator can be improved with a digital predistortion technique which then enables evaluation of an ultra-low-distortion DAS. The article also demonstrates how to use a notch filter to eliminate the fundamental tone and thus improve signal analyzer linearity.

Test results demonstrate that digital predistortion improves 8.2 dB THD of the MAX11905DIFEVKIT from -112 dB to -120.2 dB.

**About the authors**

Srudeep Patil is a Senior Applications Engineer working with Op amps, Comparators, and Current-sense amplifiers, ADCs and Voltage References at Maxim Integrated since July 2011. He resolves customer issues with technical lab support and works on new product launches by performing IC road tests and writing the data sheets along with the application notes. Srudeep has an MSEE with major academic focus on Analog/RF VLSI. Prior to joining Maxim, he worked with NXP Semiconductors as an intern in their analog team working on ADCs and amplifiers.

Carmelo Morello is a Senior Business Manager for the Industrial and Healthcare business unit at Maxim Integrated. He oversees business for the industrial and telecom markets. Morello was an analog field application engineer and R&D designer of high-precision and high-speed signal chain circuits in well-known international companies before joining Maxim. He received a Master’s Degree in Electronic Engineering from Pavia University, Italy.