DAC/ADC distortion measurement based on missing-tone method

Fig 5. 1 Measurement setup for the response, noise and distortions of DAC and ADC

Electrical back-to-back setup are established to measure the response, noise and distortions of DAC and ADC as shown in Fig 5. 1. DAC is set with 64Gsps sampling rate, and directly connected to the ADC by the short matched cables. ADC is set also with 64Gsps sampling rate and with same external clock source of 2GHz from the frequency synthesizer. This setup measures the total characters of DAC and ADC, which is used to identify the distortions of DAC and ADC. Obviously, it is not able to separate the response, noise and distortions of DAC or ADC individually from the total characters. To do it, high speed arbitrary waveform generator is needed as the input to measure the ADC, and high speed DSO is needed as the receiver to measure the DAC. Here the total characters of DAC and ADC are measured for the modeling, and divided into two half for each based on that the specifications of DAC and ADC are almost same.

At the first, the filter response of DAC and ADC are measured using the previous DMT channel probing scheme that is to estimate the filter response by PRBS modulated QPSK signals and the MMSE method. The settings of this DMT probing signal are subcarrier number 4096, CP number 16, and clipping ratio 3.16. In order to improve the measurement accuracy, more than 375 DMT symbols are averaged in estimating the filter response.

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Fig 5. 2 Measured results of filter response of DAC and ADC

Measured results of the filter response of DAC and ADC is shown in Fig 5. 2 in the frequency domain. The resolution is 7.8125MHz. The overall 3dB bandwidth of DAC and ADC is measured 12GHz, and no serious amplitude/phase ripples are observed. The measured phase response ripple within 125MHz bandwidth is shown in the histogram in Fig 5. 3. Seen from the figure, phase ripple of 0Hz to 25GHz is less than 20 degree. Such small phase ripple within each DMT subcarrier bandwidth would not have considerable performance variation. Therefore, in the following individual modeling of DAC or ADC, the phase-frequency responses are discarded in the further modeling and evaluation.

Fig 5. 3 Measured phase response ripple of DAC and ADC

To confirm the measured filter response is independent with test signal. Two other DMT signals with subcarrier number 512 and 1024, and a 1024 incoherent comb signal were also used to measure the filter responses for comparison. The results of these measured filter responses are shown and compared Fig 5. 4, Fig 5. 5 and Fig 5. 6. As can be seen, the measured filter responses are agreed with each other and independent with the test signal.

Fig 5. 4 Measured amplitude response by DMT signal and comb signal. sc1024: subcarrier number 1024

Fig 5. 5 Measured amplitude response difference with different subcarrier numbers

Fig 5. 6 Measured phase response difference with different subcarrier numbers

To measure the static noise of DAC and ADC, no signal input is set for the DAC in the setup of Fig 5. 1. The spectrum of noise floor are shown in Fig 5. 7. As can be seen, the noise floor is at -45dBV but with many spurs existing. Here the unit of power spectrum density is dBV which is related to volts by dBV  20 log ( )₁₀V . Many spurs are observed in the noise floor spectrum with 200MHz spacing which is possibly from the divided frequency of the clock signal of 2GHz.

These spurs are significantly different with the additive Gaussian white noise and may cause significant penalty for the transmission performance, which would be investigated in later sections in detail. Because this noise is measured with no signal input, it is also called signal-independent noise.

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Fig 5. 7 Measured noise floor of DAC and ADC with no signal input

To measure the dynamic noise of DAC and ADC with DMT signal input, missing-tone method is proposed. Because of the existence of various distortions in the DAC and ADC implementation, the dynamic noise when input the DMT signal is expected to be significantly different from the static noise floor. Missing-tone method is to measure the dynamic noise spectrum of a small frequency range by inputting the missing-tone signals. One example of missing-tone signal spectrum at the DAC and ADC output is shown in Fig 5. 8 to explain the measure method. The input signal is the ordinary DMT signal with some frequency tones missing which is from 1GHz to 5GHz in Fig 5. 8. At the DAC and ADC output, the spectrum between 1GHz and 5GHz shows the dynamic noise spectrum. Actually, the center 1GHz spectrum in the 4GHz missing band in Fig 5. 8 is regarded as the dynamic noise spectrum because the edge band spectrum may be interfered by the signal spectrum. In the practical measurement setup, the missing band position is swept along the frequency axis to obtain the whole spectrum of dynamic noise spectrum.

Fig 5. 8 Output signal spectrum at the DAC and ADC output by the DMT missing-tone method Measured results of the dynamic noise spectrum is shown in Fig 5. 9. Because it is measured with DMT missing-tone signal input, it measures the total noise including both signal-independent noise and signal-dependent noise. As can be seen, with DMT missing-tone signal input, the total noise spectrum is much higher that the independent noise, which means the signal-dependent noise may be the dominant noise of the DAC and ADC in the communication systems.

On the other hand, many spurs are observed in the total noise spectrum. The amplitude of the spurs are varying between the measured signal-independent noise and total noise.

Fig 5. 9 Measured total noise spectrum of DAC and ADC

To confirm the accuracy of the measured total noise spectrum by the missing-tone method, the redundant measurements were performed for comparison with different missing bandwidth, different DMT subcarrier numbers on different dates. The power of total noise in the center 1GHz band of the missing band is used as the indicators. Results are shown in Fig 5. 10. As can be seen, the measured total noise spectrum by missing-tone method is independent on the missing bandwidth, the DMT subcarrier number and the different measurement dates.

Fig 5. 10 Experiment results to confirm the measured total noise spectrum by missing-tone method independent on: a) missing bandwidth; b) & c) DMT subcarrier number; d) & e) dates.

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Fig 5. 11 Extracted distortions for the DAC and ADC from experiment

To assist the comparison and analysis, the measured total noise spectrum shown in Fig 5. 9 is divided into three kinds of distortions: narrow-band interference, white noise floor, and colored noise. Firstly, narrow-band interference spectrum is separated by judging if power spectrum density is 5dB larger than its neighbors, which are the spurs in the total noise spectrum. Then white noise floor was obtained by removing narrow-band interference from the signal-independent noise spectrum. And the remainder of noise in Fig 5. 9 would be regarded as colored noise, which is also the signal-dependent noise. Spectrums of all the separated distortions are shown in Fig 5.

11. In the following, the impact of these distortions on the performance of optical DMT system and optical PAM system would be investigated separately, based on the sophisticated simulation model for the DAC and ADC using these measured distortions.