AN-1483: Harmonic Analysis Using the ADE9000

Introduction

Traditionally, harmonic analysis requires complex computations and processing. Harmonic analysis goes to an order of processing data in which a fixed analog-to-digital converter (ADC) sampling rate is used, then a window is applied into the data to account for the fact that the data is not sampled coherently. Lastly, a Fourier transform is performed, which can be difficult, because the number of samples of the data is not an exact amount of 2n integral numbers.

The ADE9000 metering IC is capable of performing the desired Fourier transform coherently or noncoherently using the waveform buffer application. Typically, this waveform buffer samples an amount of data and gives a set of values for a Fourier transform process. The output generated contains the fundamental signal plus all harmonics.

Another concern in harmonic analysis is that the signal being measured in the ADE9000 passes digital filtering, and the gain varies over frequency, thus attenuating the measurements at higher frequencies more noticeable beyond 500 Hz. Proper gain compensation factors must be introduced in measuring those frequencies affected by this process.

This application note discusses the ways of performing harmonic analysis and the gain compensation analysis using the EVAL-ADE9000EBZ evaluation board.

Coherent vs. Noncoherent Sampling

To obtain the fundamental and harmonic contents of the signal after the transformation process, it is essential to sample the signal in a way that it gives a perfectly generated output in root mean squared (rms) of the energy contents of each frequency.

Noncoherent sampling in the ADE9000 uses the waveform buffer to read enough samples for a fast Fourier transform (FFT). The timing clock and the size of the sample set is the main concern for noncoherent sampling. The energy content is concentrated at a single frequency if proper amounts of samples are generated for an FFT. It can be obtained by using an external clock, probably operating at the same timing with the generated signal and the input clock of the ADE9000. The requirement is also to generate a sample set that ends with the same exact point in the waveform where sampling starts. By doing this, each content of the signal is concentrated only to one specific point, thus measuring the rms values accurately.

Figure 1 shows an FFT response if noncoherent sampling is performed without taking into consideration the timing and the integral number of line periods. However, Figure 2 shows that when sampling starts and ends at the exact line period together with the clock sync, the content of the signal is concentrated on its specific frequency.

Figure 1. Response of a Third Harmonic of a Noncoherent Sampling Without Integral Number of Periods Using the ADE9000, NI PXI 4461 Signal Generator, and EVAL-ADE9000EBZ.

Figure 2. Third Harmonic of a 50 Hz Signal Noncoherent Sampling with Integral Number of Periods Using ADE9000, NI PXI 4461 Signal Generator, and EVAL-ADE9000EBZ.

The ADE9000 simplifies noncoherent signal processing by constantly tracking the power line frequency and using this information to resample the data to provide 128 points of data per power line, thus making the sampling coherent.

Coherent sampling also uses the waveform buffer and performs resampling of the original set of values. Each set contains 128 (128 × 4 maximum) interpolated samples providing one complete line cycle, which makes the number of samples an integral number of 2n power, thus making Fourier transform easy to compute. Interpolation introduces small errors that increase with the range of the harmonic (see Figure 3).

Figure 3. Response (in dB) of a Fundamental and Fifth Harmonic on Current Channel B Using 128 Samples/Line Cycle.

This application note discusses harmonic analysis using both noncoherent and coherent sampling modes.

Measuring Fundamental and Harmonic Contents

In performing harmonic analysis in the ADE9000, an FFT can be performed using a microcontroller or any software capable of performing signal processing (like LabVIEW®). Before measurement, a precalibration must be done using the ADE9000 Calibration Tool.


Harmonic Analysis using Noncoherent Sampling


The main register for measuring the harmonic content of the signal is the waveform buffer register.

Configure the register WFB_CFG with the following operations to control it in the desired waveform buffer setting to perform a noncoherent sampling mode. Make sure that the chip is precalibrated and working with the digital signal processor (DSP) on. See the ADE9000 Technical Reference Manual.

To set the waveform buffer, perform the following procedure:

  1. Write 0x03F8 to WFB_CFB (Address 0x4A0) to configure the waveform.
  2. Write 0'0b0 to WF_IN_EN (Bit 12) to disable waveform in neutral channel to be read through the serial peripheral interface (SPI).
  3. Write 0'b11 to WF_SRC (Bits[9:8]) to enable current and voltage channel waveform samples processed at 8 kSPS by the DSP.
  4. Write 0'b11 to WF_MODE (Bits[7:6]) to enable continuous fill on the buffer. See the ADE9000 Technical Reference Manual for more information on continuous filling mode.
  5. Write 0'b1 to WF_CAP_SEL (Bit 5) to enable the fixed data rate sampling (noncoherent).
  6. Write 0'b1 to WF_CAP_EN (Bit 4) to start waveform capturer.
  7. Write 0'b0000 for all channels to BURST_CHAN (Bits[3.0]) to select channels. See the ADE9000 data sheet for other channels.

Figure 4 shows the different sources of the waveform buffer. Waveform samples presented in this application note are captured from the output of the DSP core at a rate of 8 kSPS. It is recommended that the BURST_CHAN bits be 0ʹb0000 to access all channels.

Figure 4. Resampling Mode and Waveform Buffer Source.

Figure 5. Continuous Mode and Ping Pong Routine for Waveform Buffer.

By setting WFB_PG_IRQEN in continuous sampling, an interrupt sets at Page 7 and Page 15, dividing the waveform buffer into two major buffers and creating a ping pong buffer. After Page 0 to Page 7 are full, an interrupt enables, and a microcontroller and a PC can read the values on those pages, while the signal is continuously sampled on the remaining Page 8 to Page 15. After Page 8 to Page 15 are full, an interrupt enables again, reading the values stored on the pages while signal is sampled again on Page 0 to Page 7. Through this ping pong routine, no part of the wave is lost in continuous sampling. The WFB_LAST_PAGE bits on the WFB_ TRIG_STAT register help determine which part of the buffer is filled to start the read routine on that part of the buffer.

To execute this process, take the following steps:

  1. Write 0x20000 to MASK0 (Address 0x405) to enable the page full interrupt.
  2. Write 0x8080 to WFB_PG_IRQWN (Address 0x4A1) to set the interrupt at Page 7 and Page 15.

Figure 6 summarizes the procedure on how to operate the noncoherent sampling mode using the waveform buffer.

Figure 6. Implementing the Noncoherent Mode Resampling.

The complete list of registers for the waveform buffer is available in the ADE9000 data sheet.

The expected values to be measured after an FFT process can be computed using the following equations:

equation1

where % Full Scalen this the percentage of the full-scale content of the signal.

Input defined in this application note are expressed in terms of percentages of the full-scale ADC output in codes.

To compute for the expected total rms values, use the following equation:

equation2

This application note provides an actual measurement of the rms of a fundamental 50 Hz with a harmonic content following the IEC62053-21 with the test conditions found in Table 1.

Table 1. IEC62053-21 Test Conditions
Test Condition Value
Fundamental Current 0.5 IMAX
Fundamental Voltage UN
Fundamental Power Factor 1
Content of the Fifth Harmonic Voltage 10% of UN
Content of the Fifth Harmonic Current 40% (0.5 IMAX)

IMAX was selected to be used as the full-scale 1 V.

equation3

UN was selected to be 20% of the full-scale code.

equation4

To compute for the expected total I rms and V rms, take the rms of the individual values:

equation5

An actual test for noncoherent mode is performed using the EVAL-ADE9000EBZ evaluation board. After the waveform sampling, the microcontroller performs an FFT in which each harmonic content is extracted. For this case, the input is a fundamental signal with a fifth harmonic same as above. For this experiment, LabVIEW has been used as a tool to calculate the FFT and output the harmonic contents of the signal. The rms values of each (fundamental and harmonics) is measured after an FFT for further analysis. The results are shown in Table 2 and Table 3.

Table 2. Phase A Current Channel RMS
Input Expected Value Measured FFT Percent Error
Fundamental 26,351,046 26,347,599 0.0131%
Fifth Harmonic 10,540,418 10,532,242 0.0776%
Table 3. Phase A Voltage Channel RMS
Input Expected Value Measured FFT Percent Error
Fundamental 10,540,418 10,547,428 0.0665%
Fifth Harmonic 1,054,042 1,054,775 0.0695%

The reading from the AIFRMS register during this experiment is 26347436, which is 0.014% off of the expected value, and the reading from the AVFRMS register is 10,548,545, which is 0.0771% off of the expected value.

Using the rms values after the FFT, the total rms for voltage and current were calculated.

equation6

The same calculation is used for the voltage.

equation7

Table 4 and Table 5 describe the comparison between the expected values of the total rms, the FFT measured total rms, and the reading on the register.

Table 4. Measured Values after FFT
Input Expected Value Measured FFT Percent Error
xI rmsTotal 28,380,945 28,374,709 0.0220%
xV rmsTotal 10,592,989 10,600,037 0.0665%
Table 5. Expected vs. Register Values
Input Expected Value Register Reading AI rms/AV rms Percent Error
xI rmsTotal 28,380,945 28,374,967 0.0211%
xV rmsTotal 10,592,989 10,599,835 0.0646%

The current total harmonic distortion can also be calculated using the following equation:

equation8

Calculate the expected ITHD using the following equation:

equation9

ITHD using the measured values from FFT can be figured by the following equation:

equation10

The AITHD register can also be read for comparison. The total harmonic distortion (THD) discussion is further elaborated on in the ADE9000 data sheet.

equation11

With the same input, the measured value on AITHD is 0x33327DC and using the formula, the %THD is 39.9978%.

Table 6. ITHD Comparison Table
Expected ITHD Computed ITHD Based on Measured (FFT) THD Based on AITHD Register
40% 40.0318% 39.9978%

The same procedure is repeated in the voltage channel, and the data in Table 7 was obtained.

Table 7. ITHD Comparison Table
Expected VTHD Computed VTHD Based on Measured (FFT) THD Based on AVTHD Register
10% 10.0147% 10.0012%

Harmonic Analysis using Coherent Sampling


There are initial configurations to be considered before performing harmonic analysis using coherent sampling. The same register, WFB_CFG, is to be configured with the same settings as with the noncoherent sampling except for the WF_CAP_SEL bit. This bit must be set to 0 to configure the waveform buffer in resampled data mode. The resampled data mode has a full scale of 18,196. The following equation can be used to obtain the expected values converted in rms:

equation12

Using the same input as the noncoherent mode and the equations for computing current and voltage resampled data and THD, a new set of expected values were obtained and compared to the measured value upon performing an FFT.

The ITHD and VTHD are also computed based on expected resampled values, measured values after the FFT, and on the AITHD and AVTHD registers.

Table 8. Current Channel A Result (Resampled)
Content Percentage Full Scale Full Scale Expected Value Measured (FFT) Percentage Error
Fundamental 50% 18,196 6433 6433 0.2493%
Fifth Harmonic 20% 18,196 2573 2565 0.3319%
Table 9. Voltage Channel A Result (Resampled)
Content Percentage Full Scale Full Scale Expected Value Measured (FFT) Percentage Error
Fundamental 20% 18,196 2573 2570 0.1167%
Fifth Harmonic 2% 18,196 257 258 0.3876%
Table 10. THD Comparison Table (Resampled)
Parameter Expected THD (Based on Resampled Values) Computed THD Based on Measured (FFT) Reading on AxTHD Register
AITHD 39.9969% 40.0499% 39.9978%
AVTHD 9.9883% 10.0585% 10.0012%

Harmonic Gain Response of the ADE9000 Digital Filter

The signal that passes through the DSP of the ADE9000 is processed through digital filtering, which has a sinc4 filter with 32 KSPS output data rate followed by a low-pass filter (LPF). Due to the digital filtering, the gain of the samples in the waveform buffer varies over frequency, thus attenuating the measurements at higher frequencies. Figure 7 shows the gain performance of the digital filter.

Figure 7. % Gain Error of ADE9000 Sinc4 + LPF Response.

Table 11 and Table 12 summarize the whole performance of the digital filter in percent gain error and the gain compensation factor of each harmonic at 50 Hz and 60 Hz.

Table 11. Sinc4 + LPF Performance Summary at 50 Hz
Harmonic No. Frequency Attenuation Factor Gain Compensation Factor
1 50 1.00000 1.00000
2 100 0.99997 1.00003
3 150 0.99992 1.00008
4 200 0.99985 1.00015
5 250 0.99976 1.00024
6 300 0.99964 1.00036
7 350 0.99948 1.00052
8 400 0.99930 1.00070
9 450 0.99908 1.00092
10 500 0.99882 1.00118
11 550 0.99851 1.00149
12 600 0.99816 1.00184
13 650 0.99777 1.00223
14 700 0.99732 1.00269
15 750 0.99683 1.00318
16 800 0.99629 1.00372
17 850 0.99571 1.00431
18 900 0.99508 1.00494
19 950 0.99441 1.00562
20 1000 0.99370 1.00634
21 1050 0.99297 1.00708
22 1100 0.99220 1.00786
23 1150 0.99141 1.00866
24 1200 0.99060 1.00949
25 1250 0.98977 1.01034
26 1300 0.98893 1.01119
27 1350 0.98808 1.01206
28 1400 0.98723 1.01294
29 1450 0.98636 1.01383
30 1500 0.98547 1.01474
31 1550 0.98457 1.01567
32 1600 0.98365 1.01662
33 1650 0.98270 1.01760
34 1700 0.98172 1.01862
35 1750 0.98069 1.01969
36 1800 0.97962 1.02080
37 1850 0.97849 1.02198
38 1900 0.97730 1.02323
39 1950 0.97605 1.02454
40 2000 0.97475 1.02590
41 2050 0.97340 1.02733
42 2100 0.97200 1.02881
43 2150 0.97058 1.03031
44 2200 0.96914 1.03184
45 2250 0.96770 1.03338
46 2300 0.96627 1.03491
47 2350 0.96486 1.03642
48 2400 0.96347 1.03792
49 2450 0.96209 1.03940
50 2500 0.96069 1.04092
51 2550 0.95925 1.04248
52 2600 0.95772 1.04415
53 2650 0.95608 1.04594
54 2700 0.95431 1.04788
55 2750 0.95244 1.04993
56 2800 0.95056 1.05201
57 2850 0.94878 1.05399
58 2900 0.94722 1.05572
59 2950 0.94572 1.05740
60 3000 0.94335 1.06005
61 3050 0.93736 1.06683
62 3100 0.92128 1.08545
63 3150 0.88338 1.13202
Table 12. Sinc4 + LPF Performance Summary at 60 Hz
Harmonic No. Frequency Attenuation Factor Gain Compensation Factor
1 60 1.00000 1.00000
2 120 0.99996 1.00004
3 180 0.99989 1.00011
4 240 0.99978 1.00022
5 300 0.99964 1.00036
6 360 0.99945 1.00055
7 420 0.99922 1.00078
8 480 0.99893 1.00107
9 540 0.99858 1.00142
10 600 0.99817 1.00183
11 660 0.99769 1.00232
12 720 0.99714 1.00287
13 780 0.99652 1.00349
14 840 0.99583 1.00419
15 900 0.99508 1.00494
16 960 0.99428 1.00575
17 1020 0.99342 1.00662
18 1080 0.99251 1.00755
19 1140 0.99157 1.00850
20 1200 0.99060 1.00949
21 1260 0.98961 1.01050
22 1320 0.98860 1.01153
23 1380 0.98757 1.01259
24 1440 0.98653 1.01365
25 1500 0.98548 1.01473
26 1560 0.98439 1.01586
27 1620 0.98328 1.01700
28 1680 0.98212 1.01821
29 1740 0.98090 1.01947
30 1800 0.97962 1.02080
31 1860 0.97826 1.02222
32 1920 0.97681 1.02374
33 1980 0.97528 1.02535
34 2040 0.97368 1.02703
35 2100 0.97201 1.02880
36 2160 0.97029 1.03062
37 2220 0.96857 1.03245
38 2280 0.96684 1.03430
39 2340 0.96514 1.03612
40 2400 0.96347 1.03792
41 2460 0.96181 1.03971
42 2520 0.96013 1.04153
43 2580 0.95835 1.04346
44 2640 0.95643 1.04555
45 2700 0.95432 1.04787
46 2760 0.95207 1.05034
47 2820 0.94983 1.05282
48 2880 0.94782 1.05505
49 2940 0.94604 1.05704
50 3000 0.94336 1.06004
51 3060 0.93525 1.06923
52 3120 0.90957 1.09942
53 3180 0.84404 1.18478
54 3240 0.72078 1.38739
55 3300 0.55810 1.79179

Gain Response of Antialias Filter


The external resistor capacitor (RC) that prevents aliasing has a response that affects the signals at frequencies higher than 2000 Hz.

Figure 8. ADE9000 Antialias Filter.

The recommended values of 1 kΩ and 22 nF theoretically follow the transfer function that provide the gain response expressed in Figure 9.

equation13

Figure 9. ADE9000 Antialias Filter Response (1 kΩ, 22 nF).

The combined effect of the sinc4 and LPF digital filter and the external antialias filter create a significant gain error to high frequencies. Table 13 and Table 14 the whole performance of the digital filters including the recommended antialias filter with proper gain compensation factors for each harmonic at 50 Hz and 60 Hz.

Table 13. Effect of Antialias (1 kΩ, 22 nF) Performance Summary at 50 Hz
Harmonic No. Frequency Attenuation Factor Gain Compensation Factor
1 50 1.00000 1.00000
2 100 0.99993 1.00007
3 150 0.99981 1.00019
4 200 0.99964 1.00036
5 250 0.99943 1.00057
6 300 0.99917 1.00083
7 350 0.99886 1.00114
8 400 0.99850 1.00150
9 450 0.99809 1.00191
10 500 0.99764 1.00237
11 550 0.99715 1.00286
12 600 0.99660 1.00341
13 650 0.99601 1.00401
14 700 0.99538 1.00464
15 750 0.99469 1.00534
16 800 0.99396 1.00608
17 850 0.99319 1.00686
18 900 0.99237 1.00769
19 950 0.99151 1.00856
20 1000 0.99060 1.00949
21 1050 0.98965 1.01046
22 1100 0.98866 1.01147
23 1150 0.98762 1.01254
24 1200 0.98654 1.01364
25 1250 0.98542 1.01480
26 1300 0.98426 1.01599
27 1350 0.98305 1.01724
28 1400 0.98181 1.01853
29 1450 0.98052 1.01987
30 1500 0.97920 1.02124
31 1550 0.97783 1.02267
32 1600 0.97643 1.02414
33 1650 0.97499 1.02565
34 1700 0.97351 1.02721
35 1750 0.97199 1.02882
36 1800 0.97044 1.03046
37 1850 0.96885 1.03215
38 1900 0.96722 1.03389
39 1950 0.96556 1.03567
40 2000 0.96387 1.03748
41 2050 0.96214 1.03935
42 2100 0.96038 1.04125
43 2150 0.95859 1.04320
44 2200 0.95676 1.04519
45 2250 0.95490 1.04723
46 2300 0.95302 1.04930
47 2350 0.95110 1.05141
48 2400 0.94916 1.05356
49 2450 0.94718 1.05577
50 2500 0.94518 1.05800
51 2550 0.94315 1.06028
52 2600 0.94109 1.06260
53 2650 0.93901 1.06495
54 2700 0.93690 1.06735
55 2750 0.93476 1.06979
56 2800 0.93261 1.07226
57 2850 0.93043 1.07477
58 2900 0.92822 1.07733
59 2950 0.92599 1.07993
60 3000 0.92375 1.08254
61 3050 0.92148 1.08521
62 3100 0.91919 1.08791
63 3150 0.91688 1.09066
Table 14. Effect of Antialias (1 kΩ, 22 nF) Performance Summary at 60 Hz
Harmonic No. Frequency Attenuation Factor Gain Compensation Factor
1 60 1.00000 1.00000
2 120 0.99990 1.00010
3 180 0.99972 1.00028
4 240 0.99948 1.00052
5 300 0.99918 1.00082
6 360 0.99980 1.00120
7 420 0.99835 1.00165
8 480 0.99784 1.00216
9 540 0.99726 1.00275
10 600 0.99661 1.00340
11 660 0.99590 1.00412
12 720 0.99512 1.00490
13 780 0.99427 1.00576
14 840 0.99336 1.00668
15 900 0.99238 1.00768
16 960 0.99134 1.00874
17 1020 0.99024 1.00986
18 1080 0.98907 1.01105
19 1140 0.98784 1.01231
20 1200 0.98655 1.01363
21 1260 0.98520 1.01502
22 1320 0.98379 1.01648
23 1380 0.98232 1.01800
24 1440 0.98079 1.01959
25 1500 0.97921 1.02123
26 1560 0.97756 1.02296
27 1620 0.97587 1.02473
28 1680 0.97411 1.02658
29 1740 0.97231 1.02848
30 1800 0.97045 1.03045
31 1860 0.96853 1.03249
32 1920 0.96657 1.03459
33 1980 0.96456 1.03674
34 2040 0.96250 1.03896
35 2100 0.96039 1.04124
36 2160 0.95823 1.04359
37 2220 0.95603 1.04599
38 2280 0.95379 1.04845
39 2340 0.95150 1.05097
40 2400 0.94917 1.05355
41 2460 0.94679 1.05620
42 2520 0.94438 1.05890
43 2580 0.94193 1.06165
44 2640 0.93944 1.06446
45 2700 0.93691 1.06734
46 2760 0.93434 1.07027
47 2820 0.93175 1.07325
48 2880 0.92912 1.07629
49 2940 0.92645 1.07939
50 3000 0.92376 1.08253
51 3060 0.92103 1.08574
52 3120 0.91827 1.08900
53 3180 0.91549 1.09231
54 3240 0.91268 1.09567
55 3300 0.90984 1.09909

A full harmonic analysis is performed on Current Channel A at 50 Hz to verify the combined effect of the antialias filter of the EVAL-ADE9000EBZ and the sinc4 + LPF. The correction factors are introduced to the measurements to compensate the attenuation introduced by the sinc4 + LPF plus antialias filter. The results are shown in Table 15 and Table 16.

Table 15. Combined Performance of Sinc4 + LPF and Antialias Filter (1 kΩ, 22 nF) at 50 Hz
Harmonic No. Frequency (50 Hz) Combined Attenuation Combined Gain Compensation Factor
1 50 1 1.00000
2 100 0.9999 1.00010
3 150 0.999723 1.00027
4 200 0.999494 1.00051
5 250 0.999184 1.00082
6 300 0.999801 1.00120
7 350 0.99834 1.00166
8 400 0.997798 1.00221
9 450 0.997173 1.00284
10 500 0.996462 1.00355
11 550 0.995662 1.00436
12 600 0.994771 1.00526
13 650 0.993788 1.00625
14 700 0.992712 1.00734
15 750 0.991542 1.00853
16 800 0.990281 1.00981
17 850 0.98893 1.01119
18 900 0.987491 1.01267
19 950 0.985969 1.01423
20 1000 0.984368 1.01588
21 1050 0.982692 1.01761
22 1100 0.980947 1.01942
23 1150 0.979137 1.02131
24 1200 0.977267 1.02326
25 1250 0.975343 1.02528
26 1300 0.973366 1.02736
27 1350 0.97134 1.02951
28 1400 0.969266 1.03171
29 1450 0.967143 1.03397
30 1500 0.964971 1.03630
31 1550 0.962747 1.03869
32 1600 0.960465 1.04116
33 1650 0.958121 1.04371
34 1700 0.955708 1.04634
35 1750 0.953221 1.04907
36 1800 0.950655 1.05191
37 1850 0.948003 1.05485
38 1900 0.945265 1.05790
39 1950 0.94244 1.06108
40 2000 0.939531 1.06436
41 2050 0.936545 1.06775
42 2100 0.933491 1.07125
43 2150 0.930383 1.07483
44 2200 0.927234 1.07848
45 2250 0.92406 1.08218
46 2300 0.920872 1.08593
47 2350 0.917679 1.08971
48 2400 0.914482 1.09352
49 2450 0.91127 1.09737
50 2500 0.908024 1.10129
51 2550 0.904714 1.10532
52 2600 0.901305 1.10950
53 2650 0.897768 1.11387
54 2700 0.894094 1.11845
55 2750 0.890311 1.12320
56 2800 0.886497 1.12804
57 2850 0.882771 1.13280
58 2900 0.879228 1.13736
59 2950 0.875728 1.14191
60 3000 0.87142 1.14755
61 3050 0.863753 1.15774
62 3100 0.84683 1.18087
63 3150 0.809953 1.23464
Table 16. Combined Performance of Sinc4 + LPF and Antialias Filter (1 kΩ, 22 nF) at 60 Hz 1
Harmonic No. Frequency (60 Hz) Combined Attenuation Combined Gain Compensation Factor
1 60 1 1.00000
2 120 0.999855 1.00015
3 180 0.999612 1.00039
4 240 0.999267 1.00073
5 300 0.998815 1.00119
6 360 0.998252 1.00175
7 420 0.997573 1.00243
8 480 0.996772 1.00324
9 540 0.995844 1.00417
10 600 0.994786 1.00524
11 660 0.993595 1.00645
12 720 0.99227 1.00779
13 780 0.990811 1.00927
14 840 0.989222 1.01090
15 900 0.987506 1.01265
16 960 0.98567 1.01454
17 1020 0.983721 1.01655
18 1080 0.981667 1.01868
19 1140 0.979518 1.02091
20 1200 0.977282 1.02325
21 1260 0.974966 1.02568
22 1320 0.972575 1.02820
23 1380 0.970115 1.03081
24 1440 0.967586 1.03350
25 1500 0.964985 1.03629
26 1560 0.962309 1.03917
27 1620 0.959549 1.04216
28 1680 0.956696 1.04526
29 1740 0.953739 1.04850
30 1800 0.950669 1.05189
31 1860 0.947477 1.05543
32 1920 0.944159 1.05914
33 1980 0.940718 1.06302
34 2040 0.937162 1.06705
35 2100 0.933505 1.07123
36 2160 0.929769 1.07554
37 2220 0.92598 1.07994
38 2280 0.922162 1.08441
39 2340 0.918332 1.08893
40 2400 0.914495 1.09350
41 2460 0.910638 1.09813
42 2520 0.906723 1.10287
43 2580 0.902696 1.10779
44 2640 0.8985 1.11297
45 2700 0.894107 1.11843
46 2760 0.88956 1.12415
47 2820 0.885002 1.12994
48 2880 0.880636 1.13554
49 2940 0.876462 1.14095
50 3000 0.871433 1.14754
51 3060 0.861391 1.16091
52 3120 0.835236 1.19727
53 3180 0.772715 1.29414
54 3240 0.65784 1.52013
55 N/A N/A N/A
56 N/A N/A N/A
57 N/A N/A N/A
58 N/A N/A N/A
59 N/A N/A N/A
60 N/A N/A N/A
61 N/A N/A N/A
62 N/A N/A N/A
63 N/A N/A N/A
1 N/A means not applicable.

Figure 10. EVAL-ADE9000EBZ Current Channel A RMS Error vs. Frequency after correction (50% Full Scale, 50 Hz).

Measured Test Results using EVAL-ADE9000EBZ

A full harmonic analysis using the EVAL-ADE9000EBZ was performed on Channel IA using the noncoherent analysis with 50% full scale for both fundamental and harmonics. After the FFT, the gain errors listed in Table 17 were obtained and compared to the gain errors of the combined sinc4 + LPF + antialias listed in Table 15. The rms contents with the errors are corrected using the compensation factors listed in Table 13. The results are shown in Table 18.

Table 17. Comparison of Typical Combined Gain Error (ADE9000 Digital Filter + Antialias) vs. Actual Measured Value Using Current Channel A at 50 Hz
Harmonic No. Frequency Actual Measured Gain Error Typical Combined Gain Error
1 50 0% 0%
2 100 0.0085% −0.010%
3 150 −0.0209% −0.027%
4 200 −0.0482% −0.051%
5 250 −0.0814% −0.082%
6 300 −0.1234% −0.120%
7 350 −0.1703% −0.166%
8 400 −0.2278% −0.220%
9 450 −0.2911% −0.283%
10 500 −0.3654% −0.354%
11 550 −0.4487% −0.434%
12 600 −0.5392% −0.523%
13 650 −0.6396% −0.621%
14 700 −0.7508% −0.729%
15 750 −0.8686% −0.846%
16 800 −0.9991% −0.972%
17 850 −1.1358% −1.107%
18 900 −1.2837% −1.251%
19 950 −1.4379% −1.403%
20 1000 −1.6026% −1.563%
21 1050 −1.7728% −1.731%
22 1100 −1.9529% −1.905%
23 1150 −2.1355% −2.086%
24 1200 −2.3255% −2.273%
25 1250 −2.5249% −2.466%
26 1300 −2.7260% −2.663%
27 1350 −2.9330% −2.866%
28 1400 −3.1420% −3.073%
29 1450 −3.3594% −3.286%
30 1500 −3.5799% −3.503%
31 1550 −3.8069% −3.725%
32 1600 −4.0397% −3.954%
33 1650 −4.2800% −4.188%
34 1700 −4.5263% −4.429%
35 1750 −4.7801% −4.678%
36 1800 −5.0414% −4.935%
37 1850 −5.3127% −5.200%
38 1900 −5.5913% −5.473%
39 1950 −5.8785% −5.756%
40 2000 −6.1742% −6.047%
41 2050 −6.4778% −6.346%
42 2100 −6.7909% −6.651%
43 2150 −7.1056% −6.962%
44 2200 −7.4254% −7.277%
45 2250 −7.7491% −7.594%
46 2300 −8.0723% −7.913%
47 2350 −8.3985% −8.232%
48 2400 −8.7237% −8.552%
49 2450 −9.0526% −8.873%
50 2500 −9.3832% −9.198%
51 2550 −9.7194% −9.529%
52 2600 −10.0646% −9.870%
53 2650 −10.4263% −10.223%
54 2700 −10.7984% −10.591%
55 2750 −11.1817% −10.969%
56 2800 −11.5689% −11.350%
57 2850 −11.9442% −11.723%
58 2900 −12.3064% −12.077%
59 2950 −12.6606% −12.427%
60 3000 −13.0965% −12.858%
61 3050 −13.8693% −13.625%
62 3100 −15.5630% −15.317%
63 3150 −19.2473% −19.005%
Table 18. Corrected Harmonic Contents Using Current Channel A at 50 Hz (50% Full Scale)
Harmonic No. Frequency Harmonic Content in RMS Gain Compensation Factor Corrected Value % Error
1 50 26348904 1 26348903.6 0.00495%
2 100 26337468 1.0001 26340102 −0.02845%
3 150 26343066 1.00027 26350178.2 0.00979%
4 200 26323856 1.00051 26337280.9 −0.03916%
5 250 26313297 1.00082 26334873.5 −0.04830%
6 300 26304634 1.0012 26336200 −0.04326%
7 350 26292245 1.00166 26335890.2 −0.04444%
8 400 26277729 1.00221 26335802.3 −0.04477%
9 450 26260805 1.00284 26335386 −0.04635%
10 500 26241411 1.00355 26334567.7 −0.04946%
11 550 26220309 1.00436 26334629.8 −0.04922%
12 600 26196100 1.00526 26333891.6 −0.05203%
13 650 26169823 1.00625 26333384.1 −0.05395%
14 700 26140410 1.00734 26332280.6 −0.05814%
15 750 26109163 1.00853 26331874.1 −0.05968%
16 800 26075242 1.00981 26331040.1 −0.06285%
17 850 26038681 1.01119 26330053.6 −0.06659%
18 900 25999739 1.01267 26329156.1 −0.07000%
19 950 25959225 1.01423 26328624.5 −0.07202%
20 1000 25916479 1.01588 26328032.6 −0.07426%
21 1050 25870936 1.01761 26326523.6 −0.07999%
22 1100 25823584 1.01942 26325077.6 −0.08548%
23 1150 25774163 1.02131 26323410.5 −0.09181%
24 1200 25723526 1.02326 26321855.2 −0.09771%
25 1250 25671636 1.02528 26320614.7 −0.10242%
26 1300 25617889 1.02736 26318794.7 −0.10932%
27 1350 25563016 1.02951 26317380.4 −0.11469%
28 1400 25506991 1.03171 26315817.3 −0.12062%
29 1450 25449687 1.03397 26314212.8 −0.12671%
30 1500 25390639 1.0363 26312319.5 −0.13390%
31 1550 25330763 1.03869 26310810.7 −0.13963%
32 1600 25268285 1.04116 26308327.5 −0.14905%
33 1650 25204549 1.04371 26306240 −0.15697%
34 1700 25139013 1.04634 26303954.7 −0.16565%
35 1750 25071823 1.04907 26302097.1 −0.17270%
36 1800 25001965 1.05191 26299817 −0.18135%
37 1850 24930558 1.05485 26297999.4 −0.18825%
38 1900 24856230 1.0579 26295405.5 −0.19810%
39 1950 24779510 1.06108 26293042.4 −0.20706%
40 2000 24700898 1.06436 26290647.4 −0.21615%
41 2050 24619876 1.06775 26287872.1 −0.22669%
42 2100 24537541 1.07125 26285841 −0.23440%
43 2150 24452885 1.07483 26282694.2 −0.24634%
44 2200 24368062 1.07848 26280467 −0.25479%
45 2250 24282321 1.08218 26277841.9 −0.26476%
46 2300 24195538 1.08593 26274661 −0.27683%
47 2350 24109229 1.08971 26272068.2 −0.28667%
48 2400 24022755 1.09352 26269362.5 −0.29694%
49 2450 23936309 1.09737 26266987.8 −0.30595%
50 2500 23848192 1.10129 26263774.9 −0.31815%
51 2550 23759036 1.10532 26261338.2 −0.32740%
52 2600 23666544 1.1095 26258030.1 −0.33995%
53 2650 23570712 1.11387 26254709.2 −0.35256%
54 2700 23471248 1.11845 26251417.5 −0.36505%
55 2750 23369748 1.1232 26248900.8 −0.37460%
56 2800 23267349 1.12804 26246500.1 −0.38371%
57 2850 23166448 1.1328 26242952.3 −0.39718%
58 2900 23070843 1.13736 26239853.9 −0.40894%
59 2950 22976865 1.14191 26237512 −0.41783%
60 3000 22861848 1.14755 26235113.5 −0.42693%
61 3050 22657995 1.15774 26232066.6 −0.43849%
62 3100 22211497 1.18087 26228890.6 −0.45055%
63 3150 21242010 1.23464 26226235.5 −0.46062%

Conclusion

The following sections describe the advantages and disadvantages of both coherent and noncoherent sampling method prior to FFT.


Noncoherent Sampling


Advantages

Accurate harmonic contents can be obtained by following a proper FFT.

Noncoherent mode can perform sampling continuously using the ping pong buffer routine.

A continuous FFT process is possible.

Disadvantages

An FFT is difficult to perform and needs a more complex routine.

If signals are generated using a function generatorto perform the analysis, proper timing, and sync must be considered between the CLK_IN of the ADE9000 and the frequency of the generators.


Coherent Sampling


Advantages

An FFT is easier to perform, because 128 samples are constantly tracked during the resampling per line cycle.

Disadvantages

Coherent sampling is less accurate than the noncoherent sampling, because the maximum codes for resampled data is 18,196 codes.

Resampling is limited to 512 samples per waveform buffer.

Performing a continuous FFT is difficult, because portions of the signal are lost when the waveform buffer calculates resampled data.

The ADE9000 simplifies harmonic analysis by using the waveform buffer register. It is possible to calculate up to the 63rd harmonic and introduce the gain compensation factors to correct the attenuation caused by the digital filtering plus effects of the antialias filter.

著者

aaron-heredia-blue-background

Aaron Heredia

Aaron Heredia is an Applications Engineer for Analog Devices. He graduated with a degree in Master of Science in Electrical Engineering majoring in Control Systems. He supported the Energy Management Products in his first two years at ADI and just recently he joined the Industrial Ethernet Group.