SSZT992 august 2017 AMC1304M05 , MSP430F67641
Mekre Mesganaw
In the second installment of this series, I briefly talked about the attenuation of frequencies due to the sinc3 digital filter. In this installment, I’ll quantify the theoretical degradation due to a sinc3 filter and talk about how the Multiphase Power Quality Measurement with Isolated Shunt Sensors Reference Design reduces this degradation when calculating total harmonic distortion (THD).
First, let’s begin by examining the equation of a typical sinc3 filter show in Figure 1:
Here fM is the delta-sigma’s modulation clock and OSR is the selected oversampling ratio. The effective sample rate of the sigma-delta converter is equal to fM/OSR.
From Figure 1, you can see that the frequency response depends on the sample rate of the sigma-delta analog-to-digital converter (ADC). Figure 2 shows the degradation of amplitude for a given frequency to ADC sample-rate ratio. The waveform in Figure 1 covers a range equal to half of the ADC sample rate, thereby covering the entire set of frequencies that the ADC could sense. In Figure 2, the waveform is normalized where the magnitude at each frequency is divided by the DC gain.
In an energy-measurement system such as an e-meter, the system has calibration performed when applying a voltage and current waveform at the fundamental frequency. Therefore, any attenuation of the amplitude at the fundamental frequency will be accounted for during gain calibration of the system. Using this information, you can calculate the attenuation registered by the energy-measurement system at a specific frequency, f, by dividing the magnitude at that specific frequency, (H(f)), by the magnitude at the fundamental frequency, (H(ffund)).
As an example of the attenuation from the sinc3 filter, let’s say that you have the following test conditions:
With these settings, the sensed contribution of the fifth harmonic scales by a factor of H(250)/H(50), which equals 0.982484702. Given these conditions, this means that the sensed fifth-harmonic current contribution is 3.929938809A, which has a percentage error of 1.782755276% from the actual contribution of 4A. As a result, the total sensed RMS current would be 10.74450646A instead of the actual value of 10.77032961A, which is a percentage error of -0.239761981%.
Similarly, the fifth-harmonic voltage contribution is 22.59714815V, which has a percentage error of 1.782755276% from the actual contribution of 23V. This means that the sensed total RMS value would be 231.1074017V instead of 231.1471393V, leading to a percentage error of -0.017191483%. Assuming the use of the THD_F definition of THD, the attenuation caused by the sinc3 filter would cause a voltage THD reading of 9.824847021% instead of 10% and a current THD reading of 39.29938809% instead of 40%.
Applying the same test conditions but changing the fundamental frequency from 50Hz to 60Hz results in a fifth harmonic of 300Hz instead of 250Hz. The degradation in accuracy is worse than the 50Hz case. Specifically, these are the calculated parameter values:
From these parameter values, you can see how there is a degradation in the results due to the attenuation of harmonics caused by the roll-off of amplitude of the sinc3 filter at higher frequencies. This attenuation is worse when higher-frequency components are present, thereby resulting in less accurate results.
The Multiphase Power Quality Measurement with Isolated Shunt Sensors Reference Design demonstrates how to reduce the effects of roll-off of the sinc3 filter. This reference design uses a successive approximation register (SAR) ADC for measuring phase voltages. For many applications, a SAR ADC can measure voltages without requiring multiple gain stages, since a large dynamic range of voltage is not often required. By using a SAR ADC instead of a delta-sigma ADC with a sinc3 filter, there is no degradation of accuracy at higher frequencies caused by the converter.
For sensing current, the reference design uses the AMC1304M05 delta-sigma modulator with the MSP430F67641’s sinc3 digital filters. This modulator-plus-digital-filter combination can run with a modulation frequency as high as 20MHz. A high modulation frequency enables both a high OSR for accuracy and a high delta-sigma sample rate. The high delta-sigma sample rate has the benefit of reducing the magnitude of attenuation at higher frequencies as Figure 2 suggests, as it shows the degradation of amplitude for a given frequency to the ADC sample-rate ratio. In the reference design, the resulting delta-sigma ADC sample rate is 19,334 samples per second. Since not all of these samples are needed, one-fifth of the ADC samples for metrology calculations leads to a final sample rate of 3,866.8 samples per second.
Now let’s see how the attenuation is affected by the higher sampling rate of 19,334 for the fundamental frequency of 60Hz. Assuming the same fundamental and harmonic current conditions as before, here are the calculated parameter values:
Thus, you can see that increasing the sample rate reduces the magnitude of attenuation at higher frequencies, thereby leading to more accurate RMS and THD readings. In addition to reducing the effects of sinc3 filter roll-off at higher frequencies, the reference design also uses shunts for each phase to reduce the degradation in accuracy present with current transformers at higher frequencies.
TI PROVIDES TECHNICAL AND RELIABILITY DATA (INCLUDING DATASHEETS), DESIGN RESOURCES (INCLUDING REFERENCE DESIGNS), APPLICATION OR OTHER DESIGN ADVICE, WEB TOOLS, SAFETY INFORMATION, AND OTHER RESOURCES “AS IS” AND WITH ALL FAULTS, AND DISCLAIMS ALL WARRANTIES, EXPRESS AND IMPLIED, INCLUDING WITHOUT LIMITATION ANY IMPLIED WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE OR NON-INFRINGEMENT OF THIRD PARTY INTELLECTUAL PROPERTY RIGHTS.
These resources are intended for skilled developers designing with TI products. You are solely responsible for (1) selecting the appropriate TI products for your application, (2) designing, validating and testing your application, and (3) ensuring your application meets applicable standards, and any other safety, security, or other requirements. These resources are subject to change without notice. TI grants you permission to use these resources only for development of an application that uses the TI products described in the resource. Other reproduction and display of these resources is prohibited. No license is granted to any other TI intellectual property right or to any third party intellectual property right. TI disclaims responsibility for, and you will fully indemnify TI and its representatives against, any claims, damages, costs, losses, and liabilities arising out of your use of these resources.
TI’s products are provided subject to TI’s Terms of Sale (www.ti.com/legal/termsofsale.html) or other applicable terms available either on ti.com or provided in conjunction with such TI products. TI’s provision of these resources does not expand or otherwise alter TI’s applicable warranties or warranty disclaimers for TI products.
Mailing Address: Texas Instruments, Post Office Box 655303, Dallas, Texas 75265
Copyright © 2023, Texas Instruments Incorporated