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C2000 ™ Σ Δ 濾波器調變器 (SDFM)

Σ Δ 濾波器調變器 (SDFM) 是 C2000 裝置上即時控制系統的重要元件。此模組負責接收數位 Sigma Delta 調變位元串流,並將其轉換為 C2000 裝置可處理的數位濾波器輸出。每個 SDFM 支援四個可配置的濾波器通道,這些通道可獨立配置以偵測過電壓 / 欠電壓情況,並提供更高解析度資料濾波器結果以用作控制環路的一部分。

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      簡報者

      Hi, and welcome to the next video in our C2000 Sigma Delta Filter Module video series. I am Manoj Kumar Santha Mohan. In this video, I'll be giving you an overview of sinc filters and how they work.

      What is a sinc filter? A sinc filter is essentially a low-pass filter that converts the input SD modulated bitstream into high resolution digital data by digital filtering and decimation. In this slide, I've shown the z transform of n-th order sinc filter and its simplified block diagram.

      Sinc filter consists of cascaded integrators and cascaded combs separated by a down sampler. Cascaded integrators are operated at SD modulated clock rate, and cascaded combs are operated at decimated rate, which is given by SD modulator clock divided by O Sampling Ratio, or OSR.

      Sinc 1 filter is a first-order filter which has an integrator and a comb. Sinc 2 filter is a second-order filter which has two cascaded integrators and combs. Sinc 3 filter is a third-order filter which has three cascaded integrators and combs.

      Now let's look at the data rate and latency of sinc filters. Data rate of sinc filters is essentially throughput of the filter. It depends upon the SD modulator data rate and other settings. The equation to calculate the data rate of sinc filter is shown below.

      It is important to note that the order of filter doesn't affect the data rate. Latency of sinc filters is defined as the amount of time taken by a sinc filter to deliver the correct filtered output which represents the input signal. Here, the order of sinc filter does affect latency.

      To understand this better, let's look at a step response of different sinc filters configured with same OSR. Now, since my data rate is independent of filter order, all the sinc filters produce a filter output every OSR cycle. In the first OSR cycle, sinc 1 settles to correct filter output, but sinc 2 and sinc 2 don't represent the correct filter output yet. In the second OSR cycle, sinc 2 settles to final output. Finally, in the third OSR cycle, sinc 3 filter settles to its final output.

      Now, when sinc 1 filter settles to its correct filter output in its first OSR cycle and provides the best settling time. Why would anyone consider sinc 2 or sinc 3? Well, the answer is higher resolution. Typically, higher-order sinc filters provide better resolution for the same OSR settings. Sinc 1 has poor filter resolution with faster settling time. And sinc 3 has better resolution at the cost of slower settling time.

      Let's take a quick look into an ideal low-pass filter. An ideal low-pass filter passes all signals below cutoff frequency and completely attenuates all signals above cutoff frequency. This slide shows the frequency response of an ideal low-pass filter. It has a pass band with a gain of 1. This means all the signals with frequencies 0 to fc will not suffer any distortion. However, stop band has a gain of 0. This means all the signals with the frequency greater than fc will be completely removed.

      Now, we should take a closer look into filter characteristics of sinc filters. This slide shows the frequency response of sinc filters for the same OSR setting of 32 and SD modulated data rate of 20 MHz.

      Pass band and stop band of sinc filter is highlighted in green and red, respectively. Unlike ideal low-pass filter, with sinc filters we see a lot of ripple in stop band. Lower the ripple in stop band, higher the resolution of the filter. And higher the ripple in stop band, lower the resolution of the filter.

      Sinc 1 has the highest stop band ripple among the three filters. And it generates its output by a weighted average of 32 SD modulated bit streams. Sinc 2 filter output is weighted average of 32 sinc 1 filter data.

      Sinc 2 filter provides better resolution when compared to sinc 1 because it averages sinc 1 filter data, which is already an average of SD modulated bitstreams. This is the reason why sinc 2 shows lesser stop band ripple when compared to sinc 1. Sinc 3 filter has the lowest stop band ripple, as it produces its filter output with a weighted average of 32 sinc 2 filter data, thereby producing highest filter resolution among the three sinc filters.

      Note that the data rate of all the sinc filters are the same, but the latency increases as the order of the filter increases. In short, increasing the order of filter increases filter resolution with more stop band attenuation.

      Let's look at another example. This slide shows the frequency response of sinc 3 filter with different OSR settings of 8, 16, and 24. The black plot is the 50 spectrum of SD modulated bitstream. This is the base band signal we are interested, or it is usually called area of interest.

      And this is the unwanted quantization noise we are trying to remove using our sinc filters. Pass band and stop band of sinc 3 filter with OSR of 8 is shown here. In this filter configuration, it produces filter output by weighted average of eight sinc 2 filter data.

      Now, what happens when we increase the OSR to 16? Well, the filter would use 16 sinc 2 filter data to produce a filter output. But how does increasing OSR affect the pass band and stop band? Pass band moves closer to the area of interest, and the stop band attenuation increases with increasing OSR. This results in a higher filter resolution.

      With OSR of 24, pass band moves even closer to the area of interest and the stop and attention increases further. In short, increasing OSR increases filter resolution by averaging more number of samples.

      Let's talk about the performance of SD modulator and sinc filter. Below two plots are taken from datasheet of SD modulator AMC1304. Plot 1 shows the relationship between measured filter resolution, shown as effective number of bits, or ENOBs, versus O sampling ratio. Plot 2 shows the relationship between ENOB versus settling time for different sinc filter types.

      Suppose an application demands the following system requirements. It requires filter resolution of six ENOBs in less than 2 microseconds of settling time for short circuit protection, and high resolution data of 12 ENOBs which will be used in control loop.

      It is clear from plot 1 that sinc 3 filter with OSR of 10 provides six ENOBs. And second plot shows that six ENOB takes 1.5 microseconds of settling time. So sinc 3 filter and OSR of 10 would satisfy short circuit protection requirement. For high resolution data, sinc 3 filter with OSR of 60 provides 12 ENOBs with a settling time of microseconds. These two plots should help developers decide on selecting filter type and OSR settings based on their application requirement.

      That concludes sinc filter overview video in our C2000 Sigma Delta Filter Module video series. For more information, please refer to the links provided in foundation materials and technical reference manual. Links found in export materials are tier designs which demonstrates the use of sigma delta modulator and SD FM for current or voltage measurements.

      Thanks for watching.

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      C2000 ™ Σ Δ 濾波器調變器 (SDFM)