1. Aliasing and Anti-aliasing Filters TIPL 4304 TI Precision Labs – ADCs
Hello, and welcome to the TI Precision Lab covering frequency domain analysis for data converters. This video introduces the concept of frequency domain aliasing. The alias is an error source that we want to avoid or minimize. The video also covers how an anti-aliasing filter can be used to minimize aliasing errors.
Created by Art Kay
Presented by Peggy Liska

2. Aliasing: Time Domain vs. Frequency Domain
In a very general sense, aliasing is an error signal that is detected when the sampling system cannot sample fast enough to properly monitor the system. You many have noticed when looking at the spokes of a spinning wheel, it appears that the wheel is moving very slowly or even backwards when you know it is moving forwards very quickly. This optical illusion happens because your eye is a sampling system that cannot perceive the rapid forward spinning motion. Your eye is seeing an alias signal. Here we introduce the concept of aliasing for data converters in both the time domain and frequency domain. On the left hand side you can see time domain aliasing. The input signal is a 900kHz sine wave shown in red. The data converter is sampling at 1Msps, so each dot on the red curve represents a sample of the input signal. Connecting the dot’s for each input sample shows the blue alias signal. The point is that looking at the sampled data it appears that we have a completely different signal at 100kHz. This erroneous signal is called an alias. For data converters you will get an alias signal whenever the input signal exceeds one half the sampling rate. This frequency limitation is called the Nyquist rate, and can be thought of as the “speed limit” for the data converter. Exceeding the Nyquist rate will always result in an alias signal, so care must be taken to assure that the input signal is band limited to less than the Nyquist rate.
The right hand side of the slide shows aliasing in the frequency domain. This is the same example shown on the left. The sampling rate is 1MHz and the input is 900kHz. Since 900kHz is above the Nyquist rate, it will produce an alias. The alias signal will appear in the signal band at the sampling frequency minus the input signal, that is falias = fs – fin = 1MHz -900kHz = 100kHz. Remember the 100kHz alias is an error as the actual input signal is at 900kHz. The process of aliasing is sometimes called folding back or mirroring of the input signal.
Nyquist frequency = fs/2, the maximum input signal without aliasing.

3. Nyquist Theorem, Sampling Frequency = 1Msps
The maximum frequency that can be applied to a sampled system without aliasing is half the sampling frequency. This maximum frequency is called the Nyquist frequency.
Here is an example of a data converter with a sampling frequency of 1Msps, so the Nyquist frequency is 0.5MHz. For this example a 3V signal is applied at 0.25MHz, and a 1V noise signal is applied at 2.6MHz. The signal at 0.25MHz is within the Nyquist band and the signal at 2.6MHz is far beyond the Nyquist frequency and will generate aliases. Remember, FFT results repeat each other in increments equal to the sampling rate. So, for this example, the frequency domain pattern will repeat itself every 1MHz. Also remember that the frequency domain is symmetrical around the Nyquist frequency. So the desired signal appears at 0.75MHz which is calculated a 0.25MHz plus the sampling rate. This repeats itself every 1MHz increment. The noise signal will be symmetrical about 2.5MHz and repeats itself every 1MHz increment.

4. Eliminate redundant information
Here we show the same example from the previous slide. The point is that in most cases everything above the Nyquist frequency is hidden as it is redundant information. So in this example we show everything form 0Hz to 0.5MHz, because the Nyquist frequency is 0.5MHz. The frequency at 0.25MHz is the desired signal and the frequency at 0.4MHz is an alias. Ideally we want to avoid any aliasing into the Nyquist band. The main way to do this is to use an anti-aliasing filter.

5. Anti-aliasing filter (fs = 1Msps)
The best way to avoid aliases is to use an anti-aliasing filter. The objective of this filter is to assure that any input signal above the Nyquist rate is significantly attenuated so that it does not show up as an alias signal. In this example, the desired input signal is at 2kHz and a noise signal is at 700kHz. The sampling rate is 1Msps for this example so the 700kHz noise signal will create an alias signal. An anti-aliasing filter is introduced to pass the desired signal and significantly attenuate the noise signal. This example is a second order filter so the attenuation is 40dB/decade. The cutoff for the filter is 10kHz which allows the input signal to pass and attenuated the noise signal by about -70dB. After the filter you can see that the noise signal has been attenuated significantly. The attenuated noise signal will still alias into the signal band for the converter, but it will ideally be below the noise floor so it will not be visible.
Sampling frequency = fs = 1Msps

6. SAR Anti-aliasing Filter Design
This slide shows a typical SAR input design with an anti-aliasing filter. In this case a second order active filter is used. The cutoff for this filter is set to 8.6kHz, so signals above the Nyquist frequency will be attenuated by at least 60dB. The active filter is followed by an RC filter called a charge bucket filter. This RC filter is often mistaken for an anti-aliasing filter, but it is not designed for this purpose. Looking at the cutoff frequency for a typical RC charge bucket filter you see that the cutoff is set to 15.8MHz. Since the Nyquist frequency is set to 500kHz, the charge bucket filter clearly doesn’t work for anti-aliasing. In the next slide we will briefly introduce the purpose of this filter and later we will cover it in depth.

7. What’s the “Charge Bucket” for?
Capacitor Charging Kickback
Sampling Signal
Source
Impedance
This slide shows a signal source directly connected to a SAR data converter switched capacitor input. Notice that the signal source has a source impedance and that the internal switch has an associated impedance. When the sampling switch S1 closes the internal sample and hold capacitor needs to charge to the level of the signal source. However, the signal source is not capable of quickly charging the internal capacitance because of the source resistance. Inspecting the signal you can see that the Voltage on CSH droops from the original signal level and is NOT accurate at the end of the sample time, t_sample. The charge bucket circuit is designed provide a quick boost to help the internal sample and hold capacitor quickly settle to it’s final value. We will cover the operation and selection of this filter later.
Signal
Source

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