You have been assigned to interface different sensors (displacement, vibration, pressure,
temperature) to the ADuC847. More specifically, you have been assigned to design the antialiasing
filters for the different analog input channels on the ADuC847 (datasheet posted on Bb
course website).
The following system-level specifications are in place:
• Single-supply operation, with operating voltage = 5 V
• Sampling frequency for the 24-bit ADC on the ADuC847 (fs) = 1 kHz
For each one of the filter “types” listed below (a) – (d), design an appropriate anti-aliasing lowpass
filter that satisfies the following specifications:
• Minimum order necessary to have appropriate attenuation in the “stop band” for 24-bit
accuracy
• 2 ≤ K ≤ 4, where K is the “constant term” associated with the filter’s transfer function
(when expressed in standard form)
• –3 dB corner frequency (fc) = 50 Hz
Note that the value you decide for K should be the same for all designed filter types (a) – (d).
(a) Cascade of identical RC low-pass sections
(b) Butterworth
(c) 1 dB Chebyshev type I
(d) Bessel
In implementing your filters at the circuit-level (verification only being expected at the SPICE
simulation level), you may use Sallen-Key and/or Multi-Feedback topologies (with appropriate
rationale expected to have been provided in your report).
Your circuit-level design should use resistor and capacitor component values that can be
purchased (digikey.com, jameco.com, mouser.com, …). You may NOT use inductors in
realizing your filters.
Your circuit-level design should also use appropriate Analog Devices operational amplifiers that
are capable of single-supply operation (with appropriate rationale expected to have been
provided for your choice(s) in your report). To assist with single-supply operation, your lowpass
filters should be “AC” devices. That is, there should be no “DC” at either the input
(where your filter connects to the sensor) or output (where your filter connects to the
ADuC847).
To provide the names of some Analog Devices single-supply operational amplifiers (there are
many more out there):
OP162/262/462, AD8605/8606/8608, AD8628, AD8656, OP196/296/496, AD8541/8542/8544,
OP777/727/747, OP181/281/481, OP193/293/493, OP196/296/496, OP191/291/491,
AD820/822/824, OP184/284/484, OP113/213/413, AD8031/8032, AD8061/8062,
AD8051/8052/8054, AD8063/823, AD8591/8592/8594, AD8531/8532/8534, AD820/822/824,
AD8551/8552/8554, AD8601/8602/8604
In selecting appropriate operational amplifier(s) for your filter designs, you may find useful the
following documents posted on the Bb course website:
• “Select the right operational amplifier for your filtering circuits,” by Bonnie C. Baker at
Microchip Technology Inc.
• “A single-supply op-amp circuit collection,” by Bruce Carter at Texas Instruments Inc.
Appropriate catalog numbers and bill of materials is expected for each filter design
To design the anti-aliasing filters for the different analog input channels on the ADuC847, you need to follow the provided specifications for each filter type (a) - (d). Here's how you can approach the design process:
(a) Cascade of identical RC low-pass sections:
For this filter type, you can use a cascade of identical RC low-pass sections to achieve the required attenuation in the stop band. The transfer function of an RC low-pass section is given by:
H(s) = 1 / (1 + sRC)
To design the filter, you need to determine the values of R and C. Here's the step-by-step process:
1. Set the corner frequency (fc) to 50 Hz.
2. Use the sampling frequency (fs) of 1 kHz to calculate the maximum allowable frequency (fmax) before aliasing occurs. The Nyquist frequency is half of the sampling frequency, so fmax = fs/2 = 500 Hz.
3. Choose the attenuation in the stop band based on the desired accuracy of the 24-bit ADC. You can start with -144 dB (24 bits).
4. Select the number of RC sections (N) based on the desired attenuation in the stop band and the order of the filter. The order of the filter is equal to N.
5. Calculate the attenuation per section (A) based on the desired attenuation and the number of sections: A = -144 dB / N.
6. Set the constant term (K) of the transfer function. It should be between 2 and 4. You can choose a value of 3 for simplicity.
7. Calculate the cutoff frequency for each section using the formula: fc(section) = ^(1/N)).
8. Choose a resistor value (R) based on the desired cutoff frequency and the desired corner frequency: R = 1 / (2πfc(section)C).
9. Choose a capacitor value (C) based on the desired cutoff frequency and the chosen resistor value.
Repeat steps 7-9 for each section of the cascade.
(b) Butterworth:
To design a Butterworth filter, you can use a Butterworth filter design table or a computer software tool. The Butterworth filter has a maximally flat response in the passband and meets the required specifications. To design a Butterworth filter, follow these steps:
1. Set the corner frequency (fc) to 50 Hz.
2. Use the sampling frequency (fs) of 1 kHz to calculate the maximum allowable frequency (fmax) before aliasing occurs. The Nyquist frequency is half of the sampling frequency, so fmax = fs/2 = 500 Hz.
3. Choose the attenuation in the stop band based on the desired accuracy of the 24-bit ADC. You can start with -144 dB (24 bits).
4. Select the filter order (N) based on the desired attenuation in the stop band. The order of the filter should be high enough to achieve the desired attenuation.
5. Use a Butterworth filter design table or a computer software tool to determine the cut-off frequency and component values for each stage of the filter.
(c) 1 dB Chebyshev type I:
To design a 1 dB Chebyshev type I filter, you can use a Chebyshev filter design table or a computer software tool. The Chebyshev filter provides a sharper roll-off at the expense of some ripple in the passband. To design a 1 dB Chebyshev type I filter, follow these steps:
1. Set the corner frequency (fc) to 50 Hz.
2. Use the sampling frequency (fs) of 1 kHz to calculate the maximum allowable frequency (fmax) before aliasing occurs. The Nyquist frequency is half of the sampling frequency, so fmax = fs/2 = 500 Hz.
3. Choose the attenuation in the stop band based on the desired accuracy of the 24-bit ADC. You can start with -144 dB (24 bits).
4. Select the filter order (N) based on the desired attenuation in the stop band. The order of the filter should be high enough to achieve the desired attenuation.
5. Choose the ripple factor (ε) based on the desired passband ripple and the attenuation in the stop band. The ripple factor determines the amount of passband ripple.
6. Use a Chebyshev filter design table or a computer software tool to determine the cut-off frequency and component values for each stage of the filter.
(d) Bessel:
To design a Bessel filter, you can use a Bessel filter design table or a computer software tool. The Bessel filter provides a maximally flat group delay response, which is important for preserving the shape of signals in the time domain. To design a Bessel filter, follow these steps:
1. Set the corner frequency (fc) to 50 Hz.
2. Use the sampling frequency (fs) of 1 kHz to calculate the maximum allowable frequency (fmax) before aliasing occurs. The Nyquist frequency is half of the sampling frequency, so fmax = fs/2 = 500 Hz.
3. Choose the attenuation in the stop band based on the desired accuracy of the 24-bit ADC. You can start with -144 dB (24 bits).
4. Select the filter order (N) based on the desired attenuation in the stop band. The order of the filter should be high enough to achieve the desired attenuation.
5. Use a Bessel filter design table or a computer software tool to determine the cut-off frequency and component values for each stage of the filter.
For selecting appropriate operational amplifiers for your filter designs, refer to the provided resources such as "Select the right operational amplifier for your filtering circuits" by Bonnie C. Baker and "A single-supply op-amp circuit collection" by Bruce Carter. Consider the single-supply operational amplifiers mentioned and choose the one(s) that meet your requirements for single-supply operation.
Remember to provide the catalog numbers and bill of materials for each filter design in your report.