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.
Designing an anti-aliasing filter requires careful consideration of the system-level specifications and filter requirements. Here is a step-by-step guide to designing the filters for each type mentioned (a) - (d):
1. Determine the filter order: The filter order is determined by the required attenuation in the stop band for 24-bit accuracy. In this case, the minimum filter order needed should be sufficient for achieving the desired stop band attenuation.
2. Choose a constant term (K): The constant term is a parameter associated with the filter's transfer function when expressed in standard form. In this case, choose a value for K that satisfies 2 ≤ K ≤ 4 and use the same value for all filter types (a) - (d).
3. Determine the -3 dB corner frequency (fc): The -3 dB corner frequency represents the frequency at which the filter's response is attenuated by 3 dB. In this case, the corner frequency should be set to 50 Hz.
(a) Cascade of identical RC low-pass sections:
For this filter type, design a cascade of identical RC low-pass sections to achieve the desired filter specifications. The transfer function of a single RC low-pass section is given by:
H(s) = K / (s + ωc)
where s is the complex frequency, K is the constant term, and ωc is the corner frequency.
To achieve the desired order and corner frequency, the transfer function of the overall filter can be expressed as a product of multiple identical RC sections:
H(s) = (K / ωc)^n / [(s/ωc + 1)^n]
where n is the filter order. For this design, determine the required number of sections (n) and calculate the values of resistors and capacitors for each section using standard filter design equations.
(b) Butterworth:
For a Butterworth filter, the transfer function can be expressed in terms of poles and zeros. The transfer function of an nth-order Butterworth filter is given by:
H(s) = K / [(s/ωc + 1)^n]
where n is the filter order. Determine the required filter order and calculate the values of resistors and capacitors using Butterworth filter design equations.
(c) 1 dB Chebyshev type I:
For a 1 dB Chebyshev type I filter, the transfer function can also be expressed in terms of poles and zeros. The transfer function of an nth-order Chebyshev type I filter is given by:
H(s) = K / [(s/ωc + 1)^n * sqrt(1 + ε^2 * Tn^2(s/ωc))]
where n is the filter order, ε is the passband ripple factor, and Tn(s/ωc) is the normalized Chebyshev polynomial of order n. Determine the required filter order and ripple factor, then calculate the values of resistors and capacitors using Chebyshev filter design equations.
(d) Bessel:
For a Bessel filter, the transfer function can be expressed using a recursive equation. The transfer function of an nth-order Bessel filter is given by:
H(s) = K / [s/ωc + (n - 1)!/(n - 1)! * (s/ωc)^2 + ... + (s/ωc)^n]
where n is the filter order. Determine the required filter order and calculate the values of resistors and capacitors using Bessel filter design equations.
For each filter type, select appropriate Analog Devices operational amplifiers that are capable of single-supply operation. Consider the requirements of the filter, such as input and output voltage range, noise, bandwidth, and slew rate, while selecting the operational amplifier. Refer to the provided documents for guidance on choosing suitable operational amplifiers.
Finally, provide the appropriate catalog numbers and a bill of materials for each filter design, including the values of resistors and capacitors, as well as the chosen operational amplifiers.
Please note that designing a complete circuit-level implementation and performing SPICE simulation is beyond the scope of this explanation. It is recommended to refer to circuit design books or consult a professional in analog filter design for further guidance.