Design an Analog Filter - Report writing - Engineering Assignment Help

Assignment Task

Introduction

Filter circuits play an important role in many electronics designs. They are primarily used to pass desired signals while blocking unwanted signals. Filters can be divided into two main categories, analog and digital filters, and each category can be further divided into many sub-groups, such as passive filters, active filters, FIR filters or IIR filters. Each sub-group of filters has their own advantages and disadvantages. Learning the difference between each filter will allow a filter design engineer to choose the best type of filter for a given application.

As for the fundamental specifications of a filter, bandwidth or 3dB cut-off frequency is obviously the most crucial one. In real-world situations, the boundaries of filters are less clearly defined, so that more detailed specifications are required apart from 3dB cut-off frequency, such as ripples in pass/stop bands, transition band/slope, etc. as shown in Figure 1 (a). For example, to implement a filter with very steep cut-off, filters of higher orders must be required, as shown in Figure 1 (b), and consequently the circuits become more complex.

Apart from filter specifications stated above, more factors are to be considered on the filter design, such as input/output impedance of the filter circuit and a load connected with it, as these affect the efficiency/performance of the filter. Furthermore, physical size, power consumption and economic cost are important to be taken into account when making a decision. In reality, filter design is a trade-off among these factors.

Filters to be Designed

In this project, we will focus on first-order analog filter design. You are required to design two types of first-order filters – passive and active ones, described below. Based on the requirements of the applications, you need to design the circuit topology, select components, conduct relevant calculations, simulate the filter performance in Multisim, and verify the performance for their applications.

Filter Type 1- Passive filter

Passive filters are filters that consist of only passive components such as resistors, capacitors, and inductors (RLC) and attenuate the signal having a gain of less than one (unity). As passive filters can handle hundreds of watts of input power, they are used in most home loudspeaker systems, such as in audio amplifiers and speaker systems to reduce any high frequency noise. For low frequency applications, RC filters are preferred since an inductor’s physical size can be very large. Here you are required to design a first-order RC passive filter for an audio application. Given that the audible range for humans is approximately 20 Hz to 20 kHz, the filter should be able to filter out noises above this frequency range. Also, in an audio application, the load of the filter normally has very low impedance, for example, a speaker with an impedance of 8Ω. Therefore, the selection of the R and C of the filter are not only required to achieve the desired 3dB cut-off frequency but also to ensure it maximally match with the impedance of the load according to the principle of maximum power transfer.

Filter Type 2 - Active Filter

Active filters use transistor and op-amp as their basic components, along with resistors and capacitors, but not inductors. Due to the high input impedance and low output impedance of op-amps, active filters eliminate the loading effect at source and load. They can also provide a certain amplification for input signals, and therefore are widely employed in biomedical systems in which the weak bioelectrical signals typically, are in the range of 100 mV – 1 V while the frequencies are below 100 Hz. The design of very low-frequency filters (10 Hz) is not straightforward, many factors to be considered in practice, such as power consumption and low noise level, physical size, large time constant of RC, especially for integrated circuit implementation. Here you are required to design a first-order active RC filter with f3dB=10Hz and gain of 10, which is to be applied to the biomedical application.

Software Platform

Multisim is a platform to be used as for the online labs. It can be accessed from Citrix Workspace or remotely access PCs.

Design Tasks

For the two types of filters required above, you need to complete and include the tasks listed below but certainly not limited to them.

1. Draw the circuit diagrams for the two types of filters. Theoretically demonstrate the performance by deriving their transfer functions, identifying zeros/poles, as well as illustrating their bode plots. How do the poles/zeros affect the magnitude and phase response of filters? How to theoretically calculate the 3dB cut-off frequency?
2. To achieve a desired 3dB cut-off frequency required by the applications, there can be a few combinations for the product of R and C. To select a proper value of R and C for the specified application, you may need to consider the output/input impedance of the filters to ensure that the filters maximumly match the load/source, mainly for the RC passive filter. Demonstrate the calculations on the selection of R and C values for the filters. What are the calculated input and output impedance for the passive filter at the 3dB cut-off frequency?
3. List the model/ components selected for the filters in a Table with basic parameters. For example, for a capacitor, you need to provide more information than just capacitance, such as electrolytic or ceramic or tantalum (with considerations of the physical size/accuracy/life span/cost), leaded type or surface mount technology (SMT) as the parasitic effects are greater for the leaded types of capacitors with increasing of signal frequency, as well as the voltage rating. For an op-amp, though there are a lot of specifications listed in the datasheet, such as voltage gain, gain bandwidth product, slew rate, input offset voltage, input resistance and common-mode rejection ratio (CMRR), what are the key specifications (i.e. illustrating 2 to 3 of them) to be considered when used for a filter design? Why? You may do some research to find out the concepts mentioned here or in datasheet to help you to answer the questions. There are a number of options available in Multisim library for op-amp, for example a common-used op-amp uA741.
4. Use AC analysis in Multisim to simulate the filter frequency response, and identify 3dB cut-off frequency, voltage gain and phase at the frequency of f3dB, as well as the transition band. Are the results of simulation close to the theoretical calculations? What is the signal frequency range to make the output voltage having maximum magnitude and minimum phase shift (could be 180° if using inverting op-amp configuration)? How many dBs are the output of the filter attenuated at the frequency of 3 times of f3dB?
5. Set the input signal with a frequency from the range found in the AC analysis in the Step 4. Use Transient analysis in Multisim to simulate the output voltage of the filters. Plot the output and input of the filter in the same graph and work out the voltage gain and phase shift. Are they the same as what obtained from the AC analysis in the Step 4? How about the Transient analysis for the filter when inputting a signal with a frequency of f3dB?
6. Impedance matching is important factor to be considered for filter design. As the active filter based on a op-amp initially has a large input impedance and small output impedance, here you will focus on simulating output and input impedance of the passive filter as function of the frequency. You can use AC analysis in Multisim by setting the output parameter as an impedance. What are the input and output impedance of the filter at 3dB cut-off frequency? How do the input and output impedance change in the frequency range of interest? With these simulations you may fine tune the values of R and C selected in the step 2 to ensure the filter having the best possible input and output impedance for the specified application.
7. When a filter connected with a source and load, in order to work properly, the input impedance of the filter should be high per to the source impedance. While the output impedance of the filter should be low per to the load. To find out why, simulate the two types of filters with different loads by using Parameter Sweep in Multisim. At what load can the filters deliver the maximum power to it? Comparing the simulation results for the two types of filters, can you identify the advantages and limits of them on this regard? You should see the benefits from an active filter being with a large input impedance and small output impedance.
8. Unlike a passive filter not requiring a power source, an active filter needs DC power supplies to operate. In this step, you are to investigate how the parameters of the active filter impact on its input power consumption. Use Parameter Sweep in Multisim to simulate the total DC power consumed by the active filter. You can choose different parameters as a variable to sweep, such as input signal amplitudes or loads. How is the power consumption of the filter affected by these factors?
9. In reality, the source is normally not a single frequency signal rather than having multiple frequencies (i.e. noises). Connect the filter with a such source to mimic the scenarios and investigate the filter response. For example, set up a signal source as ????(????)=????1sin(2????????????)+????2sin(2????*5????????), where f is the signal frequency and v1, v2 are the amplitude. The first item in the Equation is to mimic the signal while the second item is to mimic the noise which is 5th order harmonic. You can set up the frequency and amplitudes based on specified applications. For the filter with the signal source defined above, use Transient and Fourier analysis in Multisim to simulate the performance of the filter. Can the filters effectively attenuate 5th order harmonic?

Assessment

This project is to use Multisim as platform to investigate the design and application of first-order RC filters. Demonstration is no longer than 8 minutes for each group and the schedule will be posted in week 12. The project will be starting in the week 10 and demonstration is scheduled in the week 13. Support and help will be available in the scheduled lab sessions via Zoom.

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