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日期：2021-11-01 10:49

Design an Analog Filter

r>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 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.

(a) (b)

Figure 1. Detailed specifications for a low pass filter response

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 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 the application.

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 and have a gain of less than one (unity). As passive filters

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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, an impedance of 8? for a speaker. Therefore, the

values of the R and C for the filter are not only required to achieve a desired 3dB cut-off frequency

but also to ensure it maximally match with the impedance of a 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 an active first-order RC filter with f3dB=10Hz and gain of 10 which is to be used in biomedical

application.

Software Platform

Multisim is a platform to be used as for other online labs. It can be accessed from Citrix Workspace

in UniConnect Cloud or remotely access PCs in J03 Lab 440. Please check UniConnect Cloud for

more details.

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, particularly 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?

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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 (considering the physical size/accuracy/life span/cost),

leaded type or surface mount technology (SMT) types as the parasitic effects are greater for

the leaded types of capacitors with increasing of a 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

large signal 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.

illustrate 2 to 3) to be considered when used for a filter design? Why? You may do some

research to find out the concepts mentioned in here or 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 f3dB, transition period, ect. 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 dB can the filter attenuate for a frequency of 3 times of

f3dB?

5. Set the input signal with a frequency from the range found in the AC analysis above (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 above? 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, particularly for a

passive RC filter. To ensure it, you may simulate output and input impedance of the filters 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 filters 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 above 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 filter with

different loads by using Parameter Sweep in Multisim. At what load can the filter 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?

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

the input power consumption of the filter. Use Parameter Sweep in Multisim to simulate the

total DC power consumed by the filter. You can choose different parameters as a variable to

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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 source to mimic the scenarios and

investigate the filter response. For example, set up a signal source as () = 1 sin(2) +

2 sin(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?

10. Note this is an extra task and not compulsory. You would have a bonus mark but subjected to

the full mark of this project. Single-pole arrangement of the first-order low pass RC filters

gives a roll-off slope of -20dB/decade attenuation of frequencies above the cut-off point at ?-

3dB. However, sometimes this slope may not be sharp enough to remove an unwanted signal

then two stages of filtering can be used. Cascade the two RC passive filters designed above

into a two-stage filter. Simulate the bode plot in Multisim for this filter. Compare the

frequency response with the first-order one (with the same RC values). Illustrate the

commons and differences from their frequency response. Comments on the results.

Assessment

This project is to use Multisim as platform to investigate the design and application of first-order RC

filters. It takes 10% of UoS and is assessed by a group report (6 marks) and zoom demonstration (4

marks). The group report should include contributions from each group member, as well as the

names, SID, lab session and group number. Each group only needs to submit one copy of the report

to Canvas. Demonstration is no longer than 8 minutes for each group and the schedule will be

posted on Canvas 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.