Overview of Assessment The purpose of this design exercise is to assess your ability to design an electronic circuit and perform a simulation analysis. There are two parts to this design exercise:

Part 1 You will design a simple circuit to meet a performance specification and test its performance using Multisim. You will then compare and evaluate the circuit’s performance against the original design specification. Part 2 You will then re-design your circuit to improve the performance and learn the importance of using simulation tools in the design cycle. It is important that you maintain a record of your work in your laboratory notebook in order to be able to write the assessment reports. The instructions in this document will guide you on what to do. NTO1038 Engineering Design and Practice Page 2 of 12 1 Background Theory 1.1 High Pass Filter You have been introduced in the lecture session to sinusoidal waveforms (sinusoids) which can have different amplitudes and frequencies. Signals representing speech and music, can be modelled as the summation of very many sinusoids at different frequencies and amplitudes. The basic idea is illustrated in Figure 1, in which two sinusoids of different frequencies are summed to produce a more complex waveform. Figure 1 Summation of Sinewaves at Different Frequencies The fact that any time-varying signal can be created from the summation of many simple sine waves at different frequencies and amplitudes is a powerful analysis tool you will encounter throughout your studies. It is sometimes useful or necessary to remove sinusoids of particular frequencies from a signal. Circuits which do this are called filters e.g. a high-pass filter allows sinusoids above a certain frequency, called the cut-off frequency, to “pass” through the filter (with little or no change), whilst those sinusoids at frequencies below the cut-off frequency are “rejected”. Figure 2 illustrates the gain response of an ideal high-pass filter. The gain G is the scaling the filter applies to the amplitude of an input sinusoid to produce the output sinusoid at a particular frequency G(f)=Vout ¿V¿ amplitudeoftheinputsinusoid V ¿ V out amplitude of the output sinusoid The value of the gain depends on the value of the frequency. For an ideal high-pass filter, the gain is ‘1’ for all frequencies above the cut-off frequency f c, and the gain is ‘0’ NTO1038 Engineering Design and Practice Page 3 of 12 for all frequencies below fc. For example, if the complex waveform on the right hand side of Figure 1 was passed through an ideal high pass filter with a cut-off frequency f c of 300 Hz, the 200Hz sinusoid would be blocked and only the 600 Hz sinusoid would pass through. Figure 2 Ideal High Pass Filter Response [1] In reality, it is very difficult to create an ideal high-pass filter response. Figure 3 illustrates the amplitude response of a practical high-pass filter. Figure 3 Practical High Pass Filter Response [1] Notice that there is no sudden, sharp point at which the filter changes from passing certain frequencies to not passing them. Instead, there is a different gain value for every frequency. The cut-off frequency is defined as that frequency at which the gain of the filter is equal to 0.7071. Sinusoids at frequencies above the cut-off frequency are scaled by gain values 1 The cut-off frequency is that frequency at which the output power is half that of the input power ( Pout=P¿×1/2); as power is proportional to (voltage) amplitude squared, the ratio of output amplitude to input amplitude is 1/√2≅0.707 i.e. V2 =V2×1/2 which becomes V❑ =V❑×1/√2 out ¿ out ¿ NTO1038 Engineering Design and Practice Page 4 of 12 greater than 0.707 and are considered “passed”; sinusoids at frequencies below the cut- off frequency are scaled by gain values smaller than 0.707 and are considered ”rejected” Figure 4 Illustrates what happens to input sinusoids at different frequencies when input to a high pass filter with a cut-off frequency of 1.6 kHz. The rms values of the sinewaves can be used to calculate the gain of the filter at each frequency. Perform the gain calculations for each frequency and relate it to the response curve in Figure 3 (if a gain value is less than 1 it is sometimes called an attenuation value). Figure 4 Example High Pass Filter Inputs and Outputs [1] Figure 5 shows an example of the typical gain response of a high-pass filter with a cut- off frequency of 30 kHz. Note that both axes are conventionally shown as log scales to allow a wide range of both frequency and gain values to be shown. Ensure you can interpret reading from a log scale graph and ask for assistance if required. NTO1038 Engineering Design and Practice Page 5 of 12 NTO1038 Engineering Design and Practice Figure 5 Example High Pass Filter Response 1.2 RL High Pass Filter The series RL circuit shown in Figure 6 acts as a high pass filter with a response curve as shown in Figure 3. The output from the circuit Vout is the voltage dropped across the inductor V L. Figure 6 Series RL High Pass Filter To understand why this circuit produces the response curve as shown in Figure 3, you need to know that inductors have a resistance-like property called reactance and that, significantly, the value of this reactance varies with frequency. Specifically, the reactance X L, measured in ohms is calculated by X L=2 πfL X L f L reactance (Ω) frequency (Hz) inductance (H) Page 6 of 12 {1} The filter circuit of Figure 6 acts somewhat like a potential divider circuit where the reactance of the inductor behaves like a ‘variable resistor’ whose value varies according with frequency. As reactance is directly proportional to frequency, at 0 Hz i.e. DC, the reactance of the inductor will be zero. For a DC voltage input, there will therefore be a short circuit through the inductor and the output voltage will be zero i.e. all of the input voltage will be dropped across the resistor. The gain of the filter is therefore zero for a DC input. Conversely, at very large frequencies, above the cut-off frequency, the reactance becomes very large relative to the resistor, and so almost the entire input signal will be dropped across the inductor i.e. the gain of the filter is approximately 1 at very high frequencies. The above explanations describe the end-points of the filter response. The variation in gain across all frequencies is given by Vout= XL V ¿ √ R 2 + X 2L The explanation for this equation will be met later in your studies. {2} As the general shape of the filter response is fixed, the implementation parameter that can be varied is the choice of cut-off frequency. The cut-off frequency for a series RL circuit is determined from the values of the two components by 1 f c cut-off frequency (Hz) fc= L ¿ L inductance(H) 2π(R) R resistance (Ω) NTO1038 Engineering Design and Practice The expression for the cut-off frequency {3} can be obtained by putting the gain value Vout/V¿ to 1/√2 into equation {2}, substituting the expression for reactance {1} into equation {2}, and solving for f. Do this to prove the expression for the cut-off frequency. 1.3 The Design Specification A circuit is to be designed to meet the following specifications: 1. Ahigh-passfilterwithacut-offfrequencyof30kHz±5%. 2. The gain Vout/V¿is less than 0.05 for frequencies below 500 Hz. Page 7 of 12 {3} 1.4 Designing an RL high-pass filter There are two components values to choose to set the cut-off frequency of the filter to complete the design. For this laboratory assignment, the value of the inductor L is given as 1 mH (a smaller selection of inductor values are typically stocked in a laboratory so the component has been pre-selected). This can be sourced from Farnell: The design problem is therefore to choose the value of R. Rearrange equation {3} to complete the design by determining the value of R to meet the design specification. Having calculated a value of R you may meet a minor problem i.e. the exact value you want will probably not be available. Resistors are normally only made in a limited range of values known as Preferred Values. The E24 series [2] shown in Figure 7 indicates the 24 values in a decade at which resistors are typically manufactured e.g. in the first decade only 10 Ω, 12 Ω, ..., 75 Ω, 91 Ω are manufactured. Figure 7 E24 Series of Preferred Values These values are replicated in every decade e.g. in the range 100 Ω to 1000 Ω the available resistors are 100 Ω, 120 Ω, ..., 750 Ω, 910 Ω; in the range 1000 Ω to 10000 Ω the values available are 1000 Ω, 1200 Ω, ..., 7500 Ω, 9100 Ω; and so on in each decade. Normal practice is to choose the Nearest Preferred Value (NPV) to the calculated value. Choose the NPV to the value of the resistance you have determined. Consider the impact the use of an NPV resistor may have on the actual the cut-off frequency of your filter when implemented. 1.5 Writing a test schedule A list of tests and measurements needs to be planned in order to validate the performance of the design. This list is called the test schedule. As the circuit has been designed to meet a specification, the specification requirements will be the basis of your test schedule. Consider the following, therefore, in drafting your test schedule. NTO1038 Engineering Design and Practice Page 8 of 12 To be able to plot the gain response of the high pass filter, measurements of gain need be made across a suitable range of frequencies. Also recall that the frequency scale of the gain response is typically plotted on a log scale, so the choice of frequencies should account for this. Choosing 3 frequency values per decade should be sufficient to achieve an acceptable plot. It is also worth considering if there are sub-ranges of frequency where more measurements may be useful. It is good practice to create a table of measurements to be taken and calculations to be performed during circuit testing. It is also good practice to have theoretical values pre-calculated to be compared against actual measured values. In addition to gathering enough data points to achieve a reasonable plot, planning specific measurements may also be necessary e.g. as the specification requires the gain to be less than 0.05 at 500 Hz, a measurement of gain at 500Hz may be useful. Another key requirement of the design specification is the cut-off frequency. Consideration of how this will be determined experimentally or from your results should be made. Making a clear schedule of measurements to be made is an essential part of good design practice. 2 Circuit Simulation Experience using Multisim will have been developed during the course. Your circuit should be drawn in Multisim and simulated to obtain the required measurements in order to evaluate the circuit performance. Two sets of experimental observations will be made: (1) using the Function Generator and the Oscilloscope tools; and (2) using the Bode analyser tool. 2.1 Using the Function Generator and Oscilloscope The experimental objective is to complete the test schedule you have planned. This involves setting one frequency at a time, then measuring the input and output rms voltages on the oscilloscope, and writing them in your lab book test schedule. The test input sine waves will be created by the Function Generator. The amplitude of the input voltage needs to be chosen: if too small, electrical noise may affect the accuracy of your results; choose as high a value as is reasonable or practical. You might be tempted to set up and measure the input voltage once at the start and then ignore it. However, it may vary as you change frequency (due to loading effects), so measure it also. NTO1038 Engineering Design and Practice Page 9 of 12 The input and output waveforms will be monitored with the two channels of the Oscilloscope. The gain response is calculated as the rms output voltages divided by input voltage at each frequency. Use the rms measurements automatically provided for each trace. Remember to make any specific measurements created as part of your test schedule. Your results should be plotted using the Excel plotting tool (or equivalent) and used to complete your test schedule measurements. 2.2 Using the Bode Analyser It is important that you learn the practical skills of making measurements by using the function generator and the oscilloscope. You will also gain important insight into the operation of the filter. The use of the Bode Analyser can, nevertheless, create the gain response of your circuit automatically for comparison and validation with your test results. The Bode tool should be set-up and run according to the training laboratory document. Appropriate maximum and minimum frequency values should be selected. Measurements can then be made from the gain response to compare with those already attained form the oscilloscope. Plots should be generated and appropriately stored. 2.3 Preliminary assessment A preliminary assessment can be made as to whether the circuit that has been implemented meets the requirements of the design specification. The requirements are: 1. AHighPassFilteringactionhasbeensuccessfullyimplemented 2. Thecut-offfrequencyofthehighpassfilteris30kHz±5% 3. Thegainresponseat500Hzandlowerfrequenciesmustbelessthan0.05. It is important to comment on what is successfully achieved. If the design partially fails, e.g. the response at specific frequencies is not met, DO NOT WORRY. In this case further analysis after the lab may be needed. 3 After the Laboratory Immediately after you have completed the design exercise, you should carefully organise all your work in preparation for writing your report; This includes calculations, simulation plots, results and notes. You are now ready to write the report. NTO1038 Engineering Design and Practice Page 10 of 12 4 Writing the report Instructions and guidance will be given in the lecture classes for this module and in the English Language and Study Skills (ELSS) module on how to write a technical report. You should follow all the layout and language conventions for technical report writing. You will have an opportunity to submit draft versions of your reports for comment and guidance before the final assessed version is submitted. The format and layout of the report for this design exercise should contain the following information. 1. Introduction Introduce the topic and the content of the report 2. Theory Include a brief explanation of a high pass filter and operating equations 3. Design Specification Reproduce the design specification 4. Design Solution Give the RL circuit and the design calculations carried out 5. Experimental Set-up Briefly describe the apparatus used and procedures followed 6. Results Present the results in tables and graphs and as individual values. 7. Analysis of results Give an assessment of how the measured results compared with expected results and state clearly whether the design specifications were met or otherwise. 8. Modified Circuit Design Propose how the circuit or components can be modified in order to meet the design specifications 9. Conclusions Review the content of the report, stating the main outcomes of the experiments and the proposed modifications concluded from the completed work. References NTO1038 Engineering Design and Practice Page 11 of 12 [1] Thomas L Floyd, “Principles of Electric Circuits Conventional Current Version”, Pearson, 2014 [2] https://en.wikipedia.org/wiki/Preferred_number#E_series NTO1038 Engineering Design and Practice Page 12 of 12