Circuits II EE221 Unit 7 Instructor: Kevin D. DonohueUseful Circuits:Cascading Filter Stages: no Loading Effects:Other Useful CircuitsAdding Outputs of Filter StagesSlide 6Midterm ProjectGeneral Design ProcessSlide 9Top-Down DesignSlide 11Time TablesEngineering NotebooksSpecifications and Problem Statement:Order of EventsCircuits IIEE221Unit 7Instructor: Kevin D. DonohueActive Filters, Connections of Filters, and Midterm ProjectUseful Circuits: Describe the transfer functions of these circuits:Non-Inverting Op Amp: gain = (1 + Rf / R1) Inverting Op Amp: gain = (- Rf / R1)Voltage Follower: gain = 1-+vi+vo-RfR1-+vi+vo-RfR1-+vi+vo-Cascading Filter Stages: no Loading Effects:Given two active filter circuits with transfer functions and , their series combination has a transfer function equal to the product of the individual transfer functions: provided that the connection between these circuits does not significantly alter the output resistance of the first circuit or the input resistance of the second circuit (i.e. no loading effects). Homework (1): In Matlab create bode plots for a first-order high-pass filter (with G = 2 and fc = 1 kHz) in series with a second order band-reject filter (with f0 = 5000 Hz, B = 500 Hz, and GDC = G = 1 ).)(ˆ2sH)(ˆ1sH)(ˆ)(ˆ)(ˆ21sHsHsHT)(ˆ)(ˆˆˆˆˆˆˆ)(ˆ212211sHsHVVVVVVsHioioTiToTVTi = V1iV1o = V2iV2o= VTo)(ˆ2sH)(ˆ1sHOther Useful CircuitsThe summing amp: The differential amp: - + vi1 vi2 viN + vo - R1 R2 RN Rf -+vi1vi2+vo-R1R2R1R2vRRvRRvRRvofififNiN   1122vRRv vo i i 212 1Adding Outputs of Filter StagesGiven two active filter circuits with transfer functions and , the TF resulting from their parallel connection is the sum of the TF (the complex TF values, not simply the magnitudes), provided that the connection of these circuits does not significantly alter the output resistance of the first circuit or the input resistance of the second circuit (i.e. no loading effects). If the outputs are connected through a summing amp with gains 1 and 2 the combined TF become:)(ˆ2sH)(ˆ1sHVTiV1oVTo)(ˆ2sH)(ˆ1sH 21ˆiioiVV2oTiTiToVsHVsHVˆ)(ˆˆ)(ˆˆ2211)(ˆ)(ˆˆˆ)(ˆ2211sHsHVVsHTiToTAdding Outputs of Filter StagesHomework (2): In Matlab create Bode plots for 2 second order bandpass filters (BPF1 with Go = 10dB and fo = 9 kHz, B = 3kHz, and BPF2 with Go = 7dB and fo = 6 kHz, B = 800Hz) connected in parallel through a summing amp with a gain of -0.5 for the output of BPF1 and a gain of -3.5 for the output of BPF2. For the magnitude plots, plot them in both dB (typical Bode plot) and linear (without the 20Log10 scaling).Homework (3): Repeat Problem 2, with different gains for the summing amp. Change the summer gain for the BPF1 node to -3 and the gain for the BPF2 node to -0.5. Compare he Bode plots with those in Homework Problem 2. Homework (4): Compute the threshold of hearing curve for your ear at the frequency points indicated in the hearing-aid project and scale it as described in the project (and on the web page) and plot it against the normal threshold of ear. Describe the environment where you did the hearing test at (quiet office using speakers, … noisy lab with headphones ….)Midterm ProjectIn this project you will design a hearing aid to correct your "client's" hearing to normal at the threshold of hearing.This project will combine your study of the AC circuit frequency response, transfer functions, passive and active filters, and filter combining to design a filters with a transfer function magnitude of a specified shape.The outcomes of this project involve the following components:Implementing a "Design Process"Using a top-down approach to solve complex designs Extending knowledge of filter design Developing plans for efficient/effective teamworkGeneral Design Process 1. Develop a set of specifications to formulate a clear and precise problem statement.2. Propose a set of potential solutions at the top-level.3. Decide on the most feasible or promising design.4. Develop solution(s) (build circuit protopypes or create computer simulations for testing).5. Optimize critical parameters of the design(s).6. Test design(s) against specifications.7. If design performance is not satisfactory, return to steps 2 through 6 (depending on the amount redesign necessary to achieve satisfactory performance). If design performance is satisfactory, complete documentation on the design process, technical description of critical components, and performance analysis.General Design Process The proposal report involves completing steps 1 through 3 and creating a time table for accomplishing steps 4 through 7.The final documentation should be complete enough for someone else to clearly compare the designed circuit’s performance with the criterion in the problem statement, build your circuit, and verify performance results.Top-Down DesignThe top-down method develops a solution by initially proposing a design in terms of functional blocks. This first and most general block diagram is called the top level. Then each functional block in the top level is broken down into more detailed and specific functional blocks to create the second level. Once the functional blocks are detailed enough so that a circuit to perform the function is easily determined, the process is finished.Example: Build a hearing aid with the following specifications .....The necessary functions (convert sound waves to electric signal, preamplify signal, filter signal, convert amplified and filtered signal back into sound waves). This suggests the following top-level Specifications for the function and input-output characteristics must be developed for each block.Also note that “top” is a relative term. This is a top-level design if your assignment was the whole hearing aid.MicrophonePre AmpCustom FilterSpeakerPower AmpTop-Down DesignAt the second design level (relative to the hearing aid as first level) each of above functional blocks are broken down into finer detail. For example, assume the transfer function of the filter block is specified. The top-level design for the filter (this is top level for your assignment, but second level the entire hearing aid) can be specified as (parallel approach - something in the