1. SE207: Modeling and Simulation General instructions

2. Objectives To be able to do Simulate systems of various types using analog computers Simulate systems of various types using digital computers( MATLAB +SIMULINK) Study and analyze responses of first and second order systems

3. Grades Lab Reports 8% Quizzes 7% --------- Total 15%

4. Attendance -1% for each unexcused absence You will not be able to submit the report if you are absent in that lab All reports must be submitted within one week (Before the start of the next lab) Food and drinks are not allowed in the lab

5. Format of the Report Cover page: includes Name, ID#, title, date, Section Introduction: Objectives Brief description of the experiment or the program Hardware needed (for the experiments) Procedure of things to be done Solution of any problems mentioned in the lab handout Program listing/ Simulation diagrams/plot of results Conclusions/comments/observations

6. SE 207: Modeling and Simulation Lab # 1: Analog Computers

7. Analog signal An analog signal are non quantized signals that are define on a time interval of interest. Analog signal Discrete-time signal

8. Analog computers Analog computers are electronic devices that performs calculations on analog signals. Main elements of Analog Computers Resistors/potentiometers Capacitors Operational Amplifiers (Op-Amp)

9. Analog Computers Can be used to solve differential equations Heavily used in World War II for computing trajectories of bombs Digital computers replace analog computers in simulating systems analog computers are still used today in some applications Advantages of analog computers over digital computers Computation time Prototyping New technologies Single chip analog computers Digital computers with analog co-processors

10. Operation Amplifier (Op-Amp) The op-amp is an electronic component The op-amp output is K times the input K is a very large number (typically 1000000) Op-amps are used in different ways to make different computing elements (summers, integrators,…) K K

11. Amplifier K Feedback resistance R f Input resistance R 1 eiei Equality is assumed when K is very large which will be the case here

12. Inverter K Feedback resistance R f Input resistance R 1 eiei When R f =R 1 then e o = ─ e i The circuit acts as inverter ( signing the sign)

13. Summer K Feedback resistance R f Input resistance R 1 e1e1 e3e3 e2e2 R2R2 R3R3

14. Integrator K Feedback Capacitor C f Input resistance R 1 e1e1 e2e2 R2R2 When the feedback element is a capacitor then the circuit acts as an integrator. The initial condition is specified by the initial charge in capacitor