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 Feedback resistance Rf Input resistance R1 K ei Equality is assumed when K is very large which will be the case here

12. Inverter Feedback resistance Rf Input resistance R1 K ei • When Rf=R1 then eo= ─ ei • The circuit acts as inverter ( signing the sign)

13. Summer Feedback resistance Rf Input resistance R1 K e1 R2 e2 R3 e3

14. Integrator Feedback Capacitor Cf Input resistance R1 K e1 R2 e2 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