Introduction to Design of Operational Amplifier Design | ECE 617, Lab Reports of Electrical and Electronics Engineering

Download Introduction to Design of Operational Amplifier Design | ECE 617 and more Lab Reports Electrical and Electronics Engineering in PDF only on Docsity! ECE617 Junior Laboratory I - 2008 Design of Operational Amplifier Circuits 1. Introduction Operational amplifiers (op-amps) have many applications in electrical and computer engineering designs. They can be used in circuits to implement: gain or power amplifiers, active filters, comparators, peak detectors, current sensors, signal generators, instrumentation amplifiers, mathematical functions, etc. Op- amps can be configured to realize most mathematical functions: • Addition • Subtraction • Multiplication • Division • Integration • Differentiation • Logarithmic This laboratory exercise will illustrate how an op-amp circuit (acting as a basic analog computer) can be configured to solve a differential equation. A good illustration of the implementation of mathematical functions with op-amps circuits is to solve the differential equation describing the input/output response of a RCL series circuit. In particular, the response of the RLC series circuit, shown in Figure 1, to an input step will be calculated. C1 10uF L1 50mH V1 10Hz 0.01V R1 30ohm + Vout _ 0 1 4 5 Figure 1, RLC Circuit Showing Input Step Voltage Source and Vout. This laboratory exercise will be performed over a two week period: • Week one: complete the pre-laboratory exercise (no in-lab session) • Week two: implement and test the circuit designed in the pre-laboratory exercise (requires going to your regularly scheduled laboratory period) 2. Pre-laboratory Exercise (week one of two) A differential equation solver circuit will be designed and simulated in the pre- laboratory exercise. First confirm that Equation 1 is the differential equation that describes the transfer function (Vout/V1) for the RLC circuit in Figure 1. Equation 1, Equation Describing the Transfer Function for the RLC Circuit The solution to this equation takes on one of three forms depending on whether the circuit is under damped, critically damped, or over damped. Review your basic circuits and differential equation textbooks if you do not recall the solutions. The solution has two parts: the transient part and the steady state part. Before the op-amp circuit is designed it would be nice to be able to plot the output's (Vout) response to the step input. That way when the circuit is simulated in Multisim the correct output response will be known. There are a number of methods that can be used including deriving the solution by hand (then use Matlab to plot the solution) and using Matlab to solve the differential equation and plot the output's response. • First Method: Derive the solution to the differential equation and plot the output response using Matlab (see sample code below). Hint, you need to determine which form the solution takes (eq2, eq3 or eq4) and value of the constants and parameters. )(21 21 dampedovereAeAVV tsts fout ++= Equation 3, Solution for Over Damped Case )(21 dampedcriticallyeDetDVV tt fout αα −− ++= Equation 4, Solution for Critically Damped Case LC VVout LCdt dVout L R dt dVout 11 12 2 =++ )()sin()cos(BV 21f dampedundertweBtweV d t d t out αα −− ++= Equation 2, Solution for Under Damped Response 3. In-Laboratory Exercise (week two of two) Construct the differential op-amp circuit designed. Apply an appropriate input signal and measure/record the output response. Record the settling time (time to reach steady state value), maximum/minimum overshoot (if any), response's oscillation frequency, decay time constant of the response's oscillation envelope, Figure 3. Multisim Transient Analysis Dialog Box and amplitude of the steady state response. Confirm that the output matches the predicted response from the Matlab analysis and Multisim simulation. Demonstrate your working circuit to the laboratory instructor. No credit will be given for this exercise without the circuit being demonstrated. 4. Report (due one week after completion of section 3) • Cover page • Abstract • Derivation used to solve the differential equation, Matlab code used to plot the output response, and plot of output response obtained • Matlab code used to solve the differential equation and plot of output response obtained • Multisim schematic and plots of input and output response • Sketch of the output response observed in the laboratory • Include the rearranged differential equation block diagram used to implement the op-amp circuit • Table comparing Matlab data, Multisim data, and in-lab measurement data for: o settling time (time to reach steady state value) o decay time constant of the responses oscillation envelope o response's oscillation frequency o maximum/minimum overshoot o amplitude of the steady state response • Summarize results obtained and the design process used