Thevenin & Norton Equivalents in Electronic Instrumentation - ENGR-4300, Fall 2000, Assignments of Engineering

Download Thevenin & Norton Equivalents in Electronic Instrumentation - ENGR-4300, Fall 2000 and more Assignments Engineering in PDF only on Docsity! Electronic Instrumentation Name _______________ ENGR-4300 Fall 2000 Section ____________ K. A. Connor Revised: 9/18/00 Rensselaer Polytechnic Institute Troy, New York, USA 1 Homework #1 (Revised 14 September) Thevenin and Norton Equivalent Circuits Due: 15 September We will not be doing a great deal of pencil and paper circuit analysis in this course. We will be relying on PSpice to determine voltages and currents for most of the circuits we will study. However, there are a few basic configurations we will need to understand a little bit better. The only way to obtain this higher level of understanding is to do the analysis ourselves. We have already seen voltage dividers under several different circumstances. There is also a circuit called a current divider, which we will also need to understand, but not right now. These two dividers are shown in the figure below, which is taken from page 10 of Gingrich. The voltage divider is also found on page 5 of the Engineer’s Mini-Notebook on Formulas, Tables and Basic Circuits. Another circuit we have seen in experiments 2 and 3 is a combination of two voltage dividers, which is called a bridge circuit. Actually it is called a Wheatstone Bridge, but we mostly forget about Mr. Wheatstone when we talk about it. There is some good basic info on circuits to be found on many, many different pages on the web. One of these sites is at the University of Guelph where you can find tutorials on such topics as DC circuits at http://www.physics.uoguelph.ca/tutorials/ohm/Q.ohm.html In this figure, taken from the Guelph tutorial, the capital E represents the voltage source (this letter is used a lot, but not as much as the capital letter V), and G represents some kind of measurement device. This circuit has been set up to determine the unknown resistor Rx, just as we did in Experiment 2. Electronic Instrumentation Name _______________ ENGR-4300 Fall 2000 Section ____________ K. A. Connor Revised: 9/18/00 Rensselaer Polytechnic Institute Troy, New York, USA 2 When we use such circuits as voltage dividers or bridges to produce a voltage of some kind, we will be using them like a voltage source. We have seen that voltage sources such as our function generator, a battery, etc. all have an internal resistance of some kind. We, therefore, can expect to require similar information about dividers or bridges when we use them as sources. It turns out that any combination of voltage or current sources and resistors can be simplified into one of the two following forms, called Thevenin and Norton Equivalents. We will only be concerned with the Thevenin equivalent for now. Note that this simple combination is the model we have used for the practical sources we have seen in the studio. Read section 1.4 of Gingrich, in which he discusses Equivalent Circuits. He does a relatively thorough example finding the Thevenin voltage and resistances for a bridge circuit. We can generalize his result for resistors labeled R1, R2, R3, RX as in the circuit from Guelph. That is, we can determine both VTh and RTh. We can also find the Thevenin voltage and resistance for the voltage divider circuit on page 5 of the Mini-Notebook on Formulas, Tables and Basic Circuits. These questions were asked last semester, so their answers can be found in the Class Reserves – which can be accessed using a link at the top of the course Syllabus webpage. Once you have looked over Gingrich and the solution to the homework from last semester, determine VTh and RTh for the following circuit. Assume that the output is taken across the points labeled A and B. 0 V1 5V R1 10 R2 10 R3 5 R4 5 A B Ans: To determine the voltage at point A relative to point B (ground), it is first necessary to determine the voltage at the unmarked point above resistor R2. To do this, we first combine R3 and R4 is series to obtain 10ohms.