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Unformatted text preview:Experiment Four: Nonlinear Circuits and Analysis Engr 361 Section 1 September/ 30/ 2013 October/ 7/ 2013 Table of Contents Abstract Introduction Major Part Results Conclusions References Abstract The purpose of this experiment is to understand better the idea of linearity in circuitry. If all circuit elements are linear, then the methods such as mesh analysis, nodal analysis, superposition, Ohm's Law, Kirchoffs Current Law, and Kirchoff's Voltage Law can be used. However, these may not be used if there are nonlinear elements in the circuit. The experimenter must use graphical or numerical analysis techniques then. This is done by ﬁnding a characteristic curve of the element, and ﬁnding the load line for that element. Introduction Again, the main idea and goal to be understood and accomplished was to understand the difference between linearity and nonlinearity in this experiment, If the circuit had ' nonlinear elements, a graphical analysis approach was followed to ﬁnd some current or voltage most likely. The two different approaches that can be used are graphical and numerical analysis, but graphical is what's used here. Voltage and current values are found to plot a characteristic curve and then a load line. This can be used to realize some component and its characteristics. Major Part Part I was centered on the idea of graphical analysis of a LBB or "little black box". This is a good concept to understand and then is realized by the following equations. This equation can be used for many nonlinear circuits of similar type. When the current value equals zero, then the equation tends to v = V. If the voltage value across the nonlinear element is zero then i = V/R. V = Ri + v and equation i = (-V/R) + (V/R) Part II is called the problem drill and was to be done by the student before coming to the lab. This would allow the student with some practice in graphical analysis and its ups and downs. These Four pages are attached for the readers delight and study of graphical analysis of circuitry. Next, the experimenter was to ﬁnd the characteristic curve for an incandescent lamp that will be used in its graphical analysis. All currents and voltages are recorded as the voltage is adjusted from zero to ﬁfty and ﬁve volt steps. This same thing is to be done with the provided 1500 ohm resistor. The characteristic curves of current versus voltage are then graphed for both the lamp and resistor. Characteristic curves for resistance versus voltage are then plotted for each element also. The two curves have about the same shape just with different "amplitudes". Part IV deals with nonlinear circuit response. This is done ﬁrst by graphical analysis of the Figure 7, Figure 8, and Figure 9. All of these circuit diagrams are attached for the reader's purposes. The experimenter was then to connect all of the three circuits and verify by direct measurement that the graphical results were correct. Lastly, the student should compare the graphical results with those directly measured. Results The measured results or data are represented herein as the data summary sheets. Sample calculations are calculated here. va = 0 then i=V/R or i=10/2=5Amps If i=0 then v=V or v=lOvolts (([theory- actual|)/theory)*100 or ((|.041—.O33|)/.04l)*100= This table is included here to show the error analysis of data taken for Circuit two Part IV. Circuit 2 . . Error Graphical AnalySIS Analysis .041A .003A 19.5% v lamp 20% i 1500 .036A .034A 5.6% Conclusions The objective and or goals of this experiment were to use graphical analysis for nonlinear components. Speciﬁcally, all goals were met with small error, and they include understanding graphical analysis, problem drill, and nonlinear circuit response work. The ﬁndings speak to the fact that some circuits cannot be realized by linear techniques. As it happens, the experimenter has other techniques that can be used including graphical and numerical analysis. References N/A '1 Z a}. . "- '- ! 'Uﬁ iv:0 (L... 'l ; :' l." W _ / \le ': ; :U'h/ ZKZﬁ '}/'O :0 V2.1 1' /ﬁ"" .: rW'.' V I r "§j17[ A v:: "27 , j-—% Uri; ; V: I :00'; ":'0: Figure 7: Circuit 1 Figure 9: Circuit 3 Exp. 4 Pg. 5 ENGR 361 and ENGR 363 Experiment Four Part III (a), (b), and ((1) Data Summary Sheets l | Calculated Resistance for 1500 Q Resistor (Q) Part 111 (0). Plot i—v curve for lamp and i-v curve for 1500 Q resistor in the laboratogy. Circuit 2 m A .1?»- Exp. 4 Pg. 12 / Name: Grading Sheet for Experiment Four Summary: Goals & objectives stated (5) LExperimental concept & procedure (5) Part 11: Problem Drill 1. Power Resistor Current X (a) 10v,2Q(1) Cb) 10v,2/3 (2(1) (c) 25v, 2.5 Q (1) (d) 25V,1.666§2(1)) ﬁr 2. Diode Circuit x (a) V = 1.3 volts (1) (b) V = 1.0 volts (1) (c) V = 0.5 volts (1) Part IV: Solutions for Voltages and Currents for 1. Lamp in series with 1500 Q (5) 2. Lamp in parallel with 1500 Q (5) 3. Lamp and 1500 Q parallel combination in series with 1000 Q (5) Report Format: go \' Mai Organization (5) Mechanics (5) Expression of Ideas (5) Mr [1 + sin(10t)] volts (5) 3. Rectiﬁer Circuit (i vs. t) 4. Parallel Circuit 1\ / A? ___power resistor current (5 ) Part III: Measurement of (a) Lamp i-v data (5) (b) 1500 Q resistor data (5) (c) plots of data (5) (d) resistance vs. voltage comments (3) Part IV: Measured Voltages and Currents for I. Lamp in series with 1500 Q (5) 2. Lamp in parallel with 1500 Q (5) 3. Lamp and 1500 Q parallel combination in series with 1000 Q (5) "é Analysis and comparison of graphical results to directly-measured results (10) Exp. 4 Pg. 10