bài thí nghiệm linear circuit CTTT

EECE 211L Experiment EECE 211L Experiment EECE 211L Experiment 12 EECE 211L Experiment 16 EECE 211L Experiment 20 EECE 211L Experiment 25 EECE 211L Experiment 29 EECE 211L Experiment 32 EECE 211L Experiment 36 EECE 211L Experiment 10 41 EECE 211L Experiment 11 45 EECE 211L Experiment 12 48 ! "# $ To learn how to assemble a simple circuit consisting of a DC power supply and resistors To learn how to measure the circuit current and resistor voltages using a multimeter To compare the measured current and voltages with those calculated by hand, and with those calculated using a PSpice simulation ! "# $ % !& Definitions for various electrical quantities is as follows: Electric current (i or I) is the flow of electric charge from one point to another, and it is defined as the rate of movement of charge past a point along a conduction path through a circuit, or i = dq/dt The unit for current is the ampere (A).One ampere= one coulomb per second Electric voltage (v or V) is the "potential difference" between two points, and it is defined as the work, or energy required, to move a charge of one coulomb from one point to another The unit for voltage is the volt (V) One volt = one joule per coulomb Resistance (R) is the "constant of proportionality" when the voltage across a circuit element is a linear function of the current through the circuit element, or v = Ri A circuit element which results in this linear response is called a resistor The unit for resistance is the Ohm( ) One Ohm = one volt per ampere The relationship v = Ri is called Ohm's Law Resistor Color Code In order to assemble a circuit with resistors it is necessary to know the resistor values The resistor color code indicated in Table and Figure can be used to estimate resistor values ' (! ) +" , ( ! # * # , ! Digital Multimeter (DMM) Adjustable DC power supply Circuit breadboard Resistors: 12k ,100 k , … " ! ,! "! Identify the make, model no., and serial number of each piece of measuring equipment This will be required on all experiments Note the color code on each resistor and determine its nominal value from the color code cards provided Set the multimeter to D.C voltage Turn on the D.C power supply and adjust the power supply to its lowest value Then measure and record the power supply output voltage Measure and record this value Adjust the voltage source accurately 20 V D.C, using the multimeter to measure voltage Mount the 12k and 100 k resistors on the circuit bread Then connect the power supply output to the two ends of the resistors Your circuit should look like the schematic diagram shown in Figure2 ) - Measure the voltage across of the two resistors Use + and – signs on the circuit diagram to indicate polarity Relate these signs to the test leads of the multimeter Measure the current through the resistors Use an arrow on the circuit diagram to indicate the direction of current Relate the direction of this arrow to the test leads of the multimeter The mA meter should be connected between the +V side of the power supply and the side of the resistor where the power supply lead was previously connected The meter and its leads act as the connection from the power supply and the resistor so that all the current flowing through the resistor must flow through the meter to get to the resistor This allows the meter to measure the same current that is flowing through the resistor To get the proper sign for the current into the positive terminal of the resistor, the positive terminal of the power supply must be connected to the mA terminal of the meter and the com terminal must be connected to the resistor Repeat the procedures above with each of the other two resistors Repeat the procedures above for V = 10 V D.C and V = 15 V D.C % ! " # Calculate the maximum expected error in each of your measurements using the information from the meter specification sheet Check Ohm's Law, by comparing your measured values of voltage (V) to the product of your measured resistance (R), measured current (I), and see if the two sides of the equation match within the expected measurement accuracy Is VMeasured = IMeasured * RMeasured ± the maximum value due to the accumulations of errors in the three measurements? (|VMeasured IMeasured * RMeasured | < the maximum value due to the accumulation of errors in the three measurements) See the supplement on measurement errors analysis at Measurement Errors Make a graph of current (y axis) versus voltage (x axis) for your 10 kOhm resistor Does the current increase linearly with the voltage? On the same graph, compare to a theoretical line of constant R Using Ohm's Law, calculate current (I) with a constant voltage of 20 V D.C for each of the three nominal resistances (1.0 K , 2.2 K , 4.7 K ,10K ) Does the current decrease linearly with resistance? Make a graph of current (y axis) versus resistance (x axis) to show your calculated and your measured results If you use a spreadsheet you can easily calculate extra data points between the values of the resistances used in the experiment and then plot a much smoother curve Plot this theoretical curve with a line between points Plot the experimental data on the same graph using symbols but no line , , " # Construct a PSpice simulation of the circuit shown in Figure using the resistor nominal values Include in your report the PSpice circuit diagram showing the predicted circuit current and node voltages Compare PSpice results with hand calculations and experimental measurements # " # Scientific conclusions supported by the data obtained in the experiment ! "# $ / ! To learn and apply Kirchhoff's Current Law (KCL) To learn and apply Kirchhoff's Voltage Law (KVL) To obtain further practice in electrical measurements Compare experimental results with those using hand calculations, MATLAB, and PSpice ! "# $ % ( / 01 !& Current Law (KCL) states that the algebraic sum of currents leaving any node or the algebraic sum of currents entering any node is zero, or: i1 + i2 + i3 in = Also KCL can be stated as the sum of the currents entering a node must equal the sum of the currents leaving a node, or i1 + i2 = i3 + i4 As you make a summation of currents, it is suggested that you use currents leaving the node as positive and the currents entering node as negative, or: i1 i2 + i3 + i4 = - / 01 Kirchhoff's Voltage Law (KVL) states that the algebraic sum of voltages around a closed path is zero, or: v1 + v2 + v3 = As you make a summation of voltages, it is suggested that you proceed around the closed path in a clockwise direction If you encounter a positive (+) sign as you first enter the circuit element, then add the value of that Conversely, if you first encounter a negative sign as you enter the circuit element, then subtract the value of that voltage +" , # # , ! Digital Multimeter (DMM) Adjustable D.C power supply Circuit bread board Resistors: 2K , 4.7K , 1K , and 3.3K ,! "! Consider the circuit shown in figure ) 3( ( Without substituting in numbers for R1, R2, R3, and R4 apply Kirchhoff's Current Law at nodes and so as to obtain two equations in terms of the two unknown node voltages V1 and V2 Simplify these equations Let R1 = 2K , R2 = 4.7K , R3 = 1K , and R4 = 3.3K in the equations of Step Solve these equations by hand for V1 and V2 Repeat, using MATLAB From V1 and V2, find Va,Vb,Vc, Ia, Ib, Ic Measure the four resistors Use these values to find V1,V2, Va, Vb,Vc, Ia, Ib, Ic as in Step Construct a PSpice simulation of the circuit in Figure using the measured values of the four resistors Run the simulation so as to show the currents and voltages indicated in Figure 3' 5* Construct the circuit shown in Figure Use the multimeter to measure the indicated three currents and five voltages Compare the results of Step with those obtained from the theoretical calculations of Steps and of the Theoretical Calculations section above Using the measured values of the three currents, check Kirchhoff's Current Law at node Use your measured values of the source voltage, Va, Vb, and Vc to check Kirchhoff's Voltage Law for the outer loop of the circuit " # # , ! # Use your measured current values to determine if KCL is verified to within the limits of the measuring equipment Also use Ohm's Law and nominal resistance values to calculate Ia, Ib, and Ic Repeat the calculations Using the measured resistance values Make a chart to compare measured current values with the two sets of calculated values Include the % differences in this chart Are the differences between the measured values and the values calculated using the measured resistance values within the accuracy limits of the DMM? Are the differences found using the nominal values for calculations within the tolerance limits of the resistors? Use your measured voltage values to determine if KVL is verified is verified to within the limits of the measuring equipment Also use measured value of Ic, measured values of resistance, and Ohm's Law to calculate Va, Vb, and Vc Make a chart to 10 7' ( ! $ $ $ Assuming the capacitor is uncharged at t = 0, the solution to (1) for t > is This is illustrated in Figure Figure Step Response of V(t) in Figure The time constant τ is a measure of the response time of the voltage V(t) Combining equation (2) in Experiment with equation (3) above, we have Equation (5) indicates that a large bandwidth is needed for a fast response 5* = After measuring R and C, construct the circuit shown in Figure Adjust the signal generator to supply a to volt pulse train with frequency of 1000 pulses/sec Vary the duty cycle to allow measurement of the time constant as shown in Figure 37 7' ( ! $ $ $ Figure RC Circuit for Experimentation Sketch V(t) and measure the time constant Compare your result for τ with that using equation (5) and the experimental value of bandwidth from Experiment ;- ! ) *! * ! = For t > the differential equation for the inductor current shown in Figure is given by Figure RL Circuit for Time Constant Determination 38 7' ( ! $ $ $ Since the inductor current at t = is 0, then the solution to (6) for t > leads to the following: Equation (8) can be related to the bandwidth of V(t) using equation (4) in Experiment The result is which is of the same form as that for the RC network; see equation (5) 5* = Measure R, RL and L and then construct the circuit shown in Figure Figure RL Circuit for Experimentation Adjust the signal generator to supply a to volt pulse train with frequency of 1000 pulses/sec Vary the duty cycle to allow measurement of the time constant in a manner similar to that for the RC network above Sketch V(t) and measure the time constant Compare your result for τ with that using equation (9) and the experimental value of bandwidth from Experiment 39 7' ( ! $ $ $ ;; , * Construct a PSpice simulation of the RC circuit shown in Figure 1using your measured values of circuit components Plot V(t) and use the cursors to estimate the time constant Compare results with theoretical and experimental results Repeat Step for the RL circuit shown in Figure 40 * / ! "# * # ! " $ , * # This experiment introduces the operational amplifier integrated circuit This device can be used to perform many tasks including signal amplification, summation, integration, differentiation and filtering +" , # # , ! Signal generator Oscilloscope Digital mulitimeter Resistor 1k , 12k Capacitor 0.1 F LM 741op amp HP E3611 dc supplies ,! "! ;( * * The LM 741op amp that will be used in this experiment is an eight pin device Figure shows the schematic symbol and how the pins are labeled Figure LM 741 Operational Amplifier Device Schematic and Labels Circuits that include an op amp can often be designed using two rules for the op amp 41 * / device The first rule is that the currents into pins and are negligibly small Vout = K(V+ V ) where K is large While the value of K is typically between 25000 and 50000, its exact value is often not needed Since Vout is limited by the supply voltage Vcc, the expression for Vout implies that │V+ V │is small Thus, the second rule usually assumed for op amp design is that V+ ≈ V For this experiment two HP E3611 dc supplies are required as shown in Figure Figure Power Supply Connections and Reference Definition We also see that Vout is measured relative to the common point between the two power supplies Although the connections between the integrated circuit and the power supplies are often omitted (See Figure 3), the integrated circuit will not work without them ;- * Build the circuit shown in Figure Use the scope to measure Vout and VAB and the phase angle of Vout relative to VAB Figure Inverting Amplifier Circuit 42 * / Calculate the magnitude of the experimental transfer function Vout/ VAB Compare the result of Step with the theoretical result: ;; # : * Build the circuit shown in Figure Figure Non inverting Amplifier Circuit Use the scope to measure Vout and VAB and the phase angle of Vout relative to VAB Calculate the magnitude of the experimental transfer function Vout/ VAB Compare the result of Step with the theoretical result: ;3 * Build the circuit shown in Figure 43 * / Figure Differentiating Amplifier Circuit Using both channels of the scope, measure Vout and VAB Compare the results of Step with the following theoretical result, Without changing the amplitude or frequency of the generator, change VAB to a triangular wave Compare your experimental Vout with theory 44 & $ ! "# $ ! To understand what happens to a circuit when it reaches a resonant frequency To understand why the current peaks at the resonant frequency To graphically show the various voltages in the circuit at resonance and on both sides of resonance ! "# $ % !& Resonance is a concept that applies to a RLC network connected to a sinusoidal source By definition, the resonant frequency is the frequency where the current and voltage are in phase at the network input terminals This is the same as the frequency where the input impedance is real Often a network is in resonance when the response (voltage or current) at some location in the circuit is a maximum While resonance could be considered for many different RLC circuits, in this experiment resonance will be examined for a series RLC circuit such as the one shown in Figure Figure Series RLC Network for Experimentation Theoretical Results The following results apply to the circuit in Figure 45 & +" , # $ # , ! Resistors: 68 ,1k ,10 k Capacitor 0.01 _F Inductor 20 mH Breadboard Oscilloscope Signal Generator (Oscillator) Digital Multi meter (DMM) ,! "! In Figure 1, let C = 0.01 `F and L = 20 mH Measure the values of C,L and the inductor resistance Using the measured values of the components, find the value of R1 that will result in a bandwidth of KHz Build the circuit in Figure using a resistance decade box for the value of R1 Adjust the signal generator to 10 volts peak to peak Calculate the theoretical resonant frequency in Hz using the measured values of circuit parameters 46 & $ Vary the frequency of the generator over the range of frequencies 6B to 15B in steps of B where B is the bandwidth in Hz For each frequency setting measure the peak to peak values of Vin and Vout using the oscilloscope Also, record Vin and Vout at the frequency where Vout/Vin is a maximum, and at the theoretical resonant frequency Using MATLAB, make a smooth graph of the theoretical magnitude of Vout/Vin (in dB) versus frequency (in Hz) over the linear frequency range to 20 KHz On the same graph, show your experimental results from Step Compare the theoretical and experimental bandwidths For the bandwidth calculation, use the 3dB points from the peak of the response # " # Your conclusions should include, but not be limited to answers to these questions: a What are your observations of the behavior of this circuit as a function of frequency? b Can you suggest some possible uses of this type of circuit? 47 ! "# $ ! This experiment introduces the transformer as a circuit element A transformer can be used to either step up or step down ac voltage It can also be used for impedance matching and to remove the dc component of signal ! "# # % !& The ideal transformer assumes (1) complete magnetic coupling of the primary and secondary windings, (2) primary and secondary inductive reactances are large compared to the terminating impedances, and (3) no power losses inside the transformer As indicated in Figure 1, the ideal model can be improved by including the winding resistances Rp in the primary and Rs in the secondary The descriptive equations for this transformer model are shown below Figure Transformer with Source and Load 48 +" , # # , ! Resistors: 10 ,47 ,150 k , decade box resistor Windings Breadboard Oscilloscope Signal Generator (Oscillator) HP 467 Digital Multi meter (DMM) ,! "! All voltages and currents referred to in this experiment are assumed to be in RMS The transformer to be studied is mounted in a box The side with two black connecting terminals will be called the transformer primary,and the other side with two blue connectors will be called the secondary The yellow, center tap, on the secondary will not be used in this experiment 3( 5* ( * This test is to be performed, at rated voltage, without wattmeters, but you should use digital instruments for measuring voltage and current Measure: V1, VRp, Vg, and I1 Figure Open Circuit Test 49 This test is to be performed, at rated current, without wattmeters, but you should use digital instruments for measuring voltage and current Measure: V1, VRp, Vg, and I1 Figure Short Circuit Test 3- 5* - Before connecting the circuit shown in Figure 1, measure the primary and secondary winding resistances Apply a volt, KHz sinusoidal signal from the output of the HP 467 to the transformer primary Do not connect a load ZL to the secondary Measure the open circuit secondary voltage Calculate the turns ratio n Connect a ZL = 47 resistor to the secondary Measure the impedance looking into the transformer primary Compare your result with theory Place a K resistor in series between the HP 467 output and the transformer primary Use a resistance decade box for ZL Vary the resistance from 10 to 150 in steps of 10 For each resistance setting, record the load voltage and calculate the load power Theoretically, find the Thevenin equivalent circuit to left of the load Use this to predict the load power as the load resistance is varied Plot a smooth curve of theoretical load power versus load resistance using MATLAB 50 On the same graph show your experimental values of load power Compare results Does the experimental peak load power occur near that predicted by theory? # " # 51 ... proportionality" when the voltage across a circuit element is a linear function of the current through the circuit element, or v = Ri A circuit element which results in this linear response is called a resistor... the behavior of this circuit as a function of frequency? b Can you suggest some possible uses of this type of circuit? 47 ! "# $ ! This experiment introduces the transformer as a circuit element... voltage Short circuits the points x and y Now, measure thecurrent flowing in the short circuited branch ‘xy’ This gives you the short circuit current Determine the Thevenin’s equivalent circuit from