EECE 211L Experiment - All

HANOI UNIVERSITY OF TECHNOLOGY

Faculty of Electrical Engineering

-----------------------------------------------

Script of

LINEAR CIRCUIT 1

Editor: Tran Thi Thao

Reviewer: Tran Hoai Linh

List of Contents EECE 211L Experiment 1.......................................................................................................... 3 EECE 211L Experiment 2.......................................................................................................... 8 EECE 211L Experiment 3........................................................................................................ 12 EECE 211L Experiment 4........................................................................................................ 16 EECE 211L Experiment 5........................................................................................................ 20 EECE 211L Experiment 6........................................................................................................ 25 EECE 211L Experiment 7........................................................................................................ 29 EECE 211L Experiment 8........................................................................................................ 32 EECE 211L Experiment 9........................................................................................................ 36 EECE 211L Experiment 10...................................................................................................... 41 EECE 211L Experiment 11...................................................................................................... 45 EECE 211L Experiment 12...................................................................................................... 48

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EECE 211L Experiment 1

Basic DC Voltage and Current Measurements

I. OBJECTIVES

1. To learn how to assemble a simple circuit consisting of a DC power supply and resistors.

2. To learn how to measure the circuit current and resistor voltages using a multimeter.

3. To compare the measured current and voltages with those calculated by hand, and with those calculated using a PSpice simulation.

II. BACKGROUND & THEORY

Definitions for various electrical quantities is as follows:

.1. 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 .

2. 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.

3. 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(Ω). 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 1 and Figure 1 can be used to estimate resistor values.

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Table 1 Resistor Color Code

Figure 1 Arrangement of Resistor Stripes Used to Determine Resistance

III. EQUIPMENT AND PARTS LIST

Digital Multimeter (DMM) Adjustable DC power supply Circuit breadboard Resistors: 12kΩ ,100 kΩ, ….

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IV. PROCEDURE

1. Identify the make, model no., and serial number of each piece of measuring equipment. This will be required on all experiments.

2. Note the color code on each resistor and determine its nominal value from the color code cards provided.

3. 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.

4. Mount the 12kΩ and 100 kΩ 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.

Figure 2 Circuit for Voltage and

Current Measurements

5. 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. 6. 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.

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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.

7. Repeat the procedures above with each of the other two resistors.

8. Repeat the procedures above for V = 10 V D.C. and V = 15 V D.C.

V. THEORETICAL CALCULATIONS

1. Calculate the maximum expected error in each of your measurements using the information from the meter specification sheet.

2. 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.

3. 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.

4. 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 KΩ, 2.2 KΩ, 4.7 KΩ,10KΩ). 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.

VI. PSPICE SIMULATION

1. Construct a PSpice simulation of the circuit shown in Figure 2 using the resistor nominal values.

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2. Include in your report the PSpice circuit diagram showing the predicted circuit current and node voltages. 3. Compare PSpice results with hand calculations and experimental measurements.

VII. CONCLUSIONS

Scientific conclusions supported by the data obtained in the experiment.

EECE 211L Experiment 2 Kirchhoff's Current and Voltage Laws

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Kirchhoff's Current and Voltage Laws

I.OBJECTIVES

1. To learn and apply Kirchhoff's Current Law (KCL).

2. To learn and apply Kirchhoff's Voltage Law (KVL).

3. To obtain further practice in electrical measurements.

4. Compare experimental results with those using hand calculations, MATLAB, and PSpice.


1. Kirchhoff's Current Law (KCL)

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 = 0

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 = 0


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2. Kirchhoff's Voltage Law (KVL)

Kirchhoff's Voltage Law (KVL) states that the algebraic sum of voltages around a closed path is zero, or:

v1 + v2 + v3 ... vn = 0

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: 2KΩ, 4.7KΩ, 1KΩ, and 3.3KΩ

IV. PROCEDURE

Consider the circuit shown in figure 1

4.1. Theoretical Calculations

1. Without substituting in numbers for R1, R2, R3, and R4 apply Kirchhoff's Current Law at nodes 1 and 2 so as to obtain two equations in terms of the two unknown node voltages V1 and V2. Simplify these equations.

Figure 1 Circuit for Voltage and Current Measurements


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2. Let R1 = 2KΩ, R2 = 4.7KΩ, R3 = 1KΩ, and R4 = 3.3KΩ in the equations of Step 1. Solve these equations by hand for V1 and V2. Repeat, using MATLAB. From V1 and V2, find Va,Vb,Vc, Ia, Ib, Ic. 3. Measure the four resistors. Use these values to find V1,V2, Va, Vb,Vc, Ia, Ib, Ic as in Step 2. 4. Construct a PSpice simulation of the circuit in Figure 1 using the measured values of the four resistors. Run the simulation so as to show the currents and voltages indicated in Figure 1. 4.2. Laboratory Experiment

1. Construct the circuit shown in Figure 1. 2. Use the multimeter to measure the indicated three currents and five voltages. 3. Compare the results of Step 2 with those obtained from the theoretical calculations of Steps 3 and 4 of the Theoretical Calculations section above. 4. Using the measured values of the three currents, check Kirchhoff's Current Law at node 2. 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.

V. CALCULATIONS AND COMPARISONS

1. 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?

2. 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


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compare these calculated voltage values with the measured voltage values. Are all differences within the expected limits of accuracy?

VI.CONCLUSIONS

Based on the results from this experiment.

EECE 211L Experiment 3-Thevenin's Equivalent Circuit and Maximum Power Transfer

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Thevenin's Equivalent Circuit and Maximum Power Transfer

For a Resistive Network

I. OBJECTIVES

1. To find experimentally the values for a Thévenin's equivalent of a circuit.

2. To check the experimental values versus calculated values.

3. To find the conditions for maximum power delivered to a load.

4. To build a Thévenin equivalent of the original circuit and check to see if it really is equivalent


2.1.Thévenin's theorem

Thévenin's theorem states that any two-terminal circuit with linear elements can be represented with an equivalent circuit containing a single voltage source in series with a single resistor. The Thévenin equivalent circuit is shown in Figure 1.

The equivalent circuit consists of an independent voltage source Voc and a series resistor Rth. Voc and Rth are computed as follows:

ocvV t =

Thévenin equivalent circuit

Figure 1. A two-terminal circuit consisting of resistances and sources

can be replaced by a Thévenin equivalent circuit


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2.2. Maximum Power Transfer

The load resistance that absorbs the maximum power from a two-terminal circuit is equal to the Thévenin resistance.

The maximum voltage at the output of a linear source is

n

ntoc

i

Rvvv ===max

The maximum current at the output of a linear source is

t

tnsc

R

viii ===max

The maximum power delivered by a linear source to a matched load resistance

sc

octt

i

v

i

vR ==

sc

Figure 2. Thévenin equivalent circuit with short circuited terminals.

Figure 3. Circuits for analysis of maximum power transfer


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RL = RT = Rn is

2244

22scocnn

T

t iviR

R

vp ===max


Variable Voltage Supply Breadboard Digital Multimeter (DMM) Fixed Resistors: 1.0 kΩ, 1.2 kΩ, 1.5 kΩ, 2-1.8 kΩ, 2.2 kΩ, 3.9 kΩ Variable Resistance: 1 kΩ 1-turn Potentiometer

IV. PROCEDURE


1. Calculate the Thevenin equivalent circuit to the left of terminals x,y. 2. Use the circuit from Step 1 to find the expression for the power dissipated in the load RL and the expression for the voltage across the load resistor. 3. Let RL vary between 0 and 20Kohm. Use MATLAB to make two separate smooth graphs: (a) Plot power dissipated in RL versus RL

Figure 4 Circuit for Thevenin Equivalent Circuit Calculation


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(b) Plot the voltage across RL versus RL. In both plots show the point on the graph corresponding to the value of RL that theoretically maximizes the load power.

4.2.Laboratory Experiment

1. Assemble the circuit in Figure 1 without RL. Use combinations of resistors from your kit to make R5 while assembling the circuit. Measure the voltage across the point’s xy. It is the open circuit 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 your measurements and compare with the theoretical data obtained earlier. 2. Remove the short circuit and place the resistor RL of value equal to the Thevinin’s resistance found by measurements. Use resistive decade box for obtaining this RL. Find the voltage across it and calculate the power dissipated in it. Compare this power to the maximum power dissipated. 3. Now, construct the Thevenin equivalent network using the closest value of resistor in your parts kit for Rth. Using a resistive decade box for RL, connect it to the Thevenin equivalent network. 4. Vary RL in increments of 500 Ohms from 0 Ohms to 10000 Ohms. For each value of RL record the load voltage. Also record the load voltage at the theoretical value of RL that maximizes the load power. For each value of load voltage calculate the load power. As RL is varied, make sure to do the measurement for RL equal to Rth. 5. Modify the graphs from Theoretical Calculations, step 3 above by superimposing your experimental results onto the theoretical graphs. Use the plot symbol "o" to denote the experimental voltage or power. Don't connect the experimental data points by connecting lines. You should end up with two graphs: (a) Theoretical and experimental power versus RL and (b) theoretical and experimental load voltage versus RL over the range 0 < RL < 20 KΩ.

V. CONCLUSIONS

Scientific conclusions supported by the data obtained in the experiment.

EECE 211L Experiment 4- Superposition Principle

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Superposition Principle

I. OBJECTIVES

Study the principle of superposition. Analyze the circuits used in this experiment numerically in the preliminary lab exercise - both “by hand (and calculator) and using PSpice. Examine experimentally same circuits in the lab and the experimental values compared to the theoretical.


Linearity and the Principle of Superposition A circuit component is called linear if the current through the component is

linearly proportional to the voltage across the component or in another word the I-V relationship is linear.

The superposition principle states that the total response is the sum of the responses to each of the independent sources acting individually. Superposition principle does not apply to any circuit that has element (s) described by nonlinear equation (s).

Time-varying currents having different frequencies will flow through linear circuits independently hence no new frequencies will be produced in the circuits.

Generally resistors, capacitors, inductors and transformers are linear components if they operate at suitably low currents and voltages. Circuit components that behave linearly at low currents and voltages may behave nonlinearly if subjected to extreme currents and voltages. (For example, a resistor operated at power levels above its rated value may heat up, causing its resistance to change and vary with the amplitude of the current and will behave as a nonlinear element. Commonly used nonlinear circuit components include diodes, and transistors operated in certain current-voltage ranges.


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This shows that at any instant of time the sum of the voltage across the resistor and the voltage across the inductor is exactly equal to the source voltage. Remember that omega is in radians per second so that the phase angle must be converted to radians before adding it to the (omega t) term inside the trig function.

III. EQUIPMENT AND PARTS

Breadboard Resistor 1 kΩ,2 kΩ, 4,7 kΩ, 3.3 kΩ. DC Source Signal Generator (Oscillator) Digital Multimeter (DMM)

IV. PROCEDURE

4.1.Theoretical Calculations

1. Using node voltage analysis, calculate the voltage V’ across 3.3Kohms resistor and the current flowing through it. 2. Now use the principle of superposition. Find the voltage across 3.3Kohms due to individual voltage sources and calculate the voltage V’. Find the current flowing through 3.3Kohms due to individual sources and the net current through it. 4.2. Laboratory Experiment

Experiment 1


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1. Assemble the circuit and measure the voltage V’ and the current through 3.3Kohms. 2. Remove one of the voltage sources in the circuit. Replace it with a short circuit. Measure the voltage across 3.3Kohms and current through it due to this source. 3. Now remove the short circuit and reconnect this source in its place in the circuit. 4. Repeat Step 2 with the other source. 5. Add the voltages measured from Step 2 and 4 keeping in mind the polarities of voltages measured and direction of current measure. 6. Compare with the theoretical calculations and comment on the results.

Experiment 2

Consider the circuits shown in the following figures would be used to investigate the principle of superposition


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1. Solve the circuit shown in Figure 1 for the voltages V1, V2, and V3 and for the currents I1, I2, and I3. Use either the node-voltage or mesh-current method. Do not use the principle of superposition. 2. Suppress (zero) VS2 in the circuit of Figure 1 by replacing it with a short circuit. Solve the resulting circuit, shown in Figure 2, for the voltages V1’, V2’, and V3’ and for the currents I1’, I2’, and I3’. 3. Suppress (zero) VS1 in the circuit of Figure 1 by replacing it with a short circuit. Solve the resulting circuit, shown in Figure 3, for the voltages V1”, V2”, and V3” and for the currents I1”, I2”, and I3”. 4. Combine the results of step 2 and step 3 using the principal of superposition and compare with the solution of step 1. 5. Use PSPICE to construct the circuits in Figure 1, 2 and 3. Run the dc analysis of all the circuits. Compare the results with the results obtained in steps 1 through 4.

V.CONCLUSIONS

Based on the experimental results.

EECE 211L Experiment 5-Function Generator and Oscilloscope Basics

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Function Generator and Oscilloscope Basics

I. OBJECTIVES

To learn how to use two important laboratory instruments: function generator and oscilloscope.

To become familiar with the oscilloscope and what it does.

To learn how to use the various controls on the Oscilloscope.


2.1.The Function Generator

Function generators are used to produce AC signals. Usually, they can produce several different waveforms including sine waves, square waves, and triangular waves. Controls on the front of the function generator provide a means to adjust the partial descriptors of the signal i.e. the frequency fo of the signal, its amplitude VA and the DC offset Vavg. The following form the basic adjustments of any function generator:

Waveform Select: Most function generators can produce three or more distinct

waveforms. Typically these include the sine, square and triangular waves. The

waveform select or consists of either a set of push buttons or a knob with several

discrete settings, one for each available waveform.

Frequency Adjust: The frequency adjust typically consists of several push buttons or a

multi position rotary switch and a continuously variable one called the vernier. The

switch or push buttons are used to select the desired range of frequencies. A decade of

frequencies is a factor range where the highest frequency is a factor of 10 larger than

the lowest frequency in that range. The vernier control is used to dial-in any frequency

within the selected range.

To ensure that there are no missing frequencies between the ranges the frequency vernier usually allows adjustment of the frequency over a range slightly more than one decade so that there is an overlap between ranges.


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Amplitude: The amplitude of the output voltage is usually set by range select buttons

and a continuously variable vernier. The smaller amplitude range is used to accurately

control small amplitude signals, e.g. testing a high gain amplifier. The higher voltage

range provides larger amplitudes, but has coarser control.

DC Offset: The controls for setting Vavg or DC Offset are quite similar to those used

for setting the output amplitude. The user typically has a couple of ranges available

with a vernier that allows the actual value to be adjusted throughout the selected range.

There may also be a switch to set the DC offset precisely to zero.

Other controls: With more sophisticated function generators the user can create

specialized waveforms and provide a synchronization signal to an oscilloscope.

The Philips PM 5132 function generator

The Philips PM 5132 function generator can be used as a source of sinusoidal, triangular, square, and pulse waveforms. When a signal from the function generator is applied to a circuit, its effect at various points in the circuit can be observed using the oscilloscope. The function generator output voltage does not correspond to an ideal source such as are often shown in an electric circuit book. The PM 5132 has a built-in output resistance. This resistance Rs cannot be removed, but it can be set to either 50Ω or 600Ω. In the first part of the experiment the Thevenin equivalent circuit of the generator will be found.

2.2. The oscilloscope

The oscilloscope that will be used in this laboratory is called a digital oscilloscope. The digital oscilloscope differs from its analog counterpart in that it “digitizes” or converts the analog input waveform into a digital signal that is stored in a semiconductor memory and then converted back into analog form for display on a conventional CRT. Typical digitizing-scope architecture applies extensive processing power to waveform acquisition, measurement, and display. A wide variety of plug-in modules are available for special timing functions and additional channels. The data are displayed most frequently in the form of individual dots that collectively make up the CRT trace. The vertical screen position of each dot is given a binary number stored in each memory location, and the horizontal screen position is derived from the binary address of that memory location.

The number of dots displayed depends on the frequency of the input signal relative to the digitizing rate, on the memory size and on the rate at which the memory contents are read out. The greater the frequency of the input signal with respect to the


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digitizing rate, the fewer the data points captured by the oscilloscope memory in a single pass and the fewer the dots available in the reconstructed waveform. Digital and analog oscilloscopes each have distinct advantages, but digital scopes are fast replacing analog scopes because they are more versatile.

An important consideration when using an oscilloscope is to remember that one of the two terminals of the probe used to measure a voltage is grounded. One of the two output terminals of the function generator is also grounded. The ground of the scope and the ground of the generator are automatically connected together since each is separately connected to the same earth ground. These automatic ground connections must be taken into consideration when using the scope. Otherwise, circuit components may be shorted out resulting in an inaccurate measurement and possible damage to the circuit. Using both channels of the scope in what is referred to as the differential mode technique can circumvent the grounding problem. This technique will be used in the second part of this experiment.


Philips PM 5132 function generator. Oscilloscope. Resistor 600 Ω , 470Ω, 750Ω. HP-467 amplifier/power supply.

IV. PROCEDURE

4.1. Laboratory Experiment 1

1. Connect the function generator directly to the oscilloscope. Adjust the generator and scope to display one cycle of the signal Vs(t) = 4sin(2000πt) volts. Set the generator output resistance to Rs = 600 Ω Sketch Vs(t). 2. Connect the generator to a resistive decade box as shown in Figure 1. Vary R until the amplitude of the voltage across R is one-half of the amplitude in Step 1. Sketch the voltage across the resistor.

Figure 1 Circuit for Thevenin Equivalent Circuit Measurement


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3. Use the results of Steps 1 and 2 to draw the Thevenin equivalent network for the function generator. 4. Set the HP-467 amplifier/power supply to operate as an amplifier of gain 1. Insert this amplifier between the function generator and the variable resistance R. Estimate the Thevenin equivalent resistance of the function generator/amplifier combination. 5. Explain why it is important to know the output resistance of the function generator you are using.

4.2. Laboratory Experiment 2

1. Set the open circuit voltage of the function generator to 20 volts peak to peak and frequency 2 KHz. 2. Connect the function generator to the two resistors as shown in Figure 2. 3. Use the scope to measure V1(t) and V2(t). Sketch V1(t) and V2(t) on the same time axis over two periods of the source voltage.


(Students should complete the first two steps of this part of the experiment before

coming to lab.)

Figure 2. Circuit for Scope Measurements


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1. Construct the circuit in Figure 2 using PSpice and the nominal values of circuit parameters. Use PSpice to plot V1(t) and V2(t) on the same time axis over two periods of the source voltage. 2. Change Rs to Rs = 0 and repeat Step 1. 3. Compare theoretical and experimental results.

V.CONCLUSIONS

Based on the experimental results

EECE 211L Experiment 6 - RC Circuit Measurements

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RC Circuit Measurements

I. OBJECTIVES

To illustrate how to experimentally determine the value of a capacitor.

To verify the rule for combining capacitors in series

To measure the phase angle between voltage signals using an oscilloscope.

To compare this angle with calculations using phasors


Capacitor Circuits

The impedance of a capacitor is given by ZC = 1/jωC = -j/ωC = jXC, where j indicatesthat the impedance of a capacitor is a purely imaginary number, XC = -1/ωC represents the imaginary portion of ZC and is called the reactance of ZC, and ω = 2πf where f is the frequency measured in Hz. In this experiment we are interested in the magnitude of the impedance of this capacitor which is given by ZC = 1/ωC. The source voltage (produced by the function generator, see Figure1) can be represented by the following expression.

V(ω,t) = VMsin(2πft) = VM sin(ωt) The voltage magnitude seen across the capacitor in an RC series network, Figures 1 and 2, is given by the following equation which is computed using the concept of voltage division. VC=V(ZC/(R+ZC))=VM(ZC/R+ZC)=VM(-XC/R+jωC) =VM(-XC/√(R2+XC

2))


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In a similar fashion it can be shown that the voltage across the resistor is given by: VR = VM(R/√(R2+XC

2)) The source is a function of time which implies that the capacitor voltage is also

a function of time. More importantly, the equation for VC shows that the voltage VC is a function of frequency.


Signal generator. Oscilloscope. Digital mulitimeter Resistor 10 kΩ , 470Ω, 750Ω. Capacitor 0.1µF, 0.33µF HP-467 amplifier/power supply.

IV. PROCEDURE

4.1. Experimental Determination of Capacitance

1. After constructing the circuit shown in Figure 3, adjust the signal generator so that the voltage at node A relative to node C is given by:

VAC(t)= 4 sin(ωt) volts

Frequency = 2KHz

Figure 3


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2. Use the scope to find the peak voltage across the capacitor. 3. Observe both VAC and VBC on the oscilloscope. Are they in time phase? From the observation on oscilloscope what will you conclude about the sum of peak voltages across each element of the loop meaning that, will the sum of peak voltages around the loop satisfy KVL? Do NOT measure to conclude this. 4. Use mulitimeter to determine the rms voltage across R. Use the multimeter to determine the rms voltage across the capacitor and rms current through it. Determine the peak voltage to rms voltage ratio across the capacitor. Also determine the rms current through the resistor using Ohms Law. Is it the same as rms current through the capacitor? 5. Calculate the magnitude of the capacitor impedance, Zc using measurements from Step 4. 6. Calculate the capacitance C using the expression, 7. Measure the value of C using the capacitance meter in the lab. Using the capacitance meter value of C as the reference, calculate the % error of the nominal value of C, and the % error of the value of C obtained from Step 6.

4.2. Series Capacitors in a Circuit

1. Construct the circuit in Figure 4. Set the generator to give VAD(t)= 4sin(ωt) volts

Frequency = 2KHz

Figure 4


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2. Measure the rms value of VBD using multimeter and the rms current through the capacitors. 3. Using measurements in step 2. determine the impedance of equivalent capacitance of two capacitors in series which is |ZCEQ|. Find the equivalent capacitance of the two capacitors in series from |ZCEQ|.

4. Compare with the theoretical value of the equivalent capacitance.

V.CONCLUSIONS


EECE 211L Experiment 7 - RLC Circuit Measurements

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RLC Circuit Measurements

I. OBJECTIVES

The main purpose of this experiment is to understand the concept of phasors.


RLC circuit:

In the following R-L-C circuit of ideal components, the current (Is) will reach a maximum when the reactances (XL and XC) are equal in magnitude, and the impedance (Zeq) reaches a minimum at a specific frequency. This frequency is called the resonant frequency.

Note the following equations which express this phenomenon mathematically.

To solve for the resonant frequency (fr), you merely set the two reactances equal as shown below.


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Solving for ω and then fr


Resistor 600Ω,1 kΩ Capacitor 0.1µF Inductor 20 mH Breadboard Oscilloscope Signal Generator (Oscillator) Digital Multi meter (DMM) IV. PROCEDURE

1. Before constructing the circuit shown in Figure 1, measure the value of the inductor resistance RL. Set the function generator to give VAB(t)= 2 sin(ωt) V. Frequency =500 Hz

2. Measure the amplitude of Vin by connecting the vertical input of oscilloscope to one channel. 3. Connect the vertical input of another channel of the oscilloscope across the capacitor.

Figure 1 RLC Circuit for Experimentation


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Measure the amplitude VC and phase of the voltage across the capacitor with reference to Vin . 4. Compute VC/Vin theoretically. Include the measured values of the inductor resistance in the theoretical computation of VC/Vin . Compare with the measurements. 5. Measure the Voltage across 1K Ohms resistor using multimeter and calculate the peak value of voltage across it and call it VR. Measure the voltage across inductor using multimeter and calculate the peak value across it and call it VL. Measure the current through the circuit using multimeter and calculate the peak current. 6. Draw a phasor diagram with VR oriented along x-axis and VC oriented along negative y-axis. Calculate the peak value of voltage drop across the resistance of the inductor RL (product of peak current with RL) and call it VRL. Draw it as another phasor along x-axis. Now orient the phasor angle of VL such that the projection of VL is VRL. Find the resultant phasor of VL VR and VC. 7. Compare the resultant phasor magnitude with the amplitude of input voltage across the series RLC.

V.CONCLUSIONS


EECE 211L Experiment 8 - RC and RL Low Pass Filters

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RC and RL Low Pass Filters

I. INTRODUCTION

Resistors, capacitors and inductors can be combined to form filters. Waveform such as those originating from voice, music, or transducers can often be decomposed into a sum of many sinusoidal signals with different frequencies.

When such a waveform is applied to a low pass filter, only the low frequency sinusoidal components pass through the filter while the high frequency components are attenuated. Such a filter could be useful for removing additive high frequency noise from a low frequency signal such as the signal from a temperature sensor.

Other types of filters include high pass, band pass and band reject filters. In this experiment, two simple low pass filters will be studied. The experimentally determined frequency responses will be compared with responses using theoretical calculations.

II. EQUIPMENT AND PARTS

Signal generator. Oscilloscope. Digital mulitimeter Resistor 470Ω. Inductor 20mH Capacitor 0.1µF HP 467 amplifier

III. PROCEDURE

3.1. RC Filter Frequency Response


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1. After measuring R and C, construct the circuit shown in Figure 1. 2. Vary the frequency of the generator over the following values: 100 Hz, 300 Hz, 600 Hz, 1000 Hz, 2000 Hz, 3000 Hz, 3500Hz, 4000Hz, 4500 Hz,5000 Hz, 6000 Hz, 10,000Hz and 50,000 Hz. For each frequency value use the scope to measure and record the amplitudes of Vin(t) and V(t). Experimentally, also find the frequency where the amplitude of V(t) is 0.707 times the amplitude of V(t) when the source frequency is close to 0. This is referred to as the experimental -3 dB frequency, or the experimental bandwidth of the circuit. Convert your voltage readings to RMS for all 14 frequencies. In addition, for each frequency in your table calculate 20*log10(V/ Vin) , where V and Vin refer to the RMS values of these voltages. 3. It can be shown that the theoretical relationship between the RMS value of V(t) and the RMS of Vin(t) is given by

In this expression V(ω) and Vin(ω) refer to the phasor representations of V(t) and Vin(t), respectively. Use MATLAB to plot

Figure 1 RC Circuit for Experimentation


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over the frequency range 100 Hz to 100 KHz. Use a 3 cycle semilog scale for the frequency axis and your measured values of R and C for the calculations. Your graph should be a solid smooth curve.

Theoretically, the expression in (1) should be -3 dB at the frequency given by

Calculate (2) using your measured R and C. Show the experimental response at this frequency point on your plot using the plot symbol "*". These are your theoretical results. 4. Use MATLAB to plot your tabulated experimental data from Step 2 on the same graph as your theoretical results. Use the plot symbol "o" for your experimental results. Don't connect the "o" by straight lines. You should now have a direct comparison of the theoretical and experimental frequency responses of the circuit. 3.2. RL Filter Frequency Response 1. Measure the values of R1, RL, and L. Then construct the circuit shown in Figure 2. 2. For the circuit in Figure 2, repeat the measurements shown earlier in Step 2 for the RC network. 3. The theoretical relationship between the RMS values of V and Vin is

(3)

Figure 2 RL Circuit for Experimentation


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As in Step 3 for the RC network, calculate and plot

over the frequency range 100 Hz to 100 KHz using 3 cycle semilog paper in MATLAB. The theoretical expression for the -3 dB frequency is given by Calculate (4) using the measured values of R and L. Indicate this frequency point in your theoretical plot of the frequency response using the plot symbol "*". 4. Use MATLAB to plot your tabulated experimental data from Step 2 on the same graph as your theoretical results. Use the plot symbol "o" for your experimental results. Don't connect the "o" by straight lines. You should now have a direct comparison of the theoretical and experimental frequency responses of the circuit Some of the results of this experiment will be used in the next experiment. You may want to make a copy of your report for this experiment before you turn it in.

EECE 95L Experiment 9 - Frequency and Time Relations for RC and RL Circuits

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Frequency and Time Relations for RC and RL Circuits

I. INTRODUCTION

In Experiment 8 the frequency responses, including the bandwidths, of low pass RC and RL circuits were experimentally determined and compared with theoretical expressions. In this experiment the pulse responses, including the time constants, of the same circuits will be measured.

Results of the two experiments can be theoretically related. In particular, the concept of bandwidth in the frequency domain can be used to predict the response time of the circuit as measured by its time constant.


Signal generator. Oscilloscope. Digital mulitimeter Resistor 470Ω. Inductor 20mH Capacitor 0.1µF HP 467 amplifier

III. PROCEDURE

3.1. RC Filter Step Response

Theoretical Result:

1. Application of Kirchhoff's Voltage Law to the circuit shown in Figure 1 leads to the following differential equation for t > 0. Figure 1 RC Circuit for Time Constant Determination


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Assuming the capacitor is uncharged at t = 0, the solution to (1) for t > 0 is

This is illustrated in Figure 2. The time constant τ is a measure of the response time of the voltage V(t). Combining equation (2) in Experiment 8 with equation (3) above, we have

Equation (5) indicates that a large bandwidth is needed for a fast response.

Experiment:

1. After measuring R and C, construct the circuit shown in Figure 3. 2. Adjust the signal generator to supply a 0 to 4 volt pulse train with frequency of 1000 pulses/sec. Vary the duty cycle to allow measurement of the time constant as shown in Figure 2.

Figure 2 Step Response of V(t) in Figure 1


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3. 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 8.

3.2. RL Filter Step Response

Theoretical Result:

For t > 0 the differential equation for the inductor current shown in Figure 4 is given by

Figure 3 RC Circuit for Experimentation

Figure 4 RL Circuit for Time Constant Determination


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Since the inductor current at t = 0 is 0, then the solution to (6) for t > 0 leads to the

following:

Equation (8) can be related to the bandwidth of V(t) using equation (4) in Experiment 8.

The result is

which is of the same form as that for the RC network; see equation (5).

Experiment:

1. Measure R, RL and L and then construct the circuit shown in Figure 5. 2. Adjust the signal generator to supply a 0 to 4 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. 3. 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 8.

Figure 5 RL Circuit for Experimentation


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3.3. PSpice Simulation 1. 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.

2. Repeat Step 1 for the RL circuit shown in Figure 4.

EECE 211L Experiment 10 - Operational Amplifier Circuits

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Operational Amplifier Circuits

I. INTRODUCTION

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 1kΩ, 12kΩ Capacitor 0.1µF LM 741op-amp HP E3611 dc supplies

III. PROCEDURE

3.1. Operational Amplifier Basics

The LM 741op-amp that will be used in this experiment is an eight pin device. Figure 1 shows the schematic symbol and how the pins are labeled. Circuits that include an op-amp can often be designed using two rules for the op-amp

Figure 1 LM 741 Operational Amplifier Device Schematic and Labels


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device. 1. The first rule is that the currents into pins 2 and 3 are negligibly small. 2. 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 2. 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. 3.2. Inverting Amplifier

1. Build the circuit shown in Figure 3. 2. Use the scope to measure Vout and VAB and the phase angle of Vout relative to VAB.

Figure 2 Power Supply Connections and Reference Definition

Figure 3 Inverting Amplifier Circuit


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3. Calculate the magnitude of the experimental transfer function Vout/ VAB. 4. Compare the result of Step 3 with the theoretical result:

3.3. Non-inverting Amplifier

1. Build the circuit shown in Figure 4. 2. Use the scope to measure Vout and VAB and the phase angle of Vout relative to VAB. 3. Calculate the magnitude of the experimental transfer function Vout/ VAB. 4. Compare the result of Step 3 with the theoretical result:

3.4. Differentiating Amplifier

1. Build the circuit shown in Figure 5.

Figure 4 Non-inverting Amplifier Circuit


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2. Using both channels of the scope, measure Vout and VAB. 3. Compare the results of Step 2 with the following theoretical result, 4. Without changing the amplitude or frequency of the generator, change VAB to a triangular wave. Compare your experimental Vout with theory.

Figure 5 Differentiating Amplifier Circuit

EECE 211L Experiment 11 - Series Resonance

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Series Resonance

I. OBJECTIVES

1. To understand what happens to a circuit when it reaches a resonant frequency. 2. To understand why the current peaks at the resonant frequency. 3. 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 1.

Theoretical Results The following results apply to the circuit in Figure 1.

Figure 1 Series RLC Network for Experimentation


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III.EQUIPMENT AND PARTS

Resistors: 68Ω,1kΩ,10 kΩ Capacitor 0.01 µF Inductor 20 mH Breadboard Oscilloscope Signal Generator (Oscillator) Digital Multi meter (DMM)

IV. PROCEDURE

1. In Figure 1, let C = 0.01 µF and L = 20 mH. Measure the values of C,L and the inductor resistance. 2. Using the measured values of the components, find the value of R1 that will result in a bandwidth of 1 KHz. Build the circuit in Figure 1 using a resistance decade box for the value of R1. Adjust the signal generator to 10 volts peak to peak. 3. Calculate the theoretical resonant frequency in Hz using the measured values of circuit parameters.


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4. 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. 5. Using MATLAB, make a smooth graph of the theoretical magnitude of Vout/Vin (in dB) versus frequency (in Hz) over the linear frequency range 0 to 20 KHz. On the same graph, show your experimental results from Step 4. Compare the theoretical and experimental bandwidths. For the bandwidth calculation, use the -3dB points from the peak of the response.

V.CONCLUSIONS

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?

EECE 211L Experiment 12 - Transformer Characteristics

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Transformer Characteristics

I. OBJECTIVES

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.

II. BACKGROUND AND THEORY

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 1 Transformer with Source and Load


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III.EQUIPMENT AND PARTS

Resistors: 10Ω,47Ω,150 kΩ, decade box resistor Windings Breadboard Oscilloscope Signal Generator (Oscillator) HP 467 Digital Multi meter (DMM) IV.PROCEDURE

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. 4.1. Experiment 1

Open Circuit Test 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.

Short circuit test

Figure 2. Open Circuit Test


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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.

4.2. Experiment 2

1. Before connecting the circuit shown in Figure 1, measure the primary and secondary winding resistances. 2. Apply a 5 volt, 2 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. 3. Connect a ZL = 47 Ω resistor to the secondary. Measure the impedance looking into the transformer primary. Compare your result with theory. 4. Place a 1 KΩ resistor in series between the HP 467 output and the transformer primary. Use a resistance decade box for ZL. Vary the resistance from 10 Ω to 150 Ω in steps of 10 Ω. 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.

Figure 3. Short Circuit Test


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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? V. CONCLUSION

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