Linear Circult Analysis Lab-Manual_ 16Jun 2016.pdf

CIRCUITS ANALYSIS – I I LAB MANUAL

DEPARTMENT OF ELECTRICAL ENGINEERING, FAST-NU, LAHORE

Lab Manual of Circuit Analysis – I I

Created by:

Ms. Beenish Fatima, Ms. Maimoona Akram, Ms. Tooba Javed

Date:

May, 2012

Last Updated by:

Ms. Akbare Yaqub

Date:

June, 2016

Approved by the HoD: Dr. Arshad Hussain Date:

January, 2016

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Sr. No.

Description

Page No.

1

List of Equipment

4

2

Experiment No.1, Introduction to Lab Equipment

5

3

Experiment No.2, a) Resistor Color Code and Measurement b) Ohm’s law, Power in DC Circuits and Resistor Power Rating

10

4

Experiment No.3, Series Resistive Circuit, Kirchhoff’s Voltage law

22

5

Experiment No.4, a) Parallel Resistive Circuit, Kirchhoff’s Current law b) Application of KCL, KVL in a series-parallel series-parall el combination circuit

26

6

Experiment No.5, Introduction to PSPICE

30

7

Experiment No.6, Finding Equivalent Resistance of a Complex Circuit

42

8

Experiment No.7, Verification of Voltage and Current Divider Theorem

44

9

Experiment No.8, Verification of Thevenin’s Theorem

47

10

Experiment No.9, Verification of Maximum Power Transfer Theorem

51

11

Experiment No.10, Verification of Superposition Theorem

55

12

Experiment No.11, Charging and Discharging of a Capacitor

58

13

Experiment No.12, Operational Amplifier

60

14

Appendix A: Lab Evaluation Criteria

66

15

Appendix B: Safety around Electricity

67

16

Appendix C: Guidelines on Preparing Lab Reports

69

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Lab Manual of Circuit Analysis – I

Sr. No.

Description

1

Breadboard

2

Capacitor (1000uF)

3

Digital multi-meter (DMM)

4

LEDs

5

Light Bulbs (6.2V, 0.5A)

6

Operational Amplifier (741)

7

Oscilloscope

8

Power Supply (0-30 V)

9

Resistors of different values (4-Band, 5-Band and Alpha-numeric)

10

Variable Resistor (5k Ω , 10k Ω)

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OBJECTIVE: Introduction to digital multi-meter, power supply and breadboard  EQUIPMENT: Digital multi-meter (DMM)  Power Supply (0-30 V)  Breadboard  BACKGROUND: DIGITAL MULTI-METER Digital multi-meter or the DMM measures voltage, current and resistance. There are separate settings for AC and DC values. The switch settings that you select will define the function of the instrument at any time. Multi-meter also has the capability of measuring other quantities such as frequency etc. The function and the usage of each instrument are explained briefly below. You can consult the instrument manual for more details. Voltmeter: The difference in electric potential (voltage) between any two nodes in a circuit is measured by connecting the probes of the voltmeter to the two nodes in question. Note that this places the voltmeter in parallel with that portion of the circuit between the measurement points as shown in Figure 1. An ideal voltmeter would have an infinite resistance so that no current is conducted through it. Thus, it would not alter the voltages at the nodes to which the voltmeter is connected.

In reality voltmeters are never ideal, but the input impedance (or internal resistance) is so high that the meter functions in a nearly ideal manner. An AC voltmeter generally measures and displays the RMS value of the time-varying component of the voltage.

Figure 1 Voltmeter connections to measure electric potential at node 2 with respect to node 0

Ammeter: Ammeters measure the flow of charge through a branch of a circuit. The meter must be inserted into the current stream, in series with the component or circuit through which the current is flowing, as shown in Figure 2. An ideal ammeter would have zero resistance so that no voltage is developed (dropped) across it when the current flows through it. Thus, according to KVL, this would

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Lab Manual of Circuit Analysis – I not affect the loop currents in the circuit being measured. An AC ammeter generally measures and displays the RMS value of the time-varying component of the current. Again, ammeters are not ideal and have some internal resistance (or input impedance), but this resistance is very small. NEVER connect an ammeter directly across a voltage source – the low resistance of the ammeter will act as a short circuit causing a large current to flow, damaging the meter.

Figure 2 Ammeter connections to measure current flowing through R3

Ohmmeter: An ohmmeter measures the net resistance of all components connected between its two probes. Ohmmeter works by forcing a small, known, and steady current to flow through the measurement probes and the element being measured. The voltage developed between the nodes connected to the ohmmeter is sensed, and (per Ohm's Law) the equivalent resistance, V/I, is displayed. When measuring the resistance of any circuit element, that element or elements must be isolated from the rest of the circuit, i.e., isolated from any component that can alter the small current delivered to the circuit by the meter or alter the voltage developed across the element of interest. For example, if the circuit itself contains any source of power, then potential difference between the probes will depend on the current supplied by the meter and the voltage or current supplied by the other source. Hence such a reading would be incorrect because the ohmmeter is influenced by the other source. In the worst case, the ohmmeter might even be damaged. Clearly the power sources must be disconnected, but other circuit components may also be a problem. In Figure-3 the meter is reading the resistance of R2 in parallel with R3.

Measuring the resistance of R3 alone would require disconnecting R3 from either node 2 or node 0. This eliminates the influence of R2 on the current delivered to R3 by the meter. Note that an ohmmeter measures only the resistance, not the complex impedance, of a circuit or element. The resistance of an ideal inductor is zero, and the resistance of an ideal capacitor is infinite.

Figure 3 Ohmmeter is connected in parallel. An ohmmeter connected as shown here will measure the net resistance between nodes 2 and 0 of the circuit

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Lab Manual of Circuit Analysis – I POWER SUPPLY DC power supply is used to generate either a constant voltage or a constant current. That is, it may be used as either a DC voltage source or a DC current source. DC means constant with respect to time. If the C.C. indicator is lighted, the corresponding variable power supply is producing a constant current. Similar is the case for the C.V. indicator which means that a constant voltage is being produced. The CURRENT/ VOLTAGE knob is used to set the output current / voltage for the variable power supply respectively. The output terminals for the power supply allow you to plug in the test leads as follows: The red terminal on the right is the positive polarity output terminal. It is indicated by a plus (+) sign above it. The black terminal on the left is the negative polarity output terminal. It is indicated by a minus ( – ) sign above it. The green terminal in the middle is the earth and chassis ground. 





Figure 4 Power supply

The tracking buttons on the power supply select the test mode of the instrument. The power supply features two tracking modes: series and parallel. If both push-button switches are disengaged (out), the two variable power supplies operate independently. If the left switch is pushed in, the instrument operates in series mode. If both switches are pushed in, the instrument operates in parallel mode. In series mode, the master power supply controls the voltage for both power supplies, which can then range from 0 to 60 V. In parallel mode, the master power supply controls both the voltage and the current for both power supplies. The current can then range from 0 to 6 A. There is another fixed 5V/ 3A output knob to provide a constant voltage of 5V. The overload indicator lights when the current on the 5 V FIXED power supply becomes too large. BREADBOARD Most of the electrical circuits built in the laboratory will be wired on "solder less breadboards" or circuit boards. The term "breadboard" originated in the early days of electronics when temporary circuits were literally wired on wooden boards about the size commonly used for slicing bread.

A typical breadboard is shown in Figure 5. Breadboard consists of a series of holes, or sockets, into which wires or leads of electrical components can be placed. There are strips of spring metal

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Lab Manual of Circuit Analysis – I underneath the plastic that serve as "tie-points", connecting individual sockets into groups. All sockets in a group will have the same electrical connection. The rectangular groups shown in Figure 5 illustrate the socket groupings or tie-points on the breadboard. The tie-points along the outside of the breadboard are referred to as “busses”. These busses provide a mechanism for distributing signals along the entire breadboard, i.e. making it easy to connect to the signals from anywhere on the breadboard.

Figure 5 Physical breadboard

Internal electrical connections in the breadboard are shown in Figure 6. Figure 7 shows some sample connections on breadboard.

Figure 6 Equivalent internal electrical connections on breadboard

Figure 7 Sample connections

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Lab Manual of Circuit Analysis – I POST LAB QUESTION:

Write a detailed report on the wiring of a circuit on the breadboard. Give examples of correctly connected components and of typical connection mistakes. Explain the internal connections of the breadboard as well.

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OBJECTIVE: To become familiar with the resistor color code and use of a multi-meter to measure resistance To prove that current (I) and voltage (V) are linearly proportional in a DC circuit. To show  that the proportionality constant is equal to the resistance R of the circuit Determine experimentally the maximum voltage that may be applied to a resistor of given  power rating 

EQUIPMENT: Digital multi-meter (DMM) with probes  5 Resistors each of different values (4-Band, 5-Band, Alpha-numeric)  DC power supply 10 V, 6V  Resistors: 120 Ω, 1 kΩ, 2.2 kΩ, 3.9 kΩ, 4.7 kΩ  Light Bulbs: 6.2V 0.5A 

BACKGROUND:

Measurement of resistance is a very common task. Ohmmeter can be used to detect a faulty component in a circuit. Also it can be used more specifically to determine the correct operation of lamps, fuses, switches and any number of other components. In this lab experiment you will use DMM (ohmmeter) to check whether a number of resistors lie within the tolerance specified by their color codes. You should also take this opportunity to get familiar with the ohmmeter portion of your DMM. Most DMMs include an ohmmeter range, usually selectable by a switch, which should be set to the ohms (Ω) position. Analog voltmeters usually have to be calibrated on each range. Though no power will be connected to your resistors in this experiment, in actual circuits, the power must always be turned off before you bring your probes into contact with the component under test. RESISTOR COLOR CODING AND STANDARD VALUES

6-band color code

5-band color code

4-band color code

3 digits, multiplier, tolerance, temperature coefficient

3 digits, multiplier, tolerance

2 digits, multiplier, tolerance

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Lab Manual of Circuit Analysis – I RESISTOR COLOR CODES

Tolerance[5]

Temperature coefficient[6]

10

± 1%

100ppm

2

100

± 2%

50ppm

Orange

3

1k

15ppm

Yellow

4

10k

25ppm

Green

5

100k

± 0.5%

Blue

6

1M

± 0.25%

Violet

7

10M

± 0.1%

Grey

8

White

9

Gold

0.1

± 5%

Silver

0.01

± 10%

Color

Digits[1-3]

Multiplier[4]

Black

0

1

Brown

1

Red

None

± 20%

ALPHA-NUMERIC LABELING OF RESISTORS

Generally on larger power resistors, the resistance value, tolerance, and even the power (wattage) rating are printed onto the actual body of the resistor instead of using the resistor color code system. Because it is very easy to "misread" the position of a decimal point or comma especially when the component is dirty, an easier system for writing and printing the resistance values of the individual resistance was developed. A type of marking with three or four character label that uses both digits and letters was introduced as alpha-numeric labeling . Two or three digits and one of the letters R , K , or M are used to identify a resistance value. The letter is used to indicate the multiplier, and its position is used to indicate decimal point position. The suffix letters "K" is for thousands or kilo ohms, the letter "M" for millions or mega ohms while the letter "R" is used where the multiplier is equal to 1; e.g. BS 1852 Codes for resistor value for 0.47Ω would be R47 or 0R47, for 4.7kΩ it would be 4k7 and for 1.0MΩ it would be 1M0Ω. Tolerance Letter Coding for Resistors:

Tolerance Codes for Resistors (±) B = 0.1% C = 0.25% D = 0.5%

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F = 1% G = 2% J = 5% K = 10% M = 20%

Also, when reading these written codes one has to be careful not to confuse the resistance letter k for kilo ohms with the tolerance letter K for 10% tolerance or the resistance letter M for mega ohms with the tolerance letter M for 20% tolerance. NUMERIC LABELING OF RESISTORS

In numeric labeling, the first two digits represent the first two numbers of the resistance value with the third digit being the multiplier, either x1, x10, x100 etc. For example: “392” = 39 x 100 ohms = 3.9 k Ω “103” = 10 x 1000 ohms = 10 k Ω “4754” = 475 x 10,000 ohms = 4.75MΩ

VARIABLE RESISTOR

The variable resistor is a three-terminal device. Any of the two terminals (let say terminal A and terminal B) have a fixed resistance between them, which is the total resistance. The third terminal (let say terminal W) acts as a moving contact (wiper). We can vary the resistance between W and A, or between W and B by moving the contact. It is applied in an electronic circuit for adjusting circuit resistance to control voltage or current of that circuit or part of that circuit. The variable resistor used to divide voltage is called a potentiometer. The variable resistor used to control current is called a rheostat. The electrical resistance is varied by sliding a wiper contact along a resistance track. Sometimes the resistance is adjusted at pre-set value as required at the time of circuit building by adjusting screw attached to it and sometimes resistance can be adjusted as when required by controlling knob connected to it.

Variable resistor symbol

Connection leads of a Variable Resistor Figure 1

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Figure 2 Variable Resistor: side view and top view

STANDARD RESISTOR VALUES 20%

10%

5%

20%

10%

5%

1.0

1.0

1.0

3.3

3.3

3.3

1.1 1.2

3.6

1.2

3.9

1.3 1.5

1.5

1.5

4.3 4.7

4.7

1.6 1.8

2.2

1.8

2.2

5.6

5.6 6.2

6.8

6.8

2.4 2.7

4.7 5.1

2.0 2.2

3.9

2.7 3.0

6.8 7.5

8.2

8.2 9.1

Note: These values can be in multiples of 1x, 10x, 100x, 1000x, etc.

PROCEDURE:

1. The color code on each resistor defines the nominal value about which the tolerance is defined. The nominal value is that value of resistance that the resistor would have if its tolerance is 0 percent. Use the color code to determine the nominal value in each case and record them in Table-I. 2. Record the tolerance and the resulting theoretical maximum and minimum values for each resistor. 3. Using DMM measure and record the actual value of each resistor, and check whether or not this value falls within the tolerance. Resistors are rarely out of tolerance; if one appears to be, it could be an error in DMM measurement. Be sure not to touch probes with your fingers when measuring resistance, since body resistance affects the readings.

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Lab Manual of Circuit Analysis – I TABLE - I (4-Band Resistors)

R 1

R 2

R 3

R 4

R 5

R 2

R 3

R 4

R 5

Nominal (value)

Tolerance

Maximum

Minimum

Measured (DMM)

TABLE - II (5-Band Resistors)

R 1 Nominal (value)

Tolerance

Maximum

Minimum

Measured (DMM)

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Lab Manual of Circuit Analysis – I TABLE - III (Alphanumeric Resistors)

R 1

R 2

R 3

R 4

R 5

Nominal (value)

Tolerance

Maximum

Minimum

Measured (DMM)

POST LAB QUESTIONS:

1. A 2.7kΩ, 10% resistor has a maximum value of a) 2.57kΩ b) 2.43kΩ c) 2.84kΩ d) 2.97kΩ 2. The minimum value that the resistor in question1 could be a) 2.57kΩ b) 2.43kΩ c) 2.84kΩ d) 2.97kΩ 3. The first three bands in resistor are colored brown, black and red. The resistance is measured and found to be 1050Ω. If the resistor is guaranteed to be within its tolerance specification, what tolerance might be indicated by its fourth (tolerance) band? a) 5% b) 10% c) 20% d) Any of these 4. A resistor having the colored bands blue-grey-orange-silver has minimum value: a) 61.2kΩ b) 68kΩ c) 63kΩ d) 64.6kΩ 5. A resistor is required for an application whose value can be no less than 7.1kΩ and no more

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Lab Manual of Circuit Analysis – I than 7.9kΩ. Determine the standard value and tolerance of the resistor you could use. Explain?

6.

A resistor having the colored bands blue-grey-orange-gold-red has maximum value: a) 66.93Ω b) 69.67Ω c) 68.3Ω d) 67.9Ω

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BACKGROUND:

OHM’S LAW Ohm’s Law is the basis of many electrical circuit calculations and is one of the most important theories you will learn: V = IR. The purpose of this experiment is to verify Ohm’s Law, which in words, simply says that the current through a resistor is proportional to the voltage across it. The way in which we accomplish this is to measure the voltage across and current through a known resistor for several different pair of values. We can then plot the data on a graph, and if the relationship is truly linear it should yield a straight line. When graphing data such as those obtained in this experiment, either the x or y-axis can be chosen to display the voltage or current values. When the y-axis is chosen as the voltage axis, and the x-axis as the current axis, we say that we are plotting V versus I. the slope of the line ∆V/∆I should be equal to the resistance R of the resistor. If on the other hand, current is plotted on the y-axis, and voltage along the x-axis, then slope of the line ∆I/∆V is equal to the conductance G of the resistor. In this experiment you will plot I in mA versus V in volts, and therefore the slope will be the conductance of the resistor. When plotting a straight line on a graph such as this, it is important that you draw the best possible straight line that you can through the data points. POWER IN DC CIRCUITS Electronic devices and circuits require energy to operate. Power is a measure (in watts) of the energy (in joules) consumed by a given device in one second. For a resistor, three equations will yield the power dissipated: P = IV, P = V²/R and P = I²R. In this experiment, you will verify these formulae and plot graphs of the power versus the current, and then power versus the voltage. The resulting curves are parabolas, and the equations of the curves are called quadratic. POWER RATING The power in a resistor is converted to heat; the resistor therefore heats up. If the resistor becomes too hot, it may “fall out” of tolerance; worse still, it could ignite and cause a fire. Therefore, it is important to be aware of resistor ’s power rating. The power rating of a resistor is the value (in watts) that must not be exceeded if the resistor is to remain within the manufacturer’s specification of ohmic value and tolerance. The power rating is a function of several variables, one of which is physical size. For example, carbon composition resistors appear in ¼ W, ½ W, 1 W, etc sizes.

The power rating actually determines the maximum voltage and current that the resistor can safely withstand. For example, if we call the power rating Pr , then we can determine the maximum safe voltage using the dc power formula,

Pr =  . Solving for , we get:  = √  × 

where Pr is the power rating of the resistor.

 × , we can solve for the maximum safe current I  = 

Similarly, using

max as

follows:

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 =  ⁄

As the power rating increases, the resistor is typically larger in volume and therefore surface area. LIGHT BULBS Light bulbs have a very simple structure. At the base, they have two metal contacts, which connect to the ends of an electrical circuit. The metal contacts are attached to two stiff wires, which are attached to a thin metal filament. The filament sits in the middle of the bulb, held up by a glass mount. The wires and the filament are housed in a glass bulb, which is filled with an inert gas, such as argon.

The filament in a light bulb is made of a long; incredibly thin length of tungsten metal. Tungsten is used in nearly all incandescent light bulbs because it is an ideal filament material. A metal must be heated to extreme temperatures before it will emit a useful amount of visible light. Most metals will actually melt before reaching such extreme temperatures. Light bulbs are manufactured with tungsten filaments because tungsten has an abnormally high melting temperature.

Figure 1

Figure 2

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Figure 3

PROCEDURE:

1. With the DMM, measure the resistance of 1 kΩ, and record this measured value in Table - I. 2. With the power supply initially off, connect the circuit in Figure 1 with R = 1 kΩ. 3. Switch on the power supply. Beginning at 0V, increase the voltage in 1 V steps up to 6V. Measure and record resulting current in Table - I. 4. Repeat this with a 6.2V light bulb as shown in Figure 3. Record this data in Table - II. 5. Use the voltage and current data together with the measured value of R to complete the rest of Table - I and Table - II for the power P. All power quantities should agree. 6. Calculate the maximum safe voltage that can be applied across the resistor mentioned in Table - III, without exceeding its power rating. 7. Calculate the maximum safe current to which the maximum safe voltage corresponds. Record this in Table - III. 8. Replace the resistor in your circuit in Figure 1. Increase the voltage until you reach maximum permissible value you calculated above. Carefully touch the resistor. Why does it feel hot? 9. Exceed the voltage by maximum permissible value and see what happens? 10. Repeat the above procedure for and resistors and complete Table - III.

1⁄4 

1⁄4 

1⁄2  1 

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Lab Manual of Circuit Analysis – I TABLE – I (For Resistor)

Vs(V)

1

2

3

4

5

6

I (mA) P = VI (mW) P = I2R(mW) P = V2/R (mW) R=1k Ω

R(measured) =

TABLE – II (For Light Bulb)

Vs(v)

1

2

3

4

5

6

I (mA) P = VI (mW) P = I2R(mW) P = V2/R (mW) TABLE – III

Power rating

Ohmic Value (Measured)

Maximum safe voltage Calculated

Measured

Maximum Safe Current (Calculated)

1⁄4W R = 0.56Ω, 1⁄2W R = 120Ω,

R = 390Ω, 1W

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Lab Manual of Circuit Analysis – I POST LAB QUESTIONS:

1. On the same scale and axis, plot graphs of current, I in mA, versus voltage, V in volts, for resistor and bulb using the data of Table I and Table II. (Assign V to x-axis and I to the yaxis.) Draw the best straight lines possible through each set of data. Determine the slope of each line; it should be equal to the conductance, G of the resistor in consideration. You can then verify the resistance of each resistor by taking the reciprocal of conductance. Do this for each set of data and record this in a table. 2. Plot graphs of power versus current and power versus voltage for the 1kΩ resistor. Include all these gra phs and tables in the ‘measurements’ section of your report. Comment on the several aspects of the behavior shown in the graphs. 3. Explain your observation about the non-ohmic behavior of light bulbs? Explain the conditions for a device to obey Ohm’s Law, and why light bulbs do not obey Ohm's Law? How is this non-ohmic behavior different from ohmic behavior?

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OBJECTIVE: To verify that the total resistance in a series connected circuit is the sum of individual  resistances 

To verif y Kirchhoff’s voltage law for DC circuits

EQUIPMENT: DC power supply  DMM   Resistors: 1kΩ, 2.2kΩ, 3.9kΩ, 4.7kΩ Light Bulbs: 6.2V 0.5A  BACKGROUND: SERIES RESISTIVE CIRCUITS When resistors are connected in series, the current that will flow is calculated from the knowledge of the total resistance. The total resistance in this case is simply the sum of individual resistors. For example in case of two resistors, total resistance R T is:

 =  +  By knowing the total resistance, the voltage required for the desired current or the current resulting from an applied voltage can easily be calculated.

KIRCHHOFF’S VOLTAGE LAW Kirchhoff’s voltage law states that the algebraic sum of voltages around a closed path is equal to zero. With regard to Figure-1, this means that

or

 + + +3 + = 0  =  +  +3 +

where V1 is the voltage across R 1 ,V2 is the voltage across R 2 ,V3 is the voltage across R 3 and V4 is the voltage across R 4. By connecting such a circuit and measuring the voltages, it should be possible to verify this relationship. In performing an experiment of this nature, you should remember that each measurement is subject to some error, and when you sum such measurements, the errors may add and produce what may appear to be an inconsistency. The important thing is that, if the instruments are perfect, we should obtain a sum of voltage drops exactly equal to the source voltage.

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Vs

V1

V2

R 1

R 2

10V

R 3

V3

R 4

V4 Figure 1

V1

V2

L1

L2

6V

L3 I

V3

L4

V4

Figure 2

PROCEDURE:

1. Using the measured values of the given resistors, use the formula for R T to determine the expected total resistance for each of the connections in Table - I. Note that an additional resistance is added each time you move to the right in the table. 2. Insert a 4.7 kΩ resistor in your breadboard and connect in series the other resistor, making up the first combination in Table - I and observe the reading. 3. Continue to add the remaining three resistors in the sequence described in the table, one at a time, recording the reading for each combination. The resistance should continue to increase until you have the value in the last column of the table. 4. Connect the circuit as shown in Figure 1. 5. Using the measured value of total resistance, calculate and record current “I” that would result from the source voltage applied. 6. Use the calculated current and resistance values to calculate the voltage drop across each of the resistors. Record these in the ‘Calculated Voltages’ row in Table - II. 7. Add the calculated voltage drops, and record this under the VSUM heading in the table. They should sum to 10V. 8. Measure the voltage across each resistor, and record these in the ‘Measured Voltages’ row in Table - II. 9. Add the measured voltages from the previous step and enter their sum in the appropriate area

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Lab Manual of Circuit Analysis – I of the table. 10. Now, connect the circuit as shown in Figure 2. 11. Measure the voltage across each bulb in the circuit, and record these in the ‘Measured Voltages’ row in Table - III. Add the measured voltages from the previous step and enter their sum in the appropriate area of the table. Also measure the total current flowing in the circuit. TABLE - I (Series Combination)

Total Resistance of Combination R T

4.7 + 3.9

Combination (kΩ)

4.7 + 3.9 + 2.2

4.7 + 3.9 + 2.2 + 1

Calculated Resistance (kΩ)

Measured Resistance (kΩ)

TABLE - II (KVL for resistors)

Calculated voltages using IR relation Measured Voltages

VSUM

ICALC (mA)

V1

V2

V3

V4

V1

V2

V3

V4

VSUM

IMEAS (mA)

V2

V3

V4

VSUM

IMEAS (mA)

TABLE - III (KVL for light bulbs)

V1 Measured Voltages

POST LAB QUESTIONS:

1. An ammeter connected in series with three resistors reads an electric current of 2A. What is the electric current through the resistor R 3?

a) 1 A

b) 2 A

c) 3 A

d) 4 A

e) 5 A

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2. Connect three light bulbs in series with a voltage source (ranging 1V to 6V). What will happen if you remove one of the light bulbs from the circuit? Explain your answer in terms of bulb brightness and current flowing through the circuit. Draw the circuit schematics as well to support your solution.

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OBJECTIVE: To verify that the total resistance in a parallel connected circuit is given by the reciprocal rule  

To verify Kirchhoff’s current law for DC circuits



To learn to apply KCL, KVL together in a series parallel combination circuit

EQUIPMENT: DC power supply  DMM   Resistors: 1kΩ, 2.2kΩ, 3.9kΩ, 4.7kΩ BACKGROUND: PARALLEL RESISTIVE CIRCUITS In a parallel circuit, each component has the same voltage drop across it, and the currents through each resistor are independent of one another. As more resistors are added in a parallel circuit, each one takes its own current from the supply independently of others. As a result, the total current increases. The power supply sees this as a reduction in the total resistance R T of the circuit. In this experiment we will determine the effect of adding more resistors to a parallel connection using ohmmeter. We will then verify the total resistance formula for parallel resistors, which is

1 = 1 + 1 + …+ 1     We will then verify the simple product over sum rule for the special case of two resistors in parallel:

  =  +  R T will always be less than the smaller of the resistances in the parallel circuit.

KIRCHHOFF’S CURRENT LAW Kirchhoff’s Current Law states that the sum of the currents into a junction is equal to the currents out of that junction. With reference to Figure-1, this implies that

 =  + +3 +

Page | 26


Figure 1

PROCEDURE: PART A 1. Measure the actual values of each of the resistors using DMM and note down these values in Table - I. 2. Using the measured values of these resistors, use the formula (the reciprocal rule) for R T to determine the expected total resistance for each of the connections in Table - II. Note that an additional resistance is added each time you move to the right in the table. 3. Insert a 4.7 kΩ resistor in your breadboard and connect in parallel the other resistor, making up the first combination in Table - II and observe the reading. 4. Continue to add resistors, one at a time, the remaining three resistors in the sequence described in the table, recording the reading for each combination. The resistance should continue to decrease until you have the value in the last column of the table. 5. Connect the circuit shown in Figure 1. 6. Measure branch currents I1, I2, I3and I4 recording all data in Table - III. 7. Also measure currents IT, I234 and I34 and record in Table - III. 8. Complete the remainder of the table by calculating each of the sums I3 + I 4, I2 +I 3+I 4, IT etc. The calculated values should compare well with the corresponding measured currents. TABLE - I (Measured Values of Resistance)

Nominal values

Resistance Values (kΩ) 2.2 3.9

1

4.7

Measured values TABLE - II (Parallel Combination)

Total Resistance of Combination R T

Combination (kΩ)

4.7 || 3.9

4.7 || 3.9 || 2.2

4.7 || 3.9 || 2.2 || 1

Calculated Resistance (kΩ) Measured Resistance (kΩ) || means “in parallel with”

Page | 27

Lab Manual of Circuit Analysis – I TABLE-III (KCL)

I1

Measured Currents (mA)

I2

I3

I34

I4

I34

I234

I234

IT

IT

Calculated Currents by KCL (mA)

PART B V5 I5

V6

1kΩ

V3

1.2kΩ

I3

V4

I6

2.2kΩ

V1

3.3kΩ

8.2kΩ

10V

I4

I1 5.6kΩ

Is

V2

I2

Figure 2

1. Implement the circuit given in Figure 2 above and measure all the voltages and currents. 2. Record the values in Table - IV given below. 3. Using these measured values, calculate the quantities given in Table - V using both KCL and KVL. TABLE - IV (KCL & KVL)

Measured Voltages Measured Currents (mA)

V1

V2

V3

V4

V5

V6

Is

I1

I2

I3

I4

I5

V5 + V6

V1 + V2

TABLE - V (KCL & KVL)

I6

V3 + V1 + V2 - V6 -V5

I4 + I5

Calculated Values

Page | 28

Lab Manual of Circuit Analysis – I POST LAB QUESTIONS:

1. Two resistors R 1 = 6Ω and R 2 = 12Ω are connected in parallel to each other and in series to R 3= 2Ω. An ammeter measures an electric current of 3A flowing though resistor R 3. What is the net voltage applied to the circuit?

a) 6 V

b) 12 V

c) 18 V

d) 24 V

e)36 V

2. What is the current through the resistor R 2 = 12Ω used in the previous problem? b) 6 A

b) 1 A

c) 3 A

d) 5 A

e) 7 A

3. The resistors in each of the circuits shown below each have the same resistance. Which of the following gives the circuits in order of increasing total resistance?

a) P, Q, S

b) Q, P, S

c) S, Q, P

d) P, S, Q

4. Connect three light bulbs in parallel with a voltage source (ranging 1V to 6V). What will happen to the overall current in the circuit and the brightness of the light bulbs if you remove one of the light bulbs from the circuit? Explain your answer in detail. Draw the circuit schematics as well to support your solution. 5. Briefly explain, with proper reasoning, whether you think the appliances in a home kitchen are wired with series or parallel connections.

Page | 29


OBJECTIVE: 

Learn to perform DC analysis using PSpice

BACKGROUND:

1. SPICE stands for Simulation Program with Integrated Circuit Emphasis 2. SPICE was originally developed at the Electronics Research Laboratory of the University of California, Berkeley (1975). As the name implies, SPICE was originally developed for designing integrated circuits. However, it can be used to analyze discrete circuits as well. 3. PSpice is a PC version of SPICE (Cadence) and HSpice is a version that runs on workstations and larger computers. 4. PSpice is case insensitive i.e. typing ‘r’ or ‘R’ will not be any different in PSpice. 5. All analysis can be done at different temperatures. The default temperature is 27˚C. 6. PSpice can do several types of circuit analysis. Here are a few: DC analysis: Calculates the DC transfer curve. AC analysis: Calculates the output as a function of frequency. A bode plot is generated.   

  

Transient analysis: Calculates the voltage and current as a function of time when a large signal is applied. Noise analysis: Analyzes noise at the input or output of the circuit. Fourier analysis: Calculates and plots the frequency spectrum. A PSpice circuit can contain components like AC & DC voltage and current sources, Resistors and Variable Resistors, Capacitors and Variable Capacitors, Inductors and Variable Inductors, Operational amplifiers, Switches, Diodes, Bipolar transistors, Transformers etc.

GETTING STARTED WITH PSPICE: Go to “Start Menu”, then “Programs”, then “PSpice Student” and then “Schematics”

Page | 30

Lab Manual of Circuit Analysis – I The following schematic editor window will appear:

DRAWING THE CIRCUIT: Following is the circuit we will use to begin our understanding about how PSpice works:

Getting the Parts: 1. The first thing is to get some or all of the parts you need and place them on your “Schematics Workspace”. This can be done by going to “Draw” and selecting “Get New Part” or by clicking

I.

or by pressing Ctrl+G. on the “get new parts” button 2. Once this box is open, select a part that you want in your circuit. This can be done by typing in the “Part Name” or the first alphabet of the part name, or scrolling down the list until you find it.

Page | 31


3. Upon selecting your parts, click on the “Place” button. Then click where you want it to be placed on the schematics workspace. Don't worry about putting it in exactly the right place, it can always be moved later. Once you have all the parts you think you need, close that box. You can always open it again later if you need more parts. II.

Get Recent Part Bin: PSpice keeps track of the most recent parts used and lists them in the Get Recent Part bin. You can save time by selecting items from this bin. Simply double click the item then place as described above.

III.

Libraries in PSpice: The parts in PSpice are arranged in the form of libraries. You do not have to worry about including the concerned libraries before you actually select Parts because PSpice Schematics Version 9.1 automatically includes all the libraries, when the “Get Part” button is pressed. Few common libraries are: analog.slb contains resistors (R), capacitors (C), inductors (L), dependent sources (E, F, G  and H) etc. 

source.slb contains various independent voltage and current sources.



port.slb contains elements such as ground etc.

Hands on Exercise 1 Get all the parts you need to draw the circuit given, on your Schematics workspace?

Find out what specific libraries contain those parts? IV.

Placing the Parts: You should have most of the parts available in your schematics workspace that you need at  this point.

Page | 32






 

To put them in the places that make the most sense (usually a rectangle works well for simple circuits), just select the part and drag it where you want it. To rotate parts so that they will fit in your circuit nicely, click on the part and click Edit "Rotate" or simply click "Ctrl+R" To flip them, click Edit "Flip" or "Ctrl+F". If any parts are left over, just select them and press "Delete".

Hands on Exercise 2 Place the parts that you have selected in Exercise 1 in a proper order on the Schematics workspace. V.

Connecting the Circuit: Now that your parts are arranged well, you'll have to connect them with wires. 



 

 



Go up to the tool bar and Go to "Draw" and select "Wire", or Select "Draw Wire" , or Press "Ctrl+W" With the pencil looking pointer, left click on one end of a part. When you move your mouse around, you should see dotted lines appear. Drag the mouse to the next part in the circuit. This will attach the other end of the wire to the next part that you want to connect and then left click again to release the wire. Repeat this until your circuit is completely wired. If you want to make a node (to make a wire go more than one place), click somewhere on the wire and then click to the part (or the other wire). Or you can go from the part to the wire. To get rid of the pencil, Right Click on the mouse. If you end up with extra dots near your parts, you probably have an extra wire, select this short wire (it will turn red), then press "Delete". If the wire doesn't look the way you want, you can make extra bends in it by clicking in different places on the way (each click will form a corner).

Hands on Exercise 3 Connect the parts using the wire that you have placed in Exercise 2. VI.

Changing the Name of the Part: You probably don't want to keep the names R 1 B , B R B 2B etc., especially if you didn't put the parts in the most logical order. To change the name, double click on the present name (C1, or R1 or whatever your part is), then a box will pop up (Edit Reference Designator). In the top window, you can type in the name for the selected part.

Please note that if you double click on the part or its value, a different box will appear. Page | 33


Hands on Exercise 4 Change the names for the parts in your circuit to the names that were shown in the original figure of the circuit given. VII.

Changing the Value of the Part: To change the value of the part (e.g. by default the value of all the resistors is 1K ohms), you can double click on the present value and a box called "Set Attribute Value" will appear. Type in the new value and press OK.

If you double click on the part itself, you can select VALUE and change it in this box.



The list of units as PSpice accepts them is as follows: F,f femto 10 -15 P,p pico 10 -12 N,n Nano 10 -9 U,u Micro 10 -6 M,m Milli 10 -3 K,k Kilo 10 +3 MEG, meg Mega 10 +6 G,g Giga 10 +9 T,t tera 10 +12

Hands on Exercise 5

Change the values for the parts in your circuit to the values that were shown in the original circuit given. SAVING Choose a name that will help you identify which problem this is. To save the circuit, click on the

save button

on the tool bar (or any other way you normally save files).

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Lab Manual of Circuit Analysis – I ELECTRIC RULE CHECK Perform an electrical rules check to be sure your circuit schematic will simulate properly. (Analysis menu, Electrical Rule Check ). If all goes well, you will see a small window flash on the screen and nothing else. If no errors are reported in your schematic, proceed to the next step. If there are errors, fix them now. Hands on Exercise 6 Do the Electrical Rule Check and Save the circuit that you have drawn? SIMULATING THE CIRCUIT Now you will simulate your circuit. Do this by going to the Analysis menu and choosing  Simulate or Press on the Toolbar

When simulation is done, a new PSPICE window will appear. Look at the Lower Left corner of the window for the results of simulation. This is what you are going to see:

  



What does PSpice mean by Floating Nodes?



Why was the Simulation Aborted?

I.

II. 







Making Sure You Have a GND: This is very important. You cannot do any simulation on the circuit if you don't have a ground. If you aren't sure where to put it, place it near the negative side of your voltage source. Reading the Output:

Select View in this window, and examine Output File. Scroll down towards the bottom of the file until you come to a series of headings that say Node Voltage. The voltage at each circuit node should be reported. Identify which node voltages are associated with which circuit elements and note them down. Scroll further down the output file. Note that the source current and total power dissipation for the circuit is also reported. The voltage source current is reported as -2.500E-04 A.

Page | 35

Lab Manual of Circuit Analysis – I Hands on Exercise 7 Find out the value of the current in the circuit manually by using the analytical methods you have learned in the Circuits Analysis-I class so far. Check if the answer agrees with PSpice analysis? III.  



 

 

Netlists: A netlist is the original way we interacted with SPICE.

The netlist contains description of the circuit that describes the parts of the circuit and the nodes with which they are connected. When PSpice creates a circuit description from your schematic, it numbers nodes, and for each component, lists the nodes to which it is connected as well as the value of the component. For example, Node 1 is designated $N001, node 2 as $N002, etc. These designations do not appear on your schematic screen but instead they reside in a file as a “netlist”. To view the netlist, click Analysis, then Examine Netlist. In the netlist, the first end of a component is connected to the first indicated node. For Example R_Ra $N_0001 $N_0002 1k means that the first end of Resistor Ra is connected with Node1 and the other is connected with Node2.

Hands on Exercise 8 Examine the Netlist for your circuit and compare these node numbers with the circuit you have drawn. PSPICE FILE EXTENSIONS PSpice file extension

Description

.SCH

Schematics diagram file.

.CIR

Control file generated by Schematics. ASCII.

.NET

Netlist (circuit description) generated by Schematics. ASCII.

.ALS

Alias file generated by Schematics. Needed for PSpice simulation.

.PRB

Control file for Probe plots. Contains settings from last run, scaling, etc.

.DAT

Complete output file generated by PSpice; input to Probe. Not readable; Normally a large file

.OUT

Readable ASCII output file from PSpice simulation. Contains dc levels, etc.

SHORTCUT TO FIND BIAS VOLTAGE AND CURRENT FROM THE TOOLBAR

You can use the ‘Enable Bias Voltage Display’ or ‘ Enable bias current display’ buttons on the Schematics workspace toolbar to find out the Bias Voltage and Currents directly instead of reading them down from the output file. Page | 36


Hands on Exercise 9 Find out the bias voltages and currents for the circuit you have drawn using the above mentioned buttons on the Schematic Window Toolbar. PRINTING To print your schematic circuit, you must first use your mouse to make a rectangle around your

circuit; this is the area of the page that will be printed. Then select print. (You can also select

).

DEPENDENT SOURCES

Voltage Controlled Voltage Source

Voltage Controlled Current Source

Current Controlled Current Source

Current Controlled Voltage Source

A controlled voltage source is one whose output voltage is controlled by the value of a voltage or current elsewhere in the circuit. A current controlled voltage source obeys the relation ,

 =   where ‘I’ is the controlling current and k is a constant having the units of resistance:  = ⁄ volts Page | 37

Lab Manual of Circuit Analysis – I per ampere, or ohms. Similarly, a controlled current source produces a current whose value depends on a voltage or a current elsewhere in the circuit. A voltage-controlled current source obeys the relation ,

 = ⁄

 =  

where V is the controlling voltage and k has the units of conductance: amperes per volt, or Siemens. All four types of controlled sources, voltage-controlled voltage source, current-controlled voltage sources, voltage-controlled current sources, and current-controlled current sources, can be modeled in PSpice. Hands on Exercise 11 The circuit shown in Figure below has a current controlled voltage source with the gain of ‘3’.

This circuit can be constructed in PSpice using part “H” as shown below:

Click the part and enter gain =3. Save and simulate it.

Page | 38

Lab Manual of Circuit Analysis – I EXERCISES (a)

Find IO using PSpice in the circuit below:

Figure - exercise (a)

(b) Find VO using PSpice in the circuit below:

Figure - exercise (b)

(c) Find VO using PSpice in the circuit below:

Figure - exercise (c)

Page | 39

Lab Manual of Circuit Analysis – I (d) Find VO using PSpice in the circuit below:

Figure - exercise (d)

(e) Draw the following circuit in PSpice:

Figure - exercise (e)

i. ii. iii. iv. v.

Discuss the contribution of each voltage source in the above circuit (active/passive). Identify the nodes in the above circuit. Find out the node voltages Verify Kirchhoff’s current law at each node. Reverse the polarity of voltage source V2 to find out the change in node voltages and currents in each element. Does KCL still hold?

Page | 40

Lab Manual of Circuit Analysis – I (f) Find IX using current dependent current source in PSpice.

Figure - exercise (f)

(g) Find VX in the circuit given.

Figure exercise – (g)

POST LAB QUESTION:

Mathematically verify the PSpice voltage and current measurements for the circuits of exercise (e) and (g) used in lab work. Solve the circuits and make appropriate tables for comparison between the theoretical calculations and PSpice measurements. Discuss the benefits of PSpice usage as well.

Page | 41


OBJECTIVE: To understand how to use DMM to measure the resistance at different points in a complex  circuit To design a simple circuit using the equivalent resistance of a complex circuit   To understand the significance of resistor’s power rating during design To calculate and measure the unknown resistance between two points  EQUIPMENT: DC Power Supply 5-10V  DMM   Resistors: 2.2Ω, 22Ω, 3.3Ω, 5.6Ω, 4.7Ω, 10Ω (two), 150Ω

Figure 1

1. Implement the given circuit, calculate and measure the following: R ab , R cd ,R de ,R cf ,R fe ,R bf and R ac TABLE - I

Unknown Resistance (Ω)

Calculated (Ω)

Measured (Ω)

R ab R cd R de R cf R fe R bf R ac

Page | 42


Figure 2

2. Calculate and measure R ab for the circuit given above and note down the readings in Table-II below. TABLE - II

Calculated (Ω)

Unknown Resistance

Measured (Ω)

R ab 3. Design a circuit, in black box, with the following requirements:

Black Box

5V

Figure 3

a) Equivalent resistance of the black box is R ab as calculated for the circuit in Figure 1. b) Input voltage (voltage supplied to black box) is 5V as shown in Figure 3 above. Use only c)

1⁄4  resistors. Design should be safe i.e. not even a single resistor should burn out or get damaged.

Page | 43


OBJECTIVE: To verify voltage and current divider theorem  EQUIPMENT: DC Power supply 5-10V  DMM  Resistors: 1kΩ, 2.2k Ω, 4.7k Ω, 5.6kΩ, 15kΩ  BACKGROUND: CURRENT DIVIDER THEOREM (CDR): The current divider theorem allows us to calculate the magnitudes of the currents in a parallel circuit, using only the total current and the resistor values. It is particularly useful when the circuit is driven by a constant current source as opposed to a constant voltage source. The formula for the current in a specific resistor in a parallel circuit in which the total current IT entering the junction is known, can be written as:





 =   where

 is the equivalent resistance of the parallel resistive circuit.

VOLTAGE DIVIDER THEOREM (VDR): Voltage dividers find many applications in electronic circuits. The requirement for voltages of different values often arises and is normally accomplished by a voltage divider circuit. The formula for the voltage in a specific resistor of a series circuit when the total voltage applied is known can be written as:







 =   where

 is the equivalent resistance of the series resistive circuit.

In this experiment, we will verify the current divider and voltage divider theorem by adjusting the source for a specified total voltage and measuring the individual resistor voltage and current. Remember that the resistor tolerance will affect your results.

Page | 44

Lab Manual of Circuit Analysis – I PROCEDURE: 1. Use current divider rule and voltage divider rule only to calculate and measure the current through and voltage across each resistor in the circuit given below. Fill Table-I and Table-II accordingly.

Figure 1

TABLE - I Calculated Data

Resistance values (Ω) Calculated current values (mA)

Calculated voltage Values (V)

2.2k

1k

5.6k

4.7k

15k

IT

I1

I2

I3

I4

V1

V2

V3

V4

V5

2.2k

1k

5.6k

4.7k

15k

IT

I1

I2

I3

I4

V1

V2

V3

V4

V5

TABLE - II Measured Data

Measured resistance values (Ω)

Measured current values (mA)

Measured voltage values (V)

Page | 45

Lab Manual of Circuit Analysis – I 2. Design a circuit, in black box, with the following requirements:

Vin

Black Box

Vout

, (voltage supplied to black box) is between 0 - 30V. b) Output voltage,  should be 2⁄5  . c) Use only 1⁄4  resistors. Design should be safe; i.e. not even a single resistor should burn a) Input voltage,

out or get damaged.

POST LAB QUESTIONS:

1. Compare between the practical and theoretical results? 2. When do we use VDR and CDR?

Page | 46


OBJECTIVE:  To verify Thevenin’s theorem in a simple DC circuit EQUIPMENT:   

Digital multi-meter (DMM) DC Power Supply (10-12 V) Resistors: 1kΩ, 3.3kΩ(two), 6.8kΩ,10kΩ, 2.2kΩ,4.7kΩ

BACKGROUND:

Thevenin’s theorem states that any linear, bilateral network can be replaced with a single voltage source in series with a single resistor. The voltage source is called Thevenin equivalent voltage and resistor is called the Thevenin equivalent resistance. To demonstrate this we will apply the theorem to the simple four resistor circuit in Figure 1. According to the theorem, we should be able to replace the circuitry to the left of terminals A-B in Figure 1 with that in Figure 2. To obtain the equivalent source voltage, you will measure the open circuit voltage. The Thevenin resistance is obtained by measuring R A-B after replacing the source voltage Vs by a short circuit. To verify that this combination is indeed equivalent, you will then connect a load to both the circuits, and verify that the resulting voltage and current are the same in both cases.

Figure 1

Figure 2

PROCEDURE:

1. For the circuit in Figure 1, calculate all the currents, voltages and powers associated with the resistors R 0, R 1, R 2 and R 3. Record the values in Table - I. 2. Now, use Thevenin’s theorem to calculate the values of Vth, R th, and PRth record them in Table - III. 3. Connect the circuit as shown in Figure 1. 4. Measure I0, I1, I2 and I3 and record the values in Table - II. 5. Measure the open-circuit voltage VAB and record this as Vth under ‘Measured’ in Table - III.

Page | 47

Lab Manual of Circuit Analysis – I 6. Replace the voltage source with a short circuit, and measure the resistance between the terminals A and B. Record this as R th under ‘Measured’ in Table - III. 7. Place a 3.3 kΩ load resistance across the terminals A and B. Calculate voltage across and current through this load resistance R L. Perform the calculations for both the actual circuit and its Thevenin equivalent. The results should be identical. Record the results under ‘Calculated’ in Table - IV. 8. Connect a 3.3 kΩ load to the terminals A and B of the circuit in Figure 1. Measure the resulting load current and voltage, and record them in Table - IV. 9. Construct the circuit of Figure 2 with the calculated values of Vth and R th. Connect a 3.3 kΩ load to the terminals A and B. Measure the resulting load current and voltage, and record them in Table - IV. They should agree closely with those in the adjacent columns. TABLE - I Calculated Data

Calculated current values (mA)

Calculated Voltage Values (V)

Calculated Power Values (mW)

I1

I2

I3

I0

V1

V2

V3

V0

P1

P2

P3

P0

I1

I2

I3

I0

V1

V2

V3

V0


Measured current values (mA)

Measured Voltage Values (V)

TABLE - III Thevenin Parameters

Calculated Vth

Measured Vth

R th R th PRth

Page | 48

Lab Manual of Circuit Analysis – I I TABLE - IV Loaded Circuit Parameters

Calculated Actual Circuit

Thevenin Equivalent

VL

VL

IL

IL

PL

Measured Actual Circuit

Thevenin Equivalent

VL

VL

IL

IL

PL

DESIGNING A THEVENIN EQUIVALENT CIRCUIT

1. For the circuit given below design the circuit such that it’s R th Ω. The resistors th = 3.9875k Ω. available are 1 k Ω, Ω, 2.2 k Ω, Ω, 3.3 k Ω and 4.7 k Ω. Ω. 2. Determine Vth for the circuit which you designed. Record these values under ‘Calculated’ in Table - V. 3. Now connect the circuit which you designed and measure Vth. Record these values under measured in Table - V. 4. Now connect conn ect a load lo ad resistance of 3.3 k Ω to both the circuits and calculate VL and IL for the actual circuit designed by you and record these values in Table - VI. 5. Now measure measu re the resulting load voltage and current and these values in table in Table - VI. They should agree closely with the values that you calculated.

Figure 3

TABLE - V Thevenin Parameters

Calculated Vth

Measured Vth

Page | 49

Lab Manual of Circuit Analysis – I I TABLE - VI Loaded Circuit Parameters

Calculated Actual Circuit

Measured

Thevenin Equivalent

Actual Circuit

Thevenin Equivalent

VL

VL

VL

VL

IL

IL

IL

IL

POST LAB QUESTIONS:

1. In Figure-1, the Thevenin resistance R th th depends on (a) VS (b) R 1, R 2, R 3 and Vs (c) R 1 and R 2 only (d) R 1, R 2 and R 3 2. In Figure-1, the Thevenin voltage Vth depends on (a) R 1, R 2, R 3 and Vs (c) R 1, R 2 and Vs

(b) Vs only (d) R 1 and Vs

3. If R 3 were increased in value, the Thevenin voltage would (a) Increase (b) Decrease (c) Remain the same (d) Insufficient Information 4. An additional resistance placed across the terminals A and B (before any load is connected) would (a) Increase R th (b) Decrease R th th th (c) Not change R th (d) Insufficient Information th 5. A resistor placed directly in parallel with the source voltage Vs does not affect R th. Why? 6. Is PRth+PL=P0+P1+P2+P3+PL for calculated circuits given in Figure 1 and Figure 2?

Page | 50


OBJECTIVE:  

To verify maximum power transfer theorem for DC circuits To determine the maximum power of a black box using Thevenin thoerem

EQUIPMENT: DC power supply 10 V  DMM with probes  Variable resistor  BACKGROUND:

In this experiment you will observe that for a given voltage source Vs with some fixed internal resistance Rs, what value of load resistor will absorb the most power from the circuit? Clearly, there are an infinite number of loads from 0 Ω (a short circuit) to ∞ Ω (an open circuit). Since a short circuit would have no voltage and an open circuit would have no current, both of these produce zero load power. The answer lies somewhere between 0 Ω and ∞ Ω. The maximum power transfer theorem tells us that resi stance tan ce shou l d be equal to the th e sour ce r esi stance tan ce f or m axi mu m power to be “Th e l oad resi absorbed by the load”

In the experiment, you will connect a variable resistor (acting as load) in series with a source resistor. In each case, you will measure VL and IL and calculate , the power in the load. You should find that this power is maximized where R L= R S. A graph is one of the best ways to illustrate the theorem. Be sure to join your data with a smooth curve (not straight-line segments) so that the true variation of power with load resistance can be observed. You will also plot the efficiency of power transfer versus the load resistance. The efficiency measures just what fraction of the total power is dissipated in the load resistance. That is,

 =  × 

Eff iciency, iciency, η = PL/PT where PL is the load power and PT is the total power (sum of power dissipated in load resistance and source resistance). You will see that when delivering maximum power to the load, the efficiency of the circuit is not maximum.

Page | 51


3.3kΩ

Vs

IL

VL

10V

RL

Figure 1

PROCEDURE:

1. For VS = 10V, and R S = 3.3 kΩ, calculate the load voltage VL, load current IL, and load power PL dissipated in the load resistor of Figure 1 for each value of R L. Note these values in Table - I. 2. Complete the table by calculating the total power (PT = VS × IL) and the circuit’s efficiency (PL/PT × 100) for each value of load resistance. 3. Connect the circuit in Figure 1 and measure the load current and voltage for each value of R L. 4. Record all measured data in Table - II. From these data, complete the table by calculating the total power and efficiency of power transfer. TABLE - I Calculated Data

R L (kΩ)

1

1.8

2.2

2.7

3.3

3.9

4.7

5.6

6.8

8.2

1.8

2.2

2.7

3.3

3.9

4.7

5.6

6.8

8.2

VL (V) IL (mA) PL (mW) PT (mW) Efficiency (%)


R L (kΩ)

1

VL (V) IL (mA) PL (mW) PT (mW) Efficiency (%)

Page | 52

Lab Manual of Circuit Analysis – I DETERMINE MAXIMUM POWER OF A BLACK BOX USING THEVENIN THOEREM

a

Vin

Black Box

b



1. Input voltage, , (voltage supplied to black box) is 10V. 2. Determine the Thevenin equivalent parameters; i.e. R th and Vth for the black box. Verify the value of R th using both the Isc method and deactivating sources method. 3. Draw the Thevenin equivalent circuit using the values determined above. 4. Connect a variable resistor between the terminals ‘a’ and ‘b’ at the output end of the black box. 5. Calculate the value of R L that would result in maximum power transfer delivered to it. Also calculate the values of corresponding voltage drop across R L and power dissipated in it. 6. Set the value of variable resistor to the value calculated above. 7. Measure the value of voltage across R L and use it to calculate the value of maximum power. Record your readings in the table below.

TABLE – III

VTH

ISC

R TH =

⁄



R TH (using deactivating sources method)

THEVENIN EQUIVALENT CIRCUIT:

Page | 53

Lab Manual of Circuit Analysis – I TABLE – IV

Calculated R L

VL

Measured PL

R L

VL

PL

POST LAB QUESTIONS: 1. Plot a graph of the load power, PL versus load resistance, R L from your measured data. Also plot a

graph of efficiency of power transfer, η versus load resistance, R L from your measured data. Include these graphs in the ‘measurements’ section of your report.

2. If the source resistance were made larger than 3.3 kΩ in this experiment, then (a) all the values of PL would be smaller than before (b) all the values of PL would be greater (c) all the values of PL would not change (d) some values of PL would be smaller and some greater 3. The power dissipated in the source resistance is always (b) = PL (d) none of these (a) ≤ PL (c) ≥ PL 4. The power dissipated in the source resistance depends on the value of the load resistance. (a) True (b) False 5. To achieve high levels of efficiency, what is the required relationship between the source and load resistance? 6. Show that the efficiency of the source is only 50 percent when supplying its maximum power.

Page | 54


OBJECTIVE: To verify the superposition theorem in a DC circuit  EQUIPMENT: DC power supplies 11V (two)  DMM with probes  Resistors: 1 k Ω, 2.2 k Ω, 3.3 k Ω  BACKGROUND:

The superposition theorem allows us to calculate the combined effects of a multi-source circuit by summing the individual effects of each source acting alone. Particular attention must be paid to current directions and voltage polarities when applying superposition. The circuit has two voltage sources, VS1 and VS2. According to superposition theorem, voltages V1, V 2 and V3 and currents I1, I 2, and I3 can be calculated by taking their values due to individual source acting alone, and then adding them. The voltage source not being considered is to be replaced with a short circuit. It is important to note that you must remove the power supply before you replace it with a short circuit. Never short-circuit a functioning power supply. Also, pay attention to the polarity of voltages due to each source so that you algebraically sum them to get the totals.

VS1

V1

V2

1kΩ

3.3kΩ

V3

11V

1kΩ

VS2

11V

V4 1.2kΩ

Figure 1

PROCEDURE:

1. Use superposition principle for the circuit in Figure 1 to calculate components of V1, V2 , V3 and V4 due to each source acting alone, and record your results in Table - I. Note that V11 is the component of V1 due to Vs1 acting alone; V12 is the component of V1 due to Vs2 acting alone, etc. Similarly, calculate components of I1, I 2, I3 and I4 due to each source acting alone and record your results in Table - I. 2. Complete Table - I by calculating the actual values of V1, V2, V 3 and V4, and I1, I2, I3 and I4 when both VS1 and VS2 are active (ON). 3. Connect the circuit in Figure 1. Remove power supply VS2 and replace it with a short circuit.

Page | 55

Lab Manual of Circuit Analysis – I Then measure the voltages V11, V21, V31 and V41 and currents I11, I21, I31 and I41 record them in Table-II, in the appropriate column. 4. Repeat above step, replacing VS1 with a short circuit and connecting VS2 in the circuit. This will enable you to measure and record V12, V22, V32 and V42 and currents I12, I22, I32 and I42. 5. Finally connect the complete circuit with both sources active. Measure and record the actual voltages V1, V2, V3 and V4 and currents I1, I2, I3 and I4. Compare your measured and calculated data. TABLE-I Calculated Data

VS1 Active

VS1 and VS2 active (Algebraic Sum)

VS2 Active

V11

V12

V1

V21

V22

V2

V31

V32

V3

V41

V42

V4

I11

I12

I1

I21

I22

I2

I31

I32

I3

I41

I42

I4

TABLE-II Measured Data

VS1 Active

VS1 and VS2 active

VS2 Active

V11

V12

V1

V21

V22

V2

V31

V32

V3

V41

V42

V4

I11

I12

I1

I21

I22

I2

I31

I32

I3

I41

I42

I4

POST LAB QUESTIONS:

1. With element values as in Figure 1, if the source VS1 were made equal to 22 V, then a. I3 would double b. I3 would have the same magnitude, but be opposite in direction c. I12, I22 and I32 would each double d. I11, I21 and I31 would each double 2. As far as the direction of current I2 is concerned, the voltages VS1 and VS2 a. Oppose each other Page | 56

Lab Manual of Circuit Analysis – I b. Aid each other c. Do neither of the above 3. If both VS1 and VS2 are increased by a factor of two, then a. All currents will double b. I2 will only double c. All currents will remain constant d. I1 and I3 will double and I2 will stay the same 4. The current I3 depends on a. The value of Vs2 b. The values of Vs2, R 3 and R 2 c. The values of Vs1, and R 1 d. All of the above 5. With values as in Figure 1, calculate the value to which Vs1 must be reduced to force the current I1 to equal zero. 6. Superposition does not work for power. For example, try using it with the power in any one of the resistors in Figure 1; that is, find the power in the resistor due to each source acting alone, add them, and compare with the power you get when you take the total current (or voltage) in this resistor and use the power formula. Which of these is the correct value for the power and why doesn't superposition work? 7. What will be the effect on the voltages and currents calculated above if the value of one of the voltage source is doubled?

Page | 57


OBJECTIVE: To observe the charging and discharging of a capacitor  EQUIPMENT: DC Power Supply 8-10V  DMM  Stop watch  Capacitor: 1000uF  Resistors: 3.3k Ω, 10kΩ, 47kΩ  BACKGROUND:

Capacitance is a measure of a capacitor’s ability to store charge. The amount of charge stored by a capacitor is given by Q = CV

The capacitor in a series RC circuit is being charged from a supply voltage Vs with the current passing through a resistor R. The voltage across the capacitor is initially zero (i.e. it is acting like a short circuit) but it increases as the capacitor charges. The capacitor is fully charged when Vc =Vs. Charging and discharging of a capacitor’s energy is never instant but takes a certain amount of time to occur with the time taken for the capacitor to charge or discharge to within a certain percentage of its maximum supply value being known as time constant. Time constant = τ (tau) = RC (in seconds) A large time constant means that a capacitor is charged slowly. After 5 time constants, the current has fallen to less than 1% of its initial value and we can say that a capacitor is fully charged. During discharging, the current decreases from its initial value of Io (which is determined by the

 = ⁄

initial voltage across the capacitor, Vo and R) i.e. . The voltage across the capacitor also decreases as the capacitor discharges. After 5*τ, voltage cross the capacitor is almost zero and capacitor is said to be fully discharged. Figure 1 shows the circuit that will be used to observe the charging and discharging of a capacitor for different values of resistors, and hence time constants, with the help of a stop watch.

Page | 58


Figure 1

PROCEDURE:

1. Connect the circuit as shown in Figure1. Set the voltage source to 8V. Make sure that you have properly placed the capacitor; taking care of its polarity. 2. For different values of resistors, calculate the time constant, τ, and the time at which the capacitor is fully charged and discharged. Note these values in the table. 3. Place the probes of DMM across the terminals of the capacitor. 4. Turn on the power supply and observe the increasing voltage during charging. Measure the time it takes to fully charge the capacitor using a stop watch. 5. Turn off the power supply when the capacitor is fully charged. Replace the power supply with short circuit (see Figure 2) and observe the decreasing voltage across the capacitor. 6. Fill the table by measuring the actual value of charging and discharging for different values of resistors for a fixed value of capacitance, C = 1000uF.

Figure 2

Page | 59

Lab Manual of Circuit Analysis – I TABLE-I Calculated & Measured Data

Calculated Values

R (Ω)

τ (sec)

Estimated charging time (sec)

Measured Values Estimated charging time (5τ)

Estimated discharging time (5τ)

3.3kΩ 10kΩ 47kΩ

Page | 60


OBJECTIVE: Observe the behavior of an operational amplifier as an inverting amplifier, and non-inverting  amplifier EQUIPMENT: DMM  Power supply  Resistors : 22kΩ, 10kΩ, variable resistor  IC: 741 op-amp  BACKGROUND:

An operational amplifier or op amp is an electronic circuit element, with inverting and non-inverting inputs, designed to be used with other circuit elements to perform a specified signal-processing operation. It is essentially a voltage amplifier having a large intrinsic DC voltage gain. Hundreds of different op amps are available in integrated-circuit (IC) form. The pin configuration of a 741 Op-amp is shown in Figure 1.

Figure 1

INVERTING AMPLIFIER:

Consider the operational amplifier circuit given in Figure 2.

Figure 2

Page | 61

Lab Manual of Circuit Analysis – I Since V+ = V- and since V+ = 0 V (grounded), then V- = 0 V (not an actual ground, but called as a virtual ground). The current I1 then can be calculated as,

I = Vi R V− = RVi Similarly,

I = V− R Vo =  RVo

Since I- = 0 A, then I1= I2. Hence

Or,

Vi =  Vo R R  Vo =  R Vi R

Since the gain is negative, the above amplifier is called inverting amplifier. NON INVERTING AMPLIFIER:

Consider the operational amplifier circuit given in Figure 3.

Figure 3

The currents I1 and I2 are calculated as:

I = RV− I = Vo R V− Since I+ = 0 A, then I1 = I2. Hence

Page | 62


V− = Vo  V− R R  Since, V+ = V- = Vi the final gain expression is obtained as:

Vo =(1+ R ) Vi R Since the gain is positive, the above amplifier is called non-inverting amplifier. PROCEDURE:

For both parts, use +12V as +Vcc and -12V as – Vcc. Part-1: Inverting Amplifier

For the amplifier circuit of Figure 2, if R 2 =22 kΩ and R 1=10 kΩ do the following measurements and calculations.

TABLE-I Calculated Data

Vi (Volts)

Vo (Volts)

Gain (Vo/Vi)

-5 -4 -3 -2 -1 0 1 2 3 4 5

Page | 63

Lab Manual of Circuit Analysis – I TABLE-II Measured Data

Vi (Volts)

Vo (Volts)

Gain (Vo/Vi)

-5 -4 -3 -2 -1 0 1 2 3 4 5

Part-2: Non Inverting Amplifier

For the amplifier circuit of Figure 3, R 2 =22 kΩ and R 1=10 kΩ, do the following measurements and calculations.

TABLE III Calculated Data

Vi (Volts)

Vo (Volts)

Gain (Vo/Vi)

-5 -4 -3 -2 -1 0 1 2 3 4 5

Page | 64

Lab Manual of Circuit Analysis – I TABLE IV Measured Data

Vi (Volts)

Vo (Volts)

Gain (Vo/Vi)

-5 -4 -3 -2 -1 0 1 2 3 4 5

POST LAB QUESTIONS:

1. Plot the voltage transfer characteristic i.e. configurations.

⁄ for both the inverting and the non-inverting 

2. What will be the effect on the output voltage, if the value of resistor R 2 is made zero, in the inverting and the non-inverting configurations.



3. In the inverting configuration, vary between -VCC and +VCC in 2V steps. Measure plot versus . What behavior does the circuit exhibit now? Explain.





 and  =

4. Replace R 2 in non-inverting configuration with a 15 kΩ variable resistor . Assume that and vary R var from 0Ω to 15 kΩ with increment of 1 kΩ. Calculate for each R var value

5

⁄ as a function of R . Explain your graph.  Simulate the inverting and non-inverting circuits using the same setup as in the experiment for different values of  , using schematics in PSpice. Compare the results with those and plot the amplification

5.



var

obtained in the experiment.

Page | 65


Labs with projects 1. Experiments and their report a. Experiment 60% b. Lab report 40% 2. Quizzes (3-4) 3. Final evaluation a. Project Implementation b. Project report and quiz

50%

15% 35% 60% 40%

Labs without projects 1. Experiments and their report a. Experiment 60% b. Lab report 40% 2. Quizzes (3-4) 3. Final Evaluation i. Experiment ii. Lab report, pre and post experiment quiz

50%

20% 30% 60% 40%

Notice: Copying and plagiarism of lab reports is a serious academic misconduct. First instance of copying may entail ZERO in that experiment. Second instance of copying may be reported to DC. This may result in awarding FAIL in the lab course.

Page | 66


In all the Electrical Engineering (EE) labs, with an aim to prevent any unforeseen accidents during conduct of lab experiments, following preventive measures and safe practices shall be adopted: 













 

 

 



Remember that the voltage of the electricity and the available electrical current in EE labs has enough power to cause death/injury by electrocution. It is around 50V/10 mA that the “cannot let go” level is reached. “The key to survival is to decrease our exposure to energized circuits.” If a person touches an energized bare wire or faulty equipment while grounded, electricity will instantly pass through the body to the ground, causing a harmful, potentially fatal, shock. Each circuit must be protected by a fuse or circuit breaker that will blow or “trip” when its safe carrying capacity is surpassed. If a fuse blows or circuit breaker trips repeatedly while in normal use (not overloaded), check for shorts and other faults in the line or devices. Do not resume use until the trouble is fixed. It is hazardous to overload electrical circuits by using extension cords and multi-plug outlets. Use extension cords only when necessary and make sure they are heavy enough for the job. Avoid creating an “octopus” by inserting several plugs into a multi-plug outlet connected to a single wall outlet. Extension cords should ONLY be used on a temporary basis in situations where fixed wiring is not feasible. Dimmed lights, reduced output from heaters and poor monitor pictures are all symptoms of an overloaded circuit. Keep the total load at any one time safely below maximum capacity. If wires are exposed, they may cause a shock to a person who comes into contact with them. Cords should not be hung on nails, run over or wrapped around objects, knotted or twisted. This may break the wire or insulation. Short circuits are usually caused by bare wires touching due to breakdown of insulation. Electrical tape or any other kind of tape is not adequate for insulation! Electrical cords should be examined visually before use for external defects such as: Fraying (worn out) and exposed wiring, loose parts, deformed or missing parts, damage to outer jacket or insulation, evidence of internal damage such as pinched or crushed outer jacket. If any defects are found the electric cords should be removed from service immediately. Pull the plug not the cord. Pulling the cord could break a wire, causing a short circuit. Plug your heavy current consuming or any other large appliances into an outlet that is not shared with other appliances. Do not tamper with fuses as this is a potential fire hazard. Do not overload circuits as this may cause the wires to heat and ignite insulation or other combustibles. Keep lab equipment properly cleaned and maintained. Ensure lamps are free from contact with flammable material. Always use lights bulbs with the recommended wattage for your lamp and equipment. Be aware of the odor of burning plastic or wire. ALWAYS follow the manufacturer recommendations when using or installing new lab equipment. Wiring installations should always be made by a licensed electrician or other qualified person. All electrical lab equipment should have the label of a testing laboratory. Be aware of missing ground prong and outlet cover, pinched wires, damaged casings on electrical outlets.

Page | 67




 







  





Inform Lab engineer / Lab assistant of any failure of safety preventive measures and safe practices as soon you notice it. Be alert and proceed with caution at all times in the laboratory. Conduct yourself in a responsible manner at all times in the EE Labs. Follow all written and verbal instructions carefully. If you do not understand a direction or part of a procedure, ASK YOUR LAB ENGINEER / LAB ASSISTANT BEFORE PROCEEDING WITH THE ACTIVITY. Never work alone in the laboratory. No student may work in EE Labs without the presence of the Lab engineer / Lab assistant. Perform only those experiments authorized by your teacher. Carefully follow all instructions, both written and oral. Unauthorized experiments are not allowed. Be prepared for your work in the EE Labs. Read all procedures thoroughly before entering the laboratory. Never fool around in the laboratory. Horseplay, practical jokes, and pranks are dangerous and prohibited. Always work in a well-ventilated area. Observe good housekeeping practices. Work areas should be kept clean and tidy at all times. Experiments must be personally monitored at all times. Do not wander around the room, distract other students, startle other students or interfere with the laboratory experiments of others. Dress properly during a laboratory activity. Long hair, dangling jewelry, and loose or baggy clothing are a hazard in the laboratory. Long hair must be tied back, and dangling jewelry and baggy clothing must be secured. Shoes must completely cover the foot. Know the locations and operating procedures of all safety equipment including fire extinguisher. Know what to do if there is a fire during a lab period; “Turn off equipment, if possible and exit EE lab immediately.”

Page | 68


Each student will maintain a lab notebook for each lab course. He will write a report for each experiment he performs in his notebook. A format has been developed for writing these lab reports. Lab Report Format

For hardware based labs, the format of the report will include: 1. Introduction: Introduce area explored in the experiment. 2. Objective: What are the learning goals of the experiment? 3. Measurements : In your own words write how the experiment is performed (Do not copy/paste the procedure). a. Issues : Which technical issues were faced during the performance of the experiment and how they were resolved? b. Graphs, if any 4. Conclusions: What conclusions can be drawn from the measurements? 5. Applications: Suggest a real world application where this experiment may apply. 6. Answers to post lab questions (if any). Sample Lab Report: Introduction

An RC circuit is a first order circuit that utilizes a capacitor as an energy storage element whereas a resistor as an energy wastage element. RC circuits are building blocks of electronic devices and their thorough understanding is important in comprehending advance engineering systems such as transistors and transmission lines. An RC circuit can be operated with both DC and AC sources. In this lab we study transient response of RC circuits with a square wave as a DC source. During the DC operation of an RC circuit the voltage across the capacitor or the resistor show energy storing (capacitor charging) and dissipating (capacitor discharging via resistor) mechanisms of the circuit. The capacitor charging or discharging curves then lead to determine time constant of the circuit where the time constant signifies time required by the RC circuit to store or waste energy. Objective:

To study transient response of a series RC circuit Measurements:

The circuit used for the experiment is shown in Fig. 1.

Page | 69


Fig.1. The circuit used in the experiment

Both input (a square wave) and output (voltage across capacitor) waveforms are monitored on an oscilloscope. The capacitor charging is observed during "on" part of the square waveform whereas the capacitor discharging is observed during "off" part of the square waveform (Fig. 2). We measure the time constant from the capacitor charging or discharging curve. While keeping the capacitor value constant, we also measure time constants with various resistor values (Table I).

INPUT VOLTAGE

VOLTAGE ACROSS A CAPACITOR

Fig. 2. Input and Output waveforms

TABLE I. Time constant as a function of th e resistor values

Resistance (Nominal)

270 Ω

330 Ω

470 Ω

1 kΩ

2.2 kΩ

3.3 kΩ

Resistance (Measured) Time constant (Calculated) Time constant (Measured) Capacitance (Measured)

Page | 70

Linear Circult Analysis Lab-Manual_ 16Jun 2016.pdf

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