circuit lab manual

Kuwait University

College of Engineering & Petroleum

Electrical Engineering Department

Designed & Edited By

Eng. Ahmed Shafik Eng. Mohamed Tawfik

Supervised By

Dr. Meshaal Al-Shaher Dr. Mona Al-Basman

Lab Schedule

Week Date

Experiment Title Quiz Pre-Lab Report From To

1 1-Feb 5-Feb Introduction and DC SPICE training

2 8-Feb 12-Feb Ex1. Ohm's Law

3 15-Feb 19-Feb Ex2. KVL and KCL Quiz 1

4 1-Mar 5-Mar Ex3. Node, Mesh and Superposition Quiz 2

5 8-Mar 12-Mar Ex4. Thevenin Equivalent Theorem Quiz 3

6 15-Mar 19-Oct First Exam

7 22-Mar 26-Mar Ex5. AC Measurements

8 29-Mar 2-Apr Ex6. Transient and Pulse Responses Quiz 4

9 5-Apr 9-Apr Ex7. Phase shift Measurements Quiz 5

10 12-Apr 16-Apr Exp 8 : Sinusoidal Steady-state power calculation Quiz 6

11 19-Apr 23-Apr Exp 9 : Power Consumption

12 26-Apr 30-Apr Final Exam

Grading PolicyPerformance + Pre-Lab 10% Reports 15% 6 Quizzes 20% 2 Exams 50% Data CD 5% Total 100%

Report Grading Policy

Cover

1

Table of Contents Objective Equipment Theory 1 Procedure + Circuit 2 Data Sheet 1 Exercise 5 Conclusion 3

References Report Format 2 Total 15

x Second Midterm is considered as Final Exam x Absence of Final Exam = FA x Absence of 3 out of 10 lab sessions = FA. x All reports and data sheets should be done by computer; no

hand writing will be accepted. x Pre-Lab = Data Sheet + Spice Simulation x Data Sheet should be signed by the lab engineer at the end of

the lab x No Mobile or calculator is allowed in the practical exams

Lab Regulations 1) Performance & Pre Lab: (10 points)

x PSpice simulation report (student name and ID must be typed, otherwise will be

discarded)

x Find Data Sheet at the end of each experiment. Theoretical part should be filled in

and printed by computer before the lab.

Note: Lab engineer has to sign the pre lab note before students leave the lab.

x Students have to leave the bench clean and switch all the equipments off before

leaving the lab.

x Food and drink is not allowed in the labs.

x Cell phone use in the labs is prohibited.

2) Data CD: (5 points)

x Students should submit at the end of the semester a CD or DVD or flash

including the following:

o Microsoft word file for each experiment report o PSpice circuit file for each experiment simulation

x The CD or DVD or Flash must be labeled with the student name and ID.

3) Attendance

x Students should attend the lab in time. Late students will not be allowed to attend

the lab and will get zero mark for (Pre Lab Note, Performance, Quiz and Report).

x Students can attend in their section only, no switching between labs will be allowed for any reason.

x Absent students for 3 out of 10 labs or more will get FA.

x Absence of Final Exam = FA

4) Report Layout:

A typical lab report should contain the following sections (in order), you can download the report sample from the site: x Cover Page x Table of Contents x Objective x Theory x Experimental Procedure + Exercise x PSpice Simulation x Data Sheet x Conclusion x References

. Writing techniques:

x Report and Pre Lab note should be written by computer. x The font and size of the normal text is TimesNewRoman 12. x The font and size of the heading and subheading is TimesNewRoman 16/14. x The report should contain page numbers. x All figures and tables should have a title caption. x The theory part should contain (figures, equations, description) for each part of the objective.

1

x To be familiar with the laboratory equipment and components.

x Verification of Ohms law.

x Series and parallel circuits.

Part I : Lab equipment and components: DC Power Supply: It is a multi-channels power source device to generate a variable DC voltage,

Figure 1-1: DC power supply sample

Function Generator (FG): It is a device to generate a variable AC signals with different wave forms (sine, square and triangle).

Figure 1-2: Function Generator

Familiarization, and Ohm's Law

Objectives

Theory

1

2

Resistor: There are two types of resistors in the lab, resistor substitution box (from 0 to 9.999 M:) and discrete resistors. See Figure 1-5 for the discrete resistor values reading table.

Resistor Substitution Box

Discrete Resistors

Figure 1-3: Resistors

4-band Color Code

Figure 1-4: 4-band color code table

3

5-band Color Code

Figure 1-5: 5-band color code table

4

Example:

(a)

(b)

Figure 1-6: Color code example

a) For the resistor of figure 1-6-a, the value can be calculated as follows:

1 2 3 4R N N N N u r Where:

Ni = band value. R = 02 x 105 + 10% = 200 K: + 10% b) For the resistor of figure 1-6-b, the value can be calculated as follows:

1 2 3 4 5R N N N N N u r Where:

Ni = band value. R = 330 x 101 + 0.1% = 3.3 K: + 0.1%

5

Inductor: There is inductance substitution box in the lab (from 0 to 9.999 H).

Figure 1-7: Inductance substitution box

Capacitor: There is capacitance substitution box in the lab (from 0 to 99.999 uF).

Figure 1-8: Capacitance substitution box

Digital Multi-Meter (DMM): DMM is a measuring instrument to measure voltage, current, ohm, frequency.

Figure 1-9: DMM sample

6

Digital Oscilloscope (CRO): CRO is a multi-channels measuring instrument to measure and display voltage wave forms with

different measurements readings.

Figure 1-10: CRO Sample

Bread Board: It is a board to connect the circuits.

Figure 1-11: Bread Board Sample

7

Part II : Ohms's Law: Ohm's Law says: The current in a circuit is directly proportional to the applied voltage.

V I R u (1)

Circuit Diagram

Relationship Between V & I (slope=1/R)

Figure 1-12: Ohms Law

Part III : Series & Parallel Circuits:

Figure 1-13: Series and Parallel Connections

I

1/R

I

V

8

Connect the circuit as shown in Figure 1-14 by the following steps:

Part I:

Figure 1-14: Circuit Diagram

1) Start PSpice [Appendix A-1] 2) Add a Resistor [Appendix A-2] (R1=2 K)

3) Add DC Voltage Source (Vs) [Appendix A-5]

4) Add Ground [Appendix A-11]

5) Connect the circuit by adding wires [Appendix A-10]

6) Add CRO current probe to measure I [Appendix A-12]

7) Select DC sweep analysis with the following parameters [Appendix A-14]

x Name = V1 x Start Value = 0 x End Value = 10 x Increment = 1

8) Simulate the circuit [Appendix A-13]

9) The following wave form will be displayed in a new window.

10) Calculate the line slope = and compare it with the theoretical value.

V_Vs

0V 0.5V 1.0V 1.5V 2.0V 2.5V 3.0V 3.5V 4.0V 4.5V 5.0V 5.5V 6.0V 6.5V 7.0V 7.5V 8.0V 8.5V 9.0V 9.5V 10.0VI(R1)

0A

0.4mA

0.8mA

1.2mA

1.6mA

2.0mA

2.4mA

2.8mA

PSpice Simulation

9

Part II:

1) Start PSpice [Appendix A-1] 2) Add Resistors [Appendix A-2] R1= R2=2K, R3=3.9 K, R4= R5=2K

3) Add DC Voltage Source (Vs) [Appendix A-5] Vs = 10 V




7) Calculate the equivalent resistor.

1) Start PSpice [Appendix A-1] 2) Add Resistors [Appendix A-2] R1= 1K, R3=3.9K, R2=1K

3) Add DC Voltage Source (Vs) [Appendix A-5] Vs = 10 V




7) Calculate the equivalent resistor.

(a)

(b)


I

I

R AB1 = =

R AB2 = =

10

Equipments:

Procedure: Part I : Ohms Law:

1) Select a discrete resistor R = 2 K, measure the resistor value

2) Connect the circuit as shown in Figure 1-16 with the shown values.

3) Vary the DC voltage source and measure I. Fill table 1-1.

Table 1-1 VS I (mA) 2 4 6 8 10

Q1: Draw V versus I, find the slope of the curve and what does the slope represent?.

Q2: Compare the slope of Q1 with the theoretical value. % 100Theoritical Measurederror Theoritical u

Q3: What are the error sources in Q2?

1) DC Voltage Source 2) Bread Board.

3) DMM 4) Discrete resistors


Experimental Work

I

R =

11

Part II: Parallel and Series Circuits:

1) Connect the circuit as shown in Figure 1-17-a, R1= R2=2K, R3=3.9K, R4= R5=2K,

Measure RAB1.

2) Connect the circuit as shown in Figure 1-17-b, R1=1K, R3=3.9K, R2=1K.

Measure RAB2.

Q4: Calculate RAB1 and RAB2 theoretically.

Q5: What is the relation between the circuit of Figure 1-17a and Figure 1-17b

(a)

(b)


RAB1=

RAB2=

A B2

12

x Verification of KVL and KCL.

x Simulating the DC circuits using PSpice.

x Measuring and calculating the equivalent resistance of different circuits.

Kirchhoffs Voltage Law (KVL) KVL states that the algebraic sum of all voltages around a closed path (or loop) is zero. Figure 2-1

shows an example for closed loop circuit.

For the circuit shown in Figure 2-1,

applying KVL:

Figure 2-1: KVL example

Kirchhoffs Current Law (KCL) Kirchhoffs current law (KCL) states that the sum of the currents entering a node is equal to the sum

of the currents leaving the node.

For the circuit shown in Figure 2-2,

applying KCL:

Figure 2-2: KCL example

KVL, KCL, and equivalent circuit resistance 2

Objectives

Theory

13

Parallel and Series Circuit Connections

1 21

...N

ab N nn

R R R R R

11 2

1 1 1 1 1...N

nab N nR R R R R

Series Connection Parallel Connection Figure 2-3: Series-Parallel Connections

Delta to Wye Conversion

Delta to Why conversion (given Ra, Rb, Rc)

Why to Delta conversion (given R1, R2, R3)

Figure 2-4: Delta Why conversions

n

n

14



1) Start PSpice [Appendix A-1] 2) Add a Resistor [Appendix A-2] (R1=1K, R2=5.1K, R3=2K, R4=1K, R5=3.9 K)

3) Add DC Voltage Source (Vdc) [Appendix A-5] (V1=12 Volt, V2=8 Volt)



6) Select the bias point simulation analysis [Appendix A-15]


8) Activate the voltage and current icons in the tool bar.

9) Fill Table 2-1.

Table 2-1 I1 I2 I3

Q1: Verify KCL at point A.

Delta to Wye Conversion

PSpice Simulation

I1

I2

I3

A

L1 L2

L3 L4 + -

+ -

+ - -

+ - -

+ - -

15


1) Start PSpice [Appendix A-1] 2) Add a Resistor [Appendix A-2]

3) Add DC Voltage Source (Vdc) between the two nodes A and B = 10 Volt[Appendix A-5]






9) Calculate the value of RAB

Rab == =

1K

3.9K

5.1K

10K

5.1K

3.9K

1K

16

Equipment:

Part A KVL & KCL:

1) Select (using color table in Appendix B-1) and measure (using DMM) the resistors values.

Fill the measured values of the resistors in Table 2-2.

Table 2-2 R1 R2 R3 R4 R5

2) Connect the circuit shown in Figure 2-5, adjust V1 = 12 V and V2 = 8 V using DMM.

3) Fill table 2-3.

Table 2-3 VR1 VR2 VR3 VR4 VR5 I1 I2 I3

Q1: Using the measured values of table 2-2 and 2-3, verify KVL for closed loops L1, L2, L3 and L4. Loop L1:

Loop L2:

Loop L3:

Loop L4:


3) DMM 4) Discrete resistors.

Experimental Work

17

Q2: Using the measured values of tables 2-2 and 2-3, verify KCL at node A.

Q3: Repeat Q1 using results of PSpice.

Part B - Delta to Wye Conversion and equivalent resistance of different circuits:


1) Connect the circuit as shown in Figure 2-7.

2) Using DMM measure Rab.

Q4: Find Rab theoretically in details (step by step with figures) and compare it with measured value in step 2 and the simulated value by PSpice.

Rab =

1K

3.9K

5.1K 5.1K

3.9K

1K

10K

18

x Verification of Nodal analysis method.

x Verification of Mesh analysis method.

x Verification of Superposition technique.

x DC circuits analysis using PSpice.

Nodal Analysis Analysis Steps:

1. Select a node as the reference node. Assign voltages v1, v2,, vn-1 to the remaining n1

nodes. The voltages are referenced with respect to the reference node.

2. Apply KCL to each of the n1 non reference nodes. Use Ohms law to express the branch

currents in terms of node voltages.

3. Solve the resulting simultaneous equations to obtain the unknown node voltages.

Example:

Figure 3-1: Nodal Example

Applying nodal equation for the circuit of Figure 3-1:

1 1 1 1 2

1 3 2

0N N N NV V V V V

R R R

2 2 2 2 1

5 4 2

0N N N NV V V V V

R R R

Nodal, Mesh and Superposition Analysis

3

Objectives

Theory

19

Mesh Analysis A mesh is a loop which does not contain any other loops within it.

Analysis steps:

1. Assign mesh currents i1, i2, . . . , in to the n meshes.

2. Apply KVL to each of the n meshes. Use Ohms law to express the voltages in terms of the

mesh currents.

3. Solve the resulting n simultaneous equations to get the mesh currents.

Example:

Figure 3-2: Mesh Loop Example

Applying mesh loop equation for the circuit of Figure 3-2:

Superposition technique: The superposition principle states that the voltage across (or current through) an element in a linear

circuit is the algebraic sum of the voltages across (or currents through) that element due to each

independent source acting alone.

Superposition steps:

1. Turn off all independent sources except one source. Find the output (voltage or current) due

to that active source using nodal or mesh analysis.

2. Repeat step 1 for each of the other independent sources.

3. Find the total contribution by adding algebraically all the contributions due to the independent

sources.

Example:

For the circuit shown in Figure 3-1, to find IR1 using super position:

20

x Disconnect the voltage source V2 and replace it with a wire (short circuit it) as shown in

Figure 3-3-a.

Solve for IR1.

x Disconnect the voltage source V1 and replace it with a wire (short circuit it) as shown in

Figure 3-3-b.

x Solve for IR1.

x IR1 = IR1 + IR1

(a) (b)

Figure 3-3: Superposition Technique Example



1) Start PSpice [Appendix A-1] 2) Add a Resistor [Appendix A-2], R1=1K:, R2=2K:, R3= 3.9K:, R4= 5.1K:, R5=2K:,

R6=1K:, R7=2K: 3) Add DC Voltage Source (Vdc) [Appendix A-5], V1 = 15 V and V2 = 12 V.


PSpice Simulation

IR1 IR1

L1 L2 L3

L4

C

21





9) Fill Table 3-1.

Table 3-1

IR5 IR3 IR7 IR4 VA VB VC

10) Deactivate V2 and simulate the circuit [Appendix A-13]

11) Fill table 3-2

Table 3-2 3

12) Deactivate V1 and simulate the circuit [Appendix A-13]

13) Fill table 3-3.

Table 3-3

" 3"

Q1: Verify superposition technique for VA and IR3.

Equipments:

Part A Nodal and Mesh Analysis

a. For the circuit shown in Figure 3.4, select (using color table in appendix B-1) and measure

(using DMM) the resistors. Fill the measured values of the resistors in table 3-4.


7) DMM 8) Discrete resistors.

Experimental Work

22

Table 3-4 R1 R2 R3 R4 R5 R6 R7

b. Connect the circuit shown in Figure 3-4, adjust V1 = 12 V and V2 = 12 V using DMM.

c. Fill table 3-5.

Table 3-5 IR5 IR3 IR7 IR4 VA VB VC

Q1: Using the measured values of table 3-4 and 3-5, verify Nodal equations for A and B.

Node A:

Node B:

Q2: Using the measured values of table 3-4 and 3-5, verify Mesh equations.

Mesh L1:

Mesh L2:

Mesh L3:

Mesh L4:

Part B Superposition technique: 1) Deactivate the voltage source V2, measure and fill table 3-6 for and 3 2) Deactivate the voltage source V1, measure and fill table 3-6 for " and 3"

3) Verify superposition technique and fill table 3-6 for and 3 Table 3-6

" 3 3" 3

23

x Verification of Thevenins Theory.

x Verification of maximum power condition.

x Determination of Thevenins Eq. Circuit using PSpice.

Thevenins Theory Thevenins theorem states that a linear two-terminal circuit can be replaced by an equivalent circuit

consisting of a voltage source VTh in series with a resistor RTh, where VTh is the open-circuit voltage

at the terminals and RTh is the input or equivalent resistance at the terminals when the independent

sources are turned off.

(a) Original Circuit (b) Thevenin Equivalent Circuit

Figure 4-1: Thevenin Theory

Maximum Power Transfer Maximum power is transferred to the load when the load resistance equals the Thevenin resistance as

seen from the load (RL = RTh).

For Figure 4-2, maximum power equation is as follows:

(1)

Thevenins Equivalent Circuit & Max. Power Transfer

4

Objectives

Theory

24

(a) The circuit used for maximum power

transfer (b) Power delivered to the load as a function

of RL

Figure 4-2: Maximum Power Circuit



1) Start PSpice [Appendix A-1] 2) Add a Resistor [Appendix A-2] R1=2K, R2=3.9K, R3=1K, RL=1K

3) Add two DC Voltage Source (Vdc) [Appendix A-5] V1=12Volt, V2=15Volt



Part 1- Finding I through RL: 1) Select the bias point simulation analysis [Appendix A-15]


x I

PSpice Simulation

y

25


Part 2: Calculating I using Thevenins Circuit A) Finding VTH

1) Change the value of RL to be 1T (high value equivalent to open circuit).


3) Activate the voltage and current icons in the tool bar. Calculate VTH = Vxy

B) Finding RTH 1) Change the value of RL to be 1f (very small value equivalent to short circuit).

2) The circuit will be as shown in Figure 4-4.



5) Calculate RTH


SC

THTH I

VR = K

Q1: Using Thevenin Equivalent Circuit, calculate IRL and compare it with the value in part 1.

=

+ =

Isc

IRL = mA

VTH = V

ISC = mA

26

Equipments:

Part 1 Finding IRL

1) Connect the circuit as shown in Figure 4-3 with the same values of resistors (using color

resistor table in Appendix B-1). Fill the measured values of the resistors in table 4-1.

Table 4-1 R1 R2 R3 R4

2) Connect the circuit shown in Figure 4-3, adjust V1 = 12 V and V2 = 15 V using DMM.

3) Measure I.

Part 2: Calculating I using Thevenins Circuit A) Finding VTH

x Remove RL from the circuit and measure VTH = Vxy

B) Finding RTH x Remove RL and replace it with a short circuit wire.

x Measure ISC.

x Calculate RTH

Q2: Using Thevenin Equivalent Circuit, calculate IRL and compare it with the value in part 1.


11) DMM 12) Discrete resistors and resistor box

Experimental Work

IRL = mA

VTH = V

ISC = mA

RTH = K

IRL = mA

27

Part 3: Maximum Power Transfer


x Let VTH = 10 V and RTH = 1000 :. x Connect the circuit as shown in Figure 4-5, where RL is a resistor box.

x Vary RL with the values of table 4-2.

x Fill table 4-2.

Table 4-2 RL (:) I PRL = I2*RL

200 800 1000 1200 1500

Q3: From table 4-2, plot PRL versus RL. What is the value of RL for maximum power. Comment?

RTH

RL VTH

I + -

RL = K PRL MAX = W

28

x To be familiar with the Digital Oscilloscope (CRO) and Function Generator (FG).

x Using P-Spice to simulate AC circuit analysis.

x AC measurements using CRO.

x Verifying the relation between Peak-Peak value and RMS values for AC circuits.

Alternating current (AC): the flow of charge is continually changing in magnitude (and direction)

with time.

Sample of AC supply waveforms:

(a) sine wave (b) square wave (c) triangle wave Figure 5-1: AC waveforms samples

AC Basics:

Figure 5-2: Sinusoidal Waveform

AC Fundamentals and Measurements

5

Objectives

Theory

VPP

VP

29

Frequency F: the number of cycles per second of a waveform in Hz. The period T: of a waveform is the duration of one cycle in seconds. 1T F

Peak Value: the peak value of a voltage or current is its maximum value with respect to zero. Peak-to-peak VPP: is the value between minimum and maximum peaks

Root Mean Square (RMS) value: The effective value of a periodic current is the dc current that delivers the same average power to a

resistor as the periodic current.

(1) Where: x is v(t) or i(t).

Table 5-1: RMS equations for different waveforms Wave Form RMS

Sinusoidal wave 2 2

PPrms

VV

Triangle wave 2 3

PPrms

VV

Square wave 2PP

rmsVV



1) Start PSpice [Appendix A-1] 2) Add 3 Resistors (R1=1K - R2=2K - R3=10K - R4=5.1K - R5=1K) [Appendix A-2]

PSpice Simulation

30

3) Add AC sine wave voltage source (Vsinpp) = 10 V [Appendix A-7]

a. VOFF = 0 b. VAMPL = 5 c. FREQ = 2 KHz



6) Add CRO probes to measure both VA and VB [Appendix A-12]

7) Adjust the transient simulation parameters [Appendix A-17]

a. Print step = 0 ns b. Final time = 1 ms c. Tick the skip initial transient solution.


9) To get the value of VA-VB , add trace [Appendix A-18]

a. Trace expression = V(A)- V(B) 10) The following wave form will be displayed in a new window.

11) Using the toggle cursor [Appendix A-19], fill table 5-2:

Table 5-2 VA PP VB PP VAB PP Period T (msec)

12) Apply KVL for loop ABA to check your result.

13) Repeat the steps from 1 to 9, modify step 3 to be square wave (VPP = 10 V, Freq. = 2 KHz) as

follows:

Time

0s 0.2ms 0.4ms 0.6ms 0.8ms 1.0msV(R5:2) V(B) V(A)

-8.0V

-4.0V

0V

4.0V

8.0V

31

a. Add square wave voltage source (Vpulse) [Appendix A-8]

i. DC=0

ii. AC=0

iii. V1= 5 V

iv. V2= -5 V

v. TD= 0

vi. TR= 1f

vii. TF= 1f

viii. PW= 12 .Freq = 0.25 msec

ix. PER= 1.Freq = 0.5 msec




16) Repeat the steps from 1 to 9, modify step 3 to be triangle wave (VPP = 10 V, Freq. = 2 KHz)

as follows:

a. Add triangle wave voltage source (Vpulse) [Appendix A-9]

i. DC=0

ii. AC=0

iii. V1= -5 V

iv. V2= +5 V

v. TD= 0

Time


-8.0V

-4.0V

0V

4.0V

8.0V

32

vi. TR= 12 .Freq = 0.25 msec

vii. TF= 12 .Freq = 0.25 msec

viii. PW= 1f

ix. PER= 1.Freq = 0.5 msec




Equipments:

Procedure: Part 1:

1) Connect the circuit as shown in Figure 5-3 with: (R1=1K - R2=2K - R3=10K -

R4=5.1K - R5=1K)

2) Adjust the function generator to get sine wave with 10 V PP and freq. = 2 KHz.

3) Fill table 5-5 by using CRO (use the math function to get VAB).

4) Fill table 5-6 by using DMM.

Time


-8.0V

-4.0V

0V

4.0V

8.0V

1) Function Generator 2) Bread Board.

3) CRO, DMM 4) Discrete resistors.

Experimental Work

33


Table 6-6 IR1 RMS VB RMS

5) From table (5-5) calculate VB (RMS) =

Part 2:

6) Adjust the function generator to get square wave with 10 V PP and freq. = 2 KHz.





9) From table 5-7, calculate VB (RMS) =

Part 3:

10) Adjust the function generator to get triangle wave with 10 V PP and freq. = 2 KHz.





34

13) From table 5-9, calculate VB (RMS) =

Q1: Is the peak to peak values of the voltage or current changed by changing the wave form?

Q2: Is the RMS values of the voltage or current changed by changing the wave form?

Why?

Q3: Find the RMS value for sine,square and triangle wave using general formula? Show your work in details

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

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

35

x Study the natural response and step response of RL/RC circuits.

x Calculate the Time ConstantW. When the dc source of an RC circuit is suddenly applied, the voltage or current source can be

modeled as a step function, and the response is known as a step response. The natural response or

transient response is the circuits temporary response that will die out with time. The forced response

or steady-state response is the behavior of the circuit a long time after an external excitation is

applied. The complete response of the circuit is the sum of the natural response and the forced

response.

Natural Response

RL Circuit RC Circuit Figure 6-1 : RL & RC Circuit

( ) , 0t

L oi t i e tW t (1)

( ) , 0t

C ov t v e tW t (2)

Where :

x eq

eq

LRW (3)

x Wis the time constant. x Io is the initial conductor current at t=0.

Where:

x eq eqR CW (4) x Wis the time constant. x Vo is the initial capacitor current at t=0.

As shown in figure 6-2 and figure 6-4:

x ( ) ( )Lx t i t for RL circuit. (5)

Natural-Response of RL/RC circuits

6

Objectives

Theory

+

Vo

- Io

36

x ( ) ( )Cx t v t for RC circuit. (6)

Figure 6-2 : Natural Response

Step Response

Figure 6-3 : Step Response of RL & RC circuit

( ) (1 ), 0ts

LVi t e tR

W t (7) ( ) (1 ), 0t

C sV t V e tW t (8)

RL Circuit RC Circuit

iL + Vc -

37

Figure 6-4 : Step Response

Time Constant W: the time required for the natural response to decay by a factor of e-1 (36.8%) as shown in figure 6-2 or the time for the step response to be 63.3% of its final value as shown in figure

6-4. Part A: RC Circuit

Figure 6-5: RC Circuit Connect the circuit as shown in figure 6-5 by the following steps:

19) Start PSpice [Appendix A-1] 20) Add Resistor [Appendix A-2] R=500

21) Add Capacitor [Appendix A-3] C=0.2uF

22) Add square wave voltage source (Vpulse) with amplitude VPP= 10 and frequency =625 Hz

[Appendix A-8]

PSpice Simulation

38

o DC=0 o AC=0 o V1= 0 o V2=10 o TD= 1f o TR= 1f o TF1f o PW= 0.8m o PER= 1.6m



25) Add CRO probes to measure both Vs and Vc [Appendix A-12]


a. Print step = 0.000001 m, Final time = 2ms. 27) Simulate the circuit [Appendix A-13]

28) The output will be displayed in a new window as shown.

11. Trace the simulation [Appendix A-18] to get the time constant W: x Trace expression = 6.32 which represents 63.2% of the final value to get the time

constant W from the intersection of the 6.32 trace with the charging voltage.

W =

12. Measure the value of VC at t = 0.2 msec, then verify this value theoretically by using equation (8). Calculate the %error.

VC = (simulation) VC = (theoretical) %error=

Time

0s 0.2ms 0.4ms 0.6ms 0.8ms 1.0ms 1.2ms 1.4ms 1.6ms 1.8ms 2.0msV(V1:+) V(C1:2) 6.32 3.62

0

5

10

39

Part B: RL Circuit

Figure 6-6: RL Circuit

1) Repeat the steps of part A, connect the circuit as shown in figure 6-6 by changing the

capacitor with an inductor=20mH and the value of R to be 2 K [Appendix A-4].

2) Trace the simulation [Appendix A-18] to get the time constant W: x Trace expression = 6.32 which represents 63.2% of the final value to get the time

constant W from the intersection of the 6.32 trace with the increasing VR response.

W =

3) Measure the value of VR at t = 0.3 msec, then verify this value theoretically by using equation (8). Calculate the %error.

VR = (simulation) VR = (theoretical) %error =

(Note: ( ) RL Vi t R , so the response of IL(t) is the same response of VR(t) divided by constant)

Equipments:

1) Resistor, capacitor, and inductor substitution box.

2) Function Generator.

3) Digital Multi-Meter DMM

4) CRO.

Experimental work

40

Procedure: Part A: RL Circuit

Figure 6-7: Circuit Diagram Figure 6-8: Pulse Voltage

1) Connect the circuit as shown in figure 6-7,

2) Adjust the function Generator to generate square wave with maximum amplitude=10 V and

minimum amplitude=0 V, Frequency=625 Hz, as shown in figure 6-8 (by adjusting the

amplitude value and the DC offset).

3) From the CRO screen, measure the value of W.

W =

4) Calculate the % error between W (Practical) and W (PSpice). W (PSpice) = %error =

5) Calculate the % error between W (Practical) and W (Theoretical). W (theoretical) = %error =

10

1.6m time

41

Part B: RC Circuit

Figure 6-9: Circuit Diagram Figure 6-10: Pulse Voltage

1) Connect the circuit as shown in figure 6-9,

2) Adjust the function Generator to generate square wave with maximum amplitude=10 V and

minimum amplitude=0 V, Frequency=625 Hz, as shown in figure 6-10 (by adjusting the

amplitude value and the DC offset).

3) From the CRO screen, measure the value of W.

W =

4) Calculate the % error between W (Practical) and W (PSpice). W (PSpice) = %error =

5) Calculate the % error between W (Practical) and W (Theoretical). W (theoretical) = %error = Q1: Define time constant? =RC (for RC circuit)

= RL (for RL circuit)

10

1.6m time

42

x Study the sine wave of AC voltage and current.

x Measure Phase Shift between voltage and current.

Phase Shift T

Phase shift is the angle between voltage and current. Passive Circuit Elements

A) Resistor

Figure 7-1: Resistor Passive Element

Figure 7-2: Time Domain Response (Voltage and Current are in phase)

Sinusoidal AC Voltage & Current for RL & RC Circuits

7

Objectives

Theory

43

Figure 7-3: Phasor Form

Figure 7-4: Phaseor Diagram (T = 0o )

B) Inductor

Figure 7-5: Inductor Passive Element

Figure 7-6: Time Domain Response (Current lags the Voltage by angle T = 90o)

V j LIZ (1)


Figure 7-8: Phasor Diagram (T = 90o )

V

I

T

I V

44

C) Capacitor

Figure 7-9: Capacitor Passive Element

Figure 7-10: Time Domain Response (Current leads Voltage by angle T = 90o)

1V Ij CZ (2)


Figure 7-12: Phasor Diagram (T = 90o )

I

T V

90o

45

D) R-L series AC circuit

Figure 7-13: RL Circuit

Figure 7-14: Time Domain Response (Current lags Voltage by angle T )

( )V j L R IZ (3)


1tan LRZT (4)

Figure 7-16: Phasor Diagram 0 90Td d

T VR

V

I

V

T Q

i

V

jZ VL

I

46

E) R-C series AC circuit

Figure 7-17: RC Circuit

Figure 7-18: Time Domain Response (Current leads Voltage by angel T)

1V R IjwC (5)

Figure 7-19 : Phasor Form

1 1tan C RT Z (6)

Figure 7-20 : Phasor Diagram 0 90Td d

T VR

V

I

T

V

V VC

I

47

Part A: RL Circuit

Figure 7-21: RL Circuit Connect the circuit as shown in figure 7-21 by the following steps:

1) Start PSpice [Appendix A-1] 2) Add Resistor (R= 2K) [Appendix A-2]

3) Add Inductor (L=200 mH) [Appendix A-4]


a. VOFF = 0 b. VAMPL = 5 c. FREQ = 1600 Hz



7) Add CRO probes to measure both Vs and VR [Appendix A-12]


d. Print step = 1000us e. Final time = 2ms f. No-Print Delay = 0.1 ms g. Tick the skip initial transient solution.



PSpice Simulation

48

11. Measure X (the time shift between Vs and Vr). 12. Calculate T (phase shift between Vs and Vr), using the following equation:

360XTT u (9)

Where T (time period) = 1/Freq.

X = T = T = VR Leads or Lags Vs ? .

Part B: RC Circuit

Figure 7-22: RC Circuit Connect the circuit as shown in figure 7-22 by the following steps:

1) Repeat the steps of part (A) except:

a. Step 2 = R = 995 [Appendix A-2]

Time

0.1ms 0.2ms 0.3ms 0.4ms 0.5ms 0.6ms 0.7ms 0.8ms 0.9ms 1.0ms 1.1ms 1.2ms 1.3ms 1.4ms 1.5ms 1.6ms 1.7ms 1.8ms 1.9ms 2.0msV(R4:2) V(V2:+)

-4.0V

-3.0V

-2.0V

-1.0V

0.0V

1.0V

2.0V

3.0V

4.0V

49

b. Step 3 = Capacitor (0.1 uF) [Appendix A-3]

c. Step 8: Adjust the transient simulation parameters [Appendix A-17]

i. Print step = 1ns ii. Final time = 4ms

iii. No-Print Delay = 2 ms iv. Tick the skip initial transient solution.

The output will be displayed in a new window as shown


360XTT u (10)



(Note : VR represents the response of I in the circuit for both RL and RC Circuit)

Time

2.0ms 2.1ms 2.2ms 2.3ms 2.4ms 2.5ms 2.6ms 2.7ms 2.8ms 2.9ms 3.0ms 3.1ms 3.2ms 3.3ms 3.4ms 3.5ms 3.6ms 3.7ms 3.8ms 3.9ms 4.0msV(V2:+) V(R4:2)

-4.0V

-3.0V

-2.0V

-1.0V

0.0V

1.0V

2.0V

3.0V

4.0V

50

Part C: RLC Circuit

Figure 7-23: RL Circuit Connect the circuit as shown in figure 7-23 by the following steps:

11) Start PSpice [Appendix A-1] 12) Add Resistor (R= 2K) [Appendix A-2]

13) Add Inductor (L=200 mH) [Appendix A-4]

14) Add Capacitor (C=0.1 uF) [Appendix A-3]

15) Add AC sine wave voltage source (Vsinpp) = 10 V[Appendix A-7]

h. VOFF = 0 i. VAMPL = 5 j. FREQ = 1600 Hz





k. Print step = 1000us l. Final time = 2ms m. No-Print Delay = 0.1 ms n. Tick the skip initial transient solution.



A B C

51


360XTT u (9)



Time

0.1ms 0.2ms 0.3ms 0.4ms 0.5ms 0.6ms 0.7ms 0.8ms 0.9ms 1.0ms 1.1ms 1.2ms 1.3ms 1.4ms 1.5ms 1.6ms 1.7ms 1.8ms 1.9ms 2.0msV(R4:2) V(V2:+)

-4.0V

-3.0V

-2.0V

-1.0V

0.0V

1.0V

2.0V

3.0V

4.0V

52

Equipments: x Resistor, capacitor, and inductor substitution boxes. x Function Generator. x Digital Multi-Meter DMM x CRO.

Procedure: Part A: RL Circuit

Figure 7-24: Circuit Diagram Figure 7-25: Sine Wave Voltage Source

1) Connect the circuit as shown in figure 7-23. (R= 2K) (L=200 mH)

2) Adjust the function Generator to generate sine wave with VPP =10 V, Frequency= 1600 Hz, (Note: be sure that the function generator is adjusted to high output impedance)

3) Measure and fill table 7-1. (VL will be measured by using the math function of the CRO)

Table 7-1 Adjust Measure Calculate

VS VR VL X (ms) T (ms) To

4) Compare T calculated with the T obtained from PSpice.

T (PSpice) = %error = (%error= %calculatedspicecalculated

TTT )

5) Compare T calculated with the theoretical T obtained from eq. (4).

T (theoretical) = %error = (%error= %ltheoretica

ltheoreticaT

TT calculated )

Note: Z = 2 S Freq.

Vpp/2

T

Experimental work

53

Part B: RC Circuit


1) Connect the circuit as shown in figure 7-24. R= 995 , C = 0.1 uF

2) Repeat the steps of part A and fill table 7-2.

Table 7-2

Adjust Measure Calculate VS VR VC X (ms) T (ms) To

3) Compare T calculated with the T obtained from PSpice.

T (PSpice) = %error = (%error= %calculatedspicecalculated

TTT )

4) Compare T calculated with the theoretical T obtained from eq. (6).

T (theoretical) = %error = (%error= %ltheoretica

ltheoreticaT

TT calculated )

Note: Z = 2 S Freq.

Vpp/2

T

54

Part C: RLC Circuit


1) Connect the circuit as shown in figure 7-28. R= 2K , C = 0.1 uF, L=200mH

2) Connect CRO ch1 to point A and ch2 to point B to measure Vs PP and VL PP = Vch1-ch2.

3) Connect CRO ch1 to point B and ch2 to point D to measure VR PP and VC PP =Vch1-ch2.

4) Connect CRO ch1 to point A and ch2 to point D to measure To between Vs and VR PP. 5) Fill table 7-3.

Table 7-3 Adjust Measure Calculate

VS VL PP VC PP VR PP X (ms) T (ms) To Pf

Q1: From table 7-3, verify KVL V = 0.

Vpp/2

T

A B D

s

55

Q2:

V Vin Vo Pt3 Pt1 Pt2

NOTE: Both signals have same frequency 1. Complete the following table.

2. Determine the frequency of the input voltage and the output current?

3. Determine the phase shift between Vin and Vo in seconds and degrees.

4. Is the current lag or lead the input voltage? State whether the circuitis RL or RC circuit

Pt # X-axis value Y-axis value 1 0.05 ms 0 2 0.55 ms 0 3 0

0

56

x Phase shift measuring between voltage and current.

x Calculation of average active, reactive, and apparent powers.

x Verification of power balance in the circuit.

x Improvement of power factor.

Power definitions P: Average active power in watts. Q: Reactive power in vars. |S|: Apparent power in VA. S: Complex power = P + j Q in VA. Power factor For max max,v IV V I IT T

v Iphase shiftT T T PF = power factor = cos(T)

We have three cases as shown in Table 8-1.

Table 8-1 Case Power Factor Phasor Diagram

T = 0 Unity power factor (V & I are in phase)

T = +ve Lagging power factor (I lags V)

T = -ve Leading power factor (I leads V)

V I

I V T

I

V T

Sinusoidal steady-state power calculations

8

Objectives

Theory

57

Power triangle S P j Q (1) Pf = cos(T) (2)

P, Q, S calculations Table 8-2

Case Equations Voltage Source

max max,v IV V I IT T

* max max max max1 1 cos sin2 2S V I V I jV IT T (3)

Resistor

2 2max max

2 2V I RP R

Q = 0, S = P (4)

Inductor

P = 0 2

2maxmax

12 2VQ I LL ZZ

S = j Q (5) Capacitor

P = 0 2

2maxmax

12 2

V cQ IcZ

Z

S = j Q (6)

Note: for any electric circuit, 0, 0, 0S P Q Power factor improvement In a typical electric circuit, the current lags the voltage as shown in Figure 8-2. By adding a capacitor

or (adjusting the existing capacitor in the circuit) T will be decreased and pf will be improved. The best value of pf is unity where T = 0.

Q

P

S

T

Figure 8-1: Power Triangle

I

V

jcZ

I V T

Figure 8-2: Lagging pf

58

Figure 8-3: PSpice Circuit Diagram


1) Start PSpice [Appendix A-1] 2) Add 2 Resistors R1= 1K, R3= 2K [Appendix A-2]

3) Add Inductor L1=100 mH[Appendix A-4]

4) Add capacitor C=0.1 uF[Appendix A-3]


x VOFF = 0 x VAMPL = 5 x FREQ = 1000





x Print step = 0 ns x Final time = 8 ms x No-Print delay = 6 ms x Step ceiling = 0.001 ms x Tick the skip initial transient solution.



PSpice Simulation

59

12) Using the toggle cursor [Appendix A-19], fill Table 8-3:

Table 8-3 VPP (R1) Difference in time (X) Phase Shift T pf (lead/lag/unity)

13) Change the value of capacitor to 0.25 uF and repeat the step 10.

14) The following wave form will be displayed in a new window:

15) Using the toggle cursor [Appendix A-19], fill Table 8-4:

Table 8-4 VPP (R1) Difference in time (X) Phase Shift T pf (lead/lag/unity)

16) Comment on the obtained power factor.

Time

6.0ms 6.2ms 6.4ms 6.6ms 6.8ms 7.0ms 7.2ms 7.4ms 7.6ms 7.8ms 8.0msV(L1:1) V(V1:+)

-5.0V

0V

5.0V

60

Equipments: 1) Function Generator

2) CRO, DMM

3) Electronic Bread Board

4) Resistor, capacitor and inductance substitution boxes.

5) Discrete resistors. Procedure: Part A Power Calculations:


1) Connect the circuit as shown in Figure 8-4 with the shown values.

2) Adjust the function generator to get sine wave with 10 VPP and freq. = 1 KHz. (Note: be sure that the

function generator is adjusted to high output impedance)

3) Connect the CRO channels to measure V1 PP and VR1 PP as shown in Figure 8-4.

4) Measure VPP (R2//L1//C1) = Ch1 Ch2

5) Fill Table 8-5.

6) Using equations 1 to 6, fill Table 8-6.

Table 8-5 V1 PP VR1 PP 'T between V1 & VR1 VPP (R2//L1//C1)

Table 8-6

360TTT' u pf

(lead/lag) PV1 QV1 PR1 PR2 QL1 QC1

Experimental Work

61

Q1: Verify average active and reactive power balance.

Part B Power factor improvement: 1) Change the capacitor value to 0.25 uf.

2) Fill Table 8-7.

Table 8-7 Measure Calculate

V1 PP VR1 PP 'T between V1 & VR1

T pf (lead/lag/unity)

Q2: explain the effect of capacitor on the pf.

62

x To be familiar with the protective devices for electric wiring.

x To study the final circuit diagram

x To study the calculation of customer electric energy cost.

The very nature of the grid system is such that power has to be transmitted over large distances. This

immediately creates a problem of voltage drop. To overcome this problem, a high voltage is used for

transmission (275 or 132 kV), the 275 kV system being known as the Super Grid. We cannot,

however, generate at such high voltages (the maximum in modern generators is 25 kV) and

transformers are used to step up the generated voltage to the transmission voltage. At the end of a

transmission line is a grid substation, where the requirements of the grid system in that area can be

controlled and where the transmission voltage is stepped down via a transformer to 132 kV. The

system voltage is then further reduced at substations to 33 000, 11 000 and 415/240 V.

Figure 9-1: Kuwait Electric Energy System

Electric Wiring & Energy Consumption

9

Objectives

Theory

275/132 KV

275 KV

415/240 V

11000/415 V

63

Distribution Board (DB): A distribution board (or panel board) is a component of an electricity supply system which divides an

electrical power feed into subsidiary circuits, while providing a protective fuse or circuit breaker for

each circuit, and safety protective devices, (RCD), in a common enclosure.

Figure 9-2: Distribution Board

64

Figure 9-3: DB 8-ways double busbar

Electric Fuse: In electronics and electrical engineering a fuse (from the Latin "fusus" meaning to melt) is a type of

sacrificial over-current protection device. Its essential component is a metal wire or strip that melts

when too much current flows, which interrupts the circuit in which it is connected. A fuse interrupts

excessive current (blows) so that further damage by overheating or fire is prevented. Wiring

regulations often define a maximum fuse current rating for particular circuits.

65

Figure 9-4: Electric Fuses

Low Voltage Circuit Breaker (LVCB) A circuit breaker is an automatically-operated electrical switch designed to protect an electrical

circuit from damage caused by overload or short circuit. Its basic function is to detect a fault

condition and, by interrupting continuity, to immediately discontinue electrical flow. Unlike a fuse,

which operates once and then has to be replaced, a circuit breaker can be reset (either manually or

automatically) to resume normal operation. Circuit breakers are made in varying sizes, from small

devices that protect an individual household appliance up to large switchgear designed to protect high

voltage circuits feeding an entire city.

Figure 9-4: Low Voltage CB

66

Fuses compared with circuit breakers Fuses have the advantages of often being less costly and simpler than a circuit breaker for similar

ratings. The blown fuse must be replaced with a new device which is less convenient than simply

resetting a breaker. Some types of circuit breakers must be maintained on a regular basis to ensure

their mechanical operation during an interruption. This is not the case with fuses, which rely on

melting processes where no mechanical operation is required for the fuse to operate under fault

conditions.

Earth Leakage CB and Residual Current Devices (RCD) x In non-technical terms if a person touches something, typically a metal part on faulty electrical

equipment, which is at a significant voltage relative to the earth, electrical current will flow

through him/her to the earth. The current that flows is too small to trip an electrical fuse which

could disconnect the electricity supply, but can be enough to kill. An ELCB detects even a small

current to earth (Earth Leakage) and disconnects the equipment (Circuit Breaker).

x Earth Leakage Circuit Breakers and Residual Current Devices are safety devices that offer that

additional protection. These two types of safety devices are used in areas that have high levels of

earth impedance. These devices have the primary purpose of reducing the risk of shock in the

event of a current flow to the earth.

Principle of operation of an RCD Figure 8-5 illustrates the construction of an RCD. In a healthy circuit, the same current passes

through the line coil and the load, and then back through the neutral coil. Hence, the magnetic effects

of line and neutral currents cancel out. In a faulty circuit, either line-to-earth or neutral-to-earth, these

currents are no longer equal. Therefore, the out-of-balance current produces some residual

magnetism in the core. As this magnetism is alternating, it links with the turns of the search coil,

inducing an electro-motive force (EMF) in it. This EMF in turn drives a current through the trip coil,

causing operation of the tripping mechanism.

Figure 9-5: RCD Circuit

67

Lighting circuits The loop-in system, this is the most common of all lighting circuitry and, as the name suggests,

circuit cables simply loop in and out of each lighting point figure 9-6.

Figure 9-6: Lighting Circuit Radial socket-outlet circuits Most domestic installations use ring final circuits to supply socket outlets, radial circuits are quite

acceptable. The recommendations for such circuits are given in table 9-1. These radial circuits are

shown in figure 9-7.

Table 9-1: Conventional Circuit Arrangements for Radial Socket outlet Circuits. Protective Device Size

Protective Device Type

Maximum Floor Area Served

Cable Size Number of Socket Outlets

30 A or 32 A any 75 m 2 4.0 m 2 unlimited

20 A any 50 m 2 2.5 m 2 unlimited

68

Figure 9-7: Radial Socket Outlet Circuit

Ring Final outlet circuits In electricity supply, a ring final circuit or ring circuit (informally also ring main or just ring) is an

electrical wiring technique developed that provides two independent conductors for live, neutral and

protective earth (ground) within a building for each connected load or socket as shown in figures 8-8-

a & 8-8-b. The ring acts like two radial circuits proceeding in opposite directions around the ring. If

the load is evenly split across the two directions, the current in each direction is half of the total,

allowing the use of wire with half the current-carrying capacity. In practice, the load does not always

split evenly, so thicker wire is used.

69

Figure 9-8-a: Ring Final Circuit

Figure 9-8-b: Ring Final Circuit

70

Power Consumption Consumers pay for the electrical energy they consume and NOT for the power. As before, the energy

is related to the power by:

Energy = Power x Time (1)

Example 1: Consider a 1200 W hairdryer. How much does it cost per month if you use it every day

for 15 minutes? The KWh in Kuwait costs 2 fils to the consumer and approximately 20

fils to the government.

Solution: We want the number of KW times the number of hours to find the energy in KWh. The

total time per month is about 15 min/day x 30 days/month = 450 min/month. = 450/60 =

7.5 h/month. So the energy used is 1.2 KW x 7.5 h = 9 KWh. Then, the cost is 180 fils.

Example 2: A refrigerator rated at 1000 W operates one third of time. What does it cost per month?

Assume 2 fils/KWh.

Solution: 1000 W = 1 KW. The number of hours that the fridge is running is 1/3 x 24 h/day x 30

days= 240 h. So. Cost = 1 KW x 240 h x 2 fils/KWh = 490 fils.

Sample of Warning Labels

71

Questions: Q1: What is the function of electric fuse? Q2: What is the function of circuit breaker? Q3: What is the function of earth leakage circuit breaker? Q4: A typical house contains air condition, clothes dryer, range, refrigerator, lighting and other

appliances. Complete table 9-1, given that cost for KWh is 4 fils. Calculate the bill of the house

for July.

Table 9-1 House Consumption in July

Item Consumption (KW)

Consumption Duration (h)

Total Consumption/Month

Cost

Air Condition 10 24

Clothes Dryer 2 2

Range 0.8 3

Refrigerator 0.5 24

Lighting 0.7 12

Total

207-spring-14-15-schedule207-spring-14-15

circuit lab manual

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