UEEA1253 SIGNALS, CIRCUITS & SYSTEMS

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Faculty of Engineering And Science

Y.C.See

chark97@hotmail.com

seeyc@utar.edu.my

Instructors

Instructor 1: See Yuen Chark Email: seeyc@utar.edu.my Level 5: East Wing 012-3385077

Instructor2: Chong Poh Kit Email:

Week 1- Week 7 (18 hrs + ) Tutorial 1-3

Week 8- Week 13/14

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Instructors

Instructor 3: Chong Zan Kai Email: seeyc@utar.edu.my

Instructor4: Lin Horn Seng Email:

Tutorial 1-3

Tutorial 4-5

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Lab session starts at Week 3 (Every Mon 9-12pm, 2-5pm,

every Tue 2-5pm and every Wed 2-5 pm)

Tutorial n Lab session starts at Week 3

ANNOUNCEMENT

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Tutorial starts at Week 3

Week 3 · Tutorial 1 (Odd)

Week 4 · Tutorial 1 (Even)

Week 5 · Tutorial 2 (Odd) · Replacement of Tutorial 2 (Even) on Saturday (14-Feb-2015) 9-12pm. Three sessions. Venue to be confirmed.

Week 6 · CNY.

Week 7 · Tutorial 3 (Odd)

Week 8 · Tutorial 3 (Even) Week 9- Mr.Lin

Syllabus

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Refer to the attachment!

Introduction Office : 5th Floor east wing

Final Exam = 60% (2+2+2) – Kampar!

Lab = 10 marks (See & Dr.Chong)

Mid Term Test = 15 marks (See)- Week 8

Assignment = 15 marks (Dr. Chong)

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CLASS Schedule

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18 Hours lectures – Wk 1- Wk7

CNY – 19-20/2 – WK 6

Lecture class resume –18th Feb 2014 (THU)

LABs & TUTORIALs start in week 3 (WED) 1 report (Lab 1 + Lab 2)

REPLACEMENT Just revision class

MID TERM OPTION 1 : 7/3/15(Sat) –8:30am-10:00am (DK3, DK4A, DK4B)

OPTION 2: 8/3/15(Sun) –2-4:00pm(DK1, DK2A, DK2B)

OPTION 3: 5/3/15(Thu) –6-8:00pm (DK1, DK2A, DK2B)

Time table

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LAB 1 & LAB 2

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REPLACEMENT HOLIDAY AND THAIPUSAM ON 2/FEB/2015 (WED) & 3/FEB/2015 (THU) WEEK3- 4 LAB SESSIONS

WEEK 4- 1 LAB SESSION (WED) WEEK 5 – 3 LAB SESSIONS (MON & TUE)

MID-TERM

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5/3/2015 (THU) @ 5:50-7:10PM VENUE: DK1(BI+ET+MH+MM) (8+7+42+5 = 62) DK2A (ME-I+EC) (ID:803003-1205143)

(54+6=60) DK2B(ME-II)(ID:1205493-1405881) (54) DK3(EEE) (59)

FACEBOOK GROUP

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https://www.facebook.com/groups/329909983870884/

Text Book Dorf, Richard C., & Svoboda, James A. (20062013). Introduction to electric circuits. (7th 9th ed.). Hoboken N.J: John Wiley & Sons.

Wadhwa, C. L. (2007). Network analysis and synthesis : (including linear system analysis)(3rd ed) New Delhi : New Age International.

References : 1.Alexander and Sadiku, (2009) 4th Ed. Fundamentals

of Electric Circuits, McGraw-Hill. ISBN: 9780071272384

2. Others…

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Expectation! SIGNALS, CIRCUITS & SYSTEMS often involves MATHS &

ELECTRICAL Perquisite - UEEA1243 Circuit Theory

Circuits elements – Capacitors & Inductors DC & AC circuit analysis Differentiation & Integral calculus Linear differentiation equation

I do revision – fast. I point you in the right direction, but you have to get

there You are expected to read and prepare before lectures. Discussion is good and always welcome

Boring for you and for me if I just talk for 120 minutes You know stuff I don’t I make mistakes Ask questions anytime If you’re confused probably others are too Let me know when I’m talking too fast

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CIRCUITS & SYSTEMS SYLLABUS

1. INTRODUCTION to Network - Revision (2)

Lumped Circuit Assumption

Nodal & Mesh analysis

Network Theorems – Thevenin , Norton…

Attenuator design (new)

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2. Time Domain Analysis (7) Energy storage elements

The source-free and step responses of RC and RL circuits.

The unit step, impulse and ramp functions. Initial and final values.

The complete response of RLC circuits.

First order circuit and second order circuit analysis

Steady-state response to sinusoidal input.

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3. Frequency Domain Analysis (9)

The Laplace transforms.

Solutions of differential equations describing a circuit.

Applications of Laplace transforms in circuit analysis.

The Fourier series and circuit applications.

The Fourier Transform and circuit applications.

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4. Two-port Networks (7) Impedance, Z, admittance, Y, hybrid, h, and transmission matrix parameters.

Relationships between matrices.

Interconnection of networks.

Network transform

Impedance transform

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5. Frequency Response and Bode Plots (2) Transfer function.

Gain and phase shifts. The decibel.

Bode plots.

Series and parallel resonance. Quality factor, bandwidth and selectivity.

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6. Filter Synthesis (8) Synthesis of one-port impedance function, positive real function, canonical forms

Types of Filters

Filter functions: Butterworth, Chebyshev

Filter synthesis

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The journey begins here…

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Path to $$

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Nature Formula Lumped circuit

Amp Digital

Combinational Logic

Clock ISA

Analog

Op-amp

Analog system

components – osc, filter….

$$

x86 etc

Language

Java C…

Software

OS

What is system?

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Collection of components that put together to serve a particular purpose.

E.g railway system, transportation system,…

Very often we are interested in finding out the response of the system under the influence of the particular input.

Single/multiple input output system

Input – current sources or voltage sources

System Input Output

Circuit Input (Excitation)

Output(Response)

Analysis and Synthesis

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Interested to find the responses or o/p at various point in a system.

Analysis: Given a circuit and its input, find the output of response.

The output is unique.

Analysis can be in Time domain or Frequency domain

Synthesis: Given an Input and an Output, find the circuit. The answer is not unique

5 volt 10 volt

Circuit ?

More than one circuit design to give a relevant output

Classification of System I

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Source

Independent

Dependent A voltage –controlled voltage source (VCVS)

A current –controlled voltage source (CCVS)

A voltage –controlled current source (VCCS)

A current –controlled current source (CCCS)

SOURCES

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Symbols for independent voltage source

Symbols for independent current source

V1 V1µ

VCVS

V1 V1g

VCCS

I1

I1α

CCCS

I1

V1γI1

CCVS

E.g.

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Classification of System II

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Circuit Type:

Linear----Nonlinear

Continuous time vs Discreet time

Time invariant (Constant parameter) ----Time variant (Variable parameter)

Passive----Active

Lumped----Distributive

Classification of system I

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Linear system vs non-linear system

a system is said to be linear if it satisfies the principle of superposition

If x1(t) y1(t) and x2(t) y2(t) then C1x1(t) + C2x2(t)

C1y1(t) + C2y2(t) where C is constant

Most of the electrical network that you learned earlier is belong to this class

Zero initial state.

Does not have extra source

LINEAR SYSTEM?

E.g.

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Classification of system II

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i

u

i

u

t1 t2

i

u

i

u

t1 t2

Linear Time Invariant

Linear Time variant

Nonlinear Time Invariant

Nonlinear Time Variant

Lumped vs. Distributed circuit

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A lumped circuit is one where all the terminal voltages and currents are functions of time only. Lumped circuit elements include resistors, capacitors, inductors, independent and dependent sources.

An distributed circuit is one where the terminal voltages and currents are functions of position as well as time. Transmission lines are distributed circuit elements

Network Theorem/Analysis

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I’m sure that you are familiar with

Kirchhoff’s law – Dorf pg 53 or Sadiku pg 37

Mesh current and nodal analysis – Dorf 108 or Sadiku pg 81

Superposition theorem – Dorf 167 or Sadiku pg 130

Thevenin’s and Norton theorems – Dorf 171 or Sadiku pg 139-150

Kirchhoff’s

Current Law. At any junction in an electric circuit the total current flowing towards that junction is equal to the total current flowing away from the junction

Voltage Law. In any closed loop in a network, the algebraic sum of the voltage drops (i.e. products of current and resistance) taken around the loop is equal to the resultant e.m.f. acting in that loop. ( ) 0k nodei =∑

( ) 0k nodev =∑

KVL and KCL

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Superposition theorem

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The principle of superposition states that for a linear circuit consisting of linear elements and independent sources, we can determine the total response by finding the response of each independent source with all other independent sources set to zero and then summing these individual responses.

Thevenin’s

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The current in any branch of a network is that which would result if an e.m.f. equal to the p.d. across a break made in the branch, were introduced into the branch, all other e.m.f. being removed and represented by the internal resistances of the sources.

Procedures remove the resistance, R from that branch,

determine the open-circuit voltage, E, across the break,

remove each source of e.m.f. and replace them by their internal resistances and then determine the resistance, r, ‘looking-in’ at the break,

determine the value of the current from the equivalent circuit

Norton

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The current that flows in any branch of a network is the same as that which would flow in the branch if it were connected across a source of electrical energy, the short-circuit current of which is equal to the current that would flow in a short-circuit across the branch, and the internal resistance of which is equal to the resistance which appears across the open-circuited branch terminals.

Procedures - to determine the current flowing in a resistance R of a branch AB of an active network: short-circuit branch AB determine the short-circuit current Isc flowing in the branch remove all sources of e.m.f. and replace them by their internal

resistance (or, if a current source exists, replace with an open-circuit), then determine the resistance r,‘looking-in’ at a break made between A and B

determine the current I flowing in resistance R from the Norton equivalent network

Thevenin? Norton? I=?

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E.g.

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Kirchhoff, Superposition, Thevenin, Norton !

Find current to 4 ohm

Mesh Analysis

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Technique in Mesh Theorem

Apply KVL to each closed loop

Express element voltages as a function of mesh current.

Nodal Analysis

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There are n nodes. Need only apply KCL to (n – 1) nodes. Why? Because only

(n – 1) independent equations.

One node is used as datum / reference / earth / ground

Apply KCL at any node except reference node.

Convert the elements current as a function of node voltage

E.G - Nodal

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Current at 2 ohm and 3 ohm?

Findings

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KCL is the basis of nodal analysis – in which the unknowns are the voltages at each of the nodes of the circuit.

KVL is the basis of mesh analysis – in which the unknowns are the currents flowing in each of the meshes of the circuit.

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Attenuator

Power

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‘The power transferred from a supply source to a load is at its maximum when the resistance of the load is equal to the internal resistance of the source.’

What should be the load R in order to have max power transfer? Application?

E.g.

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Stereo amplifier design

Is the above diagram looks similar?

THEVENIN!

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Impedance matching

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is an important consideration in electronic and communications devices which normally involve small amounts of power.

E.g.Coupling an aerial to a transmitter or receiver, or coupling a loudspeaker to an amplifier.

Also, the importance of matching a load to a source for maximum power transfer is extremely important in microwaves, as well as all manner of lower frequency applications such as electrical generating plants and solar cells.

Impedance matching (2)

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Characteristic impedance

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The source and load impedances should equal the characteristic impedance of the transmission line, as this minimizes signal reflections

For any passive two port network it’s found that a particular value of load impedance can always be found which will produce an input impedance having the same value as the load impedance.

Symmetrical network

Notes

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Attenuator

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A device for introducing a specified loss between a signal source and a matched load without upsetting the impedance relationship necessary for matching.

The loss introduced is constant irrespective of frequency - pure resistances.

There are many ways in which resistors can be arranged in attenuator circuits with the Potential Divider Circuit being the simplest type of passive attenuator circuit.

Let’s do some maths

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Characteristic Impedance for T network

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If the output terminal is open circuited – then

If short circuited then

Characteristic impedance,

How about this?

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Start “looking in” at the input port

Π

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If the output terminal is open circuited – then

If short circuited then

Before moving on let’s find out dB

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The decibel, abbreviated to "dB", is generally defined as the logarithm measure of the voltage, current or power ratio and represents one tenth 1/10th of a Bel. In other words it takes 10 decibels to make one bel

Ratio (1)

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Now assume an ideal attenuator - R

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For T attenuators

If symmetrical -

T…

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Find I1, V,V2,and N

Using

Find R1 and R2

T…

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T-pad attenuator

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For Π attenuator

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From and

The attenuation factor

Π

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and

Π

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To find R1-

Π

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From

=>

Π attenuator

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E.g.

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Design a T-section symmetrical attenuator pad to provide a voltage attenuation of 20 dB and having a characteristic impedance of 600Ω.

Insertion loss (1)

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Insertion loss (2)

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generator E connected directly to a load ZL and the current flowing be IL and the p.d. across the load VL. z is the internal impedance of the source.

2-port network is connected - The current through the load, shown as I2, and the p.d. across the load, shown as V2, will generally be less than current IL and voltage VL

Insertion loss (3)

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When the two-port network is terminated in its characteristic impedance Z0 the network is said to be matched. In this case the input impedance is also Z0, thus the insertion loss is simply the ratio of input to output voltage (=V1/V2).

For a network terminated in its characteristic impedance

Challenging question

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A 𝜋𝜋 attenuator has a series resistor of 1000Ω are parallel with two 500Ω . Determine Its characteristic impedance The insertion load when matching load is achieved.

2012 question

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The resistances R1 and R2 in Figure Q1(a) are given by the following formula:

where N is the insertion loss ratio. Find the values of resistors R1 and R2 to obtain 3dB insertion loss. Assume R0=50 ohm.

(5 marks)

01 11 R

NNR+−

= 022 12 R

NNR−

=

Switched Attenuator

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Instead of having just one attenuator to achieve the required degree of attenuation, individual attenuator pads can be connected or cascaded together to increase the amount of attenuation in given steps of attenuation.

By switching in the appropriate attenuators, the attenuation can be increased or decreased in fixed steps as shown below.

EXAMPLE

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Here, there are four independent resistive attenuator networks cascaded together in a series ladder network with each attenuator having a value twice that of its predecessor, (1-2-4-8).

Each attenuator network may be switched "in" or "out" of the signal path as required by the associated switch producing a step adjustment attenuator circuit that can be switched from 0dB to -15dB in 1dB steps and the total circuit attenuation is the sum of all four attenuators switched "in".

So for example an attenuation of -5dB would require switches SW1 and SW3 to be connected, and an attenuation of -12dB would require switches SW3 and SW4 to be connected, and so on.

2013 Questions (Kampar)

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D dB 20/10DN =

011 R

NNRa −+

= 0

2

21 R

NNRb

−=

1 1.1220 869.67 5.77 2 1.2589 436.25 11.61 4 1.5849 220.97 23.85 8 2.5119 116.14 52.84

(8 marks) The four independent pi-attenuator networks are cascaded together in a series ladder

network. Each attenuator network can be switched in and out of the signal path as required by the associated switch producing a step adjustment attenuator circuit that can be switched from 0dB to 15dB in 1dB step.

(2 marks) The total circuit attenuation is the sum of all four attenuators switched in. For

example, an attenuation of 10dB would require the 2dB and 8dB attenuator networks to be connected as shown in the figure above. (2 marks)

Rb

Ra Ra

Rb

Ra Ra

Rb

Ra Ra

Rb

Ra Ra 1dB 2dB 4dB 8dB

2014 Questions (I)-HOMEWORK

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Q1. (a) Based on the given formula in Table Q1 (a), choose the related equation and design a Π attenuator, given that the voltage attenuation is 18dB with characteristic impedance of 600Ω.

011a

NR RN+

=−

011c

NR RN−

=+

2

01

2bNR R

N−

= 02

21d

NR RN

=−

Table Q1(a)

(6 marks)

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2014 Questions (II) HOMEWORK

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Q2. (a) Figure Q2 (a) shows an attenuator inserted between a source VS and a load RL. Design the attenuator (i.e. determine R1 and R2) to obtain 10dB attenuation if the image impedance of the attenuator is R0 = 50Ω. Use the following formula:

01 11 R

NNR+−

= 022 12 R

NNR−

=

Next, use mesh or node analysis to verify that the voltage at the load RL exhibits 10dB attenuation. (15 marks)

Figure Q2 (a)

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References

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Dorf, Richard C., & Svoboda, James A. (2014). Introduction to electric circuits. (8th ed.). Hoboken, NJ: John Wiley & Sons.

Alexander, Charles K., & Sadiku, Matthew N.O. (2007). Fundamentals of electric circuits. Boston: McGraw-Hill Higher Education.

Hayt, William; Kemmerly, Jack E. (1971), Engineering Circuit Analysis (2nd ed.), McGraw-Hill, ISBN 0-07-027382-0

John Bird. (2007) Electrical circuit theory and technology.Newness

J.David Irwin, R.Mark Nelms (2010) Basic Engineering Circuit Analysis. Wiley