Binary Phase Shift Keying 205q2h

UNIVERSITY OF TRIPOLI FACULITY OF ENGINEERING ELECTRICAL AND ELECTRONIC ENGINEERING DEPARTMENT

DIGITAL CARRIER MODULATION BINARY PHASE SHIFT KEYING (BPSK) EE-491 L

By MUAD B. BAHROUN 02108253

Under Supervision of DR. AHMED S. ASHUR Spring 2016

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ABSTRACT

The Circuits that have been used in this project, are Modulator and Demodulator, and herby to demonstrate how the modulator works by choosing a desired digital data signal with low bit rate to be transmitted, on the phase output of an analog sinusoidal signal called Carrier that have greater frequency than the data signal, by using switching device (Transistor) and an operational amplifier. And to demonstrate the demodulator works by adding the modulated signal to a the same carrier, to distinguish where the data high and low state are located over a time, then to find the peak values of the signal that have been added, by using envelope detector device, then a decision device of fixed threshold point, is to be decided whether the signal is high and low.

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-List of Contents CHAPTER ONE…………………………………………………………………...........(4) 1.1 INTRODUCTION………………………………………………………………………….(5) 1.2 Binary-Phase Shift Keying (BPSK) Modulation and Demodulation………………….(5) 1.3-The Mathematical Model………………………………………………….……………..(6) 1.3.1 Generation of BPSK Signal……………………………………………………(6) 1.3.2 Power Spectral Density and Bandwidth………………………...……………(6) 1.3.3 Demodulation of BPSK Signal……………………………………………...…(7)

CHAPTER TWO……………………………………………………………...…………(8) 2.1 COMPONENTS…………………………………………………………………….……(9) 2.2 Modulation Circuit……………………………………………………………………….(9) 2.2.1 The Theory of Operation…………………………………………………..…(12) 2.3 Demodulation Circuit……………………………………………………………………(12) 2.3.1 The Theory of Operation……………………………………………………..(13)

CHAPTER THREE…………………………………………………………………..(15) 3.1 BPSK Modulator circuit………………………………………………………………....(16) 3.2 BPSK Demodulator circuit……………………………………………………………...(16)

CHAPTER FOUR……………………………………………………………………..(17) 4.1-BPSK Modulator circuit……………………………………………………………..…..(18) 4.2-BPSK Demodulator circuit…………………………………………………………...…(18) 4.3 Components of the Circuits…………………………………………………………….(19) 4.3.1 Resistor…………………………………………………………………………(19) 4.3.2 Capacitor…………………………………………………………………..…...(20) 4.3.3 OP-AMP………………………………………………………………………..(21) 4.3.4 Diode……………………………………………………………………………(22) 4.3.5 Transistor………………………………………………………………………(22) 4.4 Readings………………………………………………………………………………….(23)

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CHAPTER FIVE………………………………………………………………………(27) 5.1 Conclusion……………………………………………………………………………….(28) 5.2 References……………………………………………………………………………….(28)

CHAPTER SIX…………………………………................................................…...(29) 6.1-LM741 OP=AMP………………………………………………………………………...(30) 6.2-2N1711 NPN TRANSISTOR…………………………………………………………...(38) 6.3-1N4001-DIODE………………………………………………………………………….(41)

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CHAPTER ONE

WHAT IS BPSK ?

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1.1-INTRODUCTION: A digital signal can modulate the amplitude, frequency, or phase of a sinusoidal Carrier wave. If the modulating waveform consists of none return to zero (NRZ) Rectangular pulses, then the modulated parameter will be switched or keyed from One discrete value to another. (Figure 1) illustrates binary amplitude-shift keying (ASK), frequency-shift keying (FSK), and phase–shift keying (PSK). In each of these Situations we need a modulator at the transmitter and at the receiver a demodulator To recover the baseband signal. Such a modulator demodulator combination is called A MODEM.

Figure 1 Binary modulated waveforms: (a) ASK, (b) FSK, and (c) PSK.

1.2- Binary-Phase Shift Keying (BPSK) Modulation and Demodulation: BPSK (also sometimes called PRK, phase reversal keying, or 2PSK) is the simplest form of phase shift keying (PSK). It uses two phases which are separated by 180° and so can also be termed 2-PSK (Figure 2). It does not particularly matter exactly where the constellation points are positioned, and in (Figure 3) they are shown on the real axis, at 0° and 180°.

Figure 2

Figure 3 Constellation Diagram

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1.3-The Mathematical Model: 1.3.1-Generation of BPSK Signal

Figure 4 Block Diagram of Phase shift keying modulator.

𝑍(𝑡) = {

𝑆1 (𝑡) = −𝐴𝑐𝑜𝑠(2𝜋𝑓𝑐 𝑡) , 0 < 𝑡 < 𝑇𝑏 (𝑏𝑘 = 0) 𝑆2 (𝑡) = 𝐴𝑐𝑜𝑠(2𝜋𝑓𝑐 𝑡) , 0 < 𝑡 < 𝑇𝑏 (𝑏𝑘 = 1)

…..Eq 1

In PSK signaling schemes waveforms Z(t) , are used to convey binary digits 0 and 1, respectively. The binary PSK waveform Z(t) can be described by 𝑍(𝑡) = 𝐷(𝑡)cos(2𝜋𝑓𝑐 𝑡)

…..Eq 2

Definitions: . A = Voltage Amplitude{𝑉𝑜𝑙𝑡}. . 𝒇𝒄 = Carrier Frequency{𝐻𝑒𝑟𝑡𝑠}. . 𝑻𝒃 = Bit duration{𝑆𝑒𝑐𝑜𝑛𝑑𝑠}. . 𝒃𝒌 = Bit Key “0 logic state” or “1 logic state”. . 𝑺𝒊 (t) = Modulated Signal at certain state. . D(t) = NRZ random binary waveform with period 𝑇𝑏 and levels (-1) and (+1). . Z(t) = General form of BPSK Modulation.

1.3.2-Power Spectral Density and Bandwidth: The power spectral density of the PSK signal can be shown to be: 𝐺𝑧 (𝑓) =

𝐴2 4

[𝐺𝐷 (𝑓 − 𝑓𝑐 ) + 𝐺𝐷 (𝑓 + 𝑓𝑐 )]

…..Eq 3

Since, D(t) is a random binary waveform with levels (-1) and (+1). The autocorrelation function and the power spectral density of D(t) are: |𝜏|

1 + 𝑇 , |𝜏| ≤ 𝑇𝑏 𝑅𝐷𝐷 (𝜏) = { 𝑏 ……Eq 4 0, 𝑂𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 And

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𝐺𝐷 (𝑓) =

𝑆𝑖𝑛2 (𝜋𝑓𝑇𝑏 ) 𝜋 2 𝑓 2 𝑇𝑏

…….Eq 5

Substituting Eq 4 into Eq 3 we obtain the PSD of Z(t) as :

𝐺𝑧 (𝑓) =

𝐴2 𝑠𝑖𝑛2 (𝜋𝑇𝑏 (𝑓−𝑓𝑐 )) 4

[

𝜋2 𝑇𝑏 (𝑓−𝑓𝑐 )

+

𝑠𝑖𝑛2 (𝜋𝑇𝑏 (𝑓+𝑓𝑐 )) 𝜋2 𝑇𝑏 (𝑓+𝑓𝑐 )

]

…Eq 6

The Transmission Bandwidth requirement for the PSK signal is:

…Eq 7

𝐵𝑇 = 2𝑟𝑏 1.3.3-Demodulation of BPSK Signal

Figure 5 Block Diagram of Phase shift keying Demodulator

Stage 1 : The input BPSK Signal is been multiplied or Summered by a carrier Signal. Note (the carrier Signal should be in phase with the BPSK Signal to avoid any error). Also if the Multiplier is used then the output is doubled the carrier frequency. else the Summer is used then the output is doubled the carrier amplitude

Stage 2 The product of two signal is been filtered by any of these methods: a . Low Filter b. envelope Detector

Stage 3 Threshold Device is deciding whether the filtered signal is “1” or “0”

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CHAPTER TWO

THE SIMULATION

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2.1-COMPONENTS: 1- Function Generator

Quantity (2)

2- 4-Channel Oscilloscope

Quantity (3)

3- LM741 (OP-AMP)

Quantity (3)

4- Resistor 1KΩ

Quantity (3)

Color Code (brown-black-red-gold) 5- Resistor 8.2KΩ

Quantity (1)

Color Code (gray-red-red-gold) 6- Capacitor 100nF

Quantity (1)

7- 1N4004 Diode

Quantity (1)

8- 2N1711 NPN Transistor

Quantity (1)

2.2-Modulation Circuit:

Figure 6 BPSK Modulator

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Figure 7 NRZ Message Signal

The Message Signal is set at 1 Volt and Frequency of 5 KHz

Figure 8 Carrier Signal

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The carrier frequency is set to 2 Volt and frequency of 40 KHz

Figure 9 VBPSK Signal Output

Figure 10 All the Signals Stages (colored)

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2.2.1-The Theory of Operation: A .Case “0” digit as input When the “0” digit as an input the Transistor is off ,then the current through R12 and R8 is nearly 0 Amps ,that means node 3 and node 10 are the same voltage as the carrier ,the op-amp is works as buffer with unity gain (Figure 6), As a results the output is in phase of the input (0° ). B .Case “1” digit as input When the “1” digit as an input the Transistor is on, then the node 3 is grounded ,due to the op-amp principle ,the node 3 and node 12 are the same due to high input impedance ,then the op-amp circuit work as inverting with gain of (-1) (Figure 6). As a results the output is out of phase of the input (180° ).

2.3-Demodulation Circuit:

Figure 11 Demodulator of BPSK

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Figure 12 All the Stages of Demodulation

2.3.1-The Theory of Operation: As we can see in (Figure 12) if the input signal is (0° ) [Green waveform], then the summer output is double the amplitude [White waveform] ,then negative cycle is removed by connected diode in series so we can fine the envelope of the signal by using RC circuit (Envelope Detector) [Violet waveform] ,then the signal is compare with a fixed value of 0.978 volt below that value the comparator is (-9) Volt which is “0” digit.[Red waveform].

In the other case if the input signal is 180° [Green waveform] , then the summer output is Zero ,then the out is “1” digit .[Red waveform].

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Figure 13 The delay time between the original message and the demodulated Signal

The Delay time is about 22.962 µS

Note: In the (Figure 13) the original message is an ideal NRZ signal, And the output have slope at both rise edge and fall edge, and that’s due to having only One fixed point as compare value.

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CHAPTER THREE

Printed Circuit Board (PCB) Design

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3.1-BPSK Modulator circuit

Figure 14 Modulator

Figure 15 Demodulator

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CHAPTER FOUR

THE CIRCUIT DESIGN

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4.1-BPSK Modulator circuit

Figure 14 Modulator

4.2-BPSK Demodulator circuit

Figure 15 Demodulator

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4.3 Components of the Circuits 4.3.1 Resistor

Figure 16 Resistors

A resistor is a two-terminal electronic component that produces a voltage across its terminals that is proportional to the electric current through it in accordance with Ohm's law: V = IR Resistors are elements of electrical networks and electronic circuits and are ubiquitous in most electronic equipment. Practical resistors can be made of various compounds and films, as well as resistance wire (wire made of a high-resistivity alloy, such as nickel/chrome).The primary characteristics of a resistor are the resistance, the tolerance, maximum working voltage and the power rating. Other characteristics include temperature coefficient, noise, and inductance. Less well-known is critical resistance, the value below which power dissipation limits the maximum permitted current flow, and above which the limit is applied voltage. Critical resistance depends upon the materials constituting the resistor as well as its physical dimensions; it's determined by design. Resistors can be integrated into hybrid and printed circuits, as well as integrated circuits. Size, and position of leads (or terminals) are relevant to equipment designers; resistors must be physically large enough not to overheat when dissipating their power

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4.3.2 Capacitor

Figure 17 Capacitors

A capacitor or condenser is a ive electronic component consisting of a pair of conductors separated by a dielectric. When a voltage potential difference exists between the conductors, an electric field is present in the dielectric. This field stores energy and produces a mechanical force between the plates. The effect is greatest between wide, flat, parallel, narrowly separated conductors. An ideal capacitor is characterized by a single constant value, capacitance, which is measured in farads. This is the ratio of the electric charge on each conductor to the potential difference between them. In practice, the dielectric between the plates es a small amount of leakage current. The conductors and leads introduce an equivalent series resistance and the dielectric has an electric field strength limit resulting in a breakdown voltage. Capacitors are widely used in electronic circuits to block the flow of direct current while allowing alternating current to , to filter out interference, to smooth the output of power supplies, and for many other purposes. They are used in resonant circuits in radio frequency equipment to select particular frequencies from a signal with many frequencies

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4.3.3 OP-AMP

Figure 18 Op-Amp Chip

Figure 19 Op-Amp Chip PINS

The Operational Amplifier is probably the most versatile Integrated Circuit available. It is very cheap especially keeping in mind the fact that it contains several hundred components. The most common Op-Amp is the 741 and it is used in many circuits. The OP AMP is a ‘Linear Amplifier’ with an amazing variety of uses. Its main purpose is to amplify (increase) a weak signal - a little like a Darlington Pair. The OP-AMP has two inputs, INVERTING ( - ) and NON-INVERTING (+), and one output at pin 6 (Figure 19).

The chip can be used in a circuit in two ways. If the voltage goes into pin two then it is known as an INVERTING AMPLIFIER. If the voltage goes into pin three then the circuit becomes a NON-INVERTING AMPLIFIER.

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4.3.4 Diode

Figure 20 Diodes

The key function of an ideal diode is to control the direction of current-flow. Current ing through a diode can only go in one direction, called the forward direction. Current trying to flow the reverse direction is blocked. They’re like the one-way valve of electronics. If the voltage across a diode is negative, no current can flow, and the ideal diode looks like an open circuit. In such a situation, the diode is said to be off or reverse biased. As long as the voltage across the diode isn’t negative, it’ll “turn on” and conduct current. Ideally* a diode would act like a short circuit (0V across it) if it was conducting current. When a diode is conducting current it’s forward biased (electronics jargon for “on”).

4.3.5 Transitor

Figure 21 Transistors

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Transistors make our electronics world go ‘round. They’re critical as a control source in just about every modern circuit. Sometimes you see them, but more-often-than-not they’re hidden deep within the die of an integrated circuit. In this tutorial we’ll introduce you to the basics of the most common transistor around: the bi-polar junction transistor (BJT).In small, discrete quantities, transistors can be used to create simple electronic switches, digital logic, and signal amplifying circuits. In quantities of thousands, millions, and even billions, transistors are interconnected and embedded into tiny chips to create computer memories, microprocessors, and other complex ICs.

4.4 Readings

-The Data Signal to be transmitted : 1 Volt/Div

100µs/Div

Type =Squire Wave 50% Duty Cycle Peak Voltage 1 X 1=1 Volt Frequency 1/(2 x 100µ)= 5 KHz

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-The Carrier Signal : 1 Volt/Div

10µs/Div

Type = Sinusoidal wave

Peak Voltage 1 X 1=1 Volt

Frequency 1/(2.5 x 10µ)= 40 KHz

-The Modulated Signal

: 1 Volt/Div

50µs/Div

Type = Sinusoidal wave

Peak Voltage 1 X 1=1 Volt

Frequency 1/(2 x 50µ)= 40 KHz

NOTE: we notice that the output amplitude is decreased when the Data signal is high due to the voltage drop across R10 and R11 (Figure 6) when the op amp circuit works as inverting. .

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-The output of the summer circuit : 1 Volt/Div

100µs/Div

Type = Composite Sinusoidal waves Max Peak Voltage 1 X (2+0.5/5)=2.1 Volt Min Peak Voltage 1 x 0.25= 0.25 Volt Frequency 1/(0.25 x 100µ)= 5 KHz

NOTE: we notice that there are two peaks values ,one is MAX and the other one is MIN, in theory the MIN should be zero voltage due to the sum of phase zero and out of phase with the same amplitude ,the value of the MIN is accruing during the time delayed of the signal which causing little phase shift from the original signal.

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-The Envelope of the Signal : 1 Volt/Div

50µs/Div

Peak to Peak Voltage 1.06 Volt Frequency 1/(4 x 50µ)= 5 KHz

NOTE: The RC value of the Envelope Detector circuit is been selected so it can charging and discharging smoothly, so we can detect the Message Signal from the summer output C1 = 100nF R4 = 1KΩ τ = R4 x C1 = 100 µSec

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CHAPTER FIVE

Summery

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5.1 Conclusion The Design of the BPSK Modulator circuit is working as it should be, the change of output phase according to the input data is neat and clear The Design of the last stage of the BPSK Demodulator circuit is not working which is a Comparator circuit, is not satisfy the Simulation outputs, so to enhance the circuit, we replace the Comparator with a Schmitt Trigger Circuit, in that case we have two threshold voltage, one to detect from high “1” to low “0” and the other one is to detect from low “0” to high “1”.

5.2 References [1] www.wikipedia.org [2] www.electroniccircuit.com [3] Communication Systems By A.Bruce Carlson & Paul B. Crilly, 4th edition [4] Communication Systems II, 1st Edition. By Osama A. Alkishriwo Copyright ©2014 John Wiley & Sons, Inc. [5] Digital Communications By Dr.Abbas

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CHAPTER SIX

DATASHEETS

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6.1-LM741 OP=AMP

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6.2-2N1711 NPN TRANSISTOR

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6.3-1N4001-DIODE

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