Mamunar Rahoman

Project Title: Signal Transmit and Receive using Frequency Modulator and PLL (Phase-Locked Loop) Demodulator.

Project duration: Undergraduate, 3rd Year 2nd Semester

Objective: The objective of this project is to create a virtual representation of a signal transmission system using an FM modulator and a PLL-based demodulator in MATLAB. The project aims to simulate the modulation and demodulation processes, analyze the system performance, and provide a visual understanding of frequency modulation and signal recovery in communication systems.

Tool used: MATLAB

Figure: Bock Diagram for MATLAB Graphical User Interface (GUI) of FM modulation and demonstration

Figure: Graphical User Interface of signal transmission system.

Abstract: Frequency modulation (FM) and demodulation are essential techniques used in various communication systems to transmit and extract information. This abstract provides an overview of the principles, processes, and applications of FM modulation and demodulation. FM is a modulation technique that involves varying the frequency of a carrier signal in proportion to the instantaneous amplitude of a modulating signal. This abstract explains the basic principles behind FM modulation, including the concepts of frequency deviation and modulation index, which determine the extent of frequency variation and the fidelity of the modulated signal. It also discusses the advantages of FM, such as its resistance to noise interference and its ability to provide high-fidelity transmission. Demodulation is the process of extracting the original modulating signal from the FM-modulated carrier. This abstract describes various demodulation techniques, including popular methods such as frequency discriminators and phase-locked loops (PLL). It highlights the importance of demodulation in recovering the original information and the challenges associated with accurate demodulation in the presence of noise and other distortions. The abstract also explores the applications of FM modulation and demodulation in different communication systems, such as FM radio broadcasting, two-way radio communication, and wireless data transmission. It emphasizes the widespread use of FM in industries ranging from entertainment to public safety, highlighting its ability to provide clear audio and robust signal transmission. In conclusion, this abstract emphasizes the significance of FM modulation and demodulation in modern communication systems. It highlights the importance of understanding the principles and techniques of FM modulation and demodulation to ensure efficient and reliable communication in various domains.

Keywords: Frequency Modulation, Frequency Demodulation, Carrier Signal, Frequency Deviation, Fidelity of Signal, Interference, Phase-Locked Loop(PLL).

Introduction: Frequency modulation (FM) and demodulation are fundamental concepts in the field of telecommunications and radio broadcasting. FM is a modulation technique used to transmit information through changes in the carrier signal's frequency, while demodulation is the process of extracting the original information from the modulated signal. In the world of wireless communication, FM has gained significant popularity due to its robustness against noise and interference. It is widely used in applications such as FM radio broadcasting, two-way radio communication, mobile communication, and even television audio transmission. FM works by varying the frequency of the carrier signal in proportion to the instantaneous amplitude of the modulating signal. The modulating signal contains the information to be transmitted, such as speech, music, or data. As the amplitude of the modulating signal changes, the frequency of the carrier signal also varies, resulting in a modulated waveform. Demodulation, on the other hand, is the process of extracting the original information from the modulated signal. The demodulator detects the variations in the carrier signal's frequency caused by the modulation and converts them back into the original modulating signal. This allows the receiver to reconstruct the original audio or data. One of the key advantages of FM is its ability to preserve signal quality even in the presence of noise. Since the information is encoded in the changes in frequency rather than the amplitude, FM signals are less susceptible to amplitude-based noise and distortion. This makes FM a preferred choice for applications where signal fidelity is crucial. The demodulation process typically involves using an FM demodulator circuit or receiver, which detects and isolates the frequency variations in the received signal. This can be achieved through various techniques such as frequency discriminators, phase-locked loops (PLL), or quadrature detectors. In conclusion, frequency modulation and demodulation play a vital role in modern telecommunications systems. FM allows for the transmission of high-quality audio and data signals while providing robustness against noise and interference. Demodulation enables the extraction of the original information from the modulated signal, enabling its utilization in various communication applications.

Mathematical Concept: Frequency modulation (FM), the amplitude of the carrier is kept constant but the frequency fc of the carrier is varied by the modulating signal. The carrier frequency fc varier at the rate of the signal frequency fs , the frequency deviation being proportional to the instantaneous amplitude of the modulation signal. The maximum frequency deviation is (fc(max)-fc) and occurs at the peak voltage of the modulating signal. Suppose a modulating sine-wave signal es=EsCos(ɷst) is used to vary the carrier frequency fc. Let the change in carrier frequency be kes where k is a constant known as the frequency deviation constant. The instantaneous carrier frequency fi is given by

fi =fc+kes

=fc+kEs cosɷs t

Frequency Modulation Wave Equation : In Frequency modulation, the carrier frequency is varied sinusoidally at signal frequency. The instantaneous deviation in frequency from the carrier is proportional to the instantaneous amplitude of the modulating signal. Thus the instantaneous angular frequency of FM is given by ;

ɷ_i=ɷ_c+Δɷ_c cosɷ_s t

Total phase angle θ=ɷt so that if ɷ is variable then,

θ=∫ɷ_t dt [integration limit 0 to t]

=∫(ɷ_t +Δɷ_c cosɷ_s t)dt [integration limit 0 to t]

Finally ,

θ=ɷ_c t+(Δɷ_c)/ɷ_s

The term (Δɷ_c)/ɷ_s is called modulation index mf

θ=ɷ_c t+m_f sinɷ_s t

The instantaneous value of FM voltage wave is given by :

e=E_c cosθ

e=E_c cos⁡(ɷ_c t+m_f sinɷ_s t) (1)

This is(Equation 1) the general voltage equation of a FM wave. The modulation index is the ratio of maximum frequency deviation (Δf) to the frequency of the modulating signal i.e

Modulation index, m_f=Δɷ_c/ɷ_s =(f_(c(max))-f_c)/f_s =Δf/f_s

For,

m_f>1 : Wide Band Modulation

m_f<1 : Narrow Band Modulation

Frequency Spectrum : If f_c and f_s are the carrier and signal frequencies respectively, then FM spectrum will have the following frequencies :

f_c ; f_c±f_s ; f_c±2f_s ; f_c±3f_s and so on.

Here, f_c f_c+f_s ; f_c+2f_s ; f_c+3f_s are the Upper Side Band and f_c-f_s ; f_c- ; f_c-3f_s are the Lower Side Band frequencies.

Figure: Block Diagram for Phase-Locked Loop Demodulator.

Frequency Demodulation using PLL: As the message signal is modulated it is necessary to demodulate the modulated signal for separating the message signal from the modulated signal. The common term is used for demodulation of Frequency modulated signal is Phase-Locked Loop feedback controlled demodulator for demodulating the Frequency Modulated signal. Figure 1.4 : Block Diagram for Phase-Locked Loop Demodulator. Here, VCO for Voltage Controlled Oscillator.The Basic aim of a PLL is to lock (or synchronize) the instantaneous angle of a VCO output to the instantaneous angle of a signal that is given as input to the PLL. In the case of demodulation of FM, the input signal to PLL is the received FM signal.

Conclusion: Now a days Frequency modulation method is most popular in live radio broadcasting. Frequency Modulation basically works by changing the carrier frequency with respect to message signal. The reason of shifting from Amplitude Modulation to Frequency Modulation is, signal to noise ration is much better for frequency modulation than amplitude modulation and also FM consume less power than AM and well defined service areas for given transmitted power. Also FM has smaller geographical interference between neighboring stations. Also there are some limitations of Frequency Modulation such as it has much more Bandwidth and its very complicated process for signal Modulation and Demodulation finally it has complex steps to transmit signal and reconstruct the transmitted signal from modulated signal using demodulator system.

Analysis:

Instantaneous Frequency vs. Time Curve

Figure 1.1: Instantaneous Frequency vs. Time Curve. A graph of fi versus time is shown in Figure. 1.1. It is important to note that it is frequency-time curve and not amplitude-time curve. The factor represents the maximum frequency deviation and is denoted by Δf i.e. Maximum frequency deviation,

Δf=kEs and fi =fc+Δfcosɷs t

MATLAB Analysis for Frequency Modulation

Figure 1.2: Simulation Analysis for Frequency Modulation. A graph of time vs. amplitude is shown in Figure 1.2. It is the instantaneous response of the carrier signal frequency while changing the amplitude of the message signal. This indicates this system is working according to the theory of frequency modulation.

Frequency Spectrum for Frequency Modulation

Figure 1.3: Frequency Spectrum for Frequency Modulated Signal. A graph of the frequency vs. frequency spectrum is shown in Figure 1.3.

MATLAB Analysis for PLL Demodulator

Figure 1.4: Simulation Analysis for PLL Demodulator. A graph of Time vs Amplitude shown in Figure 1.3 . It is the output response of modulated signal at the different point the PLL demodulator. Finally at the outer end of the PLL demodulator reconstruct the transmitted signal from the Frequency signal.

Reference :

B. P. Lathi, Zhi Ding - Modern Digital and Analog Communication Systems 4th Edn 2009, 5.1 Non-Linear Modulation , 5.4 Demodulation of FM Signal.
PLL Demodulator Code from internet.

Learnings:

Gained hands-on experience in simulating a complete FM communication system using MATLAB, including both modulation and demodulation processes.
Learned the practical implementation of FM modulation, including understanding frequency deviation, modulation index, and signal waveform generation.
Developed skills in Phase-Locked Loop (PLL) demodulation and understanding its role in recovering the original message signal from a modulated carrier.
Enhanced understanding of signal spectra, including sidebands, bandwidth considerations, and their implications for communication systems.
Strengthened knowledge of numerical and graphical simulation techniques in MATLAB for analyzing signal behavior and system performance.
Improved ability to connect theoretical concepts with practical implementation, including troubleshooting issues such as signal distortion, noise effects, and system synchronization.

My role in this project: I was responsible for the complete design and implementation of the FM communication system in MATLAB. This included simulating the FM modulation process, developing the PLL-based demodulator, and verifying the recovered message signal. I also handled MATLAB coding, waveform visualization, and frequency spectrum analysis. Through this project, I ensured accurate system behavior and demonstrated the practical application of theoretical communication concepts.

NOTE: To run the exe file, make sure MATLAB is installed on your system.

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