Exp 4 SIMULINK HL24 PDF

University of Sharjah College of Engineering Electrical Engineering Department TELECOMMUNICATION SYSTEMS I LAB. 0402347 Experiment # 4 Analog Modulation and Demodulation Using SIMULINK 1 Contents 1. Objective...

University of Sharjah College of Engineering Electrical Engineering Department TELECOMMUNICATION SYSTEMS I LAB. 0402347 Experiment # 4 Analog Modulation and Demodulation Using SIMULINK 1 Contents 1. Objectives................................................................................................................... 3 2. Introduction....................................................................................................................... 3 2.1 Amplitude Modulation (AM)...............................................................................................3 2.2 Frequency Modulation (FM)................................................................................................4 2.3 Frequency Division Multiplexing (FDM).................................................................................8 3. Modulation Features of the SIMULIK Communications Toolbox.................................... 9 4. Lab Work.................................................................................................................. 10 2  Analog Modulation and Demodulation Using SIMULINK 1. Objectives In this experiment, students will have the opportunity to utilize Simulink for the following purposes: ▪ Implementing AM modulator and demodulator. ▪ Implementing Frequency Division Multiplexing (FDM) system. ▪ Implementing FM modulator and demodulator. 2. Introduction Modulation is the act of translating some low-frequency or base-band signal (voice, music, data) to a higher frequency. Why do we modulate signals? There are at least two reasons: to allow the simultaneous transmission of two or more baseband signals by translating them to different frequencies and to take advantage of the greater efficiency and smaller size of higher-frequency antennas. 2.1 Amplitude Modulation (AM) In the amplitude modulation (AM) process, the amplitude of a high-frequency sinusoidal, known as carrier, is changed in direct proportion to the instantaneous amplitude of the message signal. Depending on the frequency contents of the modulated signal AM can be classified into three categories: 1. Conventional AM 2. Double sideband-suppressed carrier (DSBSC) 3. Single sideband-suppressed carrier (SSSC) The mathematical representation of a conventional AM-transmitted signal which carries the message and the carrier is s(t ) = Ac 1 + m(t )cos(wc t ) (1) Where m(t) is the message signal, μ is called the modulation index and ωc =2πfc is the carrier frequency. To save transmitted power the carrier can be suppressed in the above scheme. Such a scheme is known as a Double sideband-suppressed carrier (DSBSC) and it can be mathematically written as: s(t ) = Ac m(t ) cos(wc t ) (2) Assuming noise-free transmission, the received signal will be 3  r (t ) = s(t ) = Ac m(t ) cos(wc t ) (3) At the receiving end, m(t) can be recovered by multiplying the received signal with the carrier and passing the output through a low pass filter (LPF). Thus, input to the filter will be r (t ) = Ac m(t ) cos(wc t )  cos(wc t ) (4) 1 + cos(2wc t )  = Ac m(t )  (5)  2  Using a LPF that can reject the high frequency component, cos(2ωct), and allow the low frequency message will produce the output proportional to the message signal as given by 1 r (t ) = Ac m(t ) (6) 2 Thus, scaling the output of LPF properly can recover the original message signal, m(t). 2.2 Frequency Modulation (FM) An alternative system to Amplitude Modulation is Frequency Modulation. In this modulation scheme the carrier frequency is shifted proportionally to the amplitude of the modulating signal. The larger the amplitude of the information signal, the further the frequency of the carrier signal is shifted from its starting point. The frequency of the information signal determines how many times a second this change in frequency occurs. This modulation process does not affect the amplitude of the carrier. The amplitude of the modulated carrier is held constant and either the phase or the time derivative of the phase of the carrier is varied linearly with the message signal m(t). Thus, the general angle modulated signal is given by: x(t) = Ac cos (2 fct +  (t) ) (8) The quantity 2 fc +  (t) = i(t) is called the instantaneous phase of x(t), while the quantity  (t) is called the phase deviation of x(t). The instantaneous angular frequency of x(t), defined as the rate of change of the instantaneous phase and having units of radians per second, is given by: di (t ) d (2f c t +  (t )) d i (t ) = = = 2f c + (9) dt dt dt The instantaneous frequency fi (t), having units of Hertz (Hz), of x(t) is accordingly given by:  (t ) 1 d (10) f (t ) = i =f + 2 2 dt i c 4 The quantity d is called the angular frequency deviation. The two basic types of angle modulation dt are Phase Modulation (PM) and Frequency Modulation (FM). VARIATION OF  (t) PRODUCES PHASE MODULATION Phase modulation implies that  (t) is proportional to the modulating signal. Thus  (t)=kpm(t), where kp is the deviation constant in radians per unit of m(t). Therefore, the time domain expression for PM is given by: x(t) = Ac cos (2 fct + kpm(t)) (11) VARIATION OF d PRODUCES FREQUENCY MODULATION dt Frequency modulation implies that d is proportional to the modulating signal. This yield: dt d (12) = 2k m(t ) f dt Thus, in FM the instantaneous frequency varies linearly with the message signal and is given by: fi = fc + kf m(t). (13) The term kf , expressed in Hertz per unit of m(t), represents the frequency sensitivity of the FM signal. The phase angle  (t) of FM signal is given by:  (t ) = 2k  m( )d t (14) f 0 Therefore, the time domain expression for FM is given by: C ( x(t ) = A cos 2f t + 2k  m( )d c f t 0 ) (15) FREQUENCY DEVIATION, MODULATION INDEX AND SPECTRUM OF FM Consider a sinusoidal modulating information signal given by: m(t) = Am cos(2 fm t ) (16) The instantaneous frequency of the resulting FM signal equals: fi(t) = fc + kf m(t) = fc + kf Am cos(2 fm t ) (17) 5 The maximum change in instantaneous frequency fi from the carrier frequency fc, is known as frequency deviation f, where it is given by:  f = kf A m (18) Frequency deviation is a useful parameter for determining the bandwidth of FM signals. For example, an information signal of peak-to-peak voltage of 6 volts and a frequency of 10kHz with a frequency constant of 15 kHz/V would cause a FM carrier to change by a total of 90 kHz (45 kHz above and below the original carrier frequency). The carrier frequency would be swept over this range 10,000 times a second. Next, the FM modulated signal is given by: x(t ) = A cos (2f t +  sin(2f t )) C c m (19) where k A f is the modulation index of the modulated signal. In general, for a non-sinusoidal = f = m f m f m m(t) signal, the modulation index is defined as: k f m(t ) max = (20) W where, W is the bandwidth of the message signal, m(t). In case of a sinusoidal message signal, the modulated signal can be represented by:  x(t ) =  A J ( ) cos(2 ( f n = − C n C + nf m )t ) (21) where Jn() is known as Bessel functions in the order n and argument . Some of the selected values of Jn() is listed in Table 1. In the frequency domain, we have: AC J n (  ) A J ( )     ( f + ( f C + nf m )) (22) X( f ) =  ( f − ( f C + nf m )) + C n n = − 2 2  6 From the equations (21) and (22), we observe that : 1. The spectrum consists of a carrier-frequency component and an infinite number of sideband components at frequencies fc  nfm (n = 1,2,3,4,5…..). 2. The relative amplitudes of the spectral lines depend on the value of Jn(), and the value of Jn() becomes very small for large values of n. 3. The number of significant spectral lines (that is, having appreciable relative amplitude) is a function of the modulation index . With  > 1, there will be many sideband lines. The amplitude spectrums of FM signals for several values of  are shown in Figure 1. 1 0.5  = 0.2 fc - fm fc fc + f m 0.5 =1 fc =5 fc Figure 1: Amplitude spectrum of sinusoidal modulated FM signals (fm fixed). 7 2.3 Frequency Division Multiplexing (FDM) Multiplexing is a technique that allows the simultaneous transmission of multiple signals through a single channel or link. In multiplexing, several signals are combined into a single composite signal and transmitted over a single channel or medium. Using multiplexing the channel bandwidth can be utilized more efficiently or more signals can be transmitted through a channel at the same time. Types of Multiplexing: Although there are several types of multiplexing techniques, but mainly there are three multiplexing techniques. 1. Frequency Division Multiplexing (FDM) 2. Time Division Multiplexing (TDM) 3. Wavelength Division Multiplexing (WDM) In Frequency Division Multiplexing, the different message signals are modulated at the different carrier frequencies. In this way, the modulated signals are separate from each other in the frequency domain. The modulated signals are combined to form the composite signal and this signal is sent over the shared medium or channel. To avoid interference between the two message signals, some guard band is also kept between the two message signals. At the receiver, using the bandpass filter, each modulated signal is separated from the composite signal and demultiplexed. By passing the demultiplexed signal through the low pass filter, it is possible to recover each message signal. 8 3. Modulation Features of the SIMULIK Communications Toolbox The available methods of modulation depend on whether the input signal is analog or digital. The figures below show the modulation techniques that the Communications Toolbox supports for analog and digital signals, respectively. As the figures suggest, some categories of techniques include named special cases Baseband vs. Passband Communication systems can be classified into two groups depending on the range of frequencies they use to transmit information. These communication systems are classified into BASEBAND or PASSBAND system. Baseband transmission sends the information signal as it is without modulation (without frequency shifting) while passband transmission shifts the signal to be transmitted in frequency to a higher frequency and then transmits it, where at the receiver the signal is shifted back to its original frequency. 9 4. Lab Work Problem 1 Use Simulink to simulate DSB-SC transmitter receiver system as shown in Fig. 3. Assume that the message signal is sinusoid with amplitude 1 and frequency 1590Hz. The carrier used has frequency 3180Hz. 1. Click on Simulink Library icon or type simulink at the MATLAB COMMAND prompt. * The Simulink Library Browser window is opened. 2. Create a new model window by clicking the Create a new model button on the Library Browser toolbar or click File >> New >> Model. * A new empty workspace window is opened. 3. Click to expand the Simulink folder at the Library Browser window. 4. Click to expand the Sources sub-folder in the Simulink folder. 5. Drag and drop the Signal Generator module into the new empty workspace window. 6. Click to expand the Discrete sub-folder in the Simulink folder. 7. Drag and drop the Zero-Order Hold module into the new empty workspace window. 8. Go to Communications System Toolbox -> Modulation -> Analog Passband Modulation sub- folder. 9. Drag and drop DSBSC AM Modulator Passband and DSBSC AM Demodulator Passband modules into the workspace window. 10. Go to DSP System Toolbox -> Filtering -> Filter Implementations sub-folder. Drag and drop the Analog Filter Design module into the workspace window. 11. Go to Simulink Extras -> Additional Sinks sub-folder. Drag and drop three Power Spectral Density modules into the workspace window. 12. Connect all the inserted modules as shown below. 10 13. Set the parameters of the different blocks in your workspace as follows: Block Model Parameters to be set Signal Generator Waveform type: Sine Amplitude: 1 Frequency: 1590 Hz Zero-Order Hold The function of this block is to convert an input signal with a continuous sample time to an output signal with a discrete sample time. Sample time =1e-5 DSBSC AM modulator Passband Carrier Frequency: 3180Hz Initial phase: 0 radian DSBSC AM Demodulator Carrier Frequency: 3180Hz Passband Initial phase: 0 radian Sample time: 1e-5 Low pass filter parameter Cutoff frequency =49000 (Fs/2 -1000 ) **Fs= 1/sampling time ( this will cancel the effect of the LPF at this stage) Analog Filter Design Filter type: Butterworth Low Pass Filter Filter Order: 4 Passband Edge: 2*pi*1590 rad/s Power Spectral Density Length of buffer: 512 Number of points for fft: 512 Plot after how many points: 512 Sample time: 1e-4 14. Set the stop time to 0.5 seconds, Run (Simulation >> Run) and observe the output waveforms in both time and frequency domains of the message, modulated and demodulated signals. Problem 2 Use Simulink to simulate FDM TX-RX system. Assume the following system parameters: Amplitude of the 1st message signal 2units Frequency of the 1st message signal 500Hz. Amplitude of the 2nd message signal 4units Frequency of the 2nd message signal 1000Hz. Frequency of the 1st carrier signal 5000Hz. Frequency of the 2nd carrier signal 10000Hz. Sample time: 1e-5 sec. Obtain the time and frequency domain display of the following signals: I. Message Signal (1 & 2) II. Modulated Signal III. Recovered Signal (1 &2) 11  1. Construct the model of FDM as shown below. 2. Adjust the parameters of the filter block. You can use Butterworth as filter type having appropriate order and passband edge frequency (cutoff frequency). Keep the simulation parameters as in proplem1. 4. Set the stop time to 0.5 seconds, Run (Simulation >> Run), and observe the output waveforms in both time and frequency domains of the message, modulated and demodulated signals. 5. Complete the table below Type (LPF or BPF) Cutoff Frequency or Pass Frequency Band Filter 1 Filter 2 Filter 3 Filter 4 12 Problem 3 Use Simulink to simulate FM transmitter receiver system. Assume that the message signal is sinusoid with amplitude 0.8 and frequency 1000Hz. The carrier used has frequency 3180 Hz. The sensitivity (Frequency constant) kf is 1250 (Hz/v) 1. Connect all the inserted modules as shown below. 2. Set the parameters of the different blocks in your workspace as follows: Block Model Parameters to be set Signal Generator Waveform type: Sine Amplitude: 0.8 Frequency: 1000 Hz FM Passband Modulator Carrier Frequency: 3180Hz & Demodulator Initial phase: 0 radian Frequency Deviation  f : Calculate Sample time: 1e-5 Power Spectral Density Length of buffer: 512 Number of points for fft: 512 Plot after how many points: 512 Sample time: 1e-4 3. Adjust the parameters of the filter block. You can use Butterworth as a filter type having appropriate order and passband edge frequency (cutoff frequency). 4. Keep the simulation parameters as in proplem1. 5. Set the stop time to 0.5 seconds, and observe the output waveforms in both time and frequency domains of the message, modulated and demodulated signals. 6. Present the calculation for the deviation ratio f, modulation index β, the values for the carrier, and two frequency components on each side of the carrier. 7. Determine the value of the Modulation constant (frequency sensitivity of the FM signal) kf so that β =0.5 (Narrow band FM) repeat step 5 and 6, and comment on your result. 8. Determine the value of the Modulation constant (frequency sensitivity of the FM signal) kf so that β =2 (Wide band FM) repeat step 5 and 6, and comment your result. 13 Submit the model you have drawn in Simulink and all the graphs you obtain after simulation with your report. 14