Category: analog Communication

Analog Communication – SSBSC Modulation In the previous chapters, we have discussed DSBSC modulation and demodulation. The DSBSC modulated signal has two sidebands. Since, the two sidebands carry the same information, there is no need to transmit both sidebands. We can eliminate one sideband. The process of suppressing one of the sidebands along with the carrier and transmitting a single sideband is called as Single Sideband Suppressed Carrier system or simply SSBSC. It is plotted as shown in the following figure. In the above figure, the carrier and the lower sideband are suppressed. Hence, the upper sideband is used for transmission. Similarly, we can suppress the carrier and the upper sideband while transmitting the lower sideband. This SSBSC system, which transmits a single sideband has high power, as the power allotted for both the carrier and the other sideband is utilized in transmitting this Single Sideband. Mathematical Expressions Let us consider the same mathematical expressions for the modulating and the carrier signals as we have considered in the earlier chapters. i.e., Modulating signal $$mleft ( t right )=A_m cosleft ( 2 pi f_mt right )$$ Carrier signal $$cleft ( t right )=A_c cosleft ( 2 pi f_ct right)$$ Mathematically, we can represent the equation of SSBSC wave as $sleft ( t right )=frac{A_mA_c}{2} cosleft [ 2 pileft ( f_c+f_m right ) tright ]$for the upper sideband Or $sleft ( t right )=frac{A_mA_c}{2} cosleft [ 2 pileft ( f_c-f_m right ) tright ]$for the lower sideband Bandwidth of SSBSC Wave We know that the DSBSC modulated wave contains two sidebands and its bandwidth is $2f_m$. Since the SSBSC modulated wave contains only one sideband, its bandwidth is half of the bandwidth of DSBSC modulated wave. i.e., Bandwidth of SSBSC modulated wave =$frac{2f_m}{2}=f_m$ Therefore, the bandwidth of SSBSC modulated wave is $f_m$ and it is equal to the frequency of the modulating signal. Power Calculations of SSBSC Wave Consider the following equation of SSBSC modulated wave. $sleft ( t right )=frac{A_mA_c}{2} cosleft [ 2 pileft ( f_c+f_m right ) tright ]$for the upper sideband Or $sleft ( t right )=frac{A_mA_c}{2} cosleft [ 2 pileft ( f_c-f_m right ) tright ]$for the lower sideband Power of SSBSC wave is equal to the power of any one sideband frequency components. $$P_t=P_{USB}=P_{LSB}$$ We know that the standard formula for power of cos signal is $$P=frac{{v_{rms}}^{2}}{R}=frac{left ( v_m/sqrt{2} right )^2}{R}$$ In this case, the power of the upper sideband is $$P_{USB}=frac{left ( A_m A_c/2sqrt{2} right )^2}{R}=frac{{A_{m}}^{2}{A_{c}}^{2}}{8R}$$ Similarly, we will get the lower sideband power same as that of the upper side band power. $$P_{LSB}= frac{{A_{m}}^{2}{A_{c}}^{2}}{8R}$$ Therefore, the power of SSBSC wave is $$P_t=P_{USB}=P_{LSB}= frac{{A_{m}}^{2}{A_{c}}^{2}}{8R}$$ Advantages Bandwidth or spectrum space occupied is lesser than AM and DSBSC waves. Transmission of more number of signals is allowed. Power is saved. High power signal can be transmitted. Less amount of noise is present. Signal fading is less likely to occur. Disadvantages The generation and detection of SSBSC wave is a complex process. The quality of the signal gets affected unless the SSB transmitter and receiver have an excellent frequency stability. Applications For power saving requirements and low bandwidth requirements. In land, air, and maritime mobile communications. In point-to-point communications. In radio communications. In television, telemetry, and radar communications. In military communications, such as amateur radio, etc. Learning working make money

Analog Communication – AM Modulators In this chapter, let us discuss about the modulators, which generate amplitude modulated wave. The following two modulators generate AM wave. Square law modulator Switching modulator Square Law Modulator Following is the block diagram of the square law modulator Let the modulating and carrier signals be denoted as $mleft ( t right )$ and $Acosleft ( 2pi f_ctright )$ respectively. These two signals are applied as inputs to the summer (adder) block. This summer block produces an output, which is the addition of the modulating and the carrier signal. Mathematically, we can write it as $$V_1t=mleft ( t right )+A_ccosleft ( 2 pi f_ct right )$$ This signal $V_1t$ is applied as an input to a nonlinear device like diode. The characteristics of the diode are closely related to square law. $V_2t=k_1V_1left ( t right )+k_2V_1^2left ( t right )$(Equation 1) Where, $k_1$ and $k_2$ are constants. Substitute $V_1left (t right )$ in Equation 1 $$V_2left (tright ) = k_1left [ mleft ( t right ) + A_c cos left ( 2 pi f_ct right ) right ] + k_2left [ mleft ( t right ) + A_c cosleft ( 2 pi f_ct right ) right ]^2$$ $Rightarrow V_2left (tright ) = k_1 mleft ( t right ) +k_1 A_c cos left ( 2 pi f_ct right ) +k_2 m^2left ( t right ) +$ $ k_2A_c^2 cos^2left ( 2 pi f_ct right )+2k_2mleft ( t right )A_c cosleft ( 2 pi f_ct right )$ $Rightarrow V_2left (tright ) = k_1 mleft ( t right ) +k_2 m^2left ( t right ) +k_2 A^2_c cos^2 left ( 2 pi f_ct right ) +$ $k_1A_cleft [ 1+left ( frac{2k_2}{k_1} right )mleft ( t right ) right ] cosleft ( 2 pi f_ct right )$ The last term of the above equation represents the desired AM wave and the first three terms of the above equation are unwanted. So, with the help of band pass filter, we can pass only AM wave and eliminate the first three terms. Therefore, the output of square law modulator is $$sleft ( t right )=k_1A_cleft [1+left ( frac{2k_2}{k_1} right ) mleft ( t right ) right ] cosleft ( 2 pi f_ct right )$$ The standard equation of AM wave is $$sleft ( t right )=A_cleft [ 1+k_amleft ( t right ) right ] cos left (2 pi f_ct right )$$ Where, $K_a$ is the amplitude sensitivity By comparing the output of the square law modulator with the standard equation of AM wave, we will get the scaling factor as $k_1$ and the amplitude sensitivity $k_a$ as $frac{2k_2}{k1}$. Switching Modulator Following is the block diagram of switching modulator. Switching modulator is similar to the square law modulator. The only difference is that in the square law modulator, the diode is operated in a non-linear mode, whereas, in the switching modulator, the diode has to operate as an ideal switch. Let the modulating and carrier signals be denoted as $mleft ( t right )$ and $cleft ( t right )= A_c cosleft ( 2pi f_ct right )$ respectively. These two signals are applied as inputs to the summer (adder) block. Summer block produces an output, which is the addition of modulating and carrier signals. Mathematically, we can write it as $$V_1left ( t right )=mleft ( t right )+cleft ( t right )= mleft ( t right )+A_c cosleft ( 2 pi f_ct right )$$ This signal $V_1left ( t right )$ is applied as an input of diode. Assume, the magnitude of the modulating signal is very small when compared to the amplitude of carrier signal $A_c$. So, the diode’s ON and OFF action is controlled by carrier signal $cleft ( t right )$. This means, the diode will be forward biased when $cleft ( t right )> 0$ and it will be reverse biased when $cleft ( t right ) Therefore, the output of the diode is $$V_2 left ( t right )=left{begin{matrix} V_1left ( t right )& if &cleft ( t right )>0 \ 0& if & cleft ( t right ) We can approximate this as $V_2left ( t right ) = V_1left ( t right )xleft ( t right )$(Equation 2) Where, $xleft ( t right )$ is a periodic pulse train with time period $T=frac{1}{f_c}$ The Fourier series representation of this periodic pulse train is $$xleft ( t right )=frac{1}{2}+frac{2}{pi }sum_{n=1}^{infty}frac{left ( -1 right )^n-1}{2n-1} cosleft (2 pi left ( 2n-1 right ) f_ct right )$$ $$Rightarrow xleft ( t right )=frac{1}{2}+frac{2}{pi} cosleft ( 2 pi f_ct right )-frac{2}{3pi } cosleft ( 6 pi f_ct right ) +….$$ Substitute, $V_1left ( t right )$ and $xleft ( t right )$ values in Equation 2. $V_2left ( t right )=left [ mleft ( t right )+A_c cosleft ( 2 pi f_ct right ) right ] left [ frac{1}{2} + frac{2}{pi} cos left ( 2 pi f_ct right )-frac{2}{3pi} cosleft ( 6 pi f_ct right )+…..right ]$ $V_2left ( t right )=frac{mleft ( t right )}{2}+frac{A_c}{2} cosleft ( 2 pi f_ct right )+frac{2mleft ( t right )}{pi} cosleft ( 2 pi f_ct right ) +frac{2A_c}{pi} cos^2left ( 2 pi f_ct right )-$ $frac{2mleft ( t right )}{3pi} cosleft ( 6 pi f_ct right )-frac{2A_c}{3pi}cos left ( 2 pi f_ct right ) cosleft ( 6 pi f_ct right )+….. $ $V_2left ( t right )=frac{A_c}{2}left ( 1+left ( frac{4}{pi A_c} right )mleft ( t right ) right ) cosleft ( 2 pi f_ct right ) + frac{mleft ( t right )}{2}+frac{2A_c}{pi} cos^2left ( 2 pi f_ct right )-$ $frac{2mleft ( t right )}{3 pi} cosleft ( 6 pi f_ct right )-frac{2A_c}{3pi} cosleft ( 2 pi f_ct right ) cosleft ( 6 pi f_ct right )+…..$ The 1st term of the above equation represents the desired AM wave and the remaining terms are unwanted terms. Thus, with the help of band pass filter, we can pass only AM wave and eliminate the remaining terms. Therefore, the output of switching

Analog Communication – VSBSC Modulation In the previous chapters, we have discussed SSBSC modulation and demodulation. SSBSC modulated signal has only one sideband frequency. Theoretically, we can get one sideband frequency component completely by using an ideal band pass filter. However, practically we may not get the entire sideband frequency component. Due to this, some information gets lost. To avoid this loss, a technique is chosen, which is a compromise between DSBSC and SSBSC. This technique is known as Vestigial Side Band Suppressed Carrier (VSBSC) technique. The word “vestige” means “a part” from which, the name is derived. VSBSC Modulation is the process, where a part of the signal called as vestige is modulated along with one sideband. The frequency spectrum of VSBSC wave is shown in the following figure. Along with the upper sideband, a part of the lower sideband is also being transmitted in this technique. Similarly, we can transmit the lower sideband along with a part of the upper sideband. A guard band of very small width is laid on either side of VSB in order to avoid the interferences. VSB modulation is mostly used in television transmissions. Bandwidth of VSBSC Modulation We know that the bandwidth of SSBSC modulated wave is $f_m$. Since the VSBSC modulated wave contains the frequency components of one side band along with the vestige of other sideband, the bandwidth of it will be the sum of the bandwidth of SSBSC modulated wave and vestige frequency $f_v$. i.e., Bandwidth of VSBSC Modulated Wave = $f_m + f_v$ Advantages Following are the advantages of VSBSC modulation. Highly efficient. Reduction in bandwidth when compared to AM and DSBSC waves. Filter design is easy, since high accuracy is not needed. The transmission of low frequency components is possible, without any difficulty. Possesses good phase characteristics. Disadvantages Following are the disadvantages of VSBSC modulation. Bandwidth is more when compared to SSBSC wave. Demodulation is complex. Applications The most prominent and standard application of VSBSC is for the transmission of television signals. Also, this is the most convenient and efficient technique when bandwidth usage is considered. Now, let us discuss about the modulator which generates VSBSC wave and the demodulator which demodulates VSBSC wave one by one. Generation of VSBSC Generation of VSBSC wave is similar to the generation of SSBSC wave. The VSBSC modulator is shown in the following figure. In this method, first we will generate DSBSC wave with the help of the product modulator. Then, apply this DSBSC wave as an input of sideband shaping filter. This filter produces an output, which is VSBSC wave. The modulating signal $mleft ( t right )$ and carrier signal $A_c cos left ( 2 pi f_ct right )$ are applied as inputs to the product modulator. Hence, the product modulator produces an output, which is the product of these two inputs. Therefore, the output of the product modulator is $$pleft ( t right )=A_c cosleft ( 2 pi f_ct right )mleft ( t right )$$ Apply Fourier transform on both sides $$Pleft ( f right )=frac{A_c}{2}left [ Mleft ( f-f_c right )+Mleft ( f+f_c right ) right ]$$ The above equation represents the equation of DSBSC frequency spectrum. Let the transfer function of the sideband shaping filter be $Hleft ( f right )$. This filter has the input $pleft ( t right )$ and the output is VSBSC modulated wave $sleft ( t right )$. The Fourier transforms of $pleft ( t right )$ and $sleft ( t right )$ are $Pleft ( t right )$ and $Sleft ( t right )$ respectively. Mathematically, we can write $Sleft ( f right )$ as $$Sleft ( t right )=Pleft ( f right )Hleft ( f right )$$ Substitute $Pleft ( f right )$ value in the above equation. $$Sleft ( f right )=frac{A_c}{2}left [ Mleft ( f-f_c right )+Mleft ( f+f_c right ) right ]Hleft ( f right )$$ The above equation represents the equation of VSBSC frequency spectrum. Demodulation of VSBSC Demodulation of VSBSC wave is similar to the demodulation of SSBSC wave. Here, the same carrier signal (which is used for generating VSBSC wave) is used to detect the message signal. Hence, this process of detection is called as coherent or synchronous detection. The VSBSC demodulator is shown in the following figure. In this process, the message signal can be extracted from VSBSC wave by multiplying it with a carrier, which is having the same frequency and the phase of the carrier used in VSBSC modulation. The resulting signal is then passed through a Low Pass Filter. The output of this filter is the desired message signal. Let the VSBSC wave be $sleft ( t right )$ and the carrier signal is $A_c cos left ( 2 pi f_ct right )$. From the figure, we can write the output of the product modulator as $$vleft ( t right )= A_c cosleft ( 2 pi f_ct right )sleft ( t right )$$ Apply Fourier transform on both sides $$Vleft ( f right )= frac{A_c}{2}left [ Sleft ( f-f_c right )+Sleft ( f+f_c right ) right ]$$ We know that$Sleft ( f right )=frac{A_c}{2}left [ Mleft ( f-f_c right ) + Mleft ( f+f_c right )right ]Hleft ( f right )$ From the above equation, let us find $Sleft ( f-f_c right )$ and $Sleft ( f+f_c right )$. $$Sleft ( f-f_c right )=frac{A_c}{2}left [ Mleft ( f-f_c-f_c right ) + Mleft ( f-f_c+f_c right )right ]Hleft ( f-f_c right )$$ $Rightarrow Sleft ( f-f_c right )=frac{A_c}{2}left [ Mleft ( f-2f_c right )+Mleft ( f right ) right ] Hleft ( f-f_c right )$ $$Sleft ( f+f_c right )=frac{A_c}{2}left [ Mleft ( f+f_c-f_c right ) +Mleft ( f+f_c+f_c right )right ] Hleft ( f+f_c right )$$ $Rightarrow Sleft ( f+f_c right )=frac{A_c}{2}left [ M left ( f right )+M left (f+2f_c right ) right ] H left ( f+f_c right )$ Substitute, $Sleft ( f-f_c right )$ and $Sleft ( f+f_c right )$ values in $Vleft (

Analog Communication Tutorial Job Search The communication based on analog signals and analog values is known as Analog Communication. This tutorial provides knowledge on the various modulation techniques that are useful in Analog Communication systems. By the completion of this tutorial, the reader will be able to understand the conceptual details involved in analog communication. Audience This tutorial is prepared for beginners who are interested in the basics of analog communication and who aspire to acquire knowledge regarding analog communication systems. Prerequisites A basic idea regarding the initial concepts of communication is enough to go through this tutorial. It will definitely help if you use our tutorial Signals and Systems as a reference. A basic knowledge of the terms involved in Electronics and Communications would be an added advantage. Learning working make money

Analog Communication – Modulation For a signal to be transmitted to a distance, without the effect of any external interferences or noise addition and without getting faded away, it has to undergo a process called as Modulation. It improves the strength of the signal without disturbing the parameters of the original signal. What is Modulation? A message carrying a signal has to get transmitted over a distance and for it to establish a reliable communication, it needs to take the help of a high frequency signal which should not affect the original characteristics of the message signal. The characteristics of the message signal, if changed, the message contained in it also alters. Hence, it is a must to take care of the message signal. A high frequency signal can travel up to a longer distance, without getting affected by external disturbances. We take the help of such high frequency signal which is called as a carrier signal to transmit our message signal. Such a process is simply called as Modulation. Modulation is the process of changing the parameters of the carrier signal, in accordance with the instantaneous values of the modulating signal. Need for Modulation Baseband signals are incompatible for direct transmission. For such a signal, to travel longer distances, its strength has to be increased by modulating with a high frequency carrier wave, which doesn’t affect the parameters of the modulating signal. Advantages of Modulation The antenna used for transmission, had to be very large, if modulation was not introduced. The range of communication gets limited as the wave cannot travel a distance without getting distorted. Following are some of the advantages for implementing modulation in the communication systems. Reduction of antenna size No signal mixing Increased communication range Multiplexing of signals Possibility of bandwidth adjustments Improved reception quality Signals in the Modulation Process Following are the three types of signals in the modulation process. Message or Modulating Signal The signal which contains a message to be transmitted, is called as a message signal. It is a baseband signal, which has to undergo the process of modulation, to get transmitted. Hence, it is also called as the modulating signal. Carrier Signal The high frequency signal, which has a certain amplitude, frequency and phase but contains no information is called as a carrier signal. It is an empty signal and is used to carry the signal to the receiver after modulation. Modulated Signal The resultant signal after the process of modulation is called as a modulated signal. This signal is a combination of modulating signal and carrier signal. Types of Modulation There are many types of modulations. Depending upon the modulation techniques used, they are classified as shown in the following figure. The types of modulations are broadly classified into continuous-wave modulation and pulse modulation. Continuous-wave Modulation In continuous-wave modulation, a high frequency sine wave is used as a carrier wave. This is further divided into amplitude and angle modulation. If the amplitude of the high frequency carrier wave is varied in accordance with the instantaneous amplitude of the modulating signal, then such a technique is called as Amplitude Modulation. If the angle of the carrier wave is varied, in accordance with the instantaneous value of the modulating signal, then such a technique is called as Angle Modulation. Angle modulation is further divided into frequency modulation and phase modulation. If the frequency of the carrier wave is varied, in accordance with the instantaneous value of the modulating signal, then such a technique is called as Frequency Modulation. If the phase of the high frequency carrier wave is varied in accordance with the instantaneous value of the modulating signal, then such a technique is called as Phase Modulation. Pulse Modulation In Pulse modulation, a periodic sequence of rectangular pulses, is used as a carrier wave. This is further divided into analog and digital modulation. In analog modulation technique, if the amplitude or duration or position of a pulse is varied in accordance with the instantaneous values of the baseband modulating signal, then such a technique is called as Pulse Amplitude Modulation (PAM) or Pulse Duration/Width Modulation (PDM/PWM), or Pulse Position Modulation (PPM). In digital modulation, the modulation technique used is Pulse Code Modulation (PCM) where the analog signal is converted into digital form of 1s and 0s. As the resultant is a coded pulse train, this is called as PCM. This is further developed as Delta Modulation (DM). These digital modulation techniques are discussed in our Digital Communications tutorial Learning working make money

Amplitude Modulation A continuous-wave goes on continuously without any intervals and it is the baseband message signal, which contains the information. This wave has to be modulated. According to the standard definition, “The amplitude of the carrier signal varies in accordance with the instantaneous amplitude of the modulating signal.” Which means, the amplitude of the carrier signal containing no information varies as per the amplitude of the signal containing information, at each instant. This can be well explained by the following figures. The first figure shows the modulating wave, which is the message signal. The next one is the carrier wave, which is a high frequency signal and contains no information. While, the last one is the resultant modulated wave. It can be observed that the positive and negative peaks of the carrier wave, are interconnected with an imaginary line. This line helps recreating the exact shape of the modulating signal. This imaginary line on the carrier wave is called as Envelope. It is the same as that of the message signal. Mathematical Expressions Following are the mathematical expressions for these waves. Time-domain Representation of the Waves Let the modulating signal be, $$mleft ( t right )=A_mcosleft ( 2pi f_mt right )$$ and the carrier signal be, $$cleft ( t right )=A_ccosleft ( 2pi f_ct right )$$ Where, $A_m$ and $A_c$ are the amplitude of the modulating signal and the carrier signal respectively. $f_m$ and $f_c$ are the frequency of the modulating signal and the carrier signal respectively. Then, the equation of Amplitude Modulated wave will be $s(t)= left [ A_c+A_mcosleft ( 2pi f_mt right ) right ]cos left ( 2pi f_ct right )$ (Equation 1) Modulation Index A carrier wave, after being modulated, if the modulated level is calculated, then such an attempt is called as Modulation Index or Modulation Depth. It states the level of modulation that a carrier wave undergoes. Rearrange the Equation 1 as below. $s(t)=A_cleft [ 1+left ( frac{A_m}{A_c} right )cos left ( 2pi f_mt right ) right ]cos left ( 2pi f_ct right )$ $Rightarrow sleft ( t right ) = A_cleft [ 1 + mu cos left ( 2 pi f_m t right ) right ] cosleft ( 2 pi f_ct right )$ (Equation 2) Where, $mu$ is Modulation index and it is equal to the ratio of $A_m$ and $A_c$. Mathematically, we can write it as $mu = frac{A_m}{A_c}$ (Equation 3) Hence, we can calculate the value of modulation index by using the above formula, when the amplitudes of the message and carrier signals are known. Now, let us derive one more formula for Modulation index by considering Equation 1. We can use this formula for calculating modulation index value, when the maximum and minimum amplitudes of the modulated wave are known. Let $A_max$ and $A_min$ be the maximum and minimum amplitudes of the modulated wave. We will get the maximum amplitude of the modulated wave, when $cos left ( 2pi f_mt right )$ is 1. $Rightarrow A_max = A_c + A_m$ (Equation 4) We will get the minimum amplitude of the modulated wave, when $cos left ( 2pi f_mt right )$ is -1. $Rightarrow A_min = A_c – A_m$ (Equation 5) Add Equation 4 and Equation 5. $$A_max + A_min = A_c+A_m+A_c-A_m = 2A_c$$ $Rightarrow A_c = frac{A_max + A_min}{2}$ (Equation 6) Subtract Equation 5 from Equation 4. $$A_max – A_min = A_c + A_m – left (A_c -A_m right )=2A_m$$ $Rightarrow A_m = frac{A_max – A_min}{2}$ (Equation 7) The ratio of Equation 7 and Equation 6 will be as follows. $$frac{A_m}{A_c} = frac{left ( A_{max} – A_{min}right )/2}{left ( A_{max} + A_{min}right )/2}$$ $Rightarrow mu = frac{A_max – A_min}{A_max + A_min}$ (Equation 8) Therefore, Equation 3 and Equation 8 are the two formulas for Modulation index. The modulation index or modulation depth is often denoted in percentage called as Percentage of Modulation. We will get the percentage of modulation, just by multiplying the modulation index value with 100. For a perfect modulation, the value of modulation index should be 1, which implies the percentage of modulation should be 100%. For instance, if this value is less than 1, i.e., the modulation index is 0.5, then the modulated output would look like the following figure. It is called as Under-modulation. Such a wave is called as an under-modulated wave. If the value of the modulation index is greater than 1, i.e., 1.5 or so, then the wave will be an over-modulated wave. It would look like the following figure. As the value of the modulation index increases, the carrier experiences a 180o phase reversal, which causes additional sidebands and hence, the wave gets distorted. Such an over-modulated wave causes interference, which cannot be eliminated. Bandwidth of AM Wave Bandwidth (BW) is the difference between the highest and lowest frequencies of the signal. Mathematically, we can write it as $$BW = f_{max} – f_{min}$$ Consider the following equation of amplitude modulated wave. $$sleft ( t right ) = A_cleft [ 1 + mu cos left ( 2 pi f_m t right ) right ] cosleft ( 2 pi f_ct right )$$ $$Rightarrow sleft ( t right ) = A_ccos left ( 2pi f_ct right )+ A_cmu cos(2pi f_ct)cos left ( 2pi f_mt right )$$ $Rightarrow sleft ( t right )= A_ccos left ( 2pi f_ct right )+frac{A_cmu }{2}cos left [ 2pi left ( f_c+f_m right ) tright ]+frac{A_cmu }{2}cos left [ 2pi left ( f_c-f_m right ) tright ]$ Hence, the amplitude modulated wave has three frequencies. Those are carrier frequency $f_c$, upper sideband frequency $f_c + f_m$ and lower sideband frequency $f_c-f_m$ Here, $f_{max}=f_c+f_m$ and $f_{min}=f_c-f_m$ Substitute, $f_{max}$ and $f_{min}$ values in bandwidth formula. $$BW=f_c+f_m-left ( f_c-f_m right )$$ $$Rightarrow BW=2f_m$$ Thus, it can be said that the bandwidth required for amplitude modulated wave is twice the frequency of the modulating signal. Power Calculations of AM Wave Consider the following equation of amplitude modulated wave. $ sleft ( t right )= A_ccos left ( 2pi f_ct right )+frac{A_cmu }{2}cos left

Analog Communication – DSBSC Modulators In this chapter, let us discuss about the modulators, which generate DSBSC wave. The following two modulators generate DSBSC wave. Balanced modulator Ring modulator Balanced Modulator Following is the block diagram of the Balanced modulator. Balanced modulator consists of two identical AM modulators. These two modulators are arranged in a balanced configuration in order to suppress the carrier signal. Hence, it is called as Balanced modulator. The same carrier signal $cleft ( t right )= A_c cos left ( 2 pi f_ct right )$ is applied as one of the inputs to these two AM modulators. The modulating signal $mleft ( t right )$ is applied as another input to the upper AM modulator. Whereas, the modulating signal $mleft ( t right )$ with opposite polarity, i.e., $-mleft ( t right )$ is applied as another input to the lower AM modulator. Output of the upper AM modulator is $$s_1left ( t right )=A_cleft [1+k_amleft ( t right ) right ] cosleft ( 2 pi f_ct right )$$ Output of the lower AM modulator is $$s_2left ( t right )=A_cleft [1-k_amleft ( t right ) right ] cosleft ( 2 pi f_ct right )$$ We get the DSBSC wave $sleft ( t right )$ by subtracting $s_2left ( t right )$ from $s_1left ( t right )$. The summer block is used to perform this operation. $s_1left ( t right )$ with positive sign and $s_2left ( t right )$ with negative sign are applied as inputs to summer block. Thus, the summer block produces an output $sleft ( t right )$ which is the difference of $s_1left ( t right )$ and $s_2left ( t right )$. $$Rightarrow sleft ( t right )=A_cleft [ 1+k_amleft ( t right ) right ] cosleft ( 2 pi f_ct right )-A_cleft [ 1-k_amleft ( t right ) right ] cosleft ( 2 pi f_ct right )$$ $$Rightarrow sleft ( t right )=A_c cosleft ( 2 pi f_ct right )+A_ck_amleft ( t right ) cosleft ( 2 pi f_ct right )- A_c cosleft ( 2 pi f_ct right )+$$ $A_ck_amleft ( t right ) cosleft ( 2 pi f_ct right )$ $Rightarrow sleft ( t right )=2A_ck_amleft ( t right ) cosleft ( 2 pi f_ct right )$ We know the standard equation of DSBSC wave is $$sleft ( t right )=A_cm left ( t right ) cosleft ( 2 pi f_ct right )$$ By comparing the output of summer block with the standard equation of DSBSC wave, we will get the scaling factor as $2k_a$ Ring Modulator Following is the block diagram of the Ring modulator. In this diagram, the four diodes $D_1$,$D_2$,$D_3$ and $D_4$ are connected in the ring structure. Hence, this modulator is called as the ring modulator. Two center tapped transformers are used in this diagram. The message signal $mleft ( t right )$ is applied to the input transformer. Whereas, the carrier signals $cleft ( t right )$ is applied between the two center tapped transformers. For positive half cycle of the carrier signal, the diodes $D_1$ and $D_3$ are switched ON and the other two diodes $D_2$ and $D_4$ are switched OFF. In this case, the message signal is multiplied by +1. For negative half cycle of the carrier signal, the diodes $D_2$ and $D_4$ are switched ON and the other two diodes $D_1$ and $D_3$ are switched OFF. In this case, the message signal is multiplied by -1. This results in $180^0$ phase shift in the resulting DSBSC wave. From the above analysis, we can say that the four diodes $D_1$, $D_2$, $D_3$ and $D_4$ are controlled by the carrier signal. If the carrier is a square wave, then the Fourier series representation of $cleft ( t right )$ is represented as $$cleft ( t right )=frac{4}{pi}sum_{n=1}^{infty }frac{left ( -1 right )^{n-1}}{2n-1} cosleft [2 pi f_ctleft ( 2n-1 right ) right ]$$ We will get DSBSC wave $sleft ( t right )$, which is just the product of the carrier signal $cleft ( t right )$ and the message signal $mleft ( t right )$ i.e., $$sleft ( t right )=frac{4}{pi}sum_{n=1}^{infty }frac{left ( -1 right )^{n-1}}{2n-1} cosleft [2 pi f_ctleft ( 2n-1 right ) right ]mleft ( t right )$$ The above equation represents DSBSC wave, which is obtained at the output transformer of the ring modulator. DSBSC modulators are also called as product modulators as they produce the output, which is the product of two input signals. Learning working make money

Analog Communication – Introduction The word communication arises from the Latin word commūnicāre, which means “to share”. Communication is the basic step for exchange of information. For example, a baby in a cradle, communicates with a cry when she needs her mother. A cow moos loudly when it is in danger. A person communicates with the help of a language. Communication is the bridge to share. Communication can be defined as the process of exchange of information through means such as words, actions, signs, etc., between two or more individuals. Parts of a Communication System Any system, which provides communication consists of the three important and basic parts as shown in the following figure. Sender is the person who sends a message. It could be a transmitting station from where the signal is transmitted. Channel is the medium through which the message signals travel to reach the destination. Receiver is the person who receives the message. It could be a receiving station where the transmitted signal is being received. Types of Signals Conveying an information by some means such as gestures, sounds, actions, etc., can be termed as signaling. Hence, a signal can be a source of energy which transmits some information. This signal helps to establish a communication between the sender and the receiver. An electrical impulse or an electromagnetic wave which travels a distance to convey a message, can be termed as a signal in communication systems. Depending on their characteristics, signals are mainly classified into two types: Analog and Digital. Analog and Digital signals are further classified, as shown in the following figure. Analog Signal A continuous time varying signal, which represents a time varying quantity can be termed as an Analog Signal. This signal keeps on varying with respect to time, according to the instantaneous values of the quantity, which represents it. Example Let us consider a tap that fills a tank of 100 liters capacity in an hour (6 AM to 7 AM). The portion of filling the tank is varied by the varying time. Which means, after 15 minutes (6:15 AM) the quarter portion of the tank gets filled, whereas at 6:45 AM, 3/4th of the tank is filled. If we try to plot the varying portions of water in the tank according to the varying time, it would look like the following figure. As the result shown in this image varies (increases) according to time, this time varying quantity can be understood as Analog quantity. The signal which represents this condition with an inclined line in the figure, is an Analog Signal. The communication based on analog signals and analog values is called as Analog Communication. Digital Signal A signal which is discrete in nature or which is non-continuous in form can be termed as a Digital signal. This signal has individual values, denoted separately, which are not based on the previous values, as if they are derived at that particular instant of time. Example Let us consider a classroom having 20 students. If their attendance in a week is plotted, it would look like the following figure. In this figure, the values are stated separately. For instance, the attendance of the class on Wednesday is 20 whereas on Saturday is 15. These values can be considered individually and separately or discretely, hence they are called as discrete values. The binary digits which has only 1s and 0s are mostly termed as digital values. Hence, the signals which represent 1s and 0s are also called as digital signals. The communication based on digital signals and digital values is called as Digital Communication. Periodic Signal Any analog or digital signal, that repeats its pattern over a period of time, is called as a Periodic Signal. This signal has its pattern continued repeatedly and is easy to be assumed or to be calculated. Example If we consider a machinery in an industry, the process that takes place one after the other is a continuous procedure. For example, procuring and grading the raw material, processing the material in batches, packing a load of products one after the other, etc., follows a certain procedure repeatedly. Such a process whether considered analog or digital, can be graphically represented as follows. Aperiodic Signal Any analog or digital signal, that doesn’t repeat its pattern over a period of time is called as Aperiodic Signal. This signal has its pattern continued but the pattern is not repeated. It is also not so easy to be assumed or to be calculated. Example The daily routine of a person, if considered, consists of various types of work which take different time intervals for different tasks. The time interval or the work doesn’t continuously repeat. For example, a person will not continuously brush his teeth from morning to night, that too with the same time period. Such a process whether considered analog or digital, can be graphically represented as follows. In general, the signals which are used in communication systems are analog in nature, which are transmitted in analog or converted to digital and then transmitted, depending upon the requirement. Learning working make money

DSBSC Demodulators The process of extracting an original message signal from DSBSC wave is known as detection or demodulation of DSBSC. The following demodulators (detectors) are used for demodulating DSBSC wave. Coherent Detector Costas Loop Coherent Detector Here, the same carrier signal (which is used for generating DSBSC signal) is used to detect the message signal. Hence, this process of detection is called as coherent or synchronous detection. Following is the block diagram of the coherent detector. In this process, the message signal can be extracted from DSBSC wave by multiplying it with a carrier, having the same frequency and the phase of the carrier used in DSBSC modulation. The resulting signal is then passed through a Low Pass Filter. Output of this filter is the desired message signal. Let the DSBSC wave be $$sleft ( t right )= A_c cosleft ( 2 pi f_ct right )m left ( t right )$$ The output of the local oscillator is $$cleft ( t right )= A_c cosleft ( 2 pi f_ct+ phi right )$$ Where, $phi$ is the phase difference between the local oscillator signal and the carrier signal, which is used for DSBSC modulation. From the figure, we can write the output of product modulator as $$vleft ( t right )=sleft ( t right )cleft ( t right )$$ Substitute, $sleft ( t right )$ and $cleft ( t right )$ values in the above equation. $$Rightarrow vleft ( t right )=A_c cos left ( 2 pi f_ct right )mleft ( t right )A_c cos left ( 2 pi f_ct + phi right )$$ $={A_{c}}^{2} cos left ( 2 pi f_ct right ) cos left ( 2 pi f_ct + phi right )mleft ( t right )$ $=frac{{A_{c}}^{2}}{2}left [ cosleft ( 4 pi f_ct+ phi right )+ cos phi right ]mleft ( t right )$ $$vleft ( t right )=frac{{A_{c}}^{2}}{2} cosphi mleft ( t right )+frac{{A_{c}}^{2}}{2} cos left ( 4 pi f_ct+ phi right )mleft ( t right )$$ In the above equation, the first term is the scaled version of the message signal. It can be extracted by passing the above signal through a low pass filter. Therefore, the output of low pass filter is $$v_0t=frac{{A_{c}}^{2}}{2} cos phi m left ( t right )$$ The demodulated signal amplitude will be maximum, when $phi=0^0$. That’s why the local oscillator signal and the carrier signal should be in phase, i.e., there should not be any phase difference between these two signals. The demodulated signal amplitude will be zero, when $phi=pm 90^0$. This effect is called as quadrature null effect. Costas Loop Costas loop is used to make both the carrier signal (used for DSBSC modulation) and the locally generated signal in phase. Following is the block diagram of Costas loop. Costas loop consists of two product modulators with common input $sleft ( t right )$, which is DSBSC wave. The other input for both product modulators is taken from Voltage Controlled Oscillator (VCO) with $-90^0$ phase shift to one of the product modulator as shown in figure. We know that the equation of DSBSC wave is $$sleft ( t right )=A_c cosleft ( 2 pi f_ct right )mleft ( t right )$$ Let the output of VCO be $$c_1left ( t right )=cosleft ( 2 pi f_ct + phiright )$$ This output of VCO is applied as the carrier input of the upper product modulator. Hence, the output of the upper product modulator is $$v_1left ( t right )=sleft ( t right )c_1left ( t right )$$ Substitute, $sleft ( t right )$ and $c_1left ( t right )$ values in the above equation. $$Rightarrow v_1left ( t right )=A_c cos left ( 2 pi f_ct right )mleft ( t right ) cosleft ( 2 pi f_ct + phi right )$$ After simplifying, we will get $v_1left ( t right )$ as $$v_1left ( t right )=frac{A_c}{2} cos phi mleft ( t right )+frac{A_c}{2} cosleft ( 4 pi f_ct + phi right )mleft ( t right )$$ This signal is applied as an input of the upper low pass filter. The output of this low pass filter is $$v_{01}left ( t right )=frac{A_c}{2} cos phi mleft ( t right )$$ Therefore, the output of this low pass filter is the scaled version of the modulating signal. The output of $-90^0$ phase shifter is $$c_2left ( t right )=cosleft ( 2 pi f_ct + phi-90^0 right )= sinleft ( 2 pi f_ct + phi right )$$ This signal is applied as the carrier input of the lower product modulator. The output of the lower product modulator is $$v_2left ( t right )=sleft ( t right )c_2left ( t right )$$ Substitute, $sleft ( t right )$ and $c_2left ( t right )$ values in the above equation. $$Rightarrow v_2left ( t right )=A_c cosleft ( 2 pi f_ct right )mleft ( t right ) sin left ( 2 pi f_ct + phi right )$$ After simplifying, we will get $v_2left ( t right )$ as $$v_2left ( t right )=frac{A_c}{2} sin phi mleft ( t right )+frac{A_c}{2} sin left ( 4 pi f_ct+ phi right )mleft ( t right )$$ This signal is applied as an input of the lower low pass filter. The output of this low pass filter is $$v_{02}left ( t right )=frac{A_c}{2} sin phi mleft ( t right )$$ The output of this Low pass filter has $-90^0$ phase difference with the output of the upper low pass filter. The outputs of these two low pass filters are applied as inputs of the phase discriminator. Based on the phase difference between these two signals, the phase discriminator produces a DC control signal. This signal is applied as an input of VCO to correct the phase error in VCO output. Therefore, the carrier signal (used for DSBSC modulation) and the locally generated signal (VCO output) are in phase. Learning working make money