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Radar Systems – Phased Array Antennas A single Antenna can radiate certain amount of power in a particular direction. Obviously, the amount of radiation power will be increased when we use group of Antennas together. The group of Antennas is called Antenna array. An Antenna array is a radiating system comprising radiators and elements. Each of this radiator has its own induction field. The elements are placed so closely that each one lies in the neighbouring one’s induction field. Therefore, the radiation pattern produced by them, would be the vector sum of the individual ones. The Antennas radiate individually and while in an array, the radiation of all the elements sum up, to form the radiation beam, which has high gain, high directivity and better performance, with minimum losses. An Antenna array is said to be Phased Antenna array if the shape and direction of the radiation pattern depends on the relative phases and amplitudes of the currents present at each Antenna of that array. Radiation Pattern Let us consider ‘n’ isotropic radiation elements, which when combined form an array. The figure given below will help you understand the same. Let the spacing between the successive elements be ‘d’ units. As shown in the figure, all the radiation elements receive the same incoming signal. So, each element produces an equal output voltage of $sin left ( omega t right)$. However, there will be an equal phase difference $Psi$ between successive elements. Mathematically, it can be written as − $$Psi=frac{2pi dsintheta }{lambda }:::::Equation:1$$ Where, $theta$ is the angle at which the incoming signal is incident on each radiation element. Mathematically, we can write the expressions for output voltages of ‘n’ radiation elements individually as $$E_1=sinleft [ omega t right]$$ $$E_2=sinleft [omega t+Psiright]$$ $$E_3=sinleft [omega t+2Psiright]$$ $$.$$ $$.$$ $$.$$ $$E_n=sinleft [omega t+left (N-1right )Psiright]$$ Where, $E_1, E_2, E_3, …, E_n$ are the output voltages of first, second, third, …, nth radiation elements respectively. $omega$ is the angular frequency of the signal. We will get the overall output voltage $E_a$ of the array by adding the output voltages of each element present in that array, since all those radiation elements are connected in linear array. Mathematically, it can be represented as − $$E_a=E_1+E_2+E_3+ …+E_n :::Equation:2$$ Substitute, the values of $E_1, E_2, E_3, …, E_n$ in Equation 2. $$E_a=sinleft [ omega t right]+sinleft [omega t+Psiright ]+sinleft [omega t+2Psiright ]+sinleft [omega t+left (n-1right )Psiright]$$ $$Rightarrow E_a=sinleft [omega t+frac{(n-1)Psi)}{2}right ]frac{sinleft [frac{nPsi}{2}right]}{sinleft [frac{Psi}{2}right ]}:::::Equation:3$$ In Equation 3, there are two terms. From first term, we can observe that the overall output voltage $E_a$ is a sine wave having an angular frequency $omega$. But, it is having a phase shift of $left (n−1right )Psi/2$. The second term of Equation 3 is an amplitude factor. The magnitude of Equation 3 will be $$left | E_a right|=left | frac{sinleft [frac{nPsi}{2}right ]}{sinleft [frac{Psi}{2}right]} right |:::::Equation:4$$ We will get the following equation by substituting Equation 1 in Equation 4. $$left | E_a right|=left | frac{sinleft [frac{npi dsintheta}{lambda}right]}{sinleft [frac{pi dsintheta}{lambda}right ]} right |:::::Equation:5$$ Equation 5 is called field intensity pattern. The field intensity pattern will have the values of zeros when the numerator of Equation 5 is zero $$sinleft [frac{npi dsintheta}{lambda}right ]=0$$ $$Rightarrow frac{npi dsintheta}{lambda}=pm mpi$$ $$Rightarrow ndsintheta=pm mlambda$$ $$Rightarrow sintheta=pm frac{mlambda}{nd}$$ Where, $m$ is an integer and it is equal to 1, 2, 3 and so on. We can find the maximum values of field intensity pattern by using L-Hospital rule when both numerator and denominator of Equation 5 are equal to zero. We can observe that if the denominator of Equation 5 becomes zero, then the numerator of Equation 5 also becomes zero. Now, let us get the condition for which the denominator of Equation 5 becomes zero. $$sinleft [frac{pi dsintheta}{lambda}right ]=0$$ $$Rightarrow frac{pi dsintheta}{lambda}=pm ppi$$ $$Rightarrow dsintheta=pm plambda$$ $$Rightarrow sintheta=pm frac{plambda}{d}$$ Where, $p$ is an integer and it is equal to 0, 1, 2, 3 and so on. If we consider $p$ as zero, then we will get the value of $sintheta$ as zero. For this case, we will get the maximum value of field intensity pattern corresponding to the main lobe. We will get the maximum values of field intensity pattern corresponding to side lobes, when we consider other values of $p$. The radiation pattern’s direction of phased array can be steered by varying the relative phases of the current present at each Antenna. This is the advantage of electronic scanning phased array. Learning working make money
Radar Systems – Quick Guide Radar Systems – Overview RADAR is an electromagnetic based detection system that works by radiating electromagnetic waves and then studying the echo or the reflected back waves. The full form of RADAR is RAdio Detection And Ranging. Detection refers to whether the target is present or not. The target can be stationary or movable, i.e., non-stationary. Ranging refers to the distance between the Radar and the target. Radars can be used for various applications on ground, on sea and in space. The applications of Radars are listed below. Controlling the Air Traffic Ship safety Sensing the remote places Military applications In any application of Radar, the basic principle remains the same. Let us now discuss the principle of radar. Basic Principle of Radar Radar is used for detecting the objects and finding their location. We can understand the basic principle of Radar from the following figure. As shown in the figure, Radar mainly consists of a transmitter and a receiver. It uses the same Antenna for both transmitting and receiving the signals. The function of the transmitter is to transmit the Radar signal in the direction of the target present. Target reflects this received signal in various directions. The signal, which is reflected back towards the Antenna gets received by the receiver. Terminology of Radar Systems Following are the basic terms, which are useful in this tutorial. Range Pulse Repetition Frequency Maximum Unambiguous Range Minimum Range Now, let us discuss about these basic terms one by one. Range The distance between Radar and target is called Range of the target or simply range, R. We know that Radar transmits a signal to the target and accordingly the target sends an echo signal to the Radar with the speed of light, C. Let the time taken for the signal to travel from Radar to target and back to Radar be ‘T’. The two way distance between the Radar and target will be 2R, since the distance between the Radar and the target is R. Now, the following is the formula for Speed. $$Speed= frac{Distance}{Time}$$ $$Rightarrow Distance=Speedtimes Time$$ $$Rightarrow 2R=Ctimes T$$ $$R=frac{CT}{2}:::::Equation:1$$ We can find the range of the target by substituting the values of C & T in Equation 1. Pulse Repetition Frequency Radar signals should be transmitted at every clock pulse. The duration between the two clock pulses should be properly chosen in such a way that the echo signal corresponding to present clock pulse should be received before the next clock pulse. A typical Radar wave form is shown in the following figure. As shown in the figure, Radar transmits a periodic signal. It is having a series of narrow rectangular shaped pulses. The time interval between the successive clock pulses is called pulse repetition time, $T_P$. The reciprocal of pulse repetition time is called pulse repetition frequency, $f_P$. Mathematically, it can be represented as $$f_P=frac{1}{T_P}:::::Equation:2$$ Therefore, pulse repetition frequency is nothing but the frequency at which Radar transmits the signal. Maximum Unambiguous Range We know that Radar signals should be transmitted at every clock pulse. If we select a shorter duration between the two clock pulses, then the echo signal corresponding to present clock pulse will be received after the next clock pulse. Due to this, the range of the target seems to be smaller than the actual range. So, we have to select the duration between the two clock pulses in such a way that the echo signal corresponding to present clock pulse will be received before the next clock pulse starts. Then, we will get the true range of the target and it is also called maximum unambiguous range of the target or simply, maximum unambiguous range. Substitute, $R=R_{un}$ and $T=T_P$ in Equation 1. $$R_{un}=frac{CT_P}{2}:::::Equation:3$$ From Equation 2, we will get the pulse repetition time, $T_P$ as the reciprocal of pulse repetition frequency, $f_P$. Mathematically, it can be represented as $$T_P=frac{1}{f_P}:::::Equation:4$$ Substitute, Equation 4 in Equation 3. $$R_{un}=frac{Cleft ( frac{1}{f_P} right )}{2}$$ $$R_{un}=frac{C}{2f_P}:::::Equation:5$$ We can use either Equation 3 or Equation 5 for calculating maximum unambiguous range of the target. We will get the value of maximum unambiguous range of the target, $R_{un}$ by substituting the values of $C$ and $T_P$ in Equation 3. Similarly, we will get the value of maximum unambiguous range of the target, $R_{un}$ by substituting the values of $C$ and $f_P$ in Equation 5. Minimum Range We will get the minimum range of the target, when we consider the time required for the echo signal to receive at Radar after the signal being transmitted from the Radar as pulse width. It is also called the shortest range of the target. Substitute, $R=R_{min}$ and $T=tau$ in Equation 1. $$R_{min}=frac{Ctau}{2}:::::Equation:6$$ We will get the value of minimum range of the target, $R_{min}$ by substituting the values of $C$ and $tau$ in Equation 6. Radar Systems – Range Equation Radar range equation is useful to know the range of the target theoretically. In this chapter, we will discuss the standard form of Radar range equation and then will discuss about the two modified forms of Radar range equation. We will get those modified forms of Radar range equation from the standard form of Radar range equation. Now, let us discuss about the derivation of the standard form of Radar range equation. Derivation of Radar Range Equation The standard form of Radar range equation is also called as simple form of Radar range equation. Now, let us derive the standard form of Radar range equation. We know that power density is nothing but the ratio of power and area. So, the power density, $P_{di}$ at a distance, R from the Radar can be mathematically represented as − $$P_{di}=frac{P_t}{4pi R^2}:::::Equation:1$$ Where, $P_t$ is the amount of power transmitted by the Radar transmitter The above power density is valid for an isotropic Antenna. In general, Radars use directional Antennas. Therefore, the power density, $P_{dd}$ due to directional Antenna will be − $$P_{dd}=frac{P_tG}{4pi R^2}:::::Equation:2$$ Target radiates the power in different directions from
Radar Systems – Doppler Effect In this chapter, we will learn about the Doppler Effect in Radar Systems. If the target is not stationary, then there will be a change in the frequency of the signal that is transmitted from the Radar and that is received by the Radar. This effect is known as the Doppler effect. According to the Doppler effect, we will get the following two possible cases − The frequency of the received signal will increase, when the target moves towards the direction of the Radar. The frequency of the received signal will decrease, when the target moves away from the Radar. Now, let us derive the formula for Doppler frequency. Derivation of Doppler Frequency The distance between Radar and target is nothing but the Range of the target or simply range, R. Therefore, the total distance between the Radar and target in a two-way communication path will be 2R, since Radar transmits a signal to the target and accordingly the target sends an echo signal to the Radar. If $lambda$ is one wave length, then the number of wave lengths N that are present in a two-way communication path between the Radar and target will be equal to $2R/lambda$. We know that one wave length $lambda$ corresponds to an angular excursion of $2pi$ radians. So, the total angle of excursion made by the electromagnetic wave during the two-way communication path between the Radar and target will be equal to $4pi R/lambda$ radians. Following is the mathematical formula for angular frequency, $omega$ − $$omega=2pi f:::::Equation:1$$ Following equation shows the mathematical relationship between the angular frequency $omega$ and phase angle $phi$ − $$omega=frac{dphi }{dt}:::::Equation:2$$ Equate the right hand side terms of Equation 1 and Equation 2 since the left hand side terms of those two equations are same. $$2pi f=frac{dphi }{dt}$$ $$Rightarrow f =frac{1}{2pi}frac{dphi }{dt}:::::Equation:3$$ Substitute,$f=f_d$ and $phi=4pi R/lambda$ in Equation 3. $$f_d =frac{1}{2pi}frac{d}{dt}left ( frac{4pi R}{lambda} right )$$ $$Rightarrow f_d =frac{1}{2pi}frac{4pi}{lambda}frac{dR}{dt}$$ $$Rightarrow f_d =frac{2V_r}{lambda}:::::Equation:4$$ Where, $f_d$ is the Doppler frequency $V_r$ is the relative velocity We can find the value of Doppler frequency $f_d$ by substituting the values of $V_r$ and $lambda$ in Equation 4. Substitute, $lambda=C/f$ in Equation 4. $$f_d =frac{2V_r}{C/f}$$ $$Rightarrow f_d =frac{2V_rf}{C}:::::Equation:5$$ Where, $f$ is the frequency of transmitted signal $C$ is the speed of light and it is equal to $3times 10^8m/sec$ We can find the value of Doppler frequency, $f_d$ by substituting the values of $V_r,f$ and $C$ in Equation 5. Note − Both Equation 4 and Equation 5 show the formulae of Doppler frequency, $f_d$. We can use either Equation 4 or Equation 5 for finding Doppler frequency, $f_d$ based on the given data. Example Problem If the Radar operates at a frequency of $5GHZ$, then find the Doppler frequency of an aircraft moving with a speed of 100KMph. Solution Given, The frequency of transmitted signal, $f=5GHZ$ Speed of aircraft (target), $V_r=100KMph$ $$Rightarrow V_r=frac{100times 10^3}{3600}m/sec$$ $$Rightarrow V_r=27.78m/sec$$ We have converted the given speed of aircraft (target), which is present in KMph into its equivalent m/sec. We know that, the speed of the light, $C=3times 10^8m/sec$ Now, following is the formula for Doppler frequency − $$f_d=frac{2Vrf}{C}$$ Substitute the values of 𝑉𝑟, $V_r,f$ and $C$ in the above equation. $$Rightarrow f_d=frac{2left ( 27.78 right )left ( 5times 10^9 right )}{3times 10^8}$$ $$Rightarrow f_d=926HZ$$ Therefore, the value of Doppler frequency, $f_d$ is $926HZ$ for the given specifications. Learning working make money
Radar Systems – Antenna Parameters An Antenna or Aerial is a transducer, which converts electrical power into electromagnetic waves and vice versa. An Antenna has the following parameters − Directivity Aperture Efficiency Antenna Efficiency Gain Now, let us discuss these parameters in detail − Directivity According to the standard definition, “The ratio of maximum radiation intensity of the subject Antenna to the radiation intensity of an isotropic or reference Antenna, radiating the same total power is called the Directivity.” Though an Antenna radiates power, the direction in which it radiates matters is of much significance. The Antenna under study is termed as subject Antenna. Its radiation intensity is focused in a particular direction, while it is transmitting or receiving. Hence, the Antenna is said to have its directivity in that particular direction. The ratio of radiation intensity in a given direction from an Antenna to the radiation intensity averaged over all directions, is termed as Directivity. If that particular direction is not specified, then the direction in which maximum intensity is observed, can be taken as the directivity of that Antenna. The directivity of a non-isotropic Antenna is equal to the ratio of the radiation intensity in a given direction to the radiation intensity of the isotropic source. Mathematically, we can write the expression for Directivity as − $$Directivity=frac{U_{Max}left (theta,phiright )}{U_0}$$ Where, $U_{Max}left (theta,phiright )$ is the maximum radiation intensity of subject Antenna $U_0$ is the radiation intensity of an isotropic Antenna. Aperture Efficiency According to the standard definition, “Aperture efficiency of an Antenna is the ratio of the effective radiating area (or effective area) to the physical area of the aperture.” An Antenna radiates power through an aperture. This radiation should be effective with minimum losses. The physical area of the aperture should also be taken into consideration, as the effectiveness of the radiation depends upon the area of the aperture, physically on the Antenna. Mathematically, we can write the expression for Aperture efficiency $epsilon_A$ as $$epsilon _A=frac{A_{eff}}{A_p}$$ Where, $A_{eff}$ is the effective area $A_P$ is the physical area Antenna Efficiency According to the standard definition, “Antenna Efficiency is the ratio of the radiated power of the Antenna to the input power accepted by the Antenna.” Any Antenna is designed to radiate power with minimum losses, for a given input. The efficiency of an Antenna explains how much an Antenna is able to deliver its output effectively with minimum losses in the transmission line. It is also called Radiation Efficiency Factor of the Antenna. Mathematically, we can write the expression for Antenna efficiency 𝜂𝑒 as − $$eta _e=frac{P_{Rad}}{P_{in}}$$ Where, $P_{Rad}$ is the amount of power radiated $P_{in}$ is the input power for the Antenna Gain According to the standard definition, “Gain of an Antenna is the ratio of the radiation intensity in a given direction to the radiation intensity that would be obtained if the power accepted by the Antenna were radiated isotropically.” Simply, Gain of an Antenna takes the Directivity of Antenna into account along with its effective performance. If the power accepted by the Antenna was radiated isotropically (that means in all directions), then the radiation intensity we get can be taken as a referential. The term Antenna gain describes how much power is transmitted in the direction of peak radiation to that of an isotropic source. Gain is usually measured in dB. Unlike Directivity, Antenna gain takes the losses that occur also into account and hence focuses on the efficiency. Mathematically, we can write the expression for Antenna Gain $G$ as − $$G=eta_eD$$ Where, $eta_e$ is the Antenna efficiency $D$ is the Directivity of the Antenna Learning working make money
Radar Systems – Delay Line Cancellers In this chapter, we will learn about Delay Line Cancellers in Radar Systems. As the name suggests, delay line introduces a certain amount of delay. So, the delay line is mainly used in Delay line canceller in order to introduce a delay of pulse repetition time. Delay line canceller is a filter, which eliminates the DC components of echo signals received from stationary targets. This means, it allows the AC components of echo signals received from non-stationary targets, i.e., moving targets. Types of Delay Line Cancellers Delay line cancellers can be classified into the following two types based on the number of delay lines that are present in it. Single Delay Line Canceller Double Delay Line Canceller In our subsequent sections, we will discuss more about these two Delay line cancellers. Single Delay Line Canceller The combination of a delay line and a subtractor is known as Delay line canceller. It is also called single Delay line canceller. The block diagram of MTI receiver with single Delay line canceller is shown in the figure below. We can write the mathematical equation of the received echo signal after the Doppler effect as − $$V_1=Asinleft [ 2pi f_dt-phi_0 right ]:::::Equation:1$$ Where, A is the amplitude of video signal $f_d$ is the Doppler frequency $phi_o$ is the phase shift and it is equal to $4pi f_tR_o/C$ We will get the output of Delay line canceller, by replacing $t$ by $t-T_P$ in Equation 1. $$V_2=Asinleft [ 2pi f_dleft ( t-T_Pright )-phi_0 right ]:::::Equation:2$$ Where, $T_P$ is the pulse repetition time We will get the subtractor output by subtracting Equation 2 from Equation 1. $$V_1-V_2=Asinleft [ 2pi f_dt-phi_0 right ]-Asinleft [ 2pi f_dleft ( t-T_Pright )-phi_0 right ]$$ $$Rightarrow V_1-V_2=2Asinleft [ frac{ 2pi f_dt-phi_0-left [ 2pi f_dleft ( t-T_P right )-phi_0 right ]}{2}right ]cosleft [ frac{ 2pi f_dt-phi_o+2pi f_dleft ( t-T_P right )-phi_0 }{2}right ]$$ $$V_1-V_2=2Asinleft [ frac{2pi f_dT_P}{2} right ]cosleft [ frac{2pi f_dleft ( 2t-T_P right )-2phi_0}{2} right ]$$ $$Rightarrow V_1-V_2=2Asinleft [ pi f_dT_p right ]cosleft [ 2pi f_dleft ( t-frac{T_P}{2} right )-phi_0 right ]:::::Equation:3$$ The output of subtractor is applied as input to Full Wave Rectifier. Therefore, the output of Full Wave Rectifier looks like as shown in the following figure. It is nothing but the frequency response of the single delay line canceller. From Equation 3, we can observe that the frequency response of the single delay line canceller becomes zero, when $pi f_dT_P$ is equal to integer multiples of $pi$ This means, $pi f_dT_P$ is equal to $npi$ Mathematically, it can be written as $$pi f_dT_P=npi$$ $$Rightarrow f_dT_P=n$$ $$Rightarrow f_d=frac{n}{T_P}:::::Equation:4$$ From Equation 4, we can conclude that the frequency response of the single delay line canceller becomes zero, when Doppler frequency $f_d$ is equal to integer multiples of reciprocal of pulse repetition time $T_P$. We know the following relation between the pulse repetition time and pulse repetition frequency. $$f_d=frac{1}{T_P}$$ $$Rightarrow frac{1}{T_P}=f_P:::::Equation:5$$ We will get the following equation, by substituting Equation 5 in Equation 4. $$Rightarrow f_d=nf_P:::::Equation:6$$ From Equation 6, we can conclude that the frequency response of the single delay line canceller becomes zero, when Doppler frequency, $f_d$ is equal to integer multiples of pulse repetition frequency $f_P$. Blind Speeds From what we learnt so far, single Delay line canceller eliminates the DC components of echo signals received from stationary targets, when $n$ is equal to zero. In addition to that, it also eliminates the AC components of echo signals received from non-stationary targets, when the Doppler frequency $f_d$ is equal to integer (other than zero) multiples of pulse repetition frequency $f_P$. So, the relative velocities for which the frequency response of the single delay line canceller becomes zero are called blind speeds. Mathematically, we can write the expression for blind speed $v_n$ as − $$v_n=frac{nlambda}{2T_P}:::::Equation:7$$ $$Rightarrow v_n=frac{nlambda f_P}{2}:::::Equation:8$$ Where, $n$ is an integer and it is equal to 1, 2, 3 and so on $lambda$ is the operating wavelength Example Problem An MTI Radar operates at a frequency of $6GHZ$ with a pulse repetition frequency of $1KHZ$. Find the first, second and third blind speeds of this Radar. Solution Given, The operating frequency of MTI Radar, $f=6GHZ$ Pulse repetition frequency, $f_P=1KHZ$. Following is the formula for operating wavelength $lambda$ in terms of operating frequency, f. $$lambda=frac{C}{f}$$ Substitute, $C=3times10^8m/sec$ and $f=6GHZ$ in the above equation. $$lambda=frac{3times10^8}{6times10^9}$$ $$Rightarrow lambda=0.05m$$ So, the operating wavelength $lambda$ is equal to $0.05m$, when the operating frequency f is $6GHZ$. We know the following formula for blind speed. $$v_n=frac{nlambda f_p}{2}$$ By substituting, $n$=1,2 & 3 in the above equation, we will get the following equations for first, second & third blind speeds respectively. $$v_1=frac{1times lambda f_p}{2}=frac{lambda f_p}{2}$$ $$v_2=frac{2times lambda f_p}{2}=2left ( frac{lambda f_p}{2} right )=2v_1$$ $$v_3=frac{3times lambda f_p}{2}=3left ( frac{lambda f_p}{2} right )=3v_1$$ Substitute the values of $lambda$ and $f_P$ in the equation of first blind speed. $$v_1=frac{0.05times 10^3}{2}$$ $$Rightarrow v_1=25m/sec$$ Therefore, the first blind speed $v_1$ is equal to $25m/sec$ for the given specifications. We will get the values of second & third blind speeds as $50m/sec$& $75m/sec$ respectively by substituting the value of 𝑣1 in the equations of second & third blind speeds. Double Delay Line Canceller We know that a single delay line canceller consists of a delay line and a subtractor. If two such delay line cancellers are cascaded together, then that combination is called Double delay line canceller. The block diagram of Double delay line canceller is shown in the following figure. Let $pleft ( t right )$ and $qleft ( t right )$ be the input and output of the first delay line canceller. We will get the following mathematical relation from first delay line canceller. $$qleft ( t right )=pleft ( t right )-pleft ( t-T_P right ):::::Equation:9$$ The output of the first delay line canceller is applied as an input to the second delay line canceller. Hence, $qleft ( t right )$ will be the input of the second delay line canceller. Let $rleft ( t right )$ be the output of
Radar Systems – Matched Filter Receiver If a filter produces an output in such a way that it maximizes the ratio of output peak power to mean noise power in its frequency response, then that filter is called Matched filter. This is an important criterion, which is considered while designing any Radar receiver. In this chapter, let us discuss the frequency response function of Matched filter and impulse response of Matched filter. Frequency Response Function of Matched Filter The frequency response of the Matched filter will be proportional to the complex conjugate of the input signal’s spectrum. Mathematically, we can write the expression for frequency response function, $Hleft (fright )$ of the Matched filter as − $$Hleft (fright )=G_aS^astleft (fright )e^{-j2pi ft_1}:::::Equation:1$$ Where, $G_a$ is the maximum gain of the Matched filter $Sleft (fright )$ is the Fourier transform of the input signal, $sleft (tright )$ $S^astleft (fright )$ is the complex conjugate of $Sleft (fright )$ $t_1$ is the time instant at which the signal observed to be maximum In general, the value of $G_a$ is considered as one. We will get the following equation by substituting $G_a=1$ in Equation 1. $$Hleft (fright )=S^astleft (fright )e^{-j2pi ft_1}:::::Equation:2$$ The frequency response function, $Hleft (fright )$ of the Matched filter is having the magnitude of $S^astleft (fright )$ and phase angle of $e^{-j2pi ft_1}$, which varies uniformly with frequency. Impulse Response of Matched Filter In time domain, we will get the output, $h(t)$ of Matched filter receiver by applying the inverse Fourier transform of the frequency response function, $H(f)$. $$hleft (tright )=int_{-infty }^{infty }Hleft (fright )e^{-j2pi ft_1}df:::::Equation:3$$ Substitute, Equation 1 in Equation 3. $$hleft (tright )=int_{-infty }^{infty }lbrace G_aS^astleft (fright )e^{-j2pi ft_1}rbrace e^{j2pi ft}df$$ $$Rightarrow hleft (tright )=int_{-infty }^{infty }G_aS^astleft (fright )e^{-j2pi fleft (t_1-tright )}df:::::Equation:4$$ We know the following relation. $$S^astleft (fright )=Sleft (-fright ):::::Equation:5$$ Substitute, Equation 5 in Equation 4. $$hleft (tright )=int_{-infty }^{infty }G_aS(-f)e^{-j2pi fleft (t_1-tright )}df$$ $$Rightarrow hleft (tright )=int_{-infty }^{infty }G_aS^left (fright )e^{j2pi fleft (t_1-tright )}df$$ $$Rightarrow hleft (tright )=G_as(t_1−t):::::Equation:6$$ In general, the value of $G_a$ is considered as one. We will get the following equation by substituting $G_a=1$ in Equation 6. $$h(t)=sleft (t_1-tright )$$ The above equation proves that the impulse response of Matched filter is the mirror image of the received signal about a time instant $t_1$. The following figures illustrate this concept. The received signal, $sleft (tright )$ and the impulse response, $hleft (tright )$ of the matched filter corresponding to the signal, $sleft (tright )$ are shown in the above figures. Learning working make money
Radar Systems – Radar Displays An electronic instrument, which is used for displaying the data visually is known as display. So, the electronic instrument which displays the information about Radar’s target visually is known as Radar display. It shows the echo signal information visually on the screen. Types of Radar Displays In this section, we will learn about the different types of Radar Displays. The Radar Displays can be classified into the following types. A-Scope It is a two dimensional Radar display. The horizontal and vertical coordinates represent the range and echo amplitude of the target respectively. In A-Scope, the deflection modulation takes place. It is more suitable for manually tracking Radar. B-Scope It is a two dimensional Radar display. The horizontal and vertical coordinates represent the azimuth angle and the range of the target respectively. In B-Scope, intensity modulation takes place. It is more suitable for military Radars. C-Scope It is a two-dimensional Radar display. The horizontal and vertical coordinates represent the azimuth angle and elevation angle respectively. In C-Scope, intensity modulation takes place. D-Scope If the electron beam is deflected or the intensity-modulated spot appears on the Radar display due to the presence of target, then it is known as blip. C-Scope becomes D-Scope, when the blips extend vertically in order to provide the distance. E-Scope It is a two-dimensional Radar display. The horizontal and vertical coordinates represent the distance and elevation angle respectively. In E-Scope, intensity modulation takes place. F-Scope If the Radar Antenna is aimed at the target, then F-Scope displays the target as a centralized blip. So, the horizontal and vertical displacements of the blip represent the horizontal and vertical aiming errors respectively. G-Scope If the Radar Antenna is aimed at the target, then G-Scope displays the target as laterally centralized blip. The horizontal and vertical displacements of the blip represent the horizontal and vertical aiming errors respectively. H-Scope It is the modified version of B-Scope in order to provide the information about elevation angle of the target. It displays the target as two blips, which are closely spaced. This can be approximated to a short bright line and the slope of this line will be proportional to the sine of the elevation angle. I-Scope If the Radar Antenna is aimed at the target, then I-Scope displays the target as a circle. The radius of this circle will be proportional to the distance of the target. If the Radar Antenna is aimed at the target incorrectly, then I-Scope displays the target as a segment instead of circle. The arc length of that segment will be inversely proportional to the magnitude of pointing error. J-Scope It is the modified version of A-Scope. It displays the target as radial deflection from time base. K-Scope It is the modified version of A-Scope. If the Radar Antenna is aimed at the target, then K-Scope displays the target as a pair of vertical deflections, which are having equal height. If the Radar Antenna is aimed at the target incorrectly, then there will be pointing error. So, the magnitude and the direction of the pointing error depends on the difference between the two vertical deflections. L-Scope If the Radar Antenna is aimed at the target, then L-Scope displays the target as two horizontal blips having equal amplitude. One horizontal blip lies to the right of central vertical time base and the other one lies to the left of central vertical time base. M-Scope It is the modified version of A-Scope. An adjustable pedestal signal has to be moved along the baseline till it coincides the signal deflections, which are coming from the horizontal position of the target. In this way, the target’s distance can be determined. N-Scope It is the modified version of K-Scope. An adjustable pedestal signal is used for measuring distance. O-Scope It is the modified version of A-Scope. We will get O-Scope, by including an adjustable notch to A-Scope for measuring distance. P-Scope It is a Radar display, which uses intensity modulation. It displays the information of echo signal as plan view. Range and azimuth angle are displayed in polar coordinates. Hence, it is called the Plan Position Indicator or the PPI display. R-Scope It is a Radar display, which uses intensity modulation. The horizontal and vertical coordinates represent the range and height of the target respectively. Hence, it is called Range-Height Indicator or RHI display. Learning working make money
Radar Systems – FMCW Radar If CW Doppler Radar uses the Frequency Modulation, then that Radar is called FMCW Doppler Radar or simply, FMCW Radar. It is also called Continuous Wave Frequency Modulated Radar or CWFM Radar. It measures not only the speed of the target but also the distance of the target from the Radar. Block Diagram of FMCW Radar FMCW Radar is mostly used as Radar Altimeter in order to measure the exact height while landing the aircraft. The following figure shows the block diagram of FMCW Radar − FMCW Radar contains two Antennas − transmitting Antenna and receiving Antenna as shown in the figure. The transmitting Antenna transmits the signal and the receiving Antenna receives the echo signal. The block diagram of the FMCW Radar looks similar to the block diagram of CW Radar. It contains few modified blocks and some other blocks in addition to the blocks that are present in the block diagram of CW Radar. The function of each block of FMCW Radar is mentioned below. FM Modulator − It produces a Frequency Modulated (FM) signal having variable frequency, $f_oleft (t right )$ and it is applied to the FM transmitter. FM Transmitter − It transmits the FM signal with the help of transmitting Antenna. The output of FM Transmitter is also connected to Mixer-I. Local Oscillator − In general, Local Oscillator is used to produce an RF signal. But, here it is used to produce a signal having an Intermediate Frequency, $f_{IF}$. The output of Local Oscillator is connected to both Mixer-I and Balanced Detector. Mixer-I − Mixer can produce both sum and difference of the frequencies that are applied to it. The signals having frequencies of $f_oleft (t right )$ and $f_{IF}$ are applied to Mixer-I. So, the Mixer-I will produce the output having frequency either $f_oleft (t right )+f_{IF}$ or $f_oleft (t right )-f_{IF}$. Side Band Filter − It allows only one side band frequencies, i.e., either upper side band frequencies or lower side band frequencies. The side band filter shown in the figure produces only lower side band frequency. i.e., $f_oleft (t right )-f_{IF}$. Mixer-II − Mixer can produce both sum and difference of the frequencies that are applied to it. The signals having frequencies of $f_oleft (t right )-f_{IF}$ and $f_oleft (t-T right )$ are applied to Mixer-II. So, the Mixer-II will produce the output having frequency either $f_oleft (t-T right )+f_oleft (t right )-f_{IF}$ or $f_oleft (t-T right )-f_oleft (t right )+f_{IF}$. IF Amplifier − IF amplifier amplifies the Intermediate Frequency (IF) signal. The IF amplifier shown in the figure amplifies the signal having frequency of $f_oleft (t-T right )-f_oleft (t right )+f_{IF}$. This amplified signal is applied as an input to the Balanced detector. Balanced Detector − It is used to produce the output signal having frequency of $f_oleft (t-T right )-f_oleft (t right )$ from the applied two input signals, which are having frequencies of $f_oleft (t-T right )-f_oleft (t right )+f_{IF}$ and $f_{IF}$. The output of Balanced detector is applied as an input to Low Frequency Amplifier. Low Frequency Amplifier − It amplifies the output of Balanced detector to the required level. The output of Low Frequency Amplifier is applied to both switched frequency counter and average frequency counter. Switched Frequency Counter − It is useful for getting the value of Doppler velocity. Average Frequency Counter − It is useful for getting the value of Range. Learning working make money
Radar Systems – Pulse Radar The Radar, which operates with pulse signal for detecting stationary targets is called Basic Pulse Radar or simply, Pulse Radar. In this chapter, let us discuss the working of Pulse Radar. Block Diagram of Pulse Radar Pulse Radar uses single Antenna for both transmitting and receiving of signals with the help of Duplexer. Following is the block diagram of Pulse Radar − Let us now see the function of each block of Pulse Radar − Pulse Modulator − It produces a pulse-modulated signal and it is applied to the Transmitter. Transmitter − It transmits the pulse-modulated signal, which is a train of repetitive pulses. Duplexer − It is a microwave switch, which connects the Antenna to both transmitter section and receiver section alternately. Antenna transmits the pulse-modulated signal, when the duplexer connects the Antenna to the transmitter. Similarly, the signal, which is received by Antenna will be given to Low Noise RF Amplifier, when the duplexer connects the Antenna to Low Noise RF Amplifier. Low Noise RF Amplifier − It amplifies the weak RF signal, which is received by Antenna. The output of this amplifier is connected to Mixer. Local Oscillator − It produces a signal having stable frequency. The output of Local Oscillator is connected to Mixer. Mixer − We know that Mixer can produce both sum and difference of the frequencies that are applied to it. Among which, the difference of the frequencies will be of Intermediate Frequency (IF) type. IF Amplifier − IF amplifier amplifies the Intermediate Frequency (IF) signal. The IF amplifier shown in the figure allows only the Intermediate Frequency, which is obtained from Mixer and amplifies it. It improves the Signal to Noise Ratio at output. Detector − It demodulates the signal, which is obtained at the output of the IF Amplifier. Video Amplifier − As the name suggests, it amplifies the video signal, which is obtained at the output of detector. Display − In general, it displays the amplified video signal on CRT screen. In this chapter, we discussed how the Pulse Radar works and how it is useful for detecting stationary targets. In our subsequent chapters, we will discuss the Radars, which are useful for detecting non-stationary targets. Learning working make money