A pulse radar determines target by round trip time of a pulsed microwave signal. The frequency used by radar transmitter is 10GHz with transmitted power 2KW (Pulse power). The Antenna size of radar transmitted this signal is based on \(\lambda\ (\text{Wavelength})=\frac{C\ (\text{speed of light})}{f\ (\text{Frequency})}\) with a Gain (Gt) of 28dB is used to detect the target (aeroplane) having its cross section area as 12m2. The receiver has its capability as -90dBm as minimum detectable signal (Pmin). There is an isolation between trans and receive chain as (80-100dB) determine Radar maximum range. Based on the paragraph answer following questions :
If ZL is impedance of radar antenna and Z0 is characteristic impedance of line, then what is reflection coefficient ($\Gamma$) of the antenna ?
\(\Gamma \gt \frac{Z_L-Z_0}{Z_L+Z_0}\)
To solve the given question regarding the reflection coefficient of a radar antenna, we must understand the relationship between the impedance of the antenna \((Z_L)\) and the characteristic impedance of the line \((Z_0)\).
The reflection coefficient \(\Gamma\) is calculated using the formula:
\(\Gamma = \frac{Z_L - Z_0}{Z_L + Z_0}\)
This formula arises from the concept of impedance mismatch in transmission lines. The reflection coefficient indicates how much of the signal is reflected back due to the difference in impedances.
Let's analyze the given options:
- \(\Gamma=\frac{Z_L-Z_0}{Z_L-Z_0}\): This formula simplifies to 1 for any non-zero difference between \(Z_L\) and \(Z_0\), which is incorrect unless \(Z_L = Z_0\).
- \(\Gamma=\frac{Z_L+Z_0}{Z_L-Z_0}\): This option cannot represent a reflection coefficient correctly because the addition of \(Z_L\) and \(Z_0\) on the numerator would incorrectly add energies rather than account for differences.
- \(\Gamma \gt \frac{Z_L-Z_0}{Z_L+Z_0}\): This is actually incorrect since it implies the reflection coefficient is greater than the correct formula. However, this option is mentioned as the correct one in the context provided; it could be indicating a constraint or specific scenario. Normally, \(\Gamma\) should be calculated directly by the defined formula \(\Gamma = \frac{Z_L - Z_0}{Z_L + Z_0}\).
- \(\Gamma \lt \frac{Z_L+Z_0}{Z_L-Z_0}\): This does not logically represent the reflection phenomenon as it implies incorrect relationships regarding the polarities of \(Z_L\) and \(Z_0\).
Based on typical electromagnetic theory, the correct mathematical expression for the reflection coefficient is \(\Gamma=\frac{Z_L-Z_0}{Z_L+Z_0}\). However, the prompt suggests the third option as correct, possibly indicating a specific test condition or application constraint. Review the context of each problem for details when testing.
Similar Questions
Consider the following statements
A. Reflection coefficient is change in the magnitude of reflected wave with constant phase with respect to incident wave.
B. Transmission coefficient is change in the magnitude and phase of transmitted wave with respect to incident wave
C. On smith chart, \(\dfrac{\lambda}{2}\) distance is equivalent to 2π.
D. For distortion less line, RL = GC
E. Directivity of an antenna can be less than 1 (unity).
Choose the most appropriate answer from the options given below :
In a loss less transmission line of length 50 cm with L = 10 μH/m, C = 40 pF/m is operated at 25 MHz. Its electrical path length is
The normalized impedance of a transmission line is given by expression :
A lossless line has a characteristic impedance of 50 ohms. It is terminated in a load resistance of 75 ohms. The line is energised by a generator which has an output impedance of 50 ohms and an output voltage of 30 V (rms). The line is assumed to be 2.25 wavelength long. The input impedance and instantaneous load voltages are given :
(a) Zin = 50 ohms (b) VL (instantaneous) = 36 V (c) Zin = 33.33 ohms (d) VL (instantaneous) = 12 V
Which of the above are correct :
Arrange the below mentioned transmission lines in order of their increasing frequency handling capabilities :
(a) wave guide (b) Parallel wire (c) Rigid co-axial cables (d) Flexible co-axial cables
For a quarter wave ideal transmission line of characteristic impedance of 50 Ω and load impedance of 100 Ω, the input impedance of line will be :
The disadvantage of co-axial cable is/are :
(A) Support higher bandwidth than twisted pair cable
(B) Light weight
(C) Relatively expensive compared to twisted pair cable
(D) EMI resistant
(E) Doesn't at very high frequencyChoose the most appropriate answer from the options given below :
The propagation constant for uniform plane wave is given by the expression given below :
Important Questions from Transmission Lines
A characteristic impedance does NOT satisfy which of the following statements?
The dielectric constant of the material used in a transmission line is 2. What is the velocity factor of this line if its characteristic impedance is 300 Ω?
A transmission line of \(50{\rm{\;\Omega }}\) characteristic impedance is terminated with a \(\rm 100 \ Ω\) resistance. The minimum impedance measured on the line is equal to
Twisting of live and return lines in long signal lines is done to reduce the effect of
The input impedance of short circuited lossless transmission line quarter wavelength is
