Category: Microwave Engineering Objective Questions

250+ TOP MCQs on Co-axial Lines Field Analysis and Answers

Microwave Engineering Multiple Choice Questions on “Co-axial Lines Field Analysis”.

1. The expression for conductance G of a coaxial transmission line with outer radius ‘b’ and inner radius ‘a’ is given by:
A. 2πωε”/ (ln b/A.
B. (R/2π)(1/a+1/B.
C. Rb/πa
D. 2Rb/a
Answer: A
Clarification: The conductance G of a coaxial transmission line is 2πωε”/ (ln b/A.. Conductance of the transmission line is inversely related to the conductance of the transmission line.

2. Expression for resistance R of a coaxial transmission line outer radius b and inner radius a is:
A. Rs/2π ( 1/a+1/B.
B. 2πω∈”/ln⁡(b/A.
C. μ/π cos-1(b/A.
D. πϵ’/cosh-1(b/A.
Answer: A
Clarification: Resistance R of a coaxial transmission line is Rs/2π ( 1/a+1/B.. Here a and b are the outer and inner radius of the transmission line. Rs are the series resistance of the coaxial cable.

3. If the outer and the inner diameter of a coaxial transmission line are 20 mm and 10 mm respectively, then the inductance /m of the transmission line is:
A. 0.13 µH
B. 0.2 µH
C. 0.3 µH
D. 0.1 µH
Answer: A
Clarification: Inductance of a coaxial transmission line is µ*ln (b/A./ 2π. Substituting the given values in the equation for inductance, the inductance is 0.13 µH.

4. If the outer circumference and the inner circumference of a transmission line are 40π and 25π units respectively, then the capacitive reactance of the coaxial transmission line is:
A. 0.376 nF
B. 0.45 nF
C. 0.9 nF
D. none of the mentioned
Answer: A
Clarification: Capacitance of a coaxial transmission line is given by the expression 2π∈/ln (b/A.. Computing the capacitance from this equation and then computing the capacitive reactance, the coaxial line has a capacitive reactance 0.376 nF.

5. For a 2 wire transmission line, if the complex part of permittivity is 2.5, then the given distance between the 2 wires is 10mm and operated at a frequency of 1.2 MHz and the radius of the line being 5mm, then the conductance of the transmission line is:
A. 0.2 µH
B. 0.1 µH
C. 0.5 µH
D. 1 µH
Answer: A
Clarification: For a two wire transmission line, inductance of the line is given by π∈/ cosh-1(D/ 2A.. Substituting the given values in the above equation, the conductance of the line is 0.2 µH.

6. Characteristics impedance of a coaxial line with external and inner diameter 5mm is:
A. 40 Ω
B. 41.58 Ω
C. 47.78 Ω
D. 54.87 Ω
Answer: B
Clarification: Characteristic impedance of the coaxial line is given by the expression ln (b/A./ 2π. Substituting the given values in the above expression, the characteristic impedance is 41.58 Ω.

7. The characteristic impedance of the transmission line if the outer diameter and inner diameter of the transmission line is 20 mm and 10 mm respectively, given the intrinsic impedance of the medium is 377 Ω, then the characteristic impedance of the transmission line is:
A. 41.58 Ω
B. 50 Ω
C. 377 Ω
D. None of the mentioned
Answer: A
Clarification: Characteristic impedance of the coaxial line is given by the expression ln (b/A./ 2π. Substituting the given values in the above expression, the characteristic impedance 41.58 Ω.

8. Flow of power in transmission line takes place through:
A. Electric field and magnetic field
B. Voltage and current
C. Voltage
D. Electric field
Answer: A
Clarification: In a transmission line, flow of power takes place through propagation of electric field and magnetic field. Alternating electric field and alternating magnetic field propagates EM wave transmitting power.

9. When a transmission line is exited by a source, total power supplied is delivered to the load.
A. True
B. False
Answer: B
Clarification: When a transmission line is excited by the source, entire power is not delivered to the load due to the various types of losses that occur in the transmission line.

10. Expression for propagation constant. γ In terms of ω is:
A. √ω2µ∈
B. ω2µ∈
C. – ω2µ∈
D. None of the mentioned
Answer: A
Clarification: Propagation constant γ for a transmission line is dependent on the operating frequency of the transmission line, and the permittivity and permeability of the medium.


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250+ TOP MCQs on Scattering Matrices and Answers

Microwave Engineering Multiple Choice Questions on “Scattering Matrices”.

1. S parameters are expressed as a ratio of:
A. Voltage and current
B. Impedance at different ports
C. Indecent and the reflected voltage waves
D. None of the mentioned
Answer: C
Clarification: S matrix can be used to represent any n port network. S parameters are defined for microwave networks. Hence instead of voltage and current measurement, the amplitude of the incident and reflected voltage waves is measured.

2. The relation between incident voltage matrix , reflected voltage matrix and S matrix for a microwave network:
A. [v-] = [s] [v+].
B. [v+] = [s] [v-].
C. [v-] [v] = [s].
D. [s] = [v] [v-].
Answer: A
Clarification: S parameter for a microwave network is defined as the ratio of reflected voltage wave to the incident voltage wave. When represented in the form of a matrix, reflected voltage matrix is the product of S parameter and the incident voltage wave at that port.

3. The specific element Sij of the scattering matrix can be determined as:
A. SIJ= Vi-/Vj+
B. SIJ= Vi+/Vj-
C. S= Vj+/Vi-
D. None of the mentioned
Answer: A
Clarification: The parameter Sij is found by driving port j with an incident wave of voltage Vj+ coming out of ports i. The incident waves on all ports except the jth port are set to zero.

4. The device used to get the measurement of S parameters of n- port micro wave network is:
A. CRO
B. Network analyzer
C. Circulator
D. Attenuator
Answer: B
Clarification: Network analyzer is a device to which any microwave network can be externally connected with the help of probes and the s parameters of the network can be obtained.

5. For a one port network , the scattering parameter S₁₁ in terms of impedance parameter Z₁₁ is:
A. (Z11-1)/ (Z11+1)
B. (Z11+1)/ (Z11-1)
C. (Z11+1) (Z11-1)
D. Z11
Answer: a
Clarification: If Z matrix of a one port network is computed, then the s matrix of the same can be computed using the Z11 coefficient. To compute the S11 parameter of the network, the relation used is (Z11-1)/ (Z11+1).

6. Scattering matrix for a reciprocal network is:
A. Symmetric
B. Unitary
C. Skew symmetric
D. Identity matrix
Answer: A
Clarification: For a reciprocal network, the input to port I and output at port j is the same as the input at port j and output measured at port i. Hence, the ports are interchangeable. As the ports are interchangeable, this is reflected in the matrix and the matrix becomes symmetric.

7. S₁₂=0.85-45⁰ and S₁₂=0.85 +45⁰ for a two port network. Then the two port network is:
A. Non-reciprocal
B. Lossless
C. Reciprocal
D. Lossy
Answer: A
Clarification: For a reciprocal network, the S matrix is symmetric. For the matrix to be symmetric, Sij=Sji. Since this condition is not satisfied in the above case, the matrix is non reciprocal.

8. Scattering matrix for a lossless matrix is:
A. Unitary
B. Symmetric
C. Identity matrix
D. Null matrix
Answer: A
Clarification: For a lossless network, the scattering matrix has to be unitary. That is, the law of conservation of energy is to be verified for this case. Using appropriate formula, this condition can be verified.

9. If the reflection co efficient of a 2 port network is 0.5 then the return network loss in the network is:
A. 6.5 dB
B. 0.15 dB
C. 6.020 dB
D. 10 dB
Answer: C
Clarification: Given the reflection coefficient of the network, return loss of the network is calculated using the formula -20 log │Г│. Substituting for reflection coefficient, the return loss of the network is 6.02 dB.

10. If the reflection co efficient of a 2 port network is 0.25 then the return network loss in the network is:
A. 12.05 dB
B. 0.15 dB
C. 20 dB
D. 10 dB
Answer: A
Clarification: Given the reflection coefficient of the network, return loss of the network is calculated using the formula -20 log │Г│. Substituting for reflection coefficient, the return loss of the network is 12.05 dB.


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250+ TOP MCQs on Excitation of Resonators and Answers

Microwave Engineering Multiple Choice Questions on “Excitation of Resonators”.

1. The level of coupling required between a resonator and its attached circuitry is a standard and independent of the application where coupling is required.
A. true
B. false
Answer: B
Clarification: The level of coupling required between a resonator and its attached circuitry depends on the application. A waveguide cavity to a frequency meter is loosely coupled to maintain high Q and good accuracy.

2. A measure of the level of coupling between a resonator and a feed is given by:
A. coupling coefficient
B. power transfer coefficient
C. voltage coefficient
D. reflection coefficient
Answer: A
Clarification: Coupling coefficient tells how the resonator is coupled to the external circuitry. A resonator can be coupled in three ways. They can be under coupled, critically coupled or over coupled.

3. To obtain maximum power transfer between a resonator and feed line, the resonator should be matched to the load at:
A. resonant frequency
B. cutoff frequency
C. zero frequency
D. none of the mentioned
Answer: A
Clarification: In order to obtain a maximum power transfer between a resonator and a feed line, the resonator should be matched to the feed line at the resonant frequency of the resonator which is coupled.

4. When impedance matching is done between a resonator and a feed line, the condition for impedance matching is:
A. R=Z0
B. R=Z0/2
C. R=2Z0
D. R=√Z0
Answer: A
Clarification: If R is the resistance of the series RLC circuit and Z0 is the characteristic impedance of the feed line, for proper coupling their impedance has to be matched. This is the condition for impedance matching between a feed line and a resonator.

5. Coupling coefficient Q can be defined as the ratio of unloaded Q to external Q.
A. true
B. false
Answer: A
Clarification: Coupling coefficient Q defined as the ratio of unloaded Q to external Q can be applied to both series resonance and parallel resonance circuits. For series resonant circuits, coupling coefficient is defined as the ratio of characteristic impedance of feed line to the resistance in the resonant circuit.

6. When the coupling coefficient is lesser than one, the resonator is over coupled to the feed line.
A. true
B. false
Answer: B
Clarification: When the coupling coefficient is less than one, the resonator is under coupled to the feed line. For a series resonant circuit, resonator is under coupled implies that the resistance in the resonator is greater than the characteristic impedance of the transmission line.

7. Direct measurement of the unloaded Q of a resonator is not possible.
A. true
B. false
Answer: A
Clarification: Direct measurement of the unloaded Q of a resonator is not possible because of the loading effect of the measurement system, but it is possible to determine unloaded Q from measurements of the frequency response of the loaded resonator when it is connected to a transmission line.

8. For practical applications cavity resonators can be modified as per the requirement of the application where it is used.
A. true
B. false
Answer: A
Clarification: Small changes in the cavity resonator can be made by changing their shape, or by introducing small pieces of dielectric or metallic materials. The resonant frequency of a cavity resonator can be easily tuned with a small screw that enters the cavity volume or by changing the size of the cavity by a movable wall.

9. When coupling coefficient is 1, the resonator is ________ to the feed line.
A. under coupled
B. over coupled
C. critically coupled
D. none of the mentioned
Answer: C
Clarification: The resonator is critically coupled to the feed line when the coupling coefficient is 1. Maximum power is transferred between the resonator and the feed line since the resistance of the resonator is equal to the characteristic impedance of the transmission line.

10. In aperture coupling, a small aperture in the transverse wall of the waveguide acts as:
A. shunt inductance
B. shunt capacitance
C. series inductance
D. series capacitance
Answer: A
Clarification: In aperture coupling, a small aperture is made in the transverse wall of the cavity which is to be coupled to an external microwave circuit. This aperture made in the transverse wall of the cavity acts as a shunt inductance.


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250+ TOP MCQs on PIN Diodes and Answers

Microwave Engineering Multiple Choice Questions on “PIN Diodes”.

1. A PIN diode consists of ______number of semiconductor layers.
A. Three
B. Two
C. Four
D. One
Answer: a
Clarification: PIN diode is a p-type, intrinsic, n-type diode consisting of narrow layer of p-type semiconductor and a narrow layer of n-type semiconductor material, with a thicker region of intrinsic or very lightly n doped semiconductor sandwiched between them.

2. The material out of which PIN diode is made is:
A. Silicon
B. Germanium
C. GaAs
D. None of the mentioned
Answer: A
Clarification: Silicon is the semiconductor normally used because of its power handling capability and it offers high resistivity for the intrinsic region. But depending on the application, these days GaAs is also used in fabricating PIN diodes.

3. The behavior of a PIN diode is entirely different from normal diodes at all frequency of operation.
A. True
B. False
Answer: B
Clarification: PIN diode acts as a ordinary diode at frequencies up to about 100MHz. at high frequencies it stops to rectify and then acts as a variable resistance.

4. The junction resistance and capacitance of the intrinsic region in a PIN diode are connected______ in the equivalent circuit of PIN diode.
A. Series
B. Parallel
C. Connected across package capacitance
D. None of the mentioned
Answer: B
Clarification: The junction capacitance Cj and junction resistance Rj of a PIN diode are connected in parallel in the equivalent circuit of a PIN diode. The package resistance and package capacitance are connected in series to these junction parameters.

5. The resistance of the PIN diode with positive bias voltage:
A. Increases
B. Decreases
C. Remains constant
D. Insufficient data
Answer: B
Clarification: When the bias is varied on the PIN diode, its microwave resistance RJ changes from a typical value of 6 KΩ under negative bias to perhaps 5 Ω under forward bias. Thus if the diode is mounted on a 50Ω coaxial line, it will not significantly load this line.

6. A PIN diode can be used in either a series or a shunt configuration to form a __________
A. Single pole single throw switch
B. Single pole double throw switch
C. Amplifier
D. Oscillator
Answer: A
Clarification: A PIN diode can be used in either a series or a shunt configuration to form a single pole single throw switch. In the series configuration, the switch is on when the diode is forward biased and off when the diode is reverse biased.

7. The working principle of series and shunt configuration single pole single throw switch is the same.
A. True
B. False
Answer: B
Clarification: In the series configuration, the switch is on when the diode is forward biased and off when the diode is reverse biased. In the shunt configuration, forward biasing the diode cuts-off the transmission while reverse biasing the diode ensures transmission from input to output.

8. Under ideal conditions, when a PIN diode is used as a switch, the switch must have _______ insertion loss in the ON state.
A. Maximum
B. Zero
C. Average
D. Insertion loss cannot be defined for a switch
Answer: B
Clarification: Ideally, when PIN diode is used as switch, the switch should have zero insertion loss in the ON state and infinite attenuation in the OFF state. These are ideal conditions. But practically a good operating switch must have low insertion loss.

9. When PIN diode is used as a switch, the expression for insertion loss of the switch is given by:
A. 10 log (Po/PL)
B. 10 log (PL/P0)
C. 10 log (PL. Pₒ)
D. None of the mentioned
Answer: A
Clarification: Insertion loss of a switch is defined as the ratio of incident power applied to the load when switch is absent to the actual power delivered to the load.

10. For a shunt configuration switch, the diode impedance is 40 Ω and the terminated line characteristic impedance is 50 Ω. Then the insertion loss of the switch is:
A. 2.2 dB
B. 4.2 dB
C. 8.4 dB
D. 3.6 dB
Answer: B
Clarification: Insertion loss of a shunt configuration switch is given by 20 log (2ZD+Z0/2ZD). Substituting the given values in the above expression, the insertion loss of the shunt configuration switch is 4.2 dB.

11. In the series configuration of a PIN diode switch, the terminated load impedance was found to be 50 Ω and the diode impedance was 60 Ω. Then the insertion loss of the switch is:
A. 4 dB
B. 2 dB
C. 3.6 dB
D. 4.8 dB
Answer: A
Clarification: Insertion loss of a shunt configuration switch is given by 20 log (2ZD+Z0/2ZD). Substituting the given values in the above equation, the insertion loss is 4 dB.

12. The number of PIN diodes used in SPST switch and SPDT switch are the same.
A. True
B. False
Answer: B
Clarification: The number of PIN diodes in SPST switch is one, while the number of PIN diodes used in single pole double throw switch is two.


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250+ TOP MCQs on Power Amplifiers and Answers

Microwave Engineering Multiple Choice Questions on “Power Amplifiers”.

1. _______________ are used in the final stages of radar and radio transmitters to increase the radiated power level.
A. Power amplifiers
B. Oscillators
C. Transistors
D. Attenuators

Answer: A
Clarification: Power amplifiers are used in the final stages of radar and radio transmitters to increase the radiated power level. Output of power amplifiers are in the range of 100-500 mW.

2. Important factors to be considered for power amplifier design are:
A. Efficiency
B. Gain
C. Thermal effect
D. All of the mentioned

Answer: D
Clarification: As per the application requirement and considering various aspects of an amplifier like efficiency, gain, thermal efficiency and inter modulation distortion, amplifiers need to be designed.

3. Amplifier efficiency is the ratio of RF output power to DC input power. This parameter determines the performance of an amplifier.
A. True
B. False

Answer: A
Clarification: Power amplifier is the primary consumer of DC power in most hand-held wireless devices, so amplifier efficiency is an important consideration. Amplifier efficiency is the ratio of RF output power to DC input power.

4. Gain of power amplifiers __________ with increase in operating frequency.
A. Increases
B. Decreases
C. Increases exponentially
D. Decreases exponentially

Answer: B
Clarification: Silicon bipolar junction transistor amplifiers in the cellular telephone band of 800-900 MHz band have power added efficiencies of about 80%. But this efficiency drops quickly with increase in the operating frequency.

5. ___________ amplifiers are linear circuits, where the transistor is biased to conduct over the entire range of the input signal cycle.
A. Class A amplifiers
B. Class B amplifiers
C. Class C amplifiers
D. None of the mentioned

Answer: A
Clarification: Class A amplifiers are linear circuits, where the transistor is biased to conduct over the entire range of the input signal cycle. Because of this, class A amplifiers theoretically have a maximum efficiency of 50%.

6. A class B amplifier consists of _______ transistors in order to conduct the input signal over the entire cycle.
A. 1
B. 2
C. 4
D. 6

Answer: B
Clarification: Class B amplifier is biased to conduct only during one-half of the input signal cycle. 2 complementary transistors are operated in a class B push pull amplifier to provide amplification over the entire cycle.

7. Power amplifiers in the increasing order of efficiency is:
A. Class A, B, C
B. Class C, A, B
C. Class B, A, C
D. Efficiency of all the 3 amplifiers is the same

Answer: A
Clarification: Class A amplifiers have an efficiency of about 50%. Class B amplifiers have an efficiency of about 78%, class C amplifiers can achieve efficiencies up to 100%. In the increasing order of efficiency, C > B> A.

8. Behavior of a transistor in power amplifiers is unpredictable at all input signal levels.
A. True
B. False

Answer: B
Clarification: A transistor behaves linearly for signal powers below 1dB compression point and so, the small –signal scattering parameters should not depend either on the input power level or the output termination impedance.

9. If the output power of an amplifier is 10 V, and the input power supplied to the amplifier is 0.229 V given that the DC voltage used is 38.5 V, efficiency of the power amplifier is:
A. 25%
B. 50%
C. 75%
D. 35%

Answer: A
Clarification: Efficiency of a power amplifier is (Pout- Pin)/ PDc Substituting the given values in the above expression, efficiency of the power amplifier is 25%.

10. If a power amplifier has an output power of 10 W, and an amplifier gain of 16.4 dB, then the input drive power is:
A. 400 mW
B. 225 mW
C. 229 mW
D. 240 mW

Answer: C
Clarification: Input drive power required to get an output of 10 W is Pout (dBm)- G (dB.. G is the gain of the amplifier. Substituting the given values in the above equation, 229 mW.

250+ TOP MCQs on Antenna Family and Answers

Microwave Engineering Multiple Choice Questions on “Antenna Family”.

1. The members of the antenna family which are made of wires of certain value in terms of operating wavelength are called:
A. Loop antennas
B. Wire antennas
C. Dipole antenna
D. Slot antennas
Answer: C
Clarification: Wires of half wavelength are termed as dipoles. Their radiation resistance is about 73 Ω. If only half of this length is used, then it is called quarter-wave monopole with a radiation resistance of 36.5 Ω.

2. The antenna in which location of the feed determines the direction of the lobe are:
A. Wire antenna
B. Loop antenna
C. Helical antenna
D. Horn antenna
Answer: A
Clarification: In a wire antenna, the location of the feed determines the direction of the lobe and the orientation of the wire determines the polarization. These wires can be thick or thin. Thickness of the wire determines the radiation resistance of the antenna.

3. Based on the size of the loops, loop antennas are classified as small and large loops. This is the only classification of loop antenna.
A. True
B. False
Answer: B
Clarification: Loop antennas are classified based on various antenna parameters. To name a few, small and large loops, circular and square loops, loops having single or multi turns, loops with turns wound using a single wire or multiple wires.

4. Antenna that does not belong to the horn antenna family among the following are:
A. Pyramidal horn
B. Conical horn
C. bi-conical horn
D. None of the mentioned
Answer: D
Clarification: All of the above mentioned antennas belong to the horn antenna family. Horn antennas may be made of pointed or rounded waveguides. The waveguides may contain disc at an end or some dielectric.

5. Patch antennas are the antennas of small size and are made of:
A. Strip line
B. Microstrip lines
C. Coaxial cables
D. Rectangular waveguide
Answer: B
Clarification: Patch antennas are microstrip antennas that can be of any shape. Patch antennas can be aperture-coupled fed or proximity fed. For obtaining circular polarization, a patch may also be doubly fed.

6. Reflector antennas are widely used to modify radiation patterns of radiating elements.
A. True
B. False
Answer: A
Clarification: Reflector antennas are used to modify radiation patterns of radiating elements. Reflector antennas are classified into two categories. They are passive reflectors and active reflectors. Based on the type of the radiating element and the modification in the radiation pattern required, accordingly either active or passive reflectors are chosen.

7. The pattern of the reflector in a reflector antenna is called:
A. Primary pattern
B. Secondary pattern
C. Reflector pattern
D. None of the mentioned
Answer: B
Clarification: In a reflector antenna, the feed pattern is called primary pattern and the pattern of the reflector is called secondary pattern. These antennas are widely employed in RADARs and other types of point to point communication links.

8. ______ antennas have gain less than reflector antennas but have more lenient tolerance on surfaces.
A. Helical antennas
B. Lens antennas
C. Array antennas
D. Slot antennas
Answer: B
Clarification: Lens antennas are complex in nature but are able to scale wider angles. In comparison to reflectors, their gain is 1 or 2 dB less, but these have more lenient tolerance on surfaces. These have less rearward reflection, relatively low loss and can be easily shaped to the desired contours.

9. Lens antennas are classified into two types. One being fast antenna, the other one is:
A. Slow antenna
B. Delay antenna
C. Dynamic antenna
D. None of the mentioned
Answer: B
Clarification: In delay lenses, the electrical path length is increased or the wave is retarded by the lens medium. Dielectric lenses and H-plane metal lenses fall in this category.

10. The antennas which offer high operational bandwidth and the antenna parameters are maintained over a wide range of antennas are called:
A. Wide band antennas
B. Array antennas
C. Parabolic antennas
D. None of the mentioned
Answer: A
Clarification: In this class of antennas, constancy of impedance and radiation characteristics is maintained over a wide range of frequencies. To be wide band or frequency independent, antennas should expand or contract in proportion to the wavelength.

11. High directivity required in RADAR communication is satisfied using this type of antennas:
A. Wide band antennas
B. Antenna arrays
C. Slot antennas
D. Patch antennas
Answer: B
Clarification: Higher directivity is the requirement in point to point communication. This can be achieved by increasing the size of the antennas in terms of electrical length. When much high directivity is required, antenna arrays are used.

12. The terminal impedance of a dipole antenna is 710 Ω. The terminal impedance of the slot antenna given the intrinsic impedance of air is 377 Ω is:
A. 100 Ω
B. 50 Ω
C. 25 Ω
D. None of the mentioned
Answer: B
Clarification: The terminal impedance ZS of the slot is given by the relation Z02/ 4Zd) Zₒ is the intrinsic impedance of the medium and ZD is the terminal impedance of the dipole. Substituting the given values in the above equation, the terminal impedance of sot is 50 Ω.

13. If the length of aperture in a pyramidal horn antenna is 10cm and δ for the design is 0.25. Then, the flaring angle of the pyramidal horn is:
A. 30⁰
B. 25.4⁰
C. 45⁰
D. 60⁰
Answer: B
Clarification: The flaring angle of pyramidal horn is given by 2cos-1(L/L+δ). Substituting the values of L and δ, flaring angle is 25.4⁰.

14. If the directivity of a square corner receiving antenna is 20 and operating at a wavelength of 0.25m, the effective aperture of a square corner antenna is:
A. 0.4 m2
B. 0.2 m2
C. 0.1 m2
D. None of the mentioned
Answer: A
Clarification: Given the directivity of the antenna, effective aperture of the antenna is given by Dλ2/4π. substituting the given values of the variables; the effective aperture of the antenna is 0.4 m2.


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