A dipole carries RMS current of about 300 A across the radiation resistance 2 Ω. What would be the power radiated by an antenna?

Question

A dipole carries RMS current of about 300 A across the radiation resistance 2 &Omega;. What would be the power radiated by an antenna?

Prepp Team · Accepted Answer

Calculating Antenna Power Radiation

The question asks us to determine the power radiated by a dipole antenna given its RMS current and radiation resistance. This is a fundamental calculation in antenna theory, relating the current flowing in the antenna to the energy it transmits as electromagnetic waves.

Understanding Power Radiation in Antennas

Antennas convert electrical power into electromagnetic waves. The power radiated by an antenna is related to the current flowing through it and its radiation resistance. Radiation resistance is a hypothetical resistance that represents the power dissipated (radiated) by the antenna as electromagnetic waves. It's defined as the ratio of the total power radiated by the antenna to the square of the RMS current at its input terminals.

The formula for calculating the power radiated ($P_{rad}$) is similar to calculating power dissipated in a resistor:

$ P_{rad} = I_{rms}^2 \times R_{rad} $

Where:

$ P_{rad} $ is the power radiated (in Watts, W)
$ I_{rms} $ is the RMS value of the current flowing into the antenna (in Amperes, A)
$ R_{rad} $ is the radiation resistance of the antenna (in Ohms, $\Omega$)

Applying the Formula to the Dipole Antenna Problem

We are given the following values for the dipole antenna:

RMS current, $ I_{rms} = 300 \text{ A} $
Radiation resistance, $ R_{rad} = 2 \text{ } \Omega $

Now, we can plug these values into the power radiation formula:

$ P_{rad} = (300 \text{ A})^2 \times 2 \text{ } \Omega $

First, calculate the square of the RMS current:

$ (300 \text{ A})^2 = 300 \times 300 \text{ A}^2 = 90000 \text{ A}^2 $

Next, multiply this by the radiation resistance:

$ P_{rad} = 90000 \text{ A}^2 \times 2 \text{ } \Omega $

$ P_{rad} = 180000 \text{ W} $

The calculated power is in Watts (W). The options are given in kilowatts (kW). To convert Watts to Kilowatts, we divide by 1000:

$ P_{rad} \text{ (in kW)} = \frac{180000 \text{ W}}{1000} $

$ P_{rad} \text{ (in kW)} = 180 \text{ kW} $

So, the power radiated by the antenna is 180 kW.

Parameter	Value	Unit
RMS Current ($I_{rms}$)	300	A
Radiation Resistance ($R_{rad}$)	2	$\Omega$
Calculated Power Radiated ($P_{rad}$)	180000	W
Calculated Power Radiated ($P_{rad}$)	180	kW

Conclusion on Antenna Power Calculation

Based on the given RMS current of 300 A and a radiation resistance of 2 $\Omega$, the power radiated by the dipole antenna is calculated to be 180 kW.

Revision Table: Antenna Power Radiation Concepts

Concept	Description	Formula/Relation
Radiation Resistance ($R_{rad}$)	Equivalent resistance representing power radiated as EM waves.	$ P_{rad} = I_{rms}^2 R_{rad} $
Input Impedance ($Z_{in}$)	Total impedance seen at antenna terminals, $ Z_{in} = R_{in} + jX_{in} $. $R_{in}$ includes $R_{rad}$ and loss resistance.	$ Z_{in} = R_{rad} + R_{loss} + jX_{A} $
Antenna Efficiency ($\eta$)	Ratio of power radiated to total power input.	$ \eta = \frac{P_{rad}}{P_{in}} = \frac{R_{rad}}{R_{rad} + R_{loss}} $
Power Input ($P_{in}$)	Total power delivered to the antenna terminals.	$ P_{in} = I_{rms}^2 (R_{rad} + R_{loss}) $

Additional Information on Antenna Characteristics

While radiation resistance helps calculate radiated power, it's important to understand that antennas also have other characteristics that affect their performance:

Loss Resistance ($R_{loss}$): This represents power dissipated as heat in the antenna structure (due to conductor resistance, dielectric losses, etc.). The total input resistance of an antenna is the sum of radiation resistance and loss resistance ($R_{in} = R_{rad} + R_{loss}$).
Antenna Efficiency: Antenna efficiency is the ratio of radiated power to the total input power. A higher efficiency means more of the input power is radiated rather than lost as heat. It is calculated as $ \eta = \frac{R_{rad}}{R_{rad} + R_{loss}} $. For an ideal antenna with no losses, $ \eta = 1 $ ($R_{loss} = 0$).
Directivity and Gain: These parameters describe how well an antenna concentrates the radiated power in a particular direction. Directivity is based on the radiation pattern assuming no losses, while gain includes the effect of antenna efficiency. Gain = Efficiency $\times$ Directivity.

Understanding these parameters is crucial for designing and analyzing antenna systems for various applications, ensuring efficient transmission of signals.

Prepp Team · Answer

135 kW

Prepp Team · Answer

200 kW

Prepp Team · Answer

90 kW

Concept	Description	Formula/Relation
Radiation Resistance (\(R_{rad}\))	Equivalent resistance representing power radiated as EM waves.	\( P_{rad} = I_{rms}^2 R_{rad} \)
Input Impedance (\(Z_{in}\))	Total impedance seen at antenna terminals, \( Z_{in} = R_{in} + jX_{in} \). \(R_{in}\) includes \(R_{rad}\) and loss resistance.	\( Z_{in} = R_{rad} + R_{loss} + jX_{A} \)
Antenna Efficiency (\(\eta\))	Ratio of power radiated to total power input.	\( \eta = \frac{P_{rad}}{P_{in}} = \frac{R_{rad}}{R_{rad} + R_{loss}} \)
Power Input (\(P_{in}\))	Total power delivered to the antenna terminals.	\( P_{in} = I_{rms}^2 (R_{rad} + R_{loss}) \)