Array gain of an antenna is

Options

A. directly proportional to power radiated by isotropic antenna
B. invesely proportional to power radiated by isotropic antenna
C. directly proportional to power radiated by practical antenna
D. inversely proportional to square of power radiated by practical antenna

Explanation

To solve the question regarding the array gain of an antenna, we need to understand the concept of array gain and how it relates to the power radiated by isotropic and practical antennas.

### Step-by-Step Solution:

1. **Understanding Array Gain**:
- Array gain refers to the increase in power gain achieved by using multiple antennas compared to a single antenna. It is a measure of how effectively the combined antennas can transmit or receive signals.

2. **Defining Isotropic Antenna**:
- An isotropic antenna is a theoretical antenna that radiates power uniformly in all directions. The power radiated by an isotropic antenna is denoted as \( P_0 \).

3. **Defining Practical Antenna**:
- A practical antenna is one that has real-world limitations and does not radiate power uniformly. The power radiated by a practical antenna is denoted as \( P_n \).

4. **Array Gain Formula**:
- The power gain \( G \) of an antenna array can be expressed in decibels (dB) using the formula:
\[ G = 10 \log \left( \frac{P_0}{P_n} \right) \]
- Here, \( P_0 \) is the power radiated by the isotropic antenna, and \( P_n \) is the power radiated by the practical antenna.

5. **Analyzing the Relationship**:
- From the formula, we can see that:
- \( G \) is directly proportional to \( P_0 \) (the power radiated by the isotropic antenna).
- \( G \) is inversely proportional to \( P_n \) (the power radiated by the practical antenna).

6. **Evaluating the Options**:
- A. Directly proportional to power radiated by isotropic antenna: **Correct**.
- B. Inversely proportional to power radiated by isotropic antenna: **Incorrect**.
- C. Directly proportional to power radiated by practical antenna: **Incorrect**.
- D. Inversely proportional to square of power radiated by practical antenna: **Incorrect**.

7. **Conclusion**:
- The correct answer is option **A**: Array gain of an antenna is directly proportional to the power radiated by an isotropic antenna.