A patch has radiation resistance of 132 Ohms. The loss resistance is 9 Ohms. The radiation efficiency of the antenna is:

1. Break Down the Problem

To compute the radiation efficiency of the antenna, we need to understand the relationship between radiation resistance, loss resistance, and radiation efficiency. The formula for radiation efficiency ($\eta$) is given by:

$\eta = \frac{R_r}{R_r + R_l}$

where:

• $R_r$ = Radiation resistance (132 Ohms)
• $R_l$ = Loss resistance (9 Ohms)

2. Relevant Concepts

The concept we need here is the definition of radiation efficiency, which is the ratio of the radiation resistance to the total resistance (sum of radiation resistance and loss resistance).

3. Analysis and Detail

Let's plug in the values into the formula.

$\eta = \frac{R_r}{R_r + R_l} = \frac{132}{132 + 9}$

Calculating the denominator:

$132 + 9 = 141$

Now substituting back into the formula:

$\eta = \frac{132}{141}$

4. Verify and Summarize

Now, we can perform the final calculation:

$\eta \approx 0.93617$

This implies that the radiation efficiency is approximately 93.62%.

Final Answer

The radiation efficiency of the antenna is approximately 93.62%.