A device with input x (t) and output y ( t) is characterized by :
`y(t) = x^(2) (t)` .
An FM signal with frequency deviation of 90 kHz and modulating signal bandwidth of 5 kHz is applied to this device . The bandwidth of the output signal is

Options

A. 370kHz
B. 190kHz
C. 380kHz
D. 95kHz

Explanation

To solve the problem step by step, we will analyze the given information and apply the appropriate formulas.

### Step 1: Understand the Input and Output Relationship
The device is characterized by the relationship:
\[ y(t) = x^2(t) \]
This means that the output signal \( y(t) \) is the square of the input signal \( x(t) \).

### Step 2: Determine the Bandwidth of the Input Signal
The input signal is an FM signal with:
- Frequency deviation (\( \Delta f \)) = 90 kHz
- Modulating signal bandwidth (\( B_m \)) = 5 kHz

The bandwidth of an FM signal can be calculated using the Carson's rule:
\[ B_x = 2(\Delta f + B_m) \]
Substituting the values:
\[ B_x = 2(90 \text{ kHz} + 5 \text{ kHz}) \]
\[ B_x = 2(95 \text{ kHz}) \]
\[ B_x = 190 \text{ kHz} \]

### Step 3: Calculate the Bandwidth of the Output Signal
Since the output signal \( y(t) \) is the square of the input signal \( x(t) \), the bandwidth of the output signal will be twice the bandwidth of the input signal:
\[ B_y = 2 \times B_x \]
Substituting the value we calculated for \( B_x \):
\[ B_y = 2 \times 190 \text{ kHz} \]
\[ B_y = 380 \text{ kHz} \]

### Final Answer
The bandwidth of the output signal \( y(t) \) is:
\[ \boxed{380 \text{ kHz}} \]

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