The power at the receiver input is -87 dBm. What is the voltage at its terminals, if its input resistance is 50 ohms.

To find the voltage at the terminals of the receiver input given the power and resistance, you can use the following formula:

\[
V = \sqrt{P \times R}
\]

Where:
- \( V \) is the voltage across the terminals.
- \( P \) is the power in watts.
- \( R \) is the resistance in ohms.

### Step 1: Convert Power from dBm to Watts

First, convert the power from dBm to watts. The formula for converting dBm to watts is:

\[
P_{\text{watts}} = 10^{\frac{P_{\text{dBm}}}{10}} \times 10^{-3}
\]

Given:
- \( P_{\text{dBm}} = -87 \, \text{dBm} \)

\[
P_{\text{watts}} = 10^{\frac{-87}{10}} \times 10^{-3} = 10^{-8.7} \times 10^{-3} \, \text{watts}
\]

### Step 2: Calculate the Voltage

Now, substitute the values into the voltage formula:

\[
V = \sqrt{P_{\text{watts}} \times R}
\]

Given:
- \( R = 50 \, \Omega \)

\[
V = \sqrt{10^{-8.7} \times 10^{-3} \times 50}
\]

Let's compute this value.

\[
V \approx \sqrt{5 \times 10^{-12.7}} \approx \sqrt{5 \times 1.995 \times 10^{-13}} \approx \sqrt{9.975 \times 10^{-13}} \approx 3.16 \times 10^{-6.5} \approx 0.707 \times 10^{-6} \text{ volts}
\]

\[
V \approx 0.707 \, \mu\text{V}
\]

Thus, the voltage at the terminals is approximately **0.707 μV**.

Would you like more details on this calculation, or have any questions?

### Related Questions:
1. How does the resistance affect the voltage at the receiver terminals?
2. What is the significance of the power level in dBm in communication systems?
3. How does the voltage change if the resistance is increased to 75 ohms?
4. How do you convert between dBm and linear scale power?
5. Why is it important to consider impedance matching in receiver systems?

**Tip:** Always ensure your power measurements are correctly converted between dBm and watts when performing calculations involving power and voltage.

Learn how to calculate the voltage at the terminals of a receiver input given a power of -87 dBm and an input resistance of 50 ohms. Understand the dBm to watts conversion and voltage calculation formulas step-by-step.

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