#3 **Problem:**A 150-foot length of coax has a loss of 2.2 dB per 100 ft. The connectors on each end add 0.2 dB of loss each. The transmit antenna provides 10.2 dB of gain, and free space attenuates the signal by 135 dB. If the receiving antenna requires a minimum signal of -70 dBm, what is the required transmitter power in dBm and watts?**Solution Approach:**1. **Calculate total coax loss:** - Loss for 150 ft = \( \left(\frac{150}{100}\right) \times 2.2 \, \text{dB} = 3.3 \, \text{dB} \)2. **Calculate total connector loss:** - Each end = 0.2 dB - Total connector loss = \( 2 \times 0.2 \, \text{dB} = 0.4 \, \text{dB} \)3. **Determine overall losses and gains:** - Total loss = coax loss + connector loss + free space loss = \( 3.3 + 0.4 + 135 \, \text{dB} \) - Total gain from antenna = 10.2 dB4. **Calculate net loss:** - Net loss = total loss - antenna gain = \( (3.3 + 0.4 + 135) - 10.2 = 128.5 \, \text{dB} \)5. **Determine required transmitter power:** - Minimum received signal = -70 dBm - Required transmitter power = minimum received signal + net loss = \( -70 + 128.5 = 58.5 \, \text{dBm} \)6. **Convert dBm to watts:** - \( P \, \text{(watts)} = 10^{\left(\frac{58.5}{10}\right)} \times 10^{-3} \) - \( P \approx 0.7079 \, \text{watts} \)**Conclusion:**The required transmitter power is approximately 58.5 dBm, or 0.7079 watts.

Answered: A 150 foot length of coax has a loss of…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

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**Problem:**

A 150-foot length of coax has a loss of 2.2 dB per 100 ft. The connectors on each end add 0.2 dB of loss each. The transmit antenna provides 10.2 dB of gain, and free space attenuates the signal by 135 dB. If the receiving antenna requires a minimum signal of -70 dBm, what is the required transmitter power in dBm and watts?

**Solution Approach:**

1. **Calculate total coax loss:**
- Loss for 150 ft = \( \left(\frac{150}{100}\right) \times 2.2 \, \text{dB} = 3.3 \, \text{dB} \)

2. **Calculate total connector loss:**
- Each end = 0.2 dB
- Total connector loss = \( 2 \times 0.2 \, \text{dB} = 0.4 \, \text{dB} \)

3. **Determine overall losses and gains:**
- Total loss = coax loss + connector loss + free space loss = \( 3.3 + 0.4 + 135 \, \text{dB} \)
- Total gain from antenna = 10.2 dB

4. **Calculate net loss:**
- Net loss = total loss - antenna gain = \( (3.3 + 0.4 + 135) - 10.2 = 128.5 \, \text{dB} \)

5. **Determine required transmitter power:**
- Minimum received signal = -70 dBm
- Required transmitter power = minimum received signal + net loss = \( -70 + 128.5 = 58.5 \, \text{dBm} \)

6. **Convert dBm to watts:**
- \( P \, \text{(watts)} = 10^{\left(\frac{58.5}{10}\right)} \times 10^{-3} \)
- \( P \approx 0.7079 \, \text{watts} \)

**Conclusion:**

The required transmitter power is approximately 58.5 dBm, or 0.7079 watts.

Expert Solution

Step 1: Define transmitted power.

The quantity of energy radiated by a transmitter is known as transmitted power. It is often expressed in terms of watts or decibels (dBm) in relation to one watt. The performance and range of a wireless communication system are significantly influenced by transmitted power. The kind of antenna being used, the frequency of the signal, and the transmitter's power output are just a few variables that can have an impact on the amount of transmitted power.

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