dB = 10 log10 (Pfinal / Pref) dB = 20 log10 (Vfinal / Vref) 1. If the source power of the original laser, or Pref is seven microwatts (1 x 106 Watts), and the total loss of a fiber link is 13 dB, how much power is delivered? 2. If the total loss of a fiber link is 84 dB and the source power of the original laser, or Pref is 1 milliwatt, how much power is delivered? 3. If 2 microvolts, or 2 x 106 volts, are measured at the end of a cable and the source voltage was 1 volt, what is the gain or loss in decibels? Is this value positive or negative? Does the value represent a gain or a loss in voltage?

Introductory Circuit Analysis (13th Edition)
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**Understanding Decibel Calculations**

**Formulas:**
- \( \text{dB} = 10 \log_{10} \left( \frac{P_{\text{final}}}{P_{\text{ref}}} \right) \)
- \( \text{dB} = 20 \log_{10} \left( \frac{V_{\text{final}}}{V_{\text{ref}}} \right) \)

**Problems:**

1. **Power Loss in a Fiber Link:**
   - The source power of the original laser (\(P_{\text{ref}}\)) is seven microwatts (\(1 \times 10^{-6}\) Watts). The total loss of the fiber link is 13 dB.
   - **Question:** How much power is delivered?

2. **Power Delivery with Significant Loss:**
   - The total loss of a fiber link is 84 dB. The source power of the original laser (\(P_{\text{ref}}\)) is 1 milliwatt.
   - **Question:** How much power is delivered?

3. **Voltage Gain or Loss:**
   - Measured voltage at the end of a cable is 2 microvolts, or \(2 \times 10^{-6}\) volts. The source voltage was 1 volt.
   - **Question:** What is the gain or loss in decibels? Is this value positive or negative? Does the value represent a gain or a loss in voltage?
Transcribed Image Text:**Understanding Decibel Calculations** **Formulas:** - \( \text{dB} = 10 \log_{10} \left( \frac{P_{\text{final}}}{P_{\text{ref}}} \right) \) - \( \text{dB} = 20 \log_{10} \left( \frac{V_{\text{final}}}{V_{\text{ref}}} \right) \) **Problems:** 1. **Power Loss in a Fiber Link:** - The source power of the original laser (\(P_{\text{ref}}\)) is seven microwatts (\(1 \times 10^{-6}\) Watts). The total loss of the fiber link is 13 dB. - **Question:** How much power is delivered? 2. **Power Delivery with Significant Loss:** - The total loss of a fiber link is 84 dB. The source power of the original laser (\(P_{\text{ref}}\)) is 1 milliwatt. - **Question:** How much power is delivered? 3. **Voltage Gain or Loss:** - Measured voltage at the end of a cable is 2 microvolts, or \(2 \times 10^{-6}\) volts. The source voltage was 1 volt. - **Question:** What is the gain or loss in decibels? Is this value positive or negative? Does the value represent a gain or a loss in voltage?
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