How many electrons are in the upper level? Problem 2
Problem 1 of chapter 6 of the course-pack. Use eqn. 2.27 for the definition of decibel.
Eqn. 2.27 : A(w)=-20log|T(jw)| db
Use the plot to calculate the repeater distance in a long haul optical communication system. Assume that a repeater is needed when the original signal has attenuated to 1% of its original value.
Do the calculations for laser wavelengths of 1) 1.55 µm 2) 1.2 µm 3) 1.8 µm
Note that intensity or energy is proportional to the square of the amplitude of the wave.
To calculate the repeater distance in a long haul optical communication system, you need to use the equation A(w) = -20log|T(jw)| dB, which is given as equation 2.27 in the course-pack.
Here's how you can solve the problem step by step:
1. Identify the values you need:
- The attenuation level where a repeater is needed (1% of the original value)
- The laser wavelengths (1.55 µm, 1.2 µm, and 1.8 µm)
2. Plug in the values into the equation:
- A(w) = -20log|T(jw)| dB
3. Calculate the attenuation level in decibels:
- Convert the attenuation level (1%) to decibels using the logarithmic relationship: 1% = -20log(T)
- Solve for T: T = 10^(-A/20)
- Substitute the T value into the equation.
4. Calculate the repeater distance:
- Since intensity or energy is proportional to the square of the amplitude of the wave, you'll need to calculate the square of the amplitude in order to convert it to intensity.
- The repeater distance is proportional to the inverse square of the signal power. Use the equation: D = sqrt(P_original / P_repeated)
5. Repeat steps 3 and 4 for each of the three laser wavelengths (1.55 µm, 1.2 µm, and 1.8 µm) to obtain the respective repeater distances.
Remember to pay attention to units and conversions throughout the calculation process.