To help you solve this problem, let's go through each part of the question systematically, analyzing the four cases presented in the diagram. I'll outline the approach for each part (a, b, c, and d) and guide you through the calculations.

Problem Breakdown and Key Concepts

1. Output Signal Level (S_o):

   • The output signal level $S_o$ is determined by the amplifier's gain and any input signal loss.

2. Carrier-to-Noise Ratio (C/N):

   • The C/N at the output can be calculated by taking into account the amplifier's noise figure and the gain, along with the signal and noise levels.

3. Equivalent Noise Figure (F_EQ):

   • The equivalent noise figure $F_{EQ}$ for the whole system can be approximated as $F_{EQ} = L_{CABLE} + F_{AMP}$ where applicable, depending on the cable loss $L_{CABLE}$ and the amplifier's noise figure $F_{AMP}$.

4. Output Carrier-to-Noise Ratio (C/N_o):

   • This is the output C/N considering the system noise contributions and signal processing.

Let's calculate these for each case provided in the diagram.

Information Available for Each Case

For each case, we have:

• Amplifier Gain $G_{AMP}$
• Amplifier Noise Figure $F_{AMP}$
• Cable Loss $L_{CABLE}$
• Input Signal Level and Input Noise Level (for calculating C/N).

Solution Steps

Case-by-Case Calculations

1. Calculate $S_o$ (Output Signal Level) $S_o = S_{IN} + G_{AMP} - L_{CABLE}$

2. Calculate $C/N$ $C/N_{OUT} = C/N_{IN} - L_{CABLE} + G_{AMP} - F_{AMP}$

3. Calculate $F_{EQ}$

   • Using $F_{EQ} = L_{CABLE} + F_{AMP}$ where applicable.

4. Calculate $C/N_o$

   • Use the values derived from $S_o$ and $C/N_{OUT}$.

Let me calculate each part for you if you'd like specific numbers for each