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Three identical amplifier, each having a spot effective input noise temperature of 125 K and available power G are cascaded. The overall spot effective input noise temperature of the cascade is 155 K. The G is
- a)3
- b)5
- c)7
- d)9
Correct answer is option 'B'. Can you explain this answer?
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Three identical amplifier, each having a spot effective input noise te...
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Understanding the Problem
In this scenario, we have three identical amplifiers with a spot effective input noise temperature of 125 K each, cascaded together. The overall spot effective input noise temperature of the cascade is given as 155 K. We need to determine the available power gain (G) for these amplifiers.
Key Concepts
- Effective Input Noise Temperature (Te): Represents the noise contribution of the amplifier.
- Cascaded Amplifiers: The total noise temperature of cascaded amplifiers can be calculated using the Friis formula, which accounts for the gain of each amplifier.
Friis Formula for Cascaded Amplifier Noise
The overall noise temperature (Te_total) for cascaded amplifiers can be calculated as follows:
Te_total = Te1 + (Te2 / G1) + (Te3 / (G1 * G2))
Where:
- Te1, Te2, Te3 are the effective input noise temperatures of the individual amplifiers.
- G1, G2 are the power gains of the first and second amplifiers, respectively.
Since the amplifiers are identical, we can simplify this to:
Te_total = Te + (Te / G) + (Te / (G^2))
Calculation Steps
1. Substitute Te = 125 K and Te_total = 155 K into the equation:
155 K = 125 K + (125 K / G) + (125 K / (G^2))
2. Rearranging gives:
30 K = (125 K / G) + (125 K / (G^2))
3. Dividing through by 125 K:
0.24 = (1 / G) + (1 / (G^2))
4. This equation can be solved to find the value of G.
Finding the Gain (G)
After solving the equation, we find that the correct option is:
- G = 5 (Option b)
This indicates that each amplifier has a power gain of 5, leading to the overall noise figure being consistent with the given effective noise temperature of the cascade.
In this scenario, we have three identical amplifiers with a spot effective input noise temperature of 125 K each, cascaded together. The overall spot effective input noise temperature of the cascade is given as 155 K. We need to determine the available power gain (G) for these amplifiers.
Key Concepts
- Effective Input Noise Temperature (Te): Represents the noise contribution of the amplifier.
- Cascaded Amplifiers: The total noise temperature of cascaded amplifiers can be calculated using the Friis formula, which accounts for the gain of each amplifier.
Friis Formula for Cascaded Amplifier Noise
The overall noise temperature (Te_total) for cascaded amplifiers can be calculated as follows:
Te_total = Te1 + (Te2 / G1) + (Te3 / (G1 * G2))
Where:
- Te1, Te2, Te3 are the effective input noise temperatures of the individual amplifiers.
- G1, G2 are the power gains of the first and second amplifiers, respectively.
Since the amplifiers are identical, we can simplify this to:
Te_total = Te + (Te / G) + (Te / (G^2))
Calculation Steps
1. Substitute Te = 125 K and Te_total = 155 K into the equation:
155 K = 125 K + (125 K / G) + (125 K / (G^2))
2. Rearranging gives:
30 K = (125 K / G) + (125 K / (G^2))
3. Dividing through by 125 K:
0.24 = (1 / G) + (1 / (G^2))
4. This equation can be solved to find the value of G.
Finding the Gain (G)
After solving the equation, we find that the correct option is:
- G = 5 (Option b)
This indicates that each amplifier has a power gain of 5, leading to the overall noise figure being consistent with the given effective noise temperature of the cascade.
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Three identical amplifier, each having a spot effective input noise temperature of 125 K and available power G are cascaded. The overall spot effective input noise temperature of the cascade is 155 K. The G isa)3b)5c)7d)9Correct answer is option 'B'. Can you explain this answer?
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