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The ratio of the open circuit voltage of a voltage amplifier (AV) to the short circuit transconductance of a (Gm) of a transconductance amplifier, given that both have the same value of the internal resistance (Ri) and the output resistance (R0), is
- a)Ri
- b)R0
- c)1/Ri
- d)1/R0
Correct answer is option 'B'. Can you explain this answer?
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The ratio of the open circuit voltage of a voltage amplifier (AV) to t...
It is a standard mathematical relation.
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The ratio of the open circuit voltage of a voltage amplifier (AV) to t...
Understanding Voltage Amplifier and Transconductance Amplifier
The problem compares the open circuit voltage of a voltage amplifier (AV) with the short circuit transconductance (Gm) of a transconductance amplifier. To understand why the correct answer is R0, we need to delve into the definitions and relationships between these parameters.
Definitions
- **Open Circuit Voltage (AV)**: This is the output voltage of the voltage amplifier when the output is not loaded, meaning the load resistance is infinite.
- **Short Circuit Transconductance (Gm)**: This represents the output current per unit of input voltage change, measured when the output is shorted (i.e., output resistance is zero).
Relationship Between Parameters
1. **Internal Resistance (Ri)**:
- Both amplifiers have the same internal resistance, which affects how much of the input signal is transferred to the output.
2. **Output Resistance (R0)**:
- This is crucial in determining how the amplifier behaves under load. For the voltage amplifier, it can be seen as providing a certain voltage output when loaded.
Ratio Derivation
- The open circuit voltage for a voltage amplifier can be expressed as:
**AV = Vout / Vin**.
- The short circuit transconductance for a transconductance amplifier can be expressed as:
**Gm = Iout / Vin**.
- Since both amplifiers have the same output resistance (R0), the relationship between the output current and voltage can be simplified.
Conclusion
Thus, the ratio of open circuit voltage (AV) to short circuit transconductance (Gm) simplifies to the output resistance R0, leading to the final answer: **R0**. This indicates that under equivalent conditions, the output performance of both amplifiers is fundamentally tied to their output resistance.
The problem compares the open circuit voltage of a voltage amplifier (AV) with the short circuit transconductance (Gm) of a transconductance amplifier. To understand why the correct answer is R0, we need to delve into the definitions and relationships between these parameters.
Definitions
- **Open Circuit Voltage (AV)**: This is the output voltage of the voltage amplifier when the output is not loaded, meaning the load resistance is infinite.
- **Short Circuit Transconductance (Gm)**: This represents the output current per unit of input voltage change, measured when the output is shorted (i.e., output resistance is zero).
Relationship Between Parameters
1. **Internal Resistance (Ri)**:
- Both amplifiers have the same internal resistance, which affects how much of the input signal is transferred to the output.
2. **Output Resistance (R0)**:
- This is crucial in determining how the amplifier behaves under load. For the voltage amplifier, it can be seen as providing a certain voltage output when loaded.
Ratio Derivation
- The open circuit voltage for a voltage amplifier can be expressed as:
**AV = Vout / Vin**.
- The short circuit transconductance for a transconductance amplifier can be expressed as:
**Gm = Iout / Vin**.
- Since both amplifiers have the same output resistance (R0), the relationship between the output current and voltage can be simplified.
Conclusion
Thus, the ratio of open circuit voltage (AV) to short circuit transconductance (Gm) simplifies to the output resistance R0, leading to the final answer: **R0**. This indicates that under equivalent conditions, the output performance of both amplifiers is fundamentally tied to their output resistance.
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The ratio of the open circuit voltage of a voltage amplifier (AV) to the short circuit transconductance of a (Gm) of a transconductance amplifier, given that both have the same value of the internal resistance (Ri) and the output resistance (R0), isa)Rib)R0c)1/Rid)1/R0Correct answer is option 'B'. Can you explain this answer?
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