Design an inverting amplifier with gain 30. If the bias voltages supplied to the op-amp are ±15 volt, what should be the maximum input voltage before entering into the saturation region.
Design an inverting amplifier with gain 30. If the bias voltages supplied to the op-amp are ±15 volt, what should be the maximum input voltage before entering into the saturation region.
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![### Designing an Inverting Amplifier with a Gain of 30
#### Problem Statement
Design an inverting amplifier with a gain of 30.
If the bias voltages supplied to the op-amp are ±15 volts, what should be the maximum input voltage before entering into the saturation region?
#### Detailed Explanation
To design an inverting amplifier using an operational amplifier (op-amp), we need to determine the relationship between the input voltage (\(V_{in}\)), the output voltage (\(V_{out}\)), and the feedback network.
For an inverting amplifier, the gain (A_v) is given by:
\[ A_v = -\frac{R_f}{R_{in}} \]
Where:
- \(R_f\) is the feedback resistor.
- \(R_{in}\) is the input resistor.
To achieve a gain of -30:
\[ \text{Gain (A_v)} = -30 \]
#### Voltage Output Equation
The output voltage (\(V_{out}\)) is related to the input voltage (\(V_{in}\)) by:
\[ V_{out} = A_v \times V_{in} \]
\[ V_{out} = -30 \times V_{in} \]
#### Saturation Condition
The op-amp will saturate when the output voltage (\(V_{out}\)) reaches the supply voltage limits, which in this case are ±15 volts.
\[ V_{out} \approx -30 \times V_{in} \leq \pm15\, \text{volts} \]
By solving for \(V_{in}\):
\[ V_{in} \leq \frac{15}{30} \]
\[ V_{in} \leq 0.5\, \text{volts} \]
#### Maximum Input Voltage
The maximum input voltage before the op-amp enters the saturation region is:
\[ V_{in(Max)} = 0.5\, \text{volts} \]
#### Conclusion
To design an inverting amplifier with a gain of 30 using an op-amp with bias voltages of ±15 volts, the maximum input voltage should be 0.5 volts to prevent the amplifier from entering the saturation region.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0062023f-64ec-498a-8360-7c79f327cf33%2Fd114623d-6649-4654-af90-12fb0e063367%2Fs4povm9_processed.png&w=3840&q=75)
Transcribed Image Text:### Designing an Inverting Amplifier with a Gain of 30
#### Problem Statement
Design an inverting amplifier with a gain of 30.
If the bias voltages supplied to the op-amp are ±15 volts, what should be the maximum input voltage before entering into the saturation region?
#### Detailed Explanation
To design an inverting amplifier using an operational amplifier (op-amp), we need to determine the relationship between the input voltage (\(V_{in}\)), the output voltage (\(V_{out}\)), and the feedback network.
For an inverting amplifier, the gain (A_v) is given by:
\[ A_v = -\frac{R_f}{R_{in}} \]
Where:
- \(R_f\) is the feedback resistor.
- \(R_{in}\) is the input resistor.
To achieve a gain of -30:
\[ \text{Gain (A_v)} = -30 \]
#### Voltage Output Equation
The output voltage (\(V_{out}\)) is related to the input voltage (\(V_{in}\)) by:
\[ V_{out} = A_v \times V_{in} \]
\[ V_{out} = -30 \times V_{in} \]
#### Saturation Condition
The op-amp will saturate when the output voltage (\(V_{out}\)) reaches the supply voltage limits, which in this case are ±15 volts.
\[ V_{out} \approx -30 \times V_{in} \leq \pm15\, \text{volts} \]
By solving for \(V_{in}\):
\[ V_{in} \leq \frac{15}{30} \]
\[ V_{in} \leq 0.5\, \text{volts} \]
#### Maximum Input Voltage
The maximum input voltage before the op-amp enters the saturation region is:
\[ V_{in(Max)} = 0.5\, \text{volts} \]
#### Conclusion
To design an inverting amplifier with a gain of 30 using an op-amp with bias voltages of ±15 volts, the maximum input voltage should be 0.5 volts to prevent the amplifier from entering the saturation region.
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