1. Calculate v3/v₁ for the circuit of Fig. 4.3 (a) V1 = tr R1 Inverter •IF Rf W Fig. 4.3 (a) V3 www R4

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**1. Calculate \( v_3/v_1 \) for the circuit of Fig. 4.3 (a)**

The diagram in Fig. 4.3 (a) represents an inverting amplifier circuit using an operational amplifier (op-amp). The circuit consists of the following components:

- **Op-Amp**: The triangle symbol represents the operational amplifier.
- **Resistors**:
  - \( R_1 \): Connected in series with the input voltage \( V_1 \).
  - \( R_f \): Feedback resistor connected between the output (V3) and the inverting input (-) of the op-amp.
  - \( R_4 \): Connected in series with the output \( V_3 \).
- **Voltage Source**:
  - \( V_1 \): Input voltage connected to the non-inverting input (+).
- The circuit acts as an inverter, changing the phase of the input signal.

To calculate the voltage gain \( v_3/v_1 \), the formula for an inverting amplifier is used:

\[
v_3/v_1 = - \frac{R_f}{R_1}
\]

This relationship shows that the gain of the circuit is determined by the ratio of the feedback resistor (\( R_f \)) to the input resistor (\( R_1 \)), with the negative sign indicating a phase inversion.
Transcribed Image Text:**1. Calculate \( v_3/v_1 \) for the circuit of Fig. 4.3 (a)** The diagram in Fig. 4.3 (a) represents an inverting amplifier circuit using an operational amplifier (op-amp). The circuit consists of the following components: - **Op-Amp**: The triangle symbol represents the operational amplifier. - **Resistors**: - \( R_1 \): Connected in series with the input voltage \( V_1 \). - \( R_f \): Feedback resistor connected between the output (V3) and the inverting input (-) of the op-amp. - \( R_4 \): Connected in series with the output \( V_3 \). - **Voltage Source**: - \( V_1 \): Input voltage connected to the non-inverting input (+). - The circuit acts as an inverter, changing the phase of the input signal. To calculate the voltage gain \( v_3/v_1 \), the formula for an inverting amplifier is used: \[ v_3/v_1 = - \frac{R_f}{R_1} \] This relationship shows that the gain of the circuit is determined by the ratio of the feedback resistor (\( R_f \)) to the input resistor (\( R_1 \)), with the negative sign indicating a phase inversion.
Expert Solution
Step 1

Given:

The inverting op-amp circuit.

The load resistance R4

The feedback resistance Rf

Input resistance R1

Output voltage V3

Input voltage V1

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