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Example 4: Derive the transfer function of the following Inverting Op-amp: VAN) V. 0 C₁= 5.6 μF LMW R₁ = 360 ΚΩ ZE F Z. i -V₁ R₂ = 220 ΚΩ WW16 v₁ (1) C₂= 0.1 μF Z₁ = R₁ R₁C₁s +1 Z₂ = R₂C₂s + 1 C₂5

Example 4: Derive the transfer function of the following Inverting Op-amp: VAN) V. 0 C₁= 5.6 μF LMW R₁ = 360 ΚΩ ZE F Z. i -V₁ R₂ = 220 ΚΩ WW16 v₁ (1) C₂= 0.1 μF Z₁ = R₁ R₁C₁s +1 Z₂ = R₂C₂s + 1 C₂5

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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DERIVE T/F OPAMP ( NEED NEAT HANDWRITTEN SOLUTION ONLY OTHERWISE DOWNVOTE).

**Example 4:** **Derive the transfer function of the following Inverting Op-amp:** The circuit consists of the following components: 1. Resistor \(R_1\) with a value of \(360 \text{ k}\Omega\) 2. Capacitor \(C_1\) with a value of \(5.6 \mu\text{F}\) 3. Resistor \(R_2\) with a value of \(220 \text{ k}\Omega\) 4. Capacitor \(C_2\) with a value of \(0.1 \mu\text{F}\) 5. An operational amplifier (op-amp) configured in the inverting mode. The input voltage is \(v_i(t)\) and the output voltage is \(v_o(t)\). The circuit is grounded at the non-inverting terminal of the op-amp. ### Impedance Calculations: \[ Z_1 = \frac{R_1}{R_1C_1s + 1} \] \[ Z_2 = \frac{R_2C_2s + 1}{C_2s} \] ### Transfer Function: Given the relationship for an inverting op-amp, \[ v_o = -\frac{Z_F}{Z_i} v_i \] where \( Z_F \) is the feedback impedance and \( Z_i \) is the input impedance. For this circuit: - The input impedance \( Z_i = Z_1 \) - The feedback impedance \( Z_F = Z_2 \) Substituting these into the transfer function formula, \[ v_o = -\frac{Z_2}{Z_1} v_i \] This represents the derived transfer function for the given inverting op-amp circuit.
Transcribed Image Text:**Example 4:** **Derive the transfer function of the following Inverting Op-amp:** The circuit consists of the following components: 1. Resistor \(R_1\) with a value of \(360 \text{ k}\Omega\) 2. Capacitor \(C_1\) with a value of \(5.6 \mu\text{F}\) 3. Resistor \(R_2\) with a value of \(220 \text{ k}\Omega\) 4. Capacitor \(C_2\) with a value of \(0.1 \mu\text{F}\) 5. An operational amplifier (op-amp) configured in the inverting mode. The input voltage is \(v_i(t)\) and the output voltage is \(v_o(t)\). The circuit is grounded at the non-inverting terminal of the op-amp. ### Impedance Calculations: \[ Z_1 = \frac{R_1}{R_1C_1s + 1} \] \[ Z_2 = \frac{R_2C_2s + 1}{C_2s} \] ### Transfer Function: Given the relationship for an inverting op-amp, \[ v_o = -\frac{Z_F}{Z_i} v_i \] where \( Z_F \) is the feedback impedance and \( Z_i \) is the input impedance. For this circuit: - The input impedance \( Z_i = Z_1 \) - The feedback impedance \( Z_F = Z_2 \) Substituting these into the transfer function formula, \[ v_o = -\frac{Z_2}{Z_1} v_i \] This represents the derived transfer function for the given inverting op-amp circuit.
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