Laboratory 4: Introduction to Operational Amplifiers

Laboratory 4: Introduction to Operational Amplifiers - Preliminary Exercises

Overview

• Focus on using operational amplifiers (op-amps) and understanding feedback configurations commonly used in electronic circuits.
• Ideal characteristics of op-amps:
  • Infinite input resistance
  • Zero output resistance
  • Infinite gain

1. Workhorse Gain Circuits

• Gain configurations to derive:
  • Gain $\frac{V<em>o}{V</em>a}$ with $V_b = 0V$
  • Gain $\frac{V<em>o}{V</em>b}$ with $V_a = 0V$
  • Gain $\frac{V<em>o}{V</em>b}$ with $Va = Vb$
• Drawing circuit diagrams for:
  • Non-inverting amplifier
  • Inverting amplifier
  • Unity gain amplifier

Questions:

• Analyze if the relation derived in Part 1(c) depends on $Rf$ or $Ri$ and justify the reasoning.
• Design amplifiers with gains of -10, +11, and +1 based on derived configurations.

2. Arithmetic Functions

• Consider the transfer function with various inputs set to zero:
  • $\frac{V<em>o}{V</em>1}$ with $V2, V3, V_4 = 0V$
  • $\frac{V<em>o}{V</em>2}$ with $V1, V3, V_4 = 0V$
  • $\frac{V<em>o}{V</em>3}$ with $V1, V2, V_4 = 0V$
  • $\frac{V<em>o}{V</em>4}$ with $V1, V2, V_3 = 0V$

Questions:

• Analyze the impact of adding an extra resistor at the inverting input
  • Does it alter the transfer function for other signal inputs (e.g. $R1$ or $R4$)?
• Discuss the construction properties of inverting versus non-inverting summing amplifiers.
• Use superposition to derive a general expression for $Vo$ as a function of $V1$, $V2$, $V3$, and $V_4$.

3. Operational Amplifiers as Instrumentation Amplifiers

• Functionality: Amplifies low-level analog signals from remote transducers (which sense physical parameters).
• Challenges: Signals affected by common-mode noise that can overpower desired signals.
• Circuit Diagram for an instrumentation amplifier is essential.

Derivation Tasks:

• Find resistor values that yield:
  • $Vo = V1 - V_2$ for good rejection of common-mode signals
  • $\frac{R<em>1R</em>2}{R<em>1 + R</em>2} = \frac{R<em>3R</em>4}{R<em>3 + R</em>4}$ to minimize op-amp errors

Identify Limitations:

• Determine the main limitations of achieving perfect rejection of common-mode signals in practice.
• Modify the circuit using two additional op-amps to mitigate identified limitations.

Summary

• Understanding and mastering op-amp circuits are crucial for designing reliable electronic systems.
• Familiarity with arithmetic functions and instrumentation amplifiers expands the adaptability in various electronic applications.