Notes on Operational Amplifiers Laboratory

Laboratory 4: Introduction to Operational Amplifiers

1. Workhorse Gain Circuits

• Operational Amplifier Characteristics:
  • Infinite input resistance
  • Zero output resistance
  • Infinite gain
• Gain Calculations:
  • Gain when Vb = 0V:
  • $\frac{V<em>o}{V</em>a}$
  • Gain when Va = 0V:
  • $\frac{V<em>o}{V</em>b}$
  • Gain when Va = Vb:
  • $\frac{V<em>o}{V</em>b}$
• Circuit Design:
  • Design structures of non-inverting, inverting, and unity gain amplifiers.
  • Understand how resistors and connections affect the gains derived in previous calculations.
• Gain Values:
  • Aim to design circuits with specific gains:
  • Gain of -10
  • Gain of +11
  • Gain of +1

2. Arithmetic Functions

• Gain Analysis:
  • Calculate gains with different signal configurations:
  • $\frac{V<em>o}{V</em>1}$ when $V<em>2, V</em>3, V_4 = 0V$
  • $\frac{V<em>o}{V</em>2}$ when $V<em>1, V</em>3, V_4 = 0V$
  • $\frac{V<em>o}{V</em>3}$ when $V<em>1, V</em>2, V_4 = 0V$
  • $\frac{V<em>o}{V</em>4}$ when $V<em>1, V</em>2, V_3 = 0V$
• Impact of Additional Resistors:
  • Additional signal input resistor inverting inputs:
  • Does it change the transfer function for other signals?
  • Additional non-inverting input resistors:
  • Investigate dependence of other solution calculations.
• Operational Amplifier Mathematical Functions:
  • Operational amplifiers are capable of performing operations like addition and subtraction of voltages.
• Summation Amplifiers:
  • Discuss the relative properties between inverting and non-inverting summing amplifiers.
• General Derivation:
  • Use superposition for deriving:
  • $V<em>o$ as a function of inputs $V</em>1, V<em>2, V</em>3, V_4$.

3. Operational Amplifiers as Instrumentation Amplifiers

• Purpose:
  • To amplify small analog signals from transducers accurately.
• Transducer Characteristics:
  • Senses physical parameters (pressure/temperature), translates them into electrical signals.
• Noise Challenges:
  • Long transmission distances lead to common-mode noise affecting the signal integrity.
• Instrumentation Amplifier Functionality:
  • Eliminates common-mode signals by subtracting ground and signal measurements from the transducer.
• Circuit Design:
  • Based upon initial design, deriving resistor values to ensure:
  • $V<em>o = V</em>1 - V_2$ for effective common-mode rejection.
  • $\frac{R<em>1R</em>2}{R<em>1 + R</em>2} = \frac{R<em>3R</em>4}{R<em>3 + R</em>4}$ to minimize op-amp errors.
• Limitations:
  • Identify potential limitations in real-world applications of these amplifiers, considering sensor outputs and operational constraints.
• Modification Ideas:
  • Suggest how to enhance the initial instrumentation amplifier using additional op-amps to resolve issues identified in practical scenarios.