EE321 - Analog Electronics Notes

Review of Op-Amps

Overview of Linear Op-Amp Circuits

• Key Types of Circuits:

  • Non-inverting amplifier

  • Inverting amplifier

  • Summing amplifier

  • Integrator

  • Difference amplifier

Negative Feedback Recap

• Function: Minimizes the error signal.

• High Gain Implications:

  • Error signal approaches zero.

  • Output equals input multiplied by some factor (K).

Feedback Network Addition

• Negative feedback continues to minimize error.

• Equation:
  $\text{Output} = \text{Input} \times K$

Non-inverting Amplifier

• Key Characteristics:

  • Output equation:
    $V<em>{OUT} = V</em>{IN} \times \left(1 + \frac{R<em>2}{R</em>1}\right)$

  • Important Rules:

  1. $I<em>+ = 0$, $I</em>- = 0$ (Input currents are zero)

  2. $V<em>+ = V</em>-$ (No voltage between inputs)

• Example: Design a non-inverting amplifier with a voltage gain of +10.

  • Solution: Set $R<em>2 = 9R</em>1$. Choosing $R<em>1 = 1k\Omega$, results in $R</em>2 = 9k\Omega$.

Inverting Amplifier

• Important Rules are similar to non-inverting:

  • Same assumptions hold about input currents and voltages.

• Output equation: $V<em>{OUT} = -V</em>{IN} \times \left(\frac{R<em>2}{R</em>1}\right)$

  • Example design for voltage gain of -10 with 1kΩ input impedance.

Summing Amplifier

• Employ Kirchhoff’s Current Law (KCL) on the V- node:

  • 
    $\text{Output} = -R \left( \frac{V<em>1}{R</em>1} + \frac{V<em>2}{R</em>2} + … + \frac{V<em>N}{R</em>N} \right)$

Integrator

• Key Assumptions:

  • Same as Inverting design (I+ = I- = 0).

• Output equation:
  $V<em>{OUT} = -\frac{1}{RC} \int V</em>{IN} dt$

Difference Amplifier

• Uses both non-inverting and inverting terminals:

  • Output equation:
    $V<em>{OUT} = \frac{R</em>1}{R<em>2} (V</em>+ - V_-)$

Ideal Op-Amp Assumptions for Analysis

1. $I<em>+ = 0$ and $I</em>- = 0$

2. $V<em>+ = V</em>-$

3. $V_{OUT} = \text{any value}$

Non-Ideal Characteristics of Op-Amps

• Real characteristics to consider:

  • Input Impedance: Greater than 1 MΩ

  • Output Impedance: Less than 100 Ω

  • Speed limitations (Slew Rate)

  • Offset Voltage

Frequency Response

• Open-loop gain is substantial at low frequencies but decreases with higher frequencies.

• Gain-Bandwidth Product: Constant across frequency range. Defined as cut-off frequency multiplied by mid-band gain.

Slew Rate

• Defined as the maximum rate of change of output. For example, a typical value for a 741 op-amp is $0.5 V/μs$.

• Important to consider with rapidly changing signals to avoid output distortion.

Non-Linear Op-Amp Applications

• Examples include:

  • Comparators

  • Schmitt triggers (hysteresis)

  • Oscillators

Summary to Remember for the Exam

• Focus on amplifier characteristics: Gain, input/output impedances, full-power bandwidth, and non-linear behavior (e.g., saturation properties).

• Comparators and their design principles.

• Slew rates and their influence on amplifier performance.

• Understand the design challenges and compensations required in both ideal and real-world circuit scenarios.

Practical Op-Amp Design

• Exercise: Create designs that navigate through theoretical assumptions to achieve practical specifications under defined limits.