9.1 Operational amplifier fundamentals

Operational amplifiers are the workhorses of analog circuits. They're versatile components that can amplify, filter, and manipulate signals in countless ways. Understanding their basics is key to mastering more complex applications in active filters and signal processing.

In this section, we'll cover the fundamentals of op-amps, including their ideal characteristics and practical limitations. We'll also explore common configurations like inverting and non-inverting amplifiers, and dive into key performance metrics that affect real-world circuit design.

Operational Amplifier Basics

Fundamental Concepts and Characteristics

• Operational amplifier functions as a high-gain electronic voltage amplifier with differential inputs and a single output
• Open-loop gain represents the amplification factor of an op-amp without feedback, typically very high (100,000 or more)
• Closed-loop gain refers to the amplification when negative feedback is applied, providing stable and predictable operation
• Input offset voltage measures the small voltage difference between inputs required to produce zero output voltage
• Bandwidth indicates the range of frequencies an op-amp can amplify effectively, usually decreasing as gain increases

Ideal Op-Amp Assumptions

• Infinite open-loop gain allows for simplified circuit analysis
• Infinite input impedance results in negligible input current
• Zero output impedance enables the op-amp to drive various loads
• Infinite bandwidth permits operation at all frequencies
• Zero input offset voltage ensures accurate amplification of small signals

Practical Op-Amp Considerations

• Finite open-loop gain limits maximum achievable amplification
• Input bias currents affect circuit performance, especially in high-impedance applications
• Limited bandwidth restricts high-frequency operation (gain-bandwidth product)
• Power supply voltages constrain the maximum output voltage swing
• Temperature variations can impact op-amp performance characteristics

Inverting and Non-Inverting Configurations

Inverting Amplifier Circuit

• Inverting amplifier configuration inverts the input signal polarity
• Input signal connects to the inverting input through a resistor
• Feedback resistor connects the output to the inverting input
• Gain determined by the ratio of feedback resistor to input resistor
• Virtual ground concept applies to the inverting input
• Closed-loop gain equation: $A_v = -\frac{R_f}{R_{in}}$

Non-Inverting Amplifier Circuit

• Non-inverting amplifier configuration maintains input signal polarity
• Input signal connects directly to the non-inverting input
• Feedback network consists of two resistors forming a voltage divider
• Gain determined by the ratio of resistors in the feedback network
• Virtual short concept applies between the inputs
• Closed-loop gain equation: $A_v = 1 + \frac{R_f}{R_1}$

Virtual Ground and Virtual Short Principles

• Virtual ground in inverting configuration keeps inverting input at ground potential
• Virtual short in non-inverting configuration equalizes voltages at both inputs
• These principles simplify circuit analysis and design
• Enable accurate prediction of circuit behavior
• Facilitate the application of negative feedback for stable operation

Key Performance Characteristics

Slew Rate and Its Impact

• Slew rate defines the maximum rate of change of the output voltage
• Measured in volts per microsecond (V/μs)
• Limits the amplifier's ability to track rapidly changing input signals
• Affects large-signal bandwidth and distortion in high-frequency applications
• Can be a critical factor in selecting op-amps for specific applications (video processing)

Common-Mode Rejection Ratio (CMRR)

• CMRR measures an op-amp's ability to reject common-mode signals
• Expressed in decibels (dB), higher values indicate better performance
• Crucial for differential amplifier applications (instrumentation amplifiers)
• Impacts the accuracy of measurements in the presence of noise or interference
• Calculated as the ratio of differential gain to common-mode gain
• CMRR equation: $CMRR = 20 \log_{10} \frac{A_d}{A_{cm}}$

Additional Performance Metrics

• Input impedance affects the loading of signal sources
• Output impedance influences the ability to drive various loads
• Power supply rejection ratio (PSRR) measures immunity to power supply variations
• Noise characteristics impact the minimum detectable signal level
• Temperature coefficients describe performance changes with temperature variations