• Operational amplifiers are fundamental building blocks in electronics

• Basic and special purpose op-amp circuits:

  • Comparators

  • Summing amplifiers

  • Integrators and differentiators

  • Instrumentation amplifiers

  • Specialized amplifiers (OTA, log/antilog)

• Applications include signal processing, digital circuits, and analog-to-digital conversion

• Specialized op-amp circuit that compares two input voltages

• Output is always in one of two states (high or low)

• Key characteristics:

  • Very fast switching times (as low as 500 ps propagation delay)

  • High open-loop gain enables detection of tiny input differences

• Used for analog-to-digital interfacing

Zero-Level Detection

• Inverting input grounded (0 V reference)

• Input signal applied to noninverting input

• Smallest input difference drives amplifier to saturation

• Can convert sine waves to square waves (squaring circuit)

Nonzero-Level Detection

• Fixed reference voltage replaces ground at inverting input

• Three reference voltage methods:

  • Battery reference

  • Voltage divider reference (\(V_{REF} = \dfrac{R_2}{R_1+R_2}(+V)\))

  • Zener diode reference (\(V_{REF} = V_Z\))

• Output switches when input crosses \(V_{REF}\)

Given \( R_1 = 8.2k\Omega \), \( R_2 = 1.0k\Omega \), \( +V = 15V \):

\[ V_{REF} = \frac{1.0k\Omega}{8.2k\Omega + 1.0k\Omega}(15V) = 1.63V \]

Output switches between \( \pm 14V \) when input crosses 1.63V.

Noise Effects and Hysteresis

• Noise (unwanted voltage fluctuations) can cause unstable switching near the threshold

• Example: A low-frequency sinusoidal voltage with noise causes erratic output

• Solution: Implement hysteresis using positive feedback

  • Upper Trigger Point (UTP): \(V_{UTP} = \dfrac{R_2}{R_1+R_2}(+V_{out(max)})\)

  • Lower Trigger Point (LTP): \(V_{LTP} = \dfrac{R_2}{R_1+R_2}(-V_{out(max)})\)

  • Hysteresis voltage: \(V_{HYS} = V_{UTP} - V_{LTP}\)

• Also called a Schmitt trigger

Output Bounding

• Limits output voltage to values less than op-amp saturation

• Methods:

  • Single zener diode: bounds one direction

  • Two zener diodes: bounds both directions (\(V_Z + 0.7V\) each way)

• Example: With 4.7V zeners, output bounds at \(\pm5.4V\)

Comparator Applications

• Over-temperature sensing:

  • Uses Wheatstone bridge with thermistor

  • Comparator detects bridge balance point

  • Triggers alarm/response when temperature exceeds threshold

• Analog-to-Digital Conversion (Flash ADC):

  • Uses parallel comparators with reference voltage ladder

  • \(2^n-1\) comparators needed for n-bit conversion

  • Priority encoder produces binary output

Summing Amplifier

• Application of inverting op-amp configuration

• Output proportional to negative sum of input voltages

• \[\begin{aligned} V_{OUT} = -\left(\dfrac{R_f}{R_1}V_{IN1} + \dfrac{R_f}{R_2}V_{IN2} + \cdots + \dfrac{R_f}{R_n}V_{INn}\right) \end{aligned}\]
  General output equation:
• \[\begin{aligned} V_{OUT} = -\dfrac{R_f}{R}(V_{IN1} + V_{IN2} + \cdots + V_{INn}) \end{aligned}\]
  For equal input resistors

Unity-Gain Summing Amplifier

• Special case where \(R_f = R\)

• \[\begin{aligned} V_{OUT} = -(V_{IN1} + V_{IN2} + \cdots + V_{INn}) \end{aligned}\]
  Output is simple inverted sum of inputs:
• \[\begin{aligned} V_{OUT} = -(2V - 3V + 4V) = -3V \end{aligned}\]
  Example: For inputs +2V, -3V, and +4V:

Averaging Amplifier

• Produces mathematical average of input voltages

• Set \(R_f/R = 1/n\) where \(n\) is number of inputs

• \[\begin{aligned} V_{OUT} = -\dfrac{1}{n}(V_{IN1} + V_{IN2} + \cdots + V_{INn}) \end{aligned}\]
  Output equation:
• \[\begin{aligned} V_{OUT} = -\dfrac{25k\Omega}{100k\Omega}(V_1 + V_2 + V_3 + V_4) = -\dfrac{1}{4}(V_1 + V_2 + V_3 + V_4) \end{aligned}\]
  : , Example: 4-input averager with

Digital-to-Analog Conversion

• Binary-weighted resistor DAC:

  • Each input resistor corresponds to binary weight

  • MSB has smallest resistor (\(R\)), next has \(2R\), then \(4R\), etc.

  • Output is analog representation of digital input

• R/2R ladder DAC:

  • Uses only two resistor values (\(R\) and \(2R\))

  • More practical for IC implementation

  • Each bit contributes half the voltage of the previous bit

Op-Amp Integrator

• Produces output proportional to integral of input

• Basic configuration:

  • Input resistor \(R_{in}\)

  • Feedback capacitor \(C\)

• \[\begin{aligned} V_{OUT} = -\dfrac{1}{R_{in}C}\int V_{IN} dt \end{aligned}\]
  Output voltage:

• Constant input produces linear ramp output

Op-Amp Integrator Example

Op-Amp Differentiator

• Produces output proportional to derivative of input

• Basic configuration:

  • Input capacitor \(C\)

  • Feedback resistor \(R_f\)

• Output voltage:

• \[\begin{aligned} V_{OUT} = -R_f C \dfrac{dV_{IN}}{dt} \end{aligned}\]

• Ramp input produces constant output

Instrumentation Amplifiers

• Amplify small signals riding on large common-mode voltages

• Key Characteristics:

  • High input impedance

  • High common-mode rejection

  • Low output offset

  • Low output impedance

• \[\begin{aligned} \text{Gain}~A_{cl} = 1 + \dfrac{2R}{R_{\text{gain}}} \quad \text{where} \quad R_1 = R_2 = R \end{aligned}\]

• Input Stage (2 Op-Amps): High \(Z_{in}\) and initial amplification

• Difference Amplifier (3rd Op-Amp): Subtracts and amplifies input signal difference

Operational Transconductance Amplifier (OTA)

• OTA is a voltage-controlled current source (VCCS)

• \[\begin{aligned} I_{\text{out}} = g_m \cdot (V_+ - V_-) \end{aligned}\]
  : into output Converts differential input

• Output is current, unlike op-amps which output voltage

• Transconductance \(g_m\) is programmable via bias current

• Key Characteristics:

  • High input impedance

  • Wide bandwidth

  • Linear transconductance over bias range

  • Suitable for analog signal processing

OTA Applications and Comparison

Applications:

• Voltage-controlled filters and oscillators

• Analog multipliers and dividers

• Audio and RF processing

• AGC circuits, function generators

OTA vs Op-Amp:

Logarithmic Amplifier (Log Amp)

• Outputs a voltage proportional to the logarithm of the input voltage

• \[\begin{aligned} V_{\text{out}} = -K \cdot \ln\left(\dfrac{V_{\text{in}}}{V_T}\right) \end{aligned}\]
  Based on the exponential I-V relationship of a diode or BJT:

• Uses an op-amp with a diode or BJT in the feedback path

Antilogarithmic Amplifier (Antilog Amp)

• Converts a logarithmic input back to a linear output

• \[\begin{aligned} V_{\text{out}} = K \cdot e^{V_{\text{in}}/V_T} \end{aligned}\]
  Uses a transistor in the input path to create an exponential relationship:
• \[\begin{aligned} \log(A) + \log(B) = \log(AB) \Rightarrow \text{Antilog} \rightarrow AB \end{aligned}\]
  Often paired with log amps for analog multiplication/division:

Isolation Amplifier

• Transmits signals across two circuits with galvanic isolation

• Prevents high voltages or ground loop currents from damaging systems

• Isolation achieved using:

  • Transformer coupling

  • Optical isolation (optocouplers)

  • Capacitive coupling

• Key Features:

  • High input-to-output isolation voltage

  • Accurate signal transmission

  • High common-mode rejection (CMR)

Isolation Amplifier Applications

• Applications:

  • Medical instrumentation (e.g., ECG, EEG)

  • Industrial process control

  • High-voltage system monitoring

  • Signal isolation in data acquisition systems

• Advantages:

  • Protects measurement devices from voltage spikes

  • Eliminates ground loops and electrical noise

  • Enables safe measurement in hazardous environments

• Note: Often integrated with analog-to-digital converters (ADCs)

Constant-Current Source

• Delivers a fixed current regardless of load resistance

• Based on Ohm’s law: \(I = \dfrac{V_{\text{ref}}}{R}\)

• Uses negative feedback to maintain stable output current

Current-to-Voltage Converter

• Also called a Transimpedance Amplifier

• Converts input current (\(I_{\text{in}}\)) to output voltage (\(V_{\text{out}}\))

• Output: \(V_{\text{out}} = -I_{\text{in}} R_f\)

• Commonly used with photodiodes and sensors

Voltage-to-Current Converter

• Also called a Voltage-Controlled Current Source (VCCS)

• Converts input voltage to output current

• Output current: \(I_{\text{out}} = \dfrac{V_{\text{in}}}{R}\)

• Useful in actuators and LED drivers

Peak Detector

• Captures and holds the peak value of an input signal

• Uses an op-amp, diode, and capacitor

• Commonly used in signal processing and instrumentation

• Operational amplifiers are versatile components in electronics, enabling a wide range of circuits:

  • Comparators for signal comparison and ADC interfacing

  • Summing, averaging, and DAC circuits for signal processing

  • Integrators and differentiators for waveform generation

  • Instrumentation amplifiers for precise measurements

  • Specialized circuits (OTA, log/antilog, isolation) for advanced applications

• Their high gain, flexibility, and reliability make op-amps essential in modern electronics

• Future exploration: Advanced op-amp designs and integration with digital systems