Operational Amplifiers Circuits

• 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)

• 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 (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

• 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 \(\pm5.4V\)

• 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

• 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

• 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:

• 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

• 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

• 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

• 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

• 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