Op-Amp and Differential Amplifier | Analog Circuits - Electronics and Communication Engineering (ECE) PDF Download

Introduction

• Op-Amp (Operational Amplifier) is a fundamental building block for handling analog electrical signals.
  
• An operational amplifier is a high gain, differential, voltage amplifier.
• OP AMP has two inputs called “+” and “-,” (or V_IN+ and V_IN-) and a single output.
• The output depends only on the difference of the voltage on the two inputs.
• If the difference of the two input voltages is V_IN , the output voltage is V_Out, then V_Out = ΔV_IN G_V
  where G_v is the (voltage) gain.
• Differential operation involves the use of opposite polarity inputs.
• Common mode operation involves the use of the same polarity inputs.
• Common-mode rejection compares the gain for differential inputs to that for common inputs.

1. Ideal Op Amp Attributes
   • Infinite Differential Gain 
   • Zero Common Mode Gam 
   • Zero Offset Voltage 
   • Zero Bias Current
2. Op Amp Inputs
   • High Input Impedance 
   • Low Bias Current 
   • Respond to Differential Mode Voltages 
   • Ignore Common Mode Voltages
3. Op Amp Output
   • Low Source Impedance
   • An ideal op-amp is usually considered the following properties, and they are considered to hold for any input voltages.
   • Infinite open loop gain
   • Infinite bandwidth (the frequency magnitude response is flat everywhere with zero phase shift)
   • Infinite input impedance
   • Zero input current (There is no leakage or bias current into the device)
   • Zero input offset voltage (when the input terminals are shorted, output is a virtual ground)
   • Infinite slew rate  (Rate of change of the output voltage is unbounded) and power bandwidth (full output voltage and current available at all frequencies).
   • Zero output impedance (R_out = 0, and so output voltage does not vary with output current)
   • Zero noise
   • Infinite CMRR (Common mode rejection ratio)
   • Infinite Power supply rejection ratio for both power supply rails.

Properties of Op-Amp

Op-Amp Classification

Differential Operational Amplifier

• A differential operational amplifier has inverting and non-inverting inputs with high input impedance and differential or open-loop gains between 1000 and 10 million.
• When the inverting input is used with negative feedback due to R₀, the closed loop gain is given by (-R₀ / R₁) and the input impedance is R₁ the output impedance is the open loop output impedance divided by loop gain.
  
  Loop gain (dB) = Open loop gain (dB) – Closed loop gain (dB)
• If a number of signals are connected to the inverting input, the output is proportional to the sum of the input signals, making possible the solution of linear algebraic and differential equations on an analog computer.
• If the non-inverting input to a differential operational amplifier is used, the input impedance is increased to a value,
  R_cm || (R_i × loop gain)
  where R_cm is the common mode impedance and R_i is the differential impedance.
• One way to increase input impedance to an amplifier utilizing the inverting input is to reduce the feedback voltage by connecting a voltage divider at the output.
• The voltage gain for a non-inverting input is:
  
• A true ideal differential amplifier the difference between two input voltages providing an output,
  
• In practice, the output also consists of an error term that is due to the common-mode input voltage = (V₁ + V₂)/2.
• Total output of a differential amplifier is:
  
  

Common Mode Rejection Ratio (CMRR)

• The common mode rejection ratio is a figure of merit of a differential amplifier, since it is the ratio of differential gain, A_d (the desired gain), to the common-mode gain A_C.
  CMRR = A_d/A_c
  or
  CMRR/_dB = 20log A_d - 20log A_c 
• Emitter-coupled differential amplifiers are the type of circuit used predominantly in IC_s, because of the manufacturing ability to closely match components, and since the devices are so closely spaced their variations due to temperature tend to cancel, providing excellent DC coupling stability.
• High values of CMRR are provided by large effective values of emitter resistance Re, in the emitter-coupled amplifier. This may be provided by a transistor or CRD to provide essentially a constant-current source in the emitter.
  

Ideal Voltage Transfer Curve

•  The graphic representation of the output equation is shown in figure in which the output voltage V₀ is plotted against differential input voltage V_d, keeping gain A_d constant.
  

Non-linear Op-Amp Circuits

1. Integrator
   • Circuit Diagram
     
   • Output Voltage:
     
2. Differentiator
   • Circuit Diagram
     
   • Output Voltage:
     
3. Non-Linear: Log-Amplifier
   • Circuit Diagram
     
   • Output Voltage:
     
   • η = recombination factor, V_t = thermal voltage, and I₀ = reverse saturation current of diode.
4. Non-Linear: Anti-log Amplifier
   • Circuit Diagram
     
   • Output Voltage:
     

Determination of Grounded Load

• 
• If Vs is applied at point A and B grounded and

Load resistance connected to ground

Capacitance Multiplier

Capacitance Multiplier Circuit

Equivalent capacitance:

This circuit is useful in creating artificially large values of capacitances while using low-valued C which is normally available.

Inductance Simulator

Inductance L_eq = CR₁R₂ Henry

Quality factor: 

Non-inverting Integrator

• The circuit shown below is a non-inverting integrator, where negative feedback exists.
• The analysis will be as follows.
  or

Non-inverting Differentiator

• It uses a single operational amplifier.
• The main feature of the circuit is that the input impedance is purely resistive.
  
  
  

Applications of Operational Amplifiers

• Inverting Amplifier
• Non-inverting Amplifier
• Differentiator
• Differential Amplifier
• Voltage follower
• Selective inversion circuit
• Current-to-voltage converter
• Active rectifier
• Integrator
• Comparator
• Filters
• Voltage comparator
• Signal Amplifier