OPERATIONAL AMPLIFIERS + - Presented by D.Satishkumar Asst. Professor, Electrical & Electronics Engineering Contact No:

Op-Amp Definition: An Op-Amp is a direct coupled high gain amplifier consisting of one or more differential amplifiers, followed by a level translator and an output stage. It is a versatile device that can be used to amplify ac as well as dc input signals & designed for computing mathematical functions such as addition, subtraction, multiplication, integration & differentiation.

Typical Op-Amp IC Packages Dual-in-Line package (DIP)Metal Can Package

Pin Configuration – IC 741 DIP-741

Schematic Diagram of Op-Amp: Vout= A( Vp-Vn) A = “open-loop” gain Very high differential gain High input impedance Low output impedance Accumulate a very high gain by multiple stages

Single-Ended Input + terminal : Source – terminal : Ground 0 o phase change + terminal : Ground – terminal : Source 180 o phase change

Ideal Operational Amplifier Vout= A( Vp-Vn ) Assumptions The Current drawn by either of the input terminals is negligible Potential Difference between the input terminals is zero A = “open-loop” gain Ip=In=0

Ideal characteristics of Op-Amp Open loop gain infinite Input impedance infinite Output impedance low Bandwidth infinite Zero offset, i.e., Vo =0 when Vp=Vn=0

Ideal Vs Practical Op-Amp

IdealPractical Open Loop gain A  10 5 Bandwidth BW  Hz Input Impedance Z in  >1M  Output Impedance Z out 0   Output Voltage V out Depends only on V d = (V +  V  ) Differential mode signal Depends slightly on average input V c = (V + +V  )/2 Common-Mode signal CMRR  dB

Common Mode Rejection Ratio (CMRR) It is the ability of an op amp to reject the signal which is present at its both inputs simultaneously i.e. the common mode signal CMRR = A OL / A CM, where A CM is common mode voltage gain defined by V out / V CM Ideally CMRR is infinite For IC 741 it is 90 dB

Inverting Amplifier The positive input is grounded. A “feedback network” composed of resistors R f and R a is connected between the inverting input, signal source and amplifier output node, respectively.

(1)Kirchhoff node equation at V + yields, (2) Kirchhoff node equation at V  yields,

The negative voltage gain implies that there is a phase shift between both dc and sinusoidal input and output signals. The inverting input of the op amp is at ground potential (although it is not connected directly to ground) and is said to be at virtual ground. (3) Setting V + = V – yields

Multiple Inputs (1)Kirchhoff node equation at V + yields,

(3) Setting V + = V – yields (2) Kirchhoff node equation at V  yields,

Noninverting Amplifier (1)Kirchhoff node equation at V + yields, (2)Kirchhoff node equation at V  yields, (3)Setting V + = V – yields or The input signal is applied to the non-inverting input terminal.

Example: Problem: Determine the output voltage and current for the given non- inverting amplifier. R 1 = 3k , R 2 = 43k , v s = +0.1 V Assumptions: Ideal op amp Analysis: Since i - =0,

Noninverting amplifierNoninverting input with voltage divider Voltage follower Less than unity gain

Non-ideal case (Inverting Amplifier)  Equivalent Circuit

Close-Loop Gain Applied KCL at V– terminal, By using the open loop gain,

The Close-Loop Gain, A v

Inverting Integrator Now replace resistors R a and R f by complex components Z a and Z f, respectively, therefore Supposing The feedback component is a capacitor C, i.e.,

The input component is a resistor R, Z a = R Therefore, the closed-loop gain (V o /V in ) become: Where What happens if Z a = 1/j  C whereas, Z f = R? Inverting differentiator

Op-Amp Differentiator

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