Op-Amp Based Circuits

Section 8.2

Topics

• Non-Inverting Amplifier• Inverting Amplifier• Integrator• Differentiator

Non-Inverting Amplifier (Ideal)

(Assumption: Ao is infinite)

Non-Inverting Amplifier (Practical)

Approximation

(Taylor seriesapproximation)

(Large, since Ao is large)

Example

Application of Inverting Amplifier

• Analog Filters• Control Systems

Inverting Amplifier

Input impedance: R2

Trade off: Input impedance versus voltage gain.

Virtual Ground Versus An Ordinary Ground

Node X is a virtual ground, but not an ordinary ground.

If X were an ordinary ground, current from Vin would bediverted from R1since R1 represents a path of high impedance.

Practical Inverting Amplifier

(Equating current in R1 and R2)

Example

Generalized Inverting Amplifier

Integrator Analysis in the Frequency Domain

(Pole at the origin)

Frequency Response of Integrator

(Pole at the origin)

(Pole frequency is obtained by setting the denominator to zero)

Integrator Analysis in the Time Domain

Example

Active Integrator Versus Passive Integrator

Current decreasesas Vout rises, leading to aslower increase in Vout.

Passive integrator approximates the behavior of an active integrator.

(Active integrator)(Passive integrator)

An Integrator with Finite Gain

Example

Frequency Domain Analysis of Differentiator

Frequency Domain Analysis

Time Domain Analysis of a Integrator

Time Domain Analysis

Example

Active Differentiator Circuit Versus Passive

Differentiator Circuit

Node X is not pinned to ground.Capacitor can not charge instantaneously.Therefore, Vout rises rapidly to V1 initially.

Practical Differentiator

Example

Voltage Adder

(Application:Noise Cancellation)