Operational Amplifiers (Op-Amps)

Operational Amplifier (Op-Amp)• Not a discrete device

(resistor, cap, ind, diode, transistor etc.)

• IC !• 2-input terminals

– Inverting and non-inverting– Output terminal– Two supply terminals

• Inexpensive – yet very useful in instrumentation applications

• We will only consider ideal op-amps !

-

+

Inverting Input

Non-inverting Input

Output

PowerSupplies

Operational Amplifiers (Op-Amps)

Ideal Op-Amps

1. Infinite open-loop voltage gain2. Infinite input impedance3. Zero output impedance4. Infinite bandwidth5. Zero input voltage offset

5 characteristics

A Simple Model for the Op-Amp• Very High Gain amplifier

with a high input and low output resistance !

• AOL: “Open-Loop” Gain (105- 107)

• RIN: input resistance (Mohms)

• ROUT: Output Resistance (10s of ohms)

v-

v+

-

+

-+

AOL(v+-v-)

RIN

ROUT

IIN

Ideal Op-Amps

1. Input currents = 02. Difference in input voltages = 0

“Golden Rules”

Input Current (IN) is zero !V+=V-

Ideal Op-Amps

1. Calculate the input voltage2. Write node equation at op-amp

input to find the output voltage

Analysis Procedure

Inverting Amplifier

Find the voltage gain Vo/Vi.

1. Calculate the input voltage2. Write node equation at op-amp

input to find the output voltage

Vb = 0Va = 0

Since Ia = 0, I1 = If

1

f

i

o

R

R

V

V

Non-Inverting Amplifier

Find the voltage gain Vo/Vi.

1. Calculate the input voltage2. Write node equation at op-amp

input to find the output voltage

Vb = Vi

Va = Vi

Since Ia = 0, I1 = If

1

f1

i

o

R

RR

V

V

Integrator

R

VI in

C t

0

CC d)(IC

1)t(V

t

0

in d)(VRC

1

By KVL, Vout = –VC

t

0

inout d)(VRC

1V

Differentiator

dt

dVC

dt

dVCI inC

C RIV Cout

dt

dVRCV in

out

Two-Stage Amplifier

Gain = Vo1/Vi Gain = Vo2/Vo1

Total Gain = (Vo1/Vi) (Vo2/Vo1) = Vo2/Vi

Example

Example

Work this Example!_________