operational amplifiers - university at buffalo amplifiers an amplifier is a signal conditioning...

OPERATIONAL AMPLIFIERS An amplifier is a signal conditioning device which alters an analog signal in a particular manner which can be described by the relationship:

( ) [ ( )]out int = h t (6.43)E E

where Eo is the output voltage, Ei is the input voltage, and h is some mathematical relationship. (a transfer function!) For many amplifiers, h = constant and the amplifier only alters the gain of the signal. Giving:

( ) ( )out vo inE t A E t

where the open loop gain of the amplifier is Avo.

( ) [ ( ) ( )]2 1o i ivot = A t - tE E E

The Ideal Op Amp

Figure 1. Equivalent circuit for an ideal operational amplifier.

1. The voltage gain is infinite: Avo = ∞

2. The input resistance is infinite: rin = ∞

3. The output resistance is zero: ro = 0

4. The bandwidth is infinite: BW = ∞

5. There is zero input offset voltage: EO = 0 if Ein = 0

AXIOMS

1. The differential input voltage is zero.

2. There is no current flow into either input terminal

3. With the loop closed, the (-) input will be driven to the potential of the (+), or reference, input.

Some Basic Amplifying Circuits

1. the inverting configuration

2. the noninverting configuration

3. the differential configuration (combination of 1. and 2.)

4. the summing Inverter configuration

5. the Integrator configuration

6. the Differentiator configuration

7. the Voltage Follower configuration

Standard Op-Amp Schematic Symbol

If we operate the amplifier in a closed loop feedback mode we can analyze the resulting circuit based on some simplifying assumptions. Consider the circuit shown in Figure 6.24a

1,

6.21a2,3

, 6.20a4. We will assume that the open

loop gain is infinite, that the input impedance is infinite, and that the output impedance is zero. For infinite input impedance, the current flowing into the amplifier becomes zero.

2 2

2

1 2

o i if

1 2

2 1o i

2

oi i

2 1o i

2

- E E E = = i

R R

+ R R = E E

R

- = /A = 0E E E

+ R R = E E

R

OperationalAmplifiers.doc Page 1 of 16 11/19/2008 1:30 PM

The closed loop gain is given by

o 2 1

i 2

+ E R RG = = (6.46)

E R

Remarkably, the closed loop gain is dependent only on the two resistances and not on the amplifier gain. Now consider the circuit shown in Figure 6.21 (e)

1

2

(note can be 0)R

2

1

i Af o A R

2

B 1 I

A B o A

io

2

o i

d [ - ]E E = C [ - ] = - = - iI E E

dt R

= = 0 iE R

- = /A = 0, so = 0E E E E

d EC = - E

dt R

1 = - dtE E

R C

(6.52)

Note the error in Eq. (6.52) in the text in the First Edition. By combining the elements shown in Figure 6.24

1, 6.21

2,3, 6.20

4, we can perform many


mathematical operations, hence the term operational amplifier. Only a rudimentary knowledge of electronics is required to design operational amplifier circuits. The performance of the circuit depends only on the circuit elements and is independent of the gain of the operational amplifier, as long as it remains constant. Thus, operational amplifiers can be made quite inexpensively.


Summary of Inverting Amplifier Characteristics

1. Gain = f

in

R

R , unlimited in range (Rf may be 0

for 0 gain, may in infinite).

2. Input Impedance = Rin.

3. If = Iin, regardless of Rf (Is=0!).

4. Summing point is a virtual ground at the same potential as the (+) input.


Inverting Amplifier


Summary of Non-Inverting Op Amp

1. Gain = in f

in

R R

R lower limit of unity gain where

Rin = ∞, or Rf = 0.

2. Input Impedance = ∞

3. If = Iin, regardless of Rf


Non-Inverting Op Amp


Summary of Differential Op Amp

1. Differential-Mode Gain (Ein1 ≠ Ein2)

1 2

fo

in in in

RE

E E R


2. Common-Mode Gain (Ein1 = Ein2) a. When

, 0

f f

in in

R R

R R

b. When

,

f f f in f in

in in in in in f

R R R R R R

R R R R R R

c. In terms of resistor match (worst case)

4

f

in f

R

R R

where δ = fractional unbalance of resistors (i.e. 1%=0.01) and Rin and Rf are the nominal resistance values.

operational amplifiers - university at buffalo amplifiers an amplifier is a signal conditioning...

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