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DC Circuits:

Operational Amplifiers Hasan Demirel

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• Op Amp is short form of operational amplifier.

• An op amp is an electronic unit that behaves like a voltage controlled voltage source.

• An operational amplifier has a very high input

impedance and a very high gain.

Op Amps: Introduction

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• Op amps can be configured in many different ways using resistors and other components.

• Most configurations use feedback.

• An op amp can be designed to perform mathematical operations of addition, subtraction, multiplication, division, differentiation, and integration.

Op Amps: Use of Op Amps

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• Amplifiers provide gains in voltage or current. • Op amps can convert current to voltage. • Op amps can provide a buffer between two

circuits. • Op amps can be used to implement

integrators and differentiators. • Op amps can be used to design filters (i.e.

lowpass and bandpass filters).

Op Amps: Applications of Op Amps

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Op Amps: Op Amp Symbol

A typical op amp: (a) pin configuration, (b) circuit symbol.

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Op Amps: Schematic diagram of op amp

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Op Amps: The Op Amp Model

Inverting input

Non-inverting input

Output

The differential input voltage The output voltage

A is the open-loop voltage gain.

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Op Amps: Typical op amp parameters

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Op Amps: • Example 5.1: A 741 op amp has an open-loop voltage gain of 2x105,

input resistance of 2 MΩ, and output resistance of 50 Ω. The op amp is used in the circuit shown in Fig. 5.6(a). Find the closed- loop gain v0/vs. Determine current i when vs = 2 V.

Figure 5.6: (a) original circuit, (b) the equivalent circuit.

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Op Amps: • Example 5.1: A 741 op amp has an open-loop voltage gain of 2x105,

input resistance of 2 MΩ, and output resistance of 50 Ω. The op amp is used in the circuit shown in Fig. 5.6(a). Find the closed- loop gain v0/vs. Determine current i when vs = 2 V.

Apply KCL at node 1:

Apply KCL at node 0:

(1)

(2)

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Op Amps: • Example 5.1: A 741 op amp has an open-loop voltage gain of 2x105,

input resistance of 2 MΩ, and output resistance of 50 Ω. The op amp is used in the circuit shown in Fig. 5.6(a). Find the closed- loop gain v0/vs. Determine current i when vs = 2 V.

Substituting v1 from Eq. (1) into Eq. (2) gives:

This is called closed-loop gain, because the 20-kΩ feedback resistor closes the loop between the output and input terminals.

From Eq. (1)

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Op Amps: Ideal Op Amp • An ideal op amp is an amplifier with infinite open-loop

gain, infinite input resistance, and zero output resistance. • To facilitate the understanding of op amp circuits, we will assume

ideal op amps. An op amp is ideal if it has the following characteristics:

1. Infinite open-loop gain, A = ∞

2. Infinite input resistance, Rin=∞

3. Zero output resistance, Ro=0

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Op Amps: Ideal Op Amp • An ideal op amp is an amplifier with infinite open-loop

gain, infinite input resistance, and zero output resistance.

1. Ideal Op Amp Model

1. Infinite open-loop gain, A = ∞

2. Infinite input resistance, Rin=∞

3. Zero output resistance, Ro=0

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Op Amps: Ideal Op Amp • Two important characteristics of the ideal op amp are:

1. The currents into both input terminals are zero. This is due to infinite input resistance. An infinite resistance between the input terminals implies that an open circuit exists there and current cannot enter the op amp.

2. The voltage across the input terminals is equal to zero.

An ideal op amp has zero current into its two input terminals and the voltage difference between the two input terminals is equal to zero.

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Op Amps: Ideal Op Amp • Example 5.2: Use the ideal op amp model to calculate the closed-loop

gain v0/vs. Find io when vs = 1 V.

(if vs = 1 V , then vo = 9V)

vo v1

KCL at inverting terminal (v1):

ss vvvvv 212

os

sos

vv

vvv

9

0540

KCL at output (vo):

33 10201040

oso

o

vvvi

mA65.010)45.02.0( 3

oi

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Op Amps: Inverting Amplifier • Both the input signal and the feedback are applied at the

inverting terminal of the op amp.

Noninverting terminal is grounded.

Applying KCL at node 1:

• An inverting amplifier reverses the polarity of the input signal while amplifying it.

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Op Amps: Inverting Amplifier • Example 5.3: Refer to the op amp in Fig. 5.12. If vi =0.5 V, calculate: (a)

the output voltage vo, and (b) the current in the 10-kW resistor.

(a)

(b)

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Op Amps: Inverting Amplifier • Practice Problem 5.3: Find the output of the op amp circuit shown in Fig.

5.13. Calculate the current through the feedback resistor.

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Op Amps: • Example 5.1: A 741 op amp has an open-loop voltage gain of 2x105, input

resistance of 2 MΩ, and output resistance of 50 Ω. The op amp is used in the circuit shown in Fig. 5.6(a). Find the closed- loop gain v0/vs. Determine current i when vs = 2 V.

• Repeat Ex. 5.1 by using ideal op amp model.

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Op Amps: Review • To solve an op amp circuit, we usually apply KCL at one or

both of the inputs. • We then use the properties of the ideal model.

The currents into both input terminals are zero.

• We solve for the op amp output voltage.

The voltage across the input terminals is equal to zero.

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Op Amps: Noninverting Amplifier • A noninverting amplifier is an op amp circuit designed to

provide a positive voltage gain.

Apply KCL at inverting terminal:

(1)

(2)

Apply eq. (1) into eq (2):

Then:

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Op Amps: Voltage Follower • A voltage follower (or unity gain amplifier) has the

output voltage equal to the input voltage.

Voltage follower is a noninverting amplifier with:

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Op Amps: Noninverting Amplifier • Example 5.5: For the op amp circuit below, calculate the output

voltage vo .

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Op Amps: Summing Amplifier (Inverting Summer)

Apply KCL at node a:

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Op Amps: Summing Amplifier (Inverting Summer)

Apply KCL at node a:

Note that

Then,

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Op Amps: Summing Amplifier (Inverting Summer) • Example 5.6: Find vo and io in the op amp circuit shown below.

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Op Amps: Difference Amplifier

Apply KCL at node a:

Apply KCL at node b:

But

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Op Amps: Difference Amplifier • Difference amplifier must reject a signal common to the two

inputs, the amplifier must have the property that vo=0, when v1= v2.

• This property exists when:

• When this property is satisfied • The op amp circuit is a difference amplifier

• If R2 = R1 and R3 = R4 •The difference amplifier becomes •A subtractor circuit:

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Op Amps: Cascaded Op Amp Circuits • A cascade connection is a head-to-tail arrangement of two or more

op amp circuits such that the output of one is the input of the next.

• The overall gain of the cascade connection is the product of the gains of the individual op amp circuits

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Op Amps: Cascaded Op Amp Circuits • Example 5.9: Find v0 and i0 in the circuit below.

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Op Amps: Cascaded Op Amp Circuits • Example 5.10: Find v1 = 1 V and v2 = 2 V, find v0 in the circuit below.