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General-purpose integrated circuit Perform addition or integration of signals Op amps are most useful when part of the output

signals is returned to the input through a feedback network.

(closed-loop condition) The characteristics of IC op amp (with resistive

feedback network) depends on the circuit configuration and the resistive values, but only weekly on the op amp.

Chapter 2 Operational amplifiers

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Outline

The ideal operational amplifier The summing-point constraints The inverting amplifier The noninverting amplifier Integrators and Differentiators Large-signal operation DC imperfection Acitve filter

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2.1 The ideal operational amplifier

Figure 2.1 Circuit symbol for the op amp.

Characteristics of an ideal operational amplifier

Input resistance Ri

voltage gain AdoL , Acm =0

Output resistance Ro=0

Figure 2.3 Op-amp symbol showing power supplies.

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The differential input voltage and the input current are zero

Ideal op-amp analysis Verify that negative feedback is

present. Using summing point constraint. Apply standard circuit analysis

principles to solve for the quantities of interest.

2.2 The summing-point constraint

v+

v-

i+c

i-

v+ = v- i+ = i-=0

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What is the value of v+?

Applying the summing point constraint, What is the value of v-?

Find expressions for the currents flowing through R1 and R2, i1 and i2, in terms of node voltages.

Applying KCL, find an equation for i1, i2 and i-

Derive the closed loop voltage gain Av=vo/vi

2.3 The inverting amplifier

Negative feedback?

Indicate v+ , v- ,i+ and i-

i2

i1

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Why is it called inverting amplifier? Input impedance and output impedance Zin=R1, Zo=0

The virtual-short-circuit (virtual open-circuit) concept

2.3 The inverting amplifier

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2.3 The inverting amplifier

Figure 2.6 An inverting amplifier that achieves high gain with a smaller range of resistor values than required for the basic inverter.P52 ）

Variation 1

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Variation 2

2.3 The inverting amplifier

Figure 2.7 Summing amplifier. See Exercise 2.1.P53

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2.3 The inverting amplifier

Example

Figure 2.9 Circuit of Exercise 2.3, p53

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2.4 The noninverting amplifier

Figure 2.11 Noninverting amplifier. P55

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2.4 The noninverting amplifier

Figure 2.12 Voltage follower.

Figure 2.14 Differential amplifier. See Exercise 2.5.P56, refer to p72 figure2.34

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Instrumentation-quality differential amplifier P72

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Voltage-current converter P73

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Current-voltage converter P74

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2.5 Integrators and Differentiators P76

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2.5 Integrators and Differentiators

Exercise: Derive the expression for the output voltage vo.

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2.6 Large-signal operation

Output voltage swing (Vomin, Vomax)

Figure 2.28 For a real op amp, clipping occurs if the output voltage reaches certain limits.

Transfer characteristic

The range of allowed output voltages before clipping occurs depends on the type of op amp in use, on the load resistance, and on the values of the power-supply voltages.

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Output current limit (Iomax, mA)

The maximum current that an op amp can supply to a load. Slew-rate limitation (105~8V/s)

The magnitude of the rate of change of the output is limited.

Full-power bandwidth~(SR,Vomax)The range of frequencies for which the op amp can produce an undistorted sinusoidal output with peak amplitude equal to the guaranteed maximum output voltage.

2.6 Large-signal operation

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2.7 DC imperfections

bias current IB

The average of the DC currents Offset current Ioff

The difference between the bias currents

Offset voltage Voff

The output voltage may not be zero for zero input voltage. The op amp behaves as if a small DC source is in series with one of the input terminal.

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2.7 DC imperfections

Cancellation of the effects of bias currents

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Pictures of Op Amps

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Frequency response (P30) The complex gain: The ratio of the phasor for the output signal to

the input signal

Bode plot (P271) How circuit functions can be quickly and easily plotted against fr

equency? (straight line approximation & smart scale)

2.8 Active Filter

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2.8 Active Filter

Logarithmic Frequency Scale

A decade is a range of frequencies for which the ratio of the highest frequency to the lowest is 10.

An octave is a two-to-one change in frequency.

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A filter circuit is designed using an operational amplifier and is A filter circuit is designed using an operational amplifier and is shown in the following figureshown in the following figure

R2 R1

~

R

C

-

+ ~VO

~Vs

Example

(1) Determine the ratio as a

function of R,C,R1,R2.

(2) Identify whether the circuit is a low-pass, high-pass or band-pass filter, and give reasons.

(3) If RC=0.1 and R1/R2=3, sketch the bode plot and find the cut-off frequency.

~~so vv

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Summary

Characteristics of an ideal op amp. The summing-point constraint applies when ideal op

amps are used in circuits with negative feedback. The steps to analyze an ideal op amp circuits. The inverting/noninverting amplifier The summing/differentiating amplifier The integrator/differentiator The design of simple op amp circuits

Exercise2.1, 2.3, 2.5, 2.6, 2.7, 2.9, 2.10, 2.18, 2.19, 2.20, 2.21, 2.22, 2.23(optional)