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Chapter 8Operational (OP) Amplifiers

Jaesung Jang

Ideal AmplifiersBasic Ideal OP amp Circuits

Active FiltersPhysical Limitations of Practical OP amps

Ref: Sedra/Smith, Microelectronic Circuits, 3rd ed., 1990, Chap. 1 & 2

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Amplifiers - Signal Amplification• One of the most important functions in electronic instrumentation is that of

amplification. The simplest signal processing task is signal amplification (Signal amplifier).

– The need for amplification arises because sensors provide signals that are said to be “weak,” that is, in the microvolt or millivolt range. Such signals are too small for reliable processing, and processing is much easier if the signal magnitude is made larger (amplification).

• When amplifying a signal, care must be taken so that the informationcontained in the signal is not changed. The ideal amplifier needs to produce an exact replica of that at the input, except for larger magnitudes.

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Ideal (Voltage) Amplifiers• In order not to lose a significant portion of the

input signal, the input resistance Ri that we can control must be much greater than RS. The ideal voltage amplifier is one with Ri = ∞ (infinite input impedance) so thevoltage ratio at the input side is independent of the source resistance.

• For a given RL one must design the amplifierso that its RO that we can control here is much smaller than RL . That is, an ideal voltage amplifier is one with Ro = 0 (zero output impedance), so the gain is independent of the load resistance. If RL = ∞, , which is the voltage gain of the unloaded amplifier, or the open-circuit voltage gain.

oAA υυ =

divider voltage:si

isi RR

R

+= υυ

Amplifier (shaded)

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Lo

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=++−→

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OP Amp• Operational amplifier (op amp) was first applied to the

amplifiers employed in analog computers to perform mathematical operations such as summing and integration. – For linear or analog systems, the IC (Integrated-Circuit) op amp plays

the same role as do the IC logic and memory elements in digital systems. Combinations of op amp and digital devices are widely used in instrumentation and control.

– One of the reasons for the popularity of the op amp is versatility. You can do almost everything with op amps!

– It is easy to design circuits with the IC op amps.– An IC op amp is made up of a large number of transistors, resistors,

and (sometimes) one capacitor.

• An op amp is basically a differential amplifier responding to the difference in the voltages of two input (positive and negative input) terminals.

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Characteristics of Ideal OP Amp• A differential amplifier has two inputs, an inverting

(−) input and a non-inverting (+) input.• It has two inputs but only one output.

• Infinite input impedance (no currents going into the op amp) and zero output impedance. (-> ideal voltage amplifier)

• The op amp responds only to the difference signal.

• Zero output voltage is induced at no difference in the voltages at two input terminals -> infinite common-mode rejection: The amplifier rejects or severely attenuates signals that are common to both inputs.

• Op amps are direct-coupled devices or dc amplifiers (low-pass amplifiers).

• Infinite bandwidth: an ideal op amp can amplify signals of any frequency with equal gain.

• Infinite open-loop voltage gain-> In almost all applications the op amp will not be used in an open-loop configuration, but in a closed-loop configuration.

External voltage source

i =0

i =0

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.10 to10 oforder on the

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� Inverting configuration: the inverting input terminal (1) is biased with voltage source is and the non-inverting terminal is usually grounded -> negative gain -> output shape is inverted with respect to the input signals.� Non-inverting configuration: the inverting input terminal (2) is biased with voltage source. -> positive gain -> output shape is not inverted with respect to the input signals.

� An inverting amplifier has a negative closed-loop voltage gain, GCL, of −−−−R2/R1. � The minus (−) sign of the gain indicates that Vin and Vout are 180° out of phase. -> inverted shape.

Analysis of Ideal OP Amps in the Inverting Configuration

( ) Gain Voltage Loop-Closed :1

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RA

I

OV −==

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Popular Op Amp Circuits� The circuit shown below is called a summing amplifier, or summer.

∑

∑

=

=

−=

=−=++++→

−=++++

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nS

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F

N

n S

S

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S

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FN

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N

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iiiii

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1

out

321

3

3

2

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:KCL

L

L

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Analysis of Ideal OP Amps in the Non-Inverting Configuration

�A non-inverting amplifier has a positive closed-loop voltage gain, GCL, of (R2/R1 + 1).

�The input signal is connected to the noninverting (+) input of the op amp, so that the input and output signals will be in phase. -> non-inverted shape.

1) toequal(or an greater th and positive always isgain The :Note

gain loop-closedamplifier inverting-Non

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==→=

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−+

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Voltage Follower

� The figure below shows a very popular op-amp circuit called a voltage follower with RF =0.� vout = vS (Voltage gain equals one.)� This circuit is also called a unity gain amplifier, buffer amplifier, or isolation amplifier.

� The name voltage follower derives from the ability of the output voltage to “follow” exactly the input voltage.

� The extremely high input impedance of the amplifier permits virtually perfect isolation between source and load and eliminates loading effects.

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Differential Amplifier

� It is often necessary to amplify the difference between two signals that are both corrupted by noise or some other form of interference. In such cases, the differential amplifier provides an invaluable tool in amplifying the desired signal while rejecting the noise.

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Active Filters

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Amplifiers Inverting :V

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Amplifiers Inverting :V

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A first-order, active, low-pass filter

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A first-order, active, high-pass filter circuit.

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12

1

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V

111

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Amplifiers Inverting :V

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=→

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=+=

−=

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out

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SS

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out

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SS

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out

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CR

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ωω

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ω

ω

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ω

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Active Filters (Cont.)

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A second-order, active, band-pass filter circuit.

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, 1

frequency dB 0 1

1111

V

V

1

1|| ,

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Amplifiers Inverting :V

V

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→==

→=

++−=

++−=

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−=

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Active Filters (Cont.)

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Integration & Differentiation

Differentiator

Integrator

dt

dvCRv

CR

v

dt

dv

R

v

dt

dvC

SSF

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F

SS

−=→−=→

=+

outout

out 0

Mathematical Operations in Analog Computers

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Real OP Amplifiers and Their Limitations• The amplifier needs dc power

supplies for their operation. The amplifier has two terminals, labeled V+

and V- for connection to the dc supplies. (Some amplifiers require only one terminal power supply.)

• The amplifier characteristics remain linear over only a limited range of input and output voltages. For an amplifier operated from two power supplies, the output voltage cannot exceed a specified positive limit and cannot decrease below a specified negative limit

limitationsupply Voltage :out+− << VvV

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Real OP Amplifiers and Their Limitations

� The differential open loop voltage gain of real op amps is finite and decrease with frequency -> finite bandwidth.

�The figure right shows the frequency response curve for a typical 741 op amp.

70.7% (3dB) of its maximum value at 10 Hz -> open loop cutoff frequency

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Real OP Amplifiers and Their Limitations

limitation rate Slew :0max

out Sdt

dv=

�The op amp can produce only a finite rate of change at its output. -> Slew rate�The slew rate (SR) is the maximum possible rate of change of the op amp output voltage.�The slew-rate specification of an op amp indicates how fast the output voltage can change. The slew rate is specified in V/µs.�The slew-rate distortion of a sine wave makes the output waveform appear triangular.

output

( )

ωωω

ω

ASdt

dvtA

dt

dv

tAtv

==→=

=

0max

outout

out

cos

sin