0195136047.pdf

232 ANALOG BUILDING BLOCKS AND OPERATIONAL AMPLIFIERS

the constant region from the high-frequency band for which the open-loop gain decreases.

fhis also called the half-power frequency since the magnitude ofAis 3 dB below its low-

frequency valueA 0. The frequencyfGBat whichAdB=0, or the magnitudeA=1, is the

gain–bandwidth productgiven byA 0 fh. Typical values offhandfGBare 10 Hz and 1 MHz,

respectively. To overcome this frequency limitation, bothinvertingandnoninvertingop-amp

stages (which are examples of feedback amplifiers) are frequently used. These will be discussed

later in examples.

Feedback circuits have a desensitizing property, which implies that variations in the values

of the op-amp parameters have little effect on the output of the circuit. “Feedback” implies

that some of the output signal is fed back to be added to the input. Another property of

feedback amplifiers is that the open-loop and closed-loop gain–bandwidth products are equal.

Referring to Figure 5.2.4, which shows the open-loop and closed-loop frequency responses, it

follows that

A 0 fh=G 0 fH (5.2.2)

whereA 0 fhis the open-loop gain–bandwidth product,fHis the closed-loop bandwidth, andG 0 is

theclosed-loop gain.The term closed loop signifies circuit performance when a path exists from

output to input, whereas open loop implies the inherent characteristics of the op amp. Thus, for

an op amp whose gain bandwidth product is 1 MHz withA 0 = 105 andfh=10 Hz, a stage

with a closed-loop gain of 10 has a bandwidthfH=100 kHz, as shown in the asymptotic Bode

diagram of Figure 5.2.4.

−20 dB/decade

|A|dB

A0 dB

(^0) fh fGB f, Hz(log scale)
Figure 5.2.3Asymptotic Bode diagram for
open-loop voltage gain.
−20 dB/decade
Open-loop response with op amp alone
Closed-loop response
with op amp in feedback circuit
|A|dB (gain magnitude)
A0 dB
0
10 102 103 104 105 106
20
40
60
80
100
f, Hz (log scale)
fh fH
G0 dB fGB
Figure 5.2.4Typical frequency response of op-amp stage.