O O
F
G
I I G
G F
V V
R
A
If A desired closed loop gain, 1
A R
V V R
1
R R
= >> = +
´
+
+
Open Loop Gain: A
Gain (dB)
100
60
40
20
0
1 10 100 1k 10k 100k 1M
Frequency (Hz)
80
120
A
Closed Loop Gain:
1 A+ b
1+Aβ
www.ti.com
Bandwidth
Figure 3. Closed Loop Bode Plot
The closed loop gain modifies the open loop gain A by 1+Aβ. Because logarithms are being used,
divisions can be accomplished by subtraction of the quantities. Therefore, at low frequencies before the
internal compensation break point, the closed loop gain in Figure 3 is 110 dB – 70 dB, or 40 dB.
The sacrifice in gain is accompanied by an increase in bandwidth. Instead of the constant (horizontal) gain
line intersecting breaking at the internal compensation frequency (about 100 Hz in Figure 2 and Figure 3);
it intersects at about 50 kHz. This decrease in gain and increase in bandwidth is a linear function known
as the gain bandwidth product, or GBP.
With VFB amplifiers, GBP is the specification of interest when looking at small signal bandwidth. Because
the VFB amplifier is dependent on the gain that is being employed, the frequency of the signal of interest
multiplied by the gain must be less than the GBP for the amplifier.
3.2 Closed Loop Bandwidth
It should be noted at this point that for both noninverting and inverting amplifier stages, the actual gain is a
function of both the closed and open loop gains. Designers may not be familiar with this fact, because in
most cases the contribution from the open loop gain is negligible. The implications of this fact are
discussed in the sections below.
3.2.1 Noninverting Closed Loop Bandwidth
Figure 4. Noninverting Gain Stage
For noninverting operational amplifier gain stages, the exact gain can be calculated by:
(2)
Where:
R
G
is the gain resistor of the stage
R
F
is the feedback resistor of the stage
5
SLOA035D–September 1999–Revised May 2015 Amplifiers and Bits: An Introduction to Selecting Amplifiers for Data
Converters
Submit Documentation Feedback
Copyright © 1999–2015, Texas Instruments Incorporated
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