(

)

2

2

2

BI

F

F

N

NI

BN

S

S

I R

4kTR

E

E

I

R

4kTR

NG

NG

æ

ö

=

+

+

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ç

÷

è

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(

)

(

)

(

)

2

2

2

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NG

I

R

4kTR NG

BI F

=

+

+

+

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4 kT

R

G

R

G

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F

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OPA656

I

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4 kT = 1.6E –20J

at 290°K

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√4kTR

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F

*

*

*

OPA656

SBOS196H – DECEMBER 2001 – REVISED SEPTEMBER 2015

www.ti.com

Application Information (continued)

Figure 31. Operational Amplifier Noise Analysis Model

The total output spot noise voltage can be computed as the square root of the squared contributing terms to the

output noise voltage. This computation is adding all the contributing noise powers at the output by superposition,

then taking the square root to get back to a spot noise voltage. Equation 1 shows the general form for this output

noise voltage using the terms shown in Figure 31.

(1)

voltage at the noninverting input as shown in Equation 2.

(2)

Putting high resistor values into Equation 2 can quickly dominate the total equivalent input referred noise. A

source impedance on the noninverting input of 3 k

Ω will add a Johnson voltage noise term equal to just that for

the amplifier itself (7 nV/

√Hz). While the JFET input of the OPA656 is ideal for high source impedance

applications, both the overall bandwidth and noise will be limited by higher source impedances in the

noninverting configuration of Figure 29.

9.1.3.2 Frequency Response Control

Voltage-feedback op amps like the OPA656 exhibit decreasing signal bandwidth as the signal gain is increased.

In theory, this relationship is described by the GBP shown in the Electrical Characteristics. Ideally, dividing GBP

by the noninverting signal gain (also called the Noise Gain, or NG) will predict the closed-loop bandwidth. In

practice, this only holds true when the phase margin approaches 90°, as it does in high-gain configurations. At

low gains (increased feedback factors), most high-speed amplifiers will exhibit a more complex response with

lower phase margin. The OPA656 is compensated to give a maximally flat 2nd-order Butterworth closed loop

response at a noninverting gain of +2 V/V (Figure 29). This results in a typical gain of +2 V/V bandwidth of 200

MHz, far exceeding that predicted by dividing the 230-MHz GBP by 2. Increasing the gain will cause the phase

margin to approach 90° and the bandwidth to more closely approach the predicted value of (GBP/NG). At a gain

of +10 V/V the OPA656 will show the 23-MHz bandwidth predicted using the simple formula and the typical GBP

of 230 MHz.

Unity-gain stable operational amplifiers like the OPA656 can also be bandlimited using a capacitor across the

feedback resistor. For the noninverting configuration of Figure 29, a capacitor across the feedback resistor will

decrease the gain with frequency down to a gain of +1 V/V. For instance, to bandlimit the gain of +2 V/V design

to 20 MHz, a 32-pF capacitor can be placed in parallel with the 250-

Ω feedback resistor. This will, however, only

decrease the gain from +2 V/V to +1 V/V. Using a feedback capacitor to limit the signal bandwidth is more

effective in the inverting configuration of Figure 30. Adding that same capacitor to the feedback of Figure 30 will

set a pole in the signal frequency response at 20 MHz, but in this case it will continue to attenuate the signal gain

to below 1. However, the output noise contribution due the input voltage noise of the OPA656 will still only be

reduced to a gain of +1 V/V with the addition of the feedback capacitor.

16

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