9.1.4 Noise Performance

The first step in the output noise analysis is to reduce the application circuit to the simplest form with equal

feedback and gain setting elements to ground. Figure 9-4 shows the simplest analysis circuit with the FDA and

resistor noise terms to be considered.

+

±

In+

2

In±

2

eno

2

RF

RG

RF

RG

enRg

2

enRf

2

enRg

2

enRf

2

eni

2

Figure 9-4. FDA Noise Analysis Circuit

The noise powers are shown in Figure 9-4 for each term. When the RF and RG (or RI) terms are matched on

each side, the total differential output noise is the root sum squared (RSS) of these separate terms. Using NG ≡

1 + RF / RG, the total output noise is given by Equation 3. Each resistor noise term is a 4kT × R power (4kT =

1.6E-20 J at 290 K).

2

2

o

ni

N

F

F

e

e NG

2 i R

2 4kTR NG

(3)

The first term is simply the differential input spot noise times the noise gain. The second term is the input current

noise terms times the feedback resistor (and because there are two uncorrelated current noise terms, the power

is two times one of them). The last term is the output noise resulting from both the RF and RG resistors, at again,

twice the value for the output noise power of each side added together. Running a wide sweep of gains when

holding RF to 2 kΩ gives the standard values and resulting noise listed in Table 9-1. When the gain increases,

the input-referred noise approaches only the gain of the FDA input voltage noise term at 3.7 nV/√ Hz.

Table 9-1. Swept Gain of the Output- and Input-Referred Spot Noise Calculations

GAIN (V/V)

RF (Ω)

RG1 (Ω)

AV

EO (nV/√ Hz)

EI (nV/√ Hz)

0.1

2000

20000

0.1

9.4

93.9

1

2000

2000

1

13.6

13.6

2

2000

1000

2

17.8

8.9

5

2000

402

4.98

29.5

5.9

10

2000

200

10

48.6

4.9

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SBOSA00B – DECEMBER 2019 – REVISED AUGUST 2020

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