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10.1.3 Noise Analysis

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 10-4 shows the simplest analysis circuit with the FDA and

resistor noise terms to be considered.

In+

In±

eno

enRg

enRf

enRg

enRf

eni

Figure 10-4. FDA Noise Analysis Circuit

The noise powers are shown in Figure 10-4 for each term. When the RF and RG 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 5. Each resistor noise term is a 4kT × R power (4kT =

1.6E-20J at 290K).

e NG

2 i R

2 4kTR NG

(5)

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), and 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 close to 1.5 kΩ and setting the input up for a 50-Ω match gives the standard values and

resulting noise listed in Table 10-2.

When the gain increases, the input-referred noise approaches only the gain of the FDA input voltage noise term

at 5 nV/√ Hz.

Table 10-2. Swept Gain of the Output- and Input-Referred Spot Noise Calculations

GAIN (V/V)

RG1

RG2

ZIN

eO (nV/√ Hz)

eI (nV/√ Hz)

0.1

1500

15000

49.9

15000

49.74

0.09973

9.15

91.53

1500

51.1

1500

49.82

0.994

14.03

1500

750

52.3

768

49.98

1.978

18.99

9.49

1500

287

54.9

316

49.6

5.014

33.20

6.64

1500

137

61.9

165

50.4

10.08

55.05

5.51

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THS4561

SBOS874D – AUGUST 2017 – REVISED FEBRUARY 2021

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