Data Sheet

ADA4950-1/ADA4950-2

Rev. B | Page 19 of 26

APPLICATIONS INFORMATION

ANALYZING AN APPLICATION CIRCUIT

The ADA4950-x uses high open-loop gain and negative feedback

to force its differential and common-mode output voltages in

such a way as to minimize the differential and common-mode

error voltages. The differential error voltage is defined as the

voltage between the differential inputs labeled +INx and −INx

(see Figure 52). For most purposes, this voltage can be assumed

to be 0. Similarly, the difference between the actual output

common-mode voltage and the voltage applied to VOCM can

also be assumed to be 0. Starting from these principles, any

application circuit can be analyzed.

SELECTING THE CLOSED-LOOP GAIN

Using the approach described in the Analyzing an Application

Circuit section, the differential gain of the circuit in Figure 52

can be determined by

G

F

dm

IN

dm

OUT

R

R

V

V

=

,

,

where the input resistors (RG) and the feedback resistors (RF) on

each side are equal.

For G = 1, the +INA and −INA inputs are used, and the +INB

and −INB inputs are left floating. The differential gain in this

case is calculated as follows:

1

500

500

=

Ω

Ω

=

=

G

F

R

R

G

For G = 2, the +INB and −INB inputs are used, and the +INA

and −INA inputs are left floating. The differential gain in this

case is calculated as follows:

2

250

500

=

Ω

Ω

=

=

G

F

R

R

G

For G = 3, the +INA and +INB inputs are connected together,

and the −INA and −INB inputs are connected together. The

differential gain in this case is calculated as follows:

3

250

||

500

500

=

Ω

Ω

Ω

=

=

G

F

R

R

G

ESTIMATING THE OUTPUT NOISE VOLTAGE

The differential output noise of the ADA4950-x can be estimated

using the noise model in Figure 53. The values of RG depend on

the selected gain. The input-referred noise voltage density, vnIN,

is modeled as a differential input, and the noise currents, inIN− and

inIN+, appear between each input and ground. The output voltage

due to vnIN is obtained by multiplying vnIN by the noise gain, GN

(defined in the GN equation that follows Table 13). The noise

currents are uncorrelated with the same mean-square value,

and each produces an output voltage that is equal to the noise

current multiplied by the associated feedback resistance. The

noise voltage density at the VOCM pin is vnCM. When the feedback

networks have the same feedback factor, as is true in most cases,

the output noise due to vnCM is common mode. Each of the four

resistors contributes (4kTRxx)1/2. The noise from the feedback

resistors appears directly at the output, and the noise from the

gain resistors appears at the output multiplied by RF/RG. Table 11

summarizes the input noise sources, the multiplication factors,

and the output-referred noise density terms.

ADA4950-x

+

RF2

vnOD

vnCM

VOCM

vnIN

RF1

RG2

RG1

vnRF1

vnRF2

vnRG1

vnRG2

inIN+

inIN–

Figure 53. Noise Model

Table 11. Output Noise Voltage Density Calculations for Matched Feedback Networks

Input Noise Contribution

Input Noise Term

Input Noise

Voltage Density

Output

Multiplication Factor

Differential Output Noise

Voltage Density Term

Differential Input

vnIN

vnIN

GN

vnO1 = GN(vnIN)

Inverting Input

inIN−

inIN− × (RF2)

1

vnO2 = (inIN−)(RF2)

Noninverting Input

inIN+

inIN+ × (RF1)

1

vnO3 = (inIN+)(RF1)

VOCM Input

vnCM

vnCM

0

vnO4 = 0 V

Gain Resistor, RG1

vnRG1

(4kTRG1)1/2

RF1/RG1

vnO5 = (RF1/RG1)(4kTRG1)1/2

Gain Resistor, RG2

vnRG2

(4kTRG2)1/2

RF2/RG2

vnO6 = (RF2/RG2)(4kTRG2)1/2

Feedback Resistor, RF1

vnRF1

(4kTRF1)1/2

1

vnO7 = (4kTRF1)1/2

Feedback Resistor, RF2

vnRF2

(4kTRF2)1/2

1

vnO8 = (4kTRF2)1/2