AD8139ACP-R2 datasheet(19/24 Pages) AD

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AD8139

Rev. A | Page 19 of 24

APPLICATIONS

ESTIMATING NOISE, GAIN, AND BANDWIDTH

WITH MATCHED FEEDBACK NETWORKS

Estimating Output Noise Voltage

The total output noise is calculated as the root-sum-squared

total of several statistically independent sources. Since the

sources are statistically independent, the contributions of each

must be individually included in the root-sum-square calcula-

tion. Table 6 lists recommended resistor values and estimates of

bandwidth and output differential voltage noise for various

closed-loop gains. For most applications, 1% resistors are

sufficient.

Table 6. Recommended Values of Gain-Setting Resistors and

Voltage Noise for Various Closed-Loop Gains

Gain

RG (Ω)

RF (Ω)

3 dB

Bandwidth

(MHz)

Total Output

Noise (nV/√Hz)

200

400

5.8

200

400

160

9.3

200

1 k

19.7

200

2 k

The differential output voltage noise contains contributions

from the AD8139’s input voltage noise and input current noise

as well as those from the external feedback networks.

The contribution from the input voltage noise spectral density

is computed as

⎟

⎠

⎞

⎜

⎝

⎛ +

Vo_n

, or equivalently, vn/β

(7)

where vn is defined as the input-referred differential voltage

noise. This equation is the same as that of traditional op amps.

The contribution from the input current noise of each input is

computed as

( )

n R

Vo_n =

(8)

where in is defined as the input noise current of one input. Each

input needs to be treated separately since the two input currents

are statistically independent processes.

The contribution from each RG is computed as

⎟

⎠

⎞

⎜

⎝

⎛

kTR

Vo_n

(9)

This result can be intuitively viewed as the thermal noise of

each RG multiplied by the magnitude of the differential gain.

The contribution from each RF is computed as

kTR

(10)

Voltage Gain

The behavior of the node voltages of the single-ended-to-

differential output topology can be deduced from the previous

definitions. Referring to Figure 57, (CF = 0) and setting VIN = 0

one can write

−

(11)

⎥⎦

⎤

⎢⎣

⎡

(12)

Solving the above two equations and setting VIP to Vi gives the

gain relationship for VO, dm/Vi.

−

(13)

An inverting configuration with the same gain magnitude can

be implemented by simply applying the input signal to VIN and

setting VIP = 0. For a balanced differential input, the gain from

VIN, dm

to VO, dm is also equal to RF/RG, where VIN, dm = VIP − VIN.

Feedback Factor Notation

When working with differential amplifiers, it is convenient to

introduce the feedback factor β, which is defined as

(14)

This notation is consistent with conventional feedback analysis

and is very useful, particularly when the two feedback loops are

not matched.

Input Common-Mode Voltage

The linear range of the VAN and VAP terminals extends to within

approximately 1 V of either supply rail. Since VAN and VAP are

essentially equal to each other, they are both equal to the ampli-

fier’s input common-mode voltage. Their range is indicated in

the Specifications tables as input common-mode range. The

voltage at VAN and VAP for the connection diagram in Figure 57

can be expressed as

ACM

⎟

⎠

⎞

⎜

⎝

⎛

⎟

⎠

⎞

⎜

⎝

⎛

OCM

)

(

(15)

where VACM is the common-mode voltage present at the

amplifier input terminals.

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