MAX412BESA datasheet(7/16 Pages) MAXIM

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Applications Information

The MAX410/MAX412/MAX414 provide low voltage-

noise performance. Obtaining low voltage noise from a

bipolar op amp requires high collector currents in the

input stage, since voltage noise is inversely proportion-

al to the square root of the input stage collector current.

However, op amp current noise is proportional to the

square root of the input stage collector current, and the

input bias current is proportional to the input stage col-

lector current. Therefore, to obtain optimum low-noise

performance, DC accuracy, and AC stability, minimize

the value of the feedback and source resistance.

Total Noise Density vs. Source Resistance

The standard expression for the total input-referred

noise of an op amp at a given frequency is:

where:

Rn = Inverting input effective series resistance

Rp = Noninverting input effective series resistance

en = Input voltage-noise density at the frequency of

interest

in = Input current-noise density at the frequency of

interest

T = Ambient temperature in Kelvin (K)

k = 1.28 x 10-23 J/K (Boltzman’s constant)

In Figure 1, Rp = R3 and Rn = R1 || R2. In a real appli-

cation, the output resistance of the source driving the

input must be included with Rp and Rn. The following

example demonstrates how to calculate the total out-

put-noise density at a frequency of 1kHz for the

MAX412 circuit in Figure 1.

Gain = 1000

4kT at +25°C = 1.64 x 10-20

Rp = 100Ω

Rn = 100Ω || 100kΩ = 99.9 W

en = 1.5nV/√Hz at 1kHz

in = 1.2pA/√Hz at 1kHz

et = [(1.5 x 10-9)2 + (100 + 99.9)2 (1.2 x 10-12)2 + (1.64

x 10-20) (100 + 99.9)]1/2 = 2.36nV/

√Hz at 1kHz

Output noise density = (100)et = 2.36µV/√Hz at 1kHz.

In general, the amplifier’s voltage noise dominates with

equivalent source resistances less than 200

Ω. As the

equivalent source resistance increases, resistor noise

becomes the dominant term, eventually making the

voltage noise contribution from the MAX410/MAX412/

MAX414 negligible. As the source resistance is further

increased, current noise becomes dominant. For exam-

ple, when the equivalent source resistance is greater

than 3k

Ω at 1kHz, the current noise component is larg-

er than the resistor noise. The graph of Total Noise

Density vs. Matched Source Resistance in the

Typical

Operating Characteristics shows this phenomenon.

Optimal MAX410/MAX412/MAX414 noise performance

and minimal total noise achieved with an equivalent

source resistance of less than 10k

Ω.

Voltage Noise Testing

RMS voltage-noise density is measured with the circuit

shown in Figure 2, using the Quan Tech model 5173

noise analyzer, or equivalent. The voltage-noise density

at 1kHz is sample tested on production units. When

measuring op-amp voltage noise, only low-value, metal

film resistors are used in the test fixture.

The 0.1Hz to 10Hz peak-to-peak noise of the

MAX410/MAX412/MAX414 is measured using the test

+(R +R )

+ 4kT (R +R )

Single/Dual/Quad, 28MHz, Low-Noise,

Low-Voltage, Precision Op Amps

_______________________________________________________________________________________

Figure 1. Total Noise vs. Source Resistance Example

100

100k

+5V

0.1

μF

100

D.U.T

0.1

μF

-5V

MAX410

MAX412

MAX414

Figure 2. Voltage-Noise Density Test Circuit

D.U.T

MAX410

MAX412

MAX414

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