MAX410/MAX412/MAX414
Single/Dual/Quad, 28MHz, Low-Noise,
Low-Voltage, Precision Op Amps
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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:
R
n
= Inverting input effective series resistance
R
p
= Noninverting input effective series resistance
e
n
= Input voltage-noise density at the frequency of
interest
i
n
= 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, R
p
= R3 and R
n
= R1 || R2. In a real appli-
cation, the output resistance of the source driving the
input must be included with R
p
and R
n
. 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
R
p
= 100Ω
R
n
= 100Ω || 100kΩ = 99.9 W
e
n
= 1.5nV/√Hz at 1kHz
i
n
= 1.2pA/√Hz at 1kHz
e
t
= [(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)e
t
= 2.36µV/√Hz at 1kHz.
In general, the amplifier’s voltage noise dominates with
equivalent source resistances less than 200Ω. 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 3kΩ 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 10kΩ.
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
