LT1115
8
1115fa
Therefore, to realize truly low noise performance it is
important to understand the interaction between voltage
noise (e
n
), current noise (i
n
) and resistor noise (r
n
).
Total Noise vs Source Resistance
The total input referred noise of an op amp is given by
e
t
= [e
n
2
+ r
n
2
+ (i
n
R
eq
)
2
]
1/2
where R
eq
is the total equivalent source resistance at
the two inputs
and r
n
= √4kTR
eq
= 0.13√R
eq
in nV/√Hz at 25°C
As a numerical example, consider the total noise at 1kHz
of the gain of 1000 amplifier shown below.
R
eq
= 100Ω + 100Ω||100k ≈ 200Ω
r
n
= 0.13√200 = 1.84nV/√Hz
e
n
= 0.85nV/√Hz
i
n
= 1.0pA/√Hz
e
t
= [0.85
2
+ 1.84
2
+ (1.0 x 2.0)
2
]
1/2
= 2.04nV/√Hz
output noise = 1000 e
t
= 2.04µV/√Hz
At very low source resistance (R
eq
< 40Ω) voltage noise
dominates. As R
eq
is increased resistor noise becomes the
largest term—as in the example above—and the LT1115’s
voltage noise becomes negligible. As R
eq
is further
increased, current noise becomes important. At 1kHz,
when R
eq
is in excess of 20kΩ, the current noise
component is larger than the resistor noise. The Total
Noise vs Matched Source Resistance plot in the Typical
Performance Characteristics section, illustrates the above
calculations.
–
+
100Ω
100k
100Ω
LT1115
LT1115 • AI01
The plot also shows that current noise is more dominant
at low frequencies, such as 10Hz. This is because resistor
noise is flat with frequency, while the 1/f corner of current
noise is typically at 250Hz. At 10Hz when R
eq
> 1kΩ, the
current noise term will exceed the resistor noise.
When the source resistance is unmatched, the Total Noise
vs Unmatched Source Resistance plot should be con-
sulted. Note that total noise is lower at source resistances
below 1kΩ because the resistor noise contribution is less.
When R
s
> 1kΩ total noise is not improved, however. This
is because bias current cancellation is used to reduce
input bias current. The cancellation circuitry injects two
correlated current noise components into the two inputs.
With matched source resistors the injected current noise
creates a common-mode voltage noise and gets rejected
by the amplifier. With source resistance in one input only,
the cancellation noise is added to the amplifier’s inherent
noise.
In summary, the LT1115 is the optimum amplifier for
noise performance—provided that the source resistance
is kept low. The following table depicts which op amp
manufactured by Linear Technology should be used to
minimize noise—as the source resistance is increased
beyond the LT1115’s level of usefulness.
Best Op Amp for Lowest Total Noise vs Source Resistance
Note 1: Source resistance is defined as matched or unmatched, e.g.,
R
S
= 1kΩ means: 1kΩ at each input, or 1kΩ at one input and zero at the
other.
SOURCE RESISTANCE BEST OP AMP
(NOTE 1) AT LOW FREQ (10Hz) WIDEBAND (1kHz)
0 to 400Ω LT1028/1115 LT1028/1115
400Ω to 4kΩ LT1007/1037 LT1028/1115
4kΩ to 40kΩ LT1001* LT1007/1037
40kΩ to 500kΩ LT1012* LT1001*
500kΩ to 5MΩ LT1012* or LT1055 LT1012*
> 5M LT1055 LT1055
*These op amps are best utilized in applications requiring less bandwidth
than audio.
APPLICATIO S I FOR ATIO
WUUU
