LT1567
14
1567fa
–
+
R2
V
OUT
R1
R
S
R
P
NOISE AT V
OUT
IN V
RMS
= V
ON
IN V/√Hz • √f
NBW
f
NBW
= NOISE BANDWIDTH
V
ON
=
IF V
SN
AND R
S
= 0
THEN
+ 1 • V
N
2
+ • (V
R1
2
+ V
SN
2
) + V
R2
2
+ (I
N
• R2)
2
2
V
S
C
S
1567 AP01
+
–
()
R2
R1 + R
S
2
()
R2
R1 + R
S
V
ON
= + 1 • V
N
2
+ • V
R1
2
+ V
R2
2
+ (I
N
• R2)
2
2
()
R2
R1
2
()
R2
R1
V
ON
is the voltage noise density in V/√Hz at the inverter’s
output.
V
N
is the op amp’s voltage noise density in V/√Hz.
I
N
is the op amp’s current noise density in A/√Hz.
V
SN
is the voltage noise density of the input voltage source
V
S
with source resistance R
S
. (If V
SN
is less than one-half
the noise of resistor R1, then the calculation error when
omitting V
SN
is less than 4.3%.)
V
R1
and V
R2
is the voltage noise density of the thermal
noise of resistors (R1 + R
S
) and R2 respectively. Resistor
R
S
is typically smaller than R1 and is omitted from noise
calculations. The voltage noise density of the thermal
noise of a resistor R is approximately 0.128x√RnV/√Hz at
25°C.
The R
P
resistor noise at the op amp’s plus input is equal
to √(kT/C
S
) and is omitted from noise calculations. (If
C
S
= 0.1µF, the R
P
noise is 0.2µV
RMS
at 25°C, k = 1.38x
10
–23
and T = 273°C + 25°C.)
The noise bandwidth (f
NBW
) is greater than a circuit’s
–3dB bandwidth. (For a 1st, 2nd or 3rd order Butterworth
filter, f
NBW
is 1.57x, 1.22x and 1.15x respectively the –
3dB bandwidth.)
V
ON
=
V
ON
= 5.29nV/√Hz
+ 1 • (1.4 •10
–9
)
2
+ • (0.128 •10
–9
• √604)
2
+ (0.128 • 10
–9
• √604)
2
+ (10
–12
• 604)
2
2
()
604
604
2
()
604
604
Example: Calculate V
ON
, the voltage noise density of an
LT1567 op amp inverter for R1 = R2 = 604Ω. With
V
N
= 1.4nV/√Hz and I
N
= 1pA/√Hz.
APPE DIX: OUTPUT OISE OF A OP A P I VERTI G A PLIFIER
UUUWUUW
