_
+
RF
RS
RG
eRg
eRf
eRs
en
IN+
Noiseless
IN
eni
eno
e
ni +
en
2
) IN )
R
S
2
) IN–
R
F
R
G
2
) 4 kTRs ) 4 kT RF RG
Where:
k = Boltzmann’s constant = 1.380658
× 1023
T = Temperature in degrees Kelvin (273 +
°C)
RF || RG = Parallel resistance of RF and RG
eno + eni AV + eni 1 )
R
F
R
G
(Noninverting Case)
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SLOS224G – JULY 1999 – REVISED MARCH 2010
NOISE CALCULATIONS AND NOISE FIGURE
Noise can cause errors on very small signals. This is especially true when amplifying small signals. The noise
model for the THS403x, shown in
Figure 52, includes all of the noise sources as follows:
en = Amplifier internal voltage noise (nV/√Hz)
IN+ = Noninverting current noise (pA/
√Hz)
IN– = Inverting current noise (pA/
√Hz)
eRx = Thermal voltage noise associated with each resistor (eRx = 4 kTRx)
Figure 52. Noise Model
The total equivalent input noise density (eni) is calculated by using the following equation:
(1)
To get the equivalent output noise of the amplifier, just multiply the equivalent input noise density (eni) by the
overall amplifier gain (AV).
(2)
As the previous equations show, to keep noise at a minimum, small-value resistors should be used. As the
closed-loop gain is increased (by reducing RG), the input noise is reduced considerably because of the parallel
resistance term. This leads to the general conclusion that the most dominant noise sources are the source
resistor (RS) and the internal amplifier noise voltage (en). Because noise is summed in a root-mean-squares
method, noise sources smaller than 25% of the largest noise source can be effectively ignored. This advantage
can greatly simplify the formula and make noise calculations much easier to calculate.
For more information on noise analysis, refer to the application note, Noise Analysis for High-Speed Op Amps
Copyright 1999–2010, Texas Instruments Incorporated
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