MT-050| Application Note

MT-050 TUTORIAL
Op Amp Total Output Noise Calculations for Second-Order System

The total output noise for a single-pole system was analyzed in Tutorial MT-049. The circuit shown in Figure 1 below represents a second-order system, where capacitor C1 represents the source capacitance, stray capacitance on the inverting input, the input capacitance of the op amp, or any combination of these. C1 causes a breakpoint in the noise gain, and C2 is the capacitor that must be added to obtain stability.
C2 C1

VN,R2

B
VN,R1 R1

4kTR1 VN,R3 R3

IN VN

4kTR2

VOUT

4kTR3

IN+

Figure 1: Op Amp Noise Model with Reactive Elements (Second-Order System) Because of C1 and C2, the noise gain is a function of frequency, and has peaking at the higher frequencies (assuming C2 is selected to make the second-order system critically damped). A flat noise gain can be achieved if one simply makes R1 C1 = R2 C2. But in the case of current-to-voltage converters, however, R1 is typically a high impedance, and the method doesn't work. Maximizing the signal bandwidth in these situations is somewhat complex and is treated in detail in Tutorial MT-059. A dc signal applied to input A (B being grounded) sees a gain of 1 + R2/R1, the low frequency noise gain. At higher frequencies, the gain from input A to the output becomes 1 + C1/C2 (the high frequency noise gain). The closed-loop bandwidth fcl is the point at which the noise gain intersects the open-loop gain. A dc signal applied to B (A being grounded) sees a gain of R2/R1, with a high frequency cutoff determined by R2-C2. Bandwidth from B to the ou
tput is 1/2R2C2.

Rev.0, 10/08, WK

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