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LT1567

1567fa

VOUT

NOISE AT VOUT IN VRMS = VON IN V/√Hz • √fNBW

fNBW = NOISE BANDWIDTH

VON =

IF VSN AND RS = 0

THEN

+ 1

• VN

2 +

• (VR1

2 + V

2) + V

2 + (I

N • R2)

1567 AP01

–

()

R1 + RS

()

R1 + RS

VON =

+ 1

• VN

2 +

• VR1

2 + V

2 + (I

N • R2)

()

()R2

VON is the voltage noise density in V/√Hz at the inverter’s

output.

VN is the op amp’s voltage noise density in V/√Hz.

IN is the op amp’s current noise density in A/√Hz.

VSN is the voltage noise density of the input voltage source

VS with source resistance RS. (If VSN is less than one-half

the noise of resistor R1, then the calculation error when

omitting VSN is less than 4.3%.)

VR1 and VR2 is the voltage noise density of the thermal

noise of resistors (R1 + RS) and R2 respectively. Resistor

RS 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

°C.

The RP resistor noise at the op amp’s plus input is equal

√(kT/CS) and is omitted from noise calculations. (If

CS = 0.1µF, the RP noise is 0.2µVRMS at 25°C, k = 1.38x

10–23 and T = 273

°C + 25°C.)

The noise bandwidth (fNBW) is greater than a circuit’s

–3dB bandwidth. (For a 1st, 2nd or 3rd order Butterworth

filter, fNBW is 1.57x, 1.22x and 1.15x respectively the –

3dB bandwidth.)

VON =

VON = 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

()

604

()604

604

Example: Calculate VON, the voltage noise density of an

LT1567 op amp inverter for R1 = R2 = 604

Ω. With

VN = 1.4nV/√Hz and IN = 1pA/√Hz.

APPE DIX: OUTPUT OISE OF A OP A P I VERTI G A PLIFIER

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