SBOSAG5 Data sheet

SBOSAG5 December 2024 – December 2024 TLV2888

PRODMIX

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sbosag5_oa

7.1.1 Basic Noise Calculations

Low-noise circuit design requires careful analysis of all noise sources. In many cases, external noise sources can dominate; consider the effect of source resistance on overall op-amp noise performance. Total noise of the circuit is the root-sum-square combination of all noise components.

The resistive portion of the source impedance produces thermal noise proportional to the square root of the resistance. The source impedance is usually fixed; consequently, select op amp and the feedback resistors that minimize the respective contributions to the total noise.

Figure 7-1 shows the noninverting op-amp circuit configurations with gain. Figure 7-2 shows the inverting op-amp circuit configurations with gain. In circuit configurations with gain, the feedback network resistors also contribute noise. In general, the current noise of the op amp reacts with the feedback resistors to create additional noise components. However, the low current noise of the TLVx888 means that the current noise contribution can be ignored.

The feedback resistor values can generally be chosen to make these noise sources negligible. Low impedance feedback resistors load the output of the amplifier. The equations for total noise are shown for both configurations.

For additional resources on noise calculations, visit TI Precision Labs.

TLV2888 Noise Calculation
in Noninverting Gain Configurations

Figure 7-1 Noise Calculation in Noninverting Gain Configurations

Equation 1.

E_{o} = e_{o} \sqrt{{B W}_{N}} [V_{R M S}]

Equation 2.

e_{o} = (1 + \frac{R_{2}}{R_{1}}) \sqrt{{e_{S}}^{2} + {e_{N}}^{2} + {(e_{R_{1} | | R_{2}})}^{2} + {(i_{N} R_{S})}^{2} + {(i_{N} \frac{R_{1} R_{2}}{R_{1} + R_{2}})}^{2}} [\frac{V}{\sqrt{H z}}]

Equation 3.

e_{S} = \sqrt{4 k_{B} T (K) R_{S}} [\frac{V}{\sqrt{H z}}]

Equation 4.

e_{R_{1} | | R_{2}} = \sqrt{4 k_{B} T (K) (\frac{R_{1} R_{2}}{R_{1} + R_{2}})} [\frac{V}{\sqrt{H z}}]

Equation 5.

k_{B} = 1.38065 \times 10^{- 23} [\frac{J}{K}]

Equation 6.

T (K) = 2.37.15 + T (° C) [K]

where

e_n is the voltage noise spectral density of the amplifier. For the TLVx888, e_n = 7.5nV/√Hz at 1kHz)
e_o is the total noise density
e_S is the thermal noise of R_S
e_{R₁ ||
R₂} is the thermal noise of R₁ || R₂
k_B is the Boltzmann constant
T(K) is the temperature in kelvins

TLV2888 Noise Calculation
in Inverting Gain Configurations

Figure 7-2 Noise Calculation in Inverting Gain Configurations

Equation 7.

E_{o} = e_{o} \sqrt{{B W}_{N}} [V_{R M S}]

Equation 8.

e_{o} = (1 + \frac{R_{2}}{R_{S} + R_{1}}) \sqrt{{e_{N}}^{2} + {(e_{R_{1} + R_{S} | | R_{2}})}^{2} + {(i_{N} \frac{(R_{S} + R_{1}) R_{2}}{R_{S} + R_{1} + R_{2}})}^{2}} [\frac{V}{\sqrt{H z}}]

Equation 9.

e_{R_{1} + R_{S} | | R_{2}} = \sqrt{4 k_{B} T (K) (\frac{(R_{S} + R_{1}) R_{2}}{R_{S} + R_{1} + R_{2}})} [\frac{V}{\sqrt{H z}}]

Equation 10.

k_{B} = 1.38065 \times 10^{- 23} [\frac{J}{K}]

Equation 11.

T (K) = 2.37.15 + T (° C) [K]

where

e_n is the voltage noise spectral density of the amplifier. For the TLVx888, e_n = 7.5nV/√Hz at 1kHz)
e_o is the total noise density
e_S is the thermal noise of R_S
e_{(R₁ + R_S)
|| R₂} is the thermal noise of (R₁ + R_S) || R₂
k_B is the Boltzmann constant
T(K) is the temperature in kelvins