SBOA585 Application note

SBOA585 March 2024 ADS127L11 , ADS127L11 , ADS127L21 , ADS127L21 , PGA855 , PGA855

4.6 PGA855 Current Noise and Source Resistance

The PGA855 input current noise density interacts with the source resistance generating voltage noise. Consider an example where a bridge sensor is measured at the inputs of the amplifier. The resistive bridge sensor has a thermal noise contribution, and the combined resistance of the filter and bridge sensor scales with the PGA input current noise density.

Figure 7-13 shows the derivation of the equivalent input source resistance in the circuit:

Figure 4-4 PGA855 Current Noise and Source Resistance

The circuit at the right of Figure 7-13 shows the simplified PGA855 noise model, where the equivalent input resistance (R_EQ) has a thermal noise density (e_NR) contribution, and the PGA input current noise density (I_{N_P}, I_{N_N}) interacts with R_EQ.

R_EQ is a function of the bridge sensor resistance (R_SEN) and the input filter resistance (R_{IN_FIL}). Equation 12 solves for the equivalent input resistance at each input terminal of the PGA855:

Equation 12.

R_{E Q} = (R_{S E N} | | R_{S E N}) + R_{I N_F I L} = \frac{R_{S E N}}{2} + R_{I N_F I L}

Equation 13 provides the resistor thermal noise spectral density at each input terminal of the PGA855, where T is the absolute temperature in degrees Kelvin, and k is Boltzman's constant, 1.3807 x 10^-23 Joule/°K:

Equation 13.

e_{N_R E Q} = \sqrt{4 \times k \times T \times R_{E Q}}

The equivalent source resistance interacts with the PGA855 current noise density, producing a voltage noise at the input of the instrumentation amplifier. Equation 14 calculates the resulting noise at each input terminal of the PGA855:

Equation 14.

e_{i N} = i_{N} \times R_{E Q}

The total current and resistor noise is computed by combining the resistor thermal noise and current noise components at each amplifier input terminal, using the root-sum-of-squares. Equation 15 provides the total current and resistor noise density:

Equation 15.

e_{i N_R} = \sqrt{({2 \times e}_{i N}^{2} + {2 \times e}_{N_R E Q}^{2})}

Equation 16 calculates the RTI current and resistor noise as a function of the effective noise bandwidth in µVRMS:

Equation 16.

E_{i N_R} = e_{i N_R} \times \sqrt{E N B W}

Table 7-6 shows the RTI current and source resistance noise of the PGA circuit, for R_SEN =2 kΩ, R_{IN_FIL} = 100Ω, and ENBW = 45.5kHz. The resistor and current noise contribution at the input remains constant with PGA gain. When referring this input noise contribution to the output, the input noise needs to be multiplied by the PGA gain.

Table 4-3 PGA855 Input-Referred Current and Source Resistance Noise

i_N (pA / √Hz)	R_EQ (Ω)	e_{N_REQ} (nV / √Hz)	e_iN (nV / √Hz)	E_{iN_R(RTI)} (µVRMS)
0.3	1.1 k	4.26	0.33	1.29