SBOA585 March   2024 ADS127L11 , ADS127L11 , ADS127L14 , ADS127L14 , ADS127L18 , ADS127L18 , ADS127L21 , ADS127L21 , PGA849 , PGA849 , PGA855 , PGA855

 

  1.   1
  2.   Abstract
  3.   Trademarks
  4. 1PGA855 and ADS127L21, 24-Bit, Delta-Sigma ADC Driver Circuit
  5. 2PGA855 Analog Front-End Filters
  6. 3ADS127Lx1 Delta-Sigma ADC and Digital Filter
  7. 4Approximate PGA855 Intrinsic Noise Analysis
    1. 4.1 Simplified Noise Model for the PGA855
    2. 4.2 PGA855 Spectral Noise Density vs Frequency
    3. 4.3 PGA855 Effective Noise Bandwidth
    4. 4.4 PGA855 Low Frequency (1/f) Noise Calculation
    5. 4.5 PGA855 Voltage Broadband Noise
    6. 4.6 PGA855 Current Noise and Source Resistance
    7. 4.7 PGA855 Total Noise
  8. 5PGA855 and ADS127Lx1 System Noise
  9. 6PGA855 and ADS127Lx1 SNR and Noise Calculator
  10. 7PGA855 and ADS127Lx1 FFT Measured Performance
  11. 8Summary
  12. 9References

4.3 PGA855 Effective Noise Bandwidth

Before calculating the RMS noise, note the noise bandwidth of the circuit is not the same as the signal bandwidth given by the filter corner, therefore the noise bandwidth must be corrected. The amount of bandwidth correction depends on the filter order.

The effective noise bandwidth (ENBW) is the bandwidth of a designed for rectangular filter that allows the same amount of power to pass, as the cumulative bandwidth of the analog filters in the circuit. Also, the ENBW is the bandwidth of a rectangular filter, which produces the equivalent integrated noise power as that of the actual filters in the design. However, the frequency response of the analog filter has a roll-off low-pass response with the slope as shown in Figure 2-2.

One method to calculate a low-pass filter’s ENBW is to calculate the noise curve using the direct-integration method of Equation 5. Alternatively, use Equation 6, which relates the Nth order low-pass filter response to the ENBW:

Equation 6. ENBWPGA855= Kn×f-3dB

In Equation 6, the Kn constant is the brick-wall correction factor for a given Nth order low-pass filter. The Kn factor is 1.57 and 1.22 for a 1st order and 2nd order low-pass filter respectively. In this circuit, the PGA855 includes three low-pass filters, but the dominant pole occurs at 677-kHz, while the other poles occur at much higher frequencies; hence, the response can be roughly approximated to a 2nd order filter with a Kn correction factor of 1.22. For more information about how this formula was derived, see the TI Precision Labs training series on operational amplifier noise (Op-Amp Noise: Calculating RMS Noise).

The effective noise bandwidth of the system can be approximated if either Equation 7, or Equation 8, is true:

Equation 7. If f-3dBADC≤ f-3dBPGA855→ ENBWSystem ≅ f-3dBADC 
Equation 8. If f-3dB(ADC) ≥ 10 ×f-3dB(PGA855)  → ENBWSystem ≅ ENBWPGA855  

Note that in Equation 8, the system ENBW can be approximated to the PGA855 ENBW, but not the PGA855 circuit cutoff frequency.

If neither Equation 7 or Equation 8 is true, such that f-3dB(ADC) is between f-3dB(PGA855) and 10 × f-3dB(ADC), determine the combined system bandwidth using integration or other numerical methods.(2)

In this circuit, the bandwidth of the PGA855 front end is 677kHz typical, while the f–3dB corner frequency of the ADS127L21 digital filter is 45.5kHz. Therefore, the system ENBW is limited by the ADC sinc4 digital-filter. Hence, an ENBW of the system of 45.5kHz can now be used to calculated the noise contribution of the analog front end circuit.