SBAA661 February   2025 LMX1205

 

  1.   1
  2.   Abstract
  3.   Trademarks
  4. 1Flicker Noise, Noise Floor, and Total Noise
    1. 1.1 Flicker Noise
    2. 1.2 Noise Floor
    3. 1.3 Total Noise
  5. 2Finding the Slew Rate
    1. 2.1 Finding the Slew Rate With an Oscilloscope
    2. 2.2 Calculating the Slew Rate From Power and Frequency
  6. 3Impact of Slew Rate on Phase Noise
    1. 3.1 Modeling of Input Clock Slew Rate, Inherent Device Noise, and Output Jitter
    2. 3.2 Slew Rate Impact on Flicker Noise and Noise Floor
  7. 4Application of Slew Rate Rules to PLL Synthesizers
    1. 4.1 PLL Flicker Noise
    2. 4.2 PLL Figure of Merit
    3. 4.3 Other Areas in PLLs Where Slew Rate has an Impact on Performance
    4. 4.4 Improving PLL Slew Rate for Better Performance
  8. 5Application of Slew Rate Rules to Data Converters
  9. 6Summary
  10. 7References
  11.   Appendix A: Relating Slew Rate, Power, and Frequency
  12.   Appendix B: Relating Slew Rate, Frequency, Jitter, and Phase Noise
  13.   Appendix C: Equations for Data Converters
    1. 8.1 Relating Sampled Signal Slew Rate to SNR
    2. 8.2 Justification That SNR Decreases 1dB per 1dB With Input Power for Slew Rate Limited Case
  14.   Appendix D: Calculations for Data Converter Example

Appendix D: Calculations for Data Converter Example

Rearrange Equation 20 to get the following:

Equation 49. 10 - S N R / 10 = 10 - S N R F i x e d / 10 + 10 - S N R J i t t e r / 10

Also, realize Equation 21 implies that if f increases from 5 to 30MHz, then SNRJitter decreases by 20 × log(6) . Now define SNR1 as the SNR with 5MHz signal and SNR2 as the SNR with 30MHz signal.

Equation 50. 10 - S N R 1 / 10 = 10 - S N R F i x e d / 10 + 10 - S N R J i t t e r / 10
Equation 51. 10 - S N R 2 / 10 = 10 - S N R F i x e d / 10 + 10 - S N R J i t t e r - 20 × l o g ⁡ ( 6 ) 10 = 10 - S N R F i x e d / 10 + 36 × 10 - S N R J i t t e r 10

Equation 50 and Equation 51 are a system of two equations and two unknowns. Subtract Equation 50 from Equation 51 and solve for SNRJitter. Realize that for the 30MHz case, is lower.

Equation 52. S N R J i t t e r = 10 × l o g 10 - S N R 2 10 - 10 - S N R 1 10 35

Once SNRJitter is known, SNRFixed can be found.

Equation 53. S N R F i x e d = 10 × l o g 10 - S N R 1 10 - 10 - S N R J i t t e r 10

Furthermore, we can rearrange Equation 47 to calculate the jitter as perceived by the data converter.

Equation 54. σ = 10 - S N R J i t t e r / 20 2 π × f

Figure 5-1 and Figure 5-2 were used to get the SNR values for the on slew rate limited case to generate Table 5-1 was calculating using Equation 52, Equation 53, and Equation 54.