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 A: Relating Slew Rate, Power, and Frequency

As a sine wave is a very common input clock, a sine wave is useful to derive the slew rate for this signal. Consider a sine wave of the form:

Equation 23. v ( t ) = A × s i n ⁡ ( 2 π × f × t )

The slew rate (SR) can be found by taking the first derivative and evaluating this at the zero crossing.

Equation 24. S R = d v d t t = 0 = 2 π × f × A × c o s ⁡ ( 2 π × f × t ) t = 0 = 2 π × f × A

Peak to Peak voltage is simply 2×A and RMS voltage is A/✓2 . It therefore follows the power is:

Equation 25. P d B m = 10 × l o g ⁡ A 2 2 × 50 Ω 0.001 = 10 × l o g ⁡ 10 × A 2

Power (in dBm) can be related by power by combining Equation 24 and Equation 25.

Equation 26. P = 10 × l o g ⁡ 10 × A 2 = 10 × l o g ⁡ 10 × S R 2 π × f 2

This can be arranged to receive the final result

Equation 27. S R =   2 π × f × 10 P 20 10