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

5 Application of Slew Rate Rules to Data Converters

For data converters, one key metric is the signal to noise ratio, SNR. The signal to noise ratio is a combination of a fixed jitter (dependent on thermal noise, resolution, and other frequency-independent factors) and a SNR due to jitter.

Equation 20. S N R = - 10 × l o g 10 ^ ( - S N R J i t t e r / 10 + 10 ^ ( - S N R F i x e d / 10

The SNR due to jitter can be calculated as follows (Section 8):

Equation 21. S N R J i t t e r = - 20 × l o g 2 π × f × σ

Furthermore, the jitter (not including sampled signal) is a combination of the clock jitter and the aperture jitter.

Equation 22. σ t = σ C l o c k 2 + σ A p e r t u r e 2

Finally, in Section 8, it is shown that the SNR for a slew rate limited case improves 1dB per 1dB with the clock power. Figure 5-1 puts these equations to actual measurements which are described in more depth in Practical Clocking Considerations That Give Your Next High-Speed Converter Design an Edge. In this case, a input clock of fixed 25MHz frequency, but variable amplitude was used to clock an analog to digital converter for both a 5MHz and 30MHz sampled signal. The slew rate limited trend lines show a dB/1dB trend and a separation between the 5MHz and 30MHz trend lines is 20×log(30MHz/5MHz) = 15.6dB. At lower amplitudes (like -15dBm), the performance is slew rate limited and we also see this same 15.6dB separation between the measurements for the 5MHz and 30MHz clocks. At higher input amplitudes, some other factors dominate that are not impacted by the slew rate. The result of this is there is not the full 15.6dB difference in the curves, but is actually closer to about 5dB at higher input power levels.

Data Converter SNR vs Input Clock Power for Rohde and Schwarz SMA100B Signal Generator Figure 5-1 Data Converter SNR vs Input Clock Power for Rohde and Schwarz SMA100B Signal Generator

To illustrate the impact of jitter on the sampled signal, the experiment was repeated with a signal generator with higher noise as shown in Figure 5-2. For both of these figures, the slew rate limited case for both sampling frequencies is degraded by 3dB by using the noisier signal generator. For the non-slew rate limited case, the signal generator makes 2dB difference for a 5MHz sampling frequency and 8dB difference for a 30MHz sampling frequency. For both figures, one can infer the portion of SNR that is fixed and the portion that is due to jitter as shown in Table 5-1. The method for doing this is presented in Section 8. In addition to the clock jitter and aperture jitter as mentioned in Equation 34, this jitter also includes that of the sampled signal.

Data Converter SNR vs Input Clock Power for Agilent 4438C Signal Generator Figure 5-2 Data Converter SNR vs Input Clock Power for Agilent 4438C Signal Generator
Table 5-1 Calculation of Inferred Jitter
Signal Generator Jitter f SNR SNRJitter SNRFixed
Rohde & Schwarz SMA100B 440.91 fs 5MHz 85 97.092 85.277
30MHz 80 81.529
Agilent 4438C 1296.71 fs 5MHz 83 87.800 84.747
30MHz 72 87.800

From the data sheet for the ADC3683, the aperture jitter is stated to be 180 fs. The jitter stated in Table 5-1 is the combination of the clock jitter and aperture jitter. In this case, the clock jitter is dominating over the aperture jitter.