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

Slew Rate Impact on Flicker Noise and Noise Floor

The inherent device noise (RMS Voltage Noise) can be thought of as a constant and the jitter results from this can be lower for higher slew rates as implied by the following equation:

Equation 6. R M S   J i t t e r   = R M S   V o l t a g e   N o i s e S l e w   R a t e

If noise of the input buffer dominates and increasing the slew rate (while holding frequency constant) improves significantly, then the phase noise is said to be slew rate limited. At some point, the phase noise from other parts of the device dominate and the phase noise is said to be not slew rate limited. At this point, increasing the slew rate brings diminishing returns, such as only 0.1dB for doubling the slew rate.

Table 3-1 shows fundamental trends for flicker noise and noise floor as a function of output frequency and slew rate. The total phase noise is the sum of the slew rate limited and non-slew rate limited phase noise sources. Derivations for this table are in Section 8.

Table 3-1 Impact of Slew Rate and Carrier Frequency on Flicker Noise and Noise Floor
Noise type Slew rate limited Not slew rate limited
Flicker noise
Equation 7. P N 20 × log f - 20 × log S R
Equation 8. P N 20 × log f
Noise floor
Equation 9. P N 10 × log f - 20 × log S R
Equation 10. P N 10 × log f

In the case of a sine wave or clipped sine wave, the slew rate is proportional to the frequency. Applying this assumption to Table 3-1 gives Table 3-2. One observation is that when the frequency is higher, the device tends to not be slew rate limited and the flicker noise increases with frequency at a faster rate than the noise floor. For this reason, flicker noise becomes a much larger consideration at high frequencies (>10GHz) for buffers.

Table 3-2 Flicker Noise and Noise Floor Trends for a Sine Wave
Noise Type Slew Rate Limited Not Slew Rate Limited
Flicker Noise
Equation 11. P N = c o n s t a n t
Equation 12. P N 20 × log f
Noise Floor
Equation 13. P N - 10 × log f
Equation 14. P N 10 × log f

Data for Table 3-3 data was taken from a graph in the Texas Instruments LMK00301 which demonstrates the behavior of a slew rate limited noise floor. As predicted, quadrupling the frequency while holding the slew rate constant results in about a 6dB degradation of the noise floor. Doubling the slew rate while keeping the frequency constant results in a 6dB improvement in the noise floor.

Table 3-3 LMK00301 Noise Floor as a Function of Slew Rate and Frequency
Slew rate (V/µs) f=156.26MHz f=625MHz
1 -148 -143.5
1.5 -152 -145.5
2 -154.5 -149
2.5 -156 -150.5

Figure 3-2 gives a hypothetical example that illustrates general trends for input buffer noise assuming a noiseless sine wave input clock of constant amplitude. The flicker noise starts out as constant versus clock frequency because the fact that the noise is slew rate limited counterbalances the general tendency to increase in frequency. After about 100MHz, the flicker noise increases due to not being slew rate limited. The noise floor is slew rate limited at lower frequencies and therefore actually improves for a while as the frequency is increased. Around 40MHz, the slew rate is sufficient and then the noise floor starts to degrade with frequency.

 Flicker Noise and Noise Floor
                    Trends With Frequency Figure 3-2 Flicker Noise and Noise Floor Trends With Frequency

Figure 3-3 shows the noise floor data taken from the Texas Instruments LMX1214 high frequency divider buffer and demonstrates the general bowl shaped trend for noise floor similar to Figure 3-2.

 LMX1214 Noise Floor Trends vs.
                    Frequency Figure 3-3 LMX1214 Noise Floor Trends vs. Frequency

Table 3-4 can be derived by assuming that frequency is constant, power is changing, and applying Equation 5 taking Table 3-1. This illustrates that both the flicker noise and noise floor are impacted in the same way by input power for this case. Figure 3-4 illustrates this in terms of a phase noise degradation.

Table 3-4 Flicker Noise and Noise Floor Assuming Slew Rate is Proportional to Frequency
Noise Type Slew Rate Limited Not Slew Rate Limited
Flicker noise
Equation 15. P N - p
Equation 16. P N =   c o n s t a n t
Noise floor
Equation 17. P N - p
Equation 18. P N =   c o n s t a n t
 Phase Noise Degradation as a
                    Function of Slew Rate Figure 3-4 Phase Noise Degradation as a Function of Slew Rate