SNAA434 March   2025 LMX2820

 

  1.   1
  2.   Abstract
  3.   Trademarks
  4. 1Introduction
  5. 2Creating Multiple Copies of the Input Signal
    1. 2.1 Skew and Slew Rate Considerations
    2. 2.2 Buffers vs. Resistive Splitters
    3. 2.3 Phase Noise Considerations With Buffers
  6. 3Considerations with Combining Outputs
    1. 3.1 Isolation Between Sources
    2. 3.2 Single-Ended vs. Differential Outputs
    3. 3.3 Losses Due to Combining
  7. 4Resistive Method for Combining Multiple Signals
    1. 4.1 General Case Where Source Output Impedance can be Different Than Load Impedance
    2. 4.2 Special Case Where Source and Load Impedance are the Same
    3. 4.3 Increasing R1 to Improve Isolation
  8. 5Impedance Matching With Reactive Circuit
  9. 6Loss Due to Phase Error
  10. 7Phase Noise Improvement by Combining Multiple Signals
    1. 7.1 Theoretical Improvement for Multiple Signals Designed for in Phase
    2. 7.2 Combining Multiple Signals With a Phase Error
  11. 8Summary
  12. 9References
  13.   A Appendix: Calculations for Resistive Matching Network
  14.   B Appendix: Calculations for Reactive Matching Network
  15.   C Appendix: Calculation of Loss Due to Phase Error

7.2 Combining Multiple Signals With a Phase Error

When a phase error is present, this decreases the signal power, but not the noise power. If this is added to the theoretical noise improvement, then the result for phase noise improvement accounting for phase error can be found..

Equation 16. L n = 10 × l o g n + 10 × l o g 1 + cos ⁡ ϕ 2                                                                                                             n   e v e n 10 × l o g n + 10 × l o g 1 n 2 + 1 - 1 n 2 1 + cos ⁡ ϕ 2 ⁡                                               n   o d d      

Figure 7-1 shows the improvement for combining multiple signals. Note that the combination of an odd number of synthesizers, especially three, seems to give a higher immunity to larger phase errors.

Phase Noise Improvement for Combining Multiple Signals Figure 7-1 Phase Noise Improvement for Combining Multiple Signals