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

4.1 General Case Where Source Output Impedance can be Different Than Load Impedance

Figure 4-1 shows a general approach of combining multiple sources to drive a single load. The assumption is that all the sources are the same amplitude and output impedance and the output impedance of a single source is equal to the load.

General Resistive Matching Network Figure 4-1 General Resistive Matching Network

The value of the matching resistor can be calculated as follows ( Appendix A ):

Equation 1. R 1   =   R S o u r c e × 2 × R L o a d × N × N - 1 N 2 × R L o a d - R S o u r c e - 1
Equation 2. R 2   =           R L o a d × 1 - 2 × R S o u r c e × N - 1 N 2 × R L o a d - R S o u r c e

This matching is possible provided that:

Equation 3. R L o a d R S o u r c e   ≥   2 × N - 1 N 2

For the purpose of analysis, a useful quantity to know the equivalent resistance of the load in parallel with N-1 sources.

Equation 4. R e q = R 1 + R S o u r c e × R 2   +   R L o a d R 1 + R S o u r c e   + N - 1 × R 2 + R L o a d

From this the relative power can be calculated.

Equation 5. P R e l a t i v e = 20 × l o g N × R e q × R L o a d   +   R S o u r c e R e q + R L o a d   +   R S o u r c e × R 2 + R L o a d

The isolation between source A and source B can be defined as the voltage that source A produces across the source impedance of source B. This can be expressed in dB.

Equation 6. I s o l a t i o n = 20 × l o g   R S o u r c e × R e q R e q + R 1   +   R S o u r c e × R 1 + R S o u r c e