Digital Phase Shifter Resolution
An N-bit digital phase shifter — the beam-steering element of a phased array — provides 2N discrete phase states spaced by one least-significant bit (LSB). The finite step causes a quantization error that raises array sidelobes. This tool gives the LSB, the number of states, the RMS quantization error, and the closest achievable setting for a target phase.
Equations & Parameters ▸
\(\text{LSB} = \dfrac{360^\circ}{2^{N}} \qquad \text{states} = 2^{N} \qquad \sigma_\phi = \dfrac{\text{LSB}}{\sqrt{12}}\)
| N | Number of control bits (typically 3–6). |
| LSB | Smallest phase step the shifter can make (degrees). |
| σφ | RMS quantization phase error for uniformly distributed rounding. |
| Target | Desired phase (deg), optional — gives the nearest achievable state and its error. |
References: R. C. Hansen, Phased Array Antennas, 2nd ed., Wiley, 2009. · R. J. Mailloux, Phased Array Antenna Handbook, 3rd ed., Artech House, 2017.
Inputs
bits
Resolutiondeg
Desired settingResults
Resolution
LSB step—
Number of states—
RMS quant. error—
Target
Nearest phase—
Error—
Diagram