What is the effect of multiple reflections in a cascaded system with poor VSWR at each interface?
Cascaded Mismatch Effects
When multiple components are cascaded, each interface between components can reflect signals. These reflections interact in complex ways that depend on the electrical lengths between all interfaces. The result is a gain versus frequency response that includes ripple contributions from every pair of mismatched interfaces.
For a system with three components and four interfaces, there are six possible reflection pairs, each creating its own ripple pattern with different period and amplitude. The total gain ripple is the vector sum of all these individual ripple contributions, making the worst case potentially large even when individual VSWR specs seem acceptable.
In practice, the most significant reflection pairs are adjacent interfaces (short electrical separation, coherent ripple over wide bandwidth). Widely separated interfaces produce finely-spaced ripple that often averages out over the measurement bandwidth. Adding attenuation between stages reduces all reflection interactions involving that junction, which is why pad attenuators between stages improve overall system flatness.
Frequently Asked Questions
How do I calculate worst-case uncertainty?
For a two-port measurement: Mismatch uncertainty = ±20·log10(1 + |Γ_source|×|Γ_load|) dB. For cascaded systems, add the individual mismatch uncertainties in an RSS (root-sum-square) fashion for typical case, or arithmetically for absolute worst case.
Can I simulate cascaded mismatch?
Yes. Use S-parameter cascading (T-matrix multiplication) with measured S-parameters for each component. Vary the interconnect lengths to see the range of possible gain ripple. This is more accurate than simple VSWR calculations because it accounts for phase information.
When does mismatch matter most?
Mismatch uncertainty is most significant in precision power measurements, gain measurements, and calibration. For communication systems, mismatch causes gain ripple that degrades EVM. For radar systems, mismatch affects transmit power accuracy and receiver gain calibration.