How does single-stub matching work?
In single-stub matching, a series line of length d moves the load admittance onto the g = 1 circle of the Smith chart, where y = 1 + jb; a shunt stub then adds susceptance −jb to reach the center. The stub may be open- or short-circuited; open stubs are easier in microstrip.[1]
How do you find d and the stub length?
On the admittance chart, rotate yL clockwise (toward generator) along its constant-|Γ| circle until it meets the g = 1 circle; the angle gives d. Read b there. An open stub with susceptance −b has length ℓ = (λ/2π)·arctan(−b) (add λ/2 if negative); a shorted stub has ℓ = (λ/2π)·arccot(b). There are two solutions per half wavelength; choose the shorter for wider bandwidth.[1]
What is double-stub matching?
Two stubs at fixed positions, adjusted in length, can match a range of loads without moving a stub; certain loads (inside a forbidden region of conductance) cannot be matched for a given spacing. Triple-stub tuners remove the forbidden region. Mechanical slug and stub tuners are used in load-pull systems.[1]
What are radial stubs?
A fan-shaped open stub that provides a broadband low impedance at its point, used for RF grounding and bias decoupling in microstrip circuits; it has lower Q than a straight stub of equivalent electrical length.
Frequently asked questions
Open or short stub?
Open stubs need no via in microstrip; short stubs are preferred in coax and where DC ground is needed.
Why choose the shortest solution?
Shorter lines change less with frequency, so the match is broader.
Do stubs work at harmonics?
Their reactance repeats every half wavelength, so behavior at harmonics must be checked.
See also
References
Online sources accessed October 21, 2026; printed works cited by edition. See all sources.
- “Microwave Engineering, 4th ed.”. D. M. Pozar, Wiley. 2012.