Here B 1 = – B L Y 0 ± Y 0 G L ( 1 ( tan β d ) 2 ) – G L 2 ( tan β d ) 2 tan β d, and B 2 = G L Y 0 ± Y 0 Y 0 G L ( 1 ( tan β d ) 2 ) – G L 2 ( tan β d ) 2 G L tan β d. ![]() The lengths of stubs are: l 1 o p e n λ = 1 2 π tan – 1 ( B 1 Y 0 ), l 2 o p e n λ = 1 2 π tan – 1 ( B 2 Y 0 ), l 1 s h o r t λ = – 1 2 π tan ( Y 0 B 1 ), l 2 s h o r t λ = – 1 2 π tan ( Y 0 B 2 ). Here G L = Y 0 1 ( tan β d ) 2 2 ( tan β d ) 2 1 ± 1 – 4 ( tan β d ) 2 ( Y 0 – B L tan β d B 1 tan β d ) 2 Y 0 2 ( 1 tan β d 2 ) 2. 11 Lecture A single stub must be repositioned to match for different loads. Then for admittance of a second stub we have: Y 2 = Y 0 G L j ( B L B 1 Y 0 tan β d ) Y 0 j ( tan β d ) ( G L j B 1 j B L ), EE334 - Double Stub Matching This is not in the book but will be on the midterm. Here is an analytical solution for double stub tuning.Īdmittance of the first stub Y 1 = G L j ( B L B 1 ), where load admittance Y L = G L j B L. Here two stubs are shunted to the main transmission line in a fixed position. Double stub tuning is schematically depicted in F igure 3. Consider the follow transmission line structure, with a shunt stub: The two design parameters of this matching network are. This type of tuning is more favourable from a practical point of view. Single stub matching using Smith chart Impedance matching in transmission lines Pdf Shunt Stub Tuning. The stubs lengths are (for short cut and open stub): l o p e n λ = 1 2 π tan – 1 Z 0 X, w h e r e X = G L 2 a – ( Y 0 – c B L ) ( B L c Y 0 ) Y 0 ( G L 2 ( B L Y 0 c ) 2 ) a n d c = B L ± G L Y 0 ( Y 0 – G L ) 2 G L Y 0 B L 2 G L – Y 0 l s h o r t λ = – 1 2 π tan – 1 X Z 0, w h e r e X = G L 2 a – ( Y 0 – c B L ) ( B L c Y 0 ) Y 0 ( G L 2 ( B L Y 0 c ) 2 ) a n d c = B L ± G L Y 0 ( Y 0 – G L ) 2 G L Y 0 B L 2 G L – Y 0.ĭouble-stub matching is a type of matching where two stubs are shunted to main transmission line on a fixed distance. Then, the distance between stub and load can be found as: d λ = 1 2 π tan – 1 Z L ± R L ( Z 0 – R L ) 2 X L 2 Z 0 R L – Z 0, i f Z L ± R L ( Z 0 – R L ) 2 X L 2 Z 0 R L – Z 0 > 0 1 2 π ( 1 tan – 1 Z L ± R L ( Z 0 – R L ) 2 X L 2 Z 0 R L – Z 0 ), i f Z L ± R L ( Z 0 – R L ) 2 X L 2 Z 0 R L – Z 0 0 1 2 π ( π tan – 1 ( B L ± G L Y 0 ( Y 0 – G L ) 2 G L Y 0 B 2 L G L – Y 0 ) ), i f B L ± G L Y 0 ( Y 0 – G L ) 2 G L Y 0 B 2 L G L – Y 0 < 0 īy v arying the parameter distance to the load, we can achieve the desired values of reactance and susceptance.įor this type of impedance, matching parameters and are important. Īdmittance and impedance are related with Y = 1 X. The parameter d is chosen so the impedance is Z = Z 0 j X, where reactance is – j X. Series stub tuning is depicted in F igure 2. For my dummy load, the matching scheme on the Smith chart is shown in Figure 3 a short series transmission line, with a stub moving clockwise to the 50 ohm. ![]() We are not in this case, physically moving down the line. The parameter d is chosen, so admittance is Y = Y 0 j B, and susceptance – j B. We sometimes think of the action of the tuning stub as allowing us to move in along the Y s Y 0 to get to the center of the Smith Chart, or to a match, as shown in Figure 6.15. Parallel stub tuning is depicted in Figure 1. If the normalized admittance of the line, at the first stub location, falls inside a certain forbidden conductance. Co– planar waveguides or slot lines are usually connected to a stub in series microstrips in parallel. ![]() ![]() A stub is usually made as part of circuit which allows the avoidance of lumped elements. \cong -0.Stub tuning is an impedance matching technique, when an open-circuited or short-circuited transmission line is connected to the main transmission line.
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