--- title: "Admittance chart and single stub for 80+j100 Ω" subject: "RF and Microwave Engineering" chapter: 2 key: "semester_7/rf_and_microwave_engineering:admittance-chart-single-stub" source: https://www.bctengineer.com/q/semester_7/rf_and_microwave_engineering/admittance-chart-single-stub site: BCT Engineering --- # Admittance chart and single stub for 80+j100 Ω RF and Microwave Engineering · Chapter 2: RF and Microwave Transmission Lines - Asked in: 2072 Asoj, 2+8 marks - Video: [Single shunt stub matching network using smith chart by Dr. Niraj Kumar VIT Chennai](https://www.youtube.com/watch?v=r78seP5upKA) — RF Design Basics - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/rf_and_microwave_engineering/admittance-chart-single-stub - Whole chapter: https://www.bctengineer.com/md/semester_7/rf_and_microwave_engineering/chapter-2 ## Question What is admittance chart? A load impedance of ZL = 80+j100 is connected to a microstrip transmission line. Find the size and placement of the matching stub. Use single stub shunt tuning short and open stubs. ## Short answer An admittance chart is the Smith chart rotated 180° reading normalized admittance g+jb. For ZL=80+j100 Ω on 50 Ω line, single shunt stub: short stub at d=0.2295λ, l=0.0867λ; open stub at d=0.3697λ, l=0.1633λ. ## Answer #### Admittance chart An **admittance chart** is the Smith chart read in normalised admittance y = g + jb instead of z. It is the impedance chart rotated by 180°. Constant-g circles touch at the short-circuit point, and the upper half then means inductive susceptance (−jb). It is used for **shunt** elements (stubs, shunt L or C), because shunt admittances simply add. A point on the Z-chart becomes its admittance when moved λ/4 (180°) around the VSWR circle. #### Single-stub design **Assumption:** the microstrip line has Z0 = 50 Ω (not stated). ZL = 80 + j100 Ω. Shunt stub, both short and open designs. #### Step 1: Normalise and plot the load ```text zL = ZL/Z0 = 1.600 + j2.000 ΓL = (zL − 1)/(zL + 1) = 0.637∠35.7° VSWR = (1 + |Γ|)/(1 − |Γ|) = 4.503 ``` Draw the constant-VSWR circle through zL (zL is at 0.2004λ WTG). #### Step 2: Convert to admittance (shunt stub) Move zL by 180° on the VSWR circle, which is the same as moving λ/4: ```text yL = 1/zL = 0.244 − j0.305 (0.4504λ WTG) ``` #### Step 3: Move toward the generator to the g = 1 circle The VSWR circle cuts the g = 1 circle at two points: ```text y1 = 1.000 + j1.651 at 0.1799λ WTG y2 = 1.000 − j1.651 at 0.3201λ WTG d1 = 0.2295λ from the load d2 = 0.3697λ from the load ``` #### Step 4: Stub susceptance and length The stub must cancel the susceptance: bstub = −b. - For a short-circuited stub: y = −j cot βl, so l = (1/2π)·cot⁻¹(−b). Measure toward the generator from the short-circuit point (y = ∞; with y plotted on an ordinary Smith chart, this is the right end, 0.25λ WTG). - For an open-circuited stub: y = j tan βl, so l = (1/2π)·tan⁻¹(b). Measure toward the generator from the open-circuit point (y = 0; the left end, 0λ WTG). ```text Sol 1: bstub = −1.6508 short stub l = 0.0867λ open stub l = 0.3367λ Sol 2: bstub = +1.6508 short stub l = 0.4133λ open stub l = 0.1633λ ``` | Solution | Stub position d | Short stub l | Open stub l | |---|---|---|---| | 1 | 0.2295λ | 0.0867λ | 0.3367λ | | 2 | 0.3697λ | 0.4133λ | 0.1633λ | **Answer (choice):** short stub, solution 1 (d = 0.2295λ, l = 0.0867λ). Open stub, solution 2 (d = 0.3697λ, l = 0.1633λ). ```text Microstrip: stub (l) || ● via (short) / open end || ===========##==== d ====[80+j100 Ω] ``` **Check:** y(d) = 1 ± j1.651. The stub cancels ±j1.651, so the line is matched (VSWR goes from 4.50 to 1). ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is the admittance chart? A. The Smith chart read in y = g + jb, the impedance chart rotated 180° B. A chart for series elements C. A chart without VSWR circles D. A chart for lossy lines Answer: A. It is the impedance chart rotated by 180° and used for shunt elements. (Key point: Admittance chart) 2. For ZL = 80 + j100 (Z0 = 50), where is the stub placed? A. At the load B. d = 0.2295λ (solution 1) or 0.3697λ (solution 2) C. d = 0.5λ D. d = 0.125λ Answer: B. The VSWR circle meets g = 1 at two points giving d1 = 0.2295λ and d2 = 0.3697λ. (Key point: Stub position) 3. At y = 1 + j1.651, the stub must supply: A. +j1.651 B. -j1 C. -j1.651 D. 0 Answer: C. The stub cancels the line susceptance. (Key point: Stub susceptance) 4. Which choice is given for the open stub? A. Solution 1 (l = 0.3367λ) B. Both C. Neither D. Solution 2 (d = 0.3697λ, l = 0.1633λ) Answer: D. Open stub solution 2 is the shorter at 0.1633λ. 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