--- title: "Immittance chart and duality parameters" subject: "RF and Microwave Engineering" chapter: 2 key: "semester_7/rf_and_microwave_engineering:immittance-chart-duality" source: https://www.bctengineer.com/q/semester_7/rf_and_microwave_engineering/immittance-chart-duality site: BCT Engineering --- # Immittance chart and duality parameters RF and Microwave Engineering · Chapter 2: RF and Microwave Transmission Lines - Asked in: 2075 Bhadra, 10 marks - Video: [Full Color Smith Chart and Lumped Element Matching - Lesson 6](https://www.youtube.com/watch?v=fIaIcJEnseA) — EMViso - 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/immittance-chart-duality - Whole chapter: https://www.bctengineer.com/md/semester_7/rf_and_microwave_engineering/chapter-2 ## Question What do you understand by immittance chart? Sketch it. List out all duality parameters vital to designing microwave networks. ## Short answer An immittance (ZY Smith) chart overlays impedance (r,x) and admittance (g,b) circles on one Γ plane, so both z and y are read directly without λ/4 rotation. It has a matched centre, OC/SC touch points, upper half inductive, lower capacitive. Key dual pairs: Z↔Y, R↔G, X↔B, L↔C, series↔shunt, open↔short, V↔I, Z-params↔Y-params, ΓV↔-ΓI, constant-r↔constant-g. ## Answer An **immittance chart** (ZY Smith chart) is a combined chart that shows both **imm**ittance forms, impedance and admittance, on the same reflection-coefficient (Γ) plane. It overlays the normal impedance Smith chart (constant r and x circles) and the admittance Smith chart (constant g and b circles). The admittance chart is the impedance chart rotated by 180°. Any point can therefore be read as z = r + jx or as y = g + jb directly, without the λ/4 rotation. #### Sketch ```text inductive (+jx, −jb) .----~~~~~~~~----. .' r-circles ↘ '. / (touch at OC) ↘ \ SC o(----------( 1 )----------)o OC y = ∞ \ g-circles ↗ / z = ∞ z = 0 '. (touch at SC) .' y = 0 '----~~~~~~~~----' capacitive (−jx, +jb) ``` #### Properties - Constant-r circles all touch at the open-circuit point (right). Constant-g circles all touch at the short-circuit point (left). - Constant-x arcs leave the right point, and constant-b arcs leave the left point. - The centre (z = y = 1) is the matched point. - Upper half: inductive in both readings (+jx, −jb). Lower half: capacitive. - A series element moves the point along a constant-r circle. A shunt element moves it along a constant-g circle. - It is used for lumped L, T and π matching networks and for amplifier input and output matching. #### Duality parameters used in microwave network design In each pair, swapping one quantity for the other turns a valid circuit relation into another valid one. | Quantity | Dual quantity | |---|---| | Impedance Z = R + jX | Admittance Y = G + jB | | Resistance R | Conductance G | | Reactance X | Susceptance B | | Inductance L | Capacitance C | | Series connection | Parallel (shunt) connection | | Open circuit | Short circuit | | Voltage V | Current I | | KVL (mesh) | KCL (node) | | Thevenin equivalent | Norton equivalent | | Z-parameters | Y-parameters | | Voltage reflection ΓV | Current reflection ΓI = −ΓV | | Voltage maximum | Current maximum (voltage minimum) | | Series stub | Shunt stub | | Constant-r circle | Constant-g circle | | Short-circuited λ/4 stub (acts open) | Open-circuited λ/4 stub (acts short) | **Why duality matters:** a design for a shunt (admittance) network can be reused for a series (impedance) network by swapping the dual quantities. On the immittance chart this swap is only a change of scale (Z or Y), not a recalculation. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is an immittance (ZY) chart? A. Impedance and admittance Smith charts overlaid on the same Γ plane B. A chart of only constant-VSWR circles C. A chart of only admittance D. A chart for lossy lines only Answer: A. It overlays the impedance chart and its 180°-rotated admittance chart, so z or y can be read directly without a λ/4 rotation. (Key point: Immittance chart) 2. On the immittance chart, which circles touch at which point? A. Constant-r at short, constant-g at open B. Constant-r circles touch at the open-circuit point; constant-g circles at the short-circuit point C. Both at the centre D. Both at the top Answer: B. r circles meet at the right (open) point, g circles at the left (short) point. (Key point: Chart properties) 3. Which element moves a point along which circle? A. Series along constant-g; shunt along constant-r B. Both along constant |Γ| C. Series element along constant-r; shunt along constant-g D. Series along constant-x Answer: C. A series reactance keeps r constant; a shunt susceptance keeps g constant. (Key point: Series vs shunt movement) 4. Which pair is a correct dual? A. Inductance - resistance B. KVL - Thevenin C. Voltage maximum - voltage maximum D. Series stub - shunt stub Answer: D. Series/shunt, L/C, open/short, Z/Y, voltage/current, KVL/KCL, Thevenin/Norton are duals. (Key point: Dual pairs) ## Related in RF and Microwave Engineering - [Short note: Immittance chart](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3Aimmittance-chart-note) — RF and Microwave Engineering, chapter 2, asked 2× - [Immittance chart sketch and scales](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3Aimmittance-chart-scales) — RF and Microwave Engineering, chapter 2 - [GaAsFET amplifier: gains, Γin, Γout, Zin, Zout](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3Agaasfet-flowchart-gains-zin-zout) — RF and Microwave Engineering, chapter 6 - [Microwave vs traditional systems and need of S-parameters](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3Amicrowave-distinction-s-parameter-need) — RF and Microwave Engineering, chapter 1 - [Bilateral/unilateral gains and design flow chart](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3Aamplifier-gains-flowchart-0-55) — RF and Microwave Engineering, chapter 6 - [Unilateral max gain with design flow chart](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3Aunilateral-gain-flowchart) — RF and Microwave Engineering, chapter 6 ## Related in other subjects - [Criteria for designing and laying out tunnels](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Ahydraulic-tunnel-design-layout) — Hydro Power, chapter 5, asked 2× - [Frequency response of networks and complex frequency](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_circuit_theory%3Afrequency-response-complex-frequency-role) — Electrical Circuit Theory, chapter 5 - [Series connection of two-port networks](https://www.bctengineer.com/question.md?key=semester_5%2Ffilter_design%3Atwo-port-series-connection) — Filter Design, chapter 4 - [Reciprocal two-port and condition in T parameters](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_circuit_theory%3Areciprocal-two-port-condition-t-parameters) — Electrical Circuit Theory, chapter 7, asked 2×