---
title: "Immittance chart sketch and scales"
subject: "RF and Microwave Engineering"
chapter: 2
key: "semester_7/rf_and_microwave_engineering:immittance-chart-scales"
source: https://www.bctengineer.com/q/semester_7/rf_and_microwave_engineering/immittance-chart-scales
site: BCT Engineering
---

# Immittance chart sketch and scales

RF and Microwave Engineering · Chapter 2: RF and Microwave Transmission Lines

- Asked in: 2072 Magh, 5 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-scales
- Whole chapter: https://www.bctengineer.com/md/semester_7/rf_and_microwave_engineering/chapter-2

## Question

Sketch an immittance chart and compare the scales.

## Short answer

An immittance chart overlays impedance and admittance Smith charts on one Γ-plane. Impedance scale (red) reads r and x: constant-r circles touch open circuit (right), upper half +jx inductive. Admittance scale (blue) reads g and b: constant-g circles touch short circuit (left), upper half –jb inductive.

## Answer

An **immittance (ZY) chart** overlays the impedance Smith chart and the admittance Smith chart (the Z-chart rotated by 180°) on one Γ-plane. It is usually printed in two colours.

```text
            +jx / −jb (inductive)
          .-~~~~~~~~~~~~-.
        /  Z: r-circles   \
 SC  ( g-circles  1   →    ) OC
 z=0   \ ←touch SC        /  z=∞
 y=∞    '-~~~~~~~~~~~~-'    y=0
            −jx / +jb (capacitive)
```

#### Comparison of scales

| Feature | Z (impedance) scale | Y (admittance) scale |
|---|---|---|
| Quantity read | r, x of z = r + jx | g, b of y = g + jb |
| Real-part circles | Constant r, touch at OC (right) | Constant g, touch at SC (left) |
| Imaginary arcs | Constant x, from the right end | Constant b, from the left end |
| Upper half | +jx (inductive) | −jb (inductive) |
| Lower half | −jx (capacitive) | +jb (capacitive) |
| Left end point | z = 0 (short) | y = ∞ (short) |
| Right end point | z = ∞ (open) | y = 0 (open) |
| Series L or C moves along | constant-r circle | — |
| Shunt L or C moves along | — | constant-g circle |
| Usual colour | Red | Blue/green |

The outer wavelength scales (WTG/WTL) and the radial scales (|Γ|, VSWR, return loss) are common to both.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. In the upper half of the immittance chart, what is read on the Z and Y scales?
   A. +jx (inductive) on Z and -jb (inductive) on Y
   B. +jx on Z and +jb on Y
   C. -jx and -jb
   D. Capacitive on both
   Answer: A. Upper half is inductive: +jx on Z, -jb on Y. (Key point: Upper half meaning)

2. Which end points apply on the left?
   A. z = ∞, y = 0
   B. z = 0, y = ∞ (short)
   C. z = 1
   D. z = y = 1
   Answer: B. Left end is the short circuit: z = 0, y = ∞. (Key point: End points)

3. Which circle does a shunt L or C move along?
   A. Constant r
   B. Constant x
   C. Constant g
   D. Constant b
   Answer: C. Shunt elements move along constant-g circles, series elements along constant-r. (Key point: Element movement)

## 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 and duality parameters](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3Aimmittance-chart-duality) — RF and Microwave Engineering, chapter 2

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