---
title: "Incremental model of a transmission line"
subject: "Telecommunications"
chapter: 2
key: "semester_8/telecommunications:transmission-line-incremental-model"
source: https://www.bctengineer.com/q/semester_8/telecommunications/transmission-line-incremental-model
site: BCT Engineering
---

# Incremental model of a transmission line

Telecommunications · Chapter 2: Transmission Media

- Asked in: 2080 Baisakh, 2 marks
- Video: [Transmission Line Equation Part 1](https://www.youtube.com/watch?v=b_VCIdXEK2I) — TutorialsPoint
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_8/telecommunications/transmission-line-incremental-model
- Whole chapter: https://www.bctengineer.com/md/semester_8/telecommunications/chapter-2

## Question

A uniform transmission line can be regarded as a cascade of infinite symmetrical sections of impedances, each of infinitesimal size. Draw an incremental length of a transmission line clearly showing the distributed inductance, capacitance, resistance and conductance per unit length.

## Short answer

An incremental line length dx has series resistance R dx and inductance L dx, plus shunt conductance G dx and capacitance C dx. These distributed parameters give series impedance Z=R+jωL and shunt admittance Y=G+jωC, with characteristic impedance Z0=sqrt(Z/Y).

## Answer

A small length $\Delta x$ of a uniform line is modelled with series resistance $R\Delta x$ and inductance $L\Delta x$, and shunt conductance $G\Delta x$ and capacitance $C\Delta x$ ($R, L, G, C$ per unit length).

```text
   i(x)   R.dx      L.dx         i(x+dx)
 o──>──[/\/\/]──[ coil ]──┬───────┬────o
 +                        │       │    +
                        [G.dx]  [C.dx]
 v(x)                     │       │   v(x+dx)
 -                        │       │    -
 o────────────────────────┴───────┴────o
 |<──────────────── dx ─────────────>|
```
Series impedance per unit length $Z = R + j\omega L$; shunt admittance $Y = G + j\omega C$; characteristic impedance $Z_0 = \sqrt{Z/Y}$.

## Check yourself

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

1. In the incremental section of length dx, which elements are in series?
   A. Resistance R dx and inductance L dx
   B. Conductance G dx and capacitance C dx
   C. Resistance R dx and capacitance C dx
   D. Inductance L dx and conductance G dx
   Answer: A. Series arm carries R dx and L dx; the shunt arm carries G dx and C dx. (Key point: Series elements)

2. Which elements form the shunt branch across the line in the model?
   A. R and L
   B. L and C
   C. G and C
   D. R and G
   Answer: C. Leakage conductance G and capacitance C connect between the two conductors. (Key point: Shunt elements)

3. What is the characteristic impedance in terms of the per-unit-length parameters?
   A. Z0 = sqrt(Y/Z)
   B. Z0 = Z + Y
   C. Z0 = sqrt(Z/Y), with Z = R + jwL and Y = G + jwC
   D. Z0 = sqrt(R/G) at all frequencies
   Answer: C. Z0 = sqrt(Z/Y) with series impedance Z = R + jwL and shunt admittance Y = G + jwC. (Key point: Z0 formula)

## Related in Telecommunications

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