The Bailey unequal-split power divider uses a 90° hybrid coupler and a T-junction, as shown below. The power division ratio is controlled by adjusting the feed position, a, along the transmission line of length b that connects ports 1 and 4 of the hybrid. A quarter-wave transformer of impedance Zo/√2 is used to match the input of the divider. (a) For b = λ/4, show that the output power division ratio is given by P3/P2 = tan² (ra/2b). (b) Using a branch-line hybrid with Zo = 50 £2, design a power divider with a division ratio of P3/P₂ = 0.5, and plot the resulting input return loss and transmission coefficients versus frequency.

The Bailey unequal-split power divider uses a 90° hybrid coupler and a T-junction, as shown below. The power division ratio is controlled by adjusting the feed position, a, along the transmission line of length b that connects ports 1 and 4 of the hybrid. A quarter-wave transformer of impedance Zo/√2 is used to match the input of the divider. (a) For b = λ/4, show that the output power division ratio is given by P3/P2 = tan² (ra/2b). (b) Using a branch-line hybrid with Zo = 50 £2, design a power divider with a division ratio of P3/P₂ = 0.5, and plot the resulting input return loss and transmission coefficients versus frequency.

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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Concept explainers

Antenna Characteristics

The antenna is an important concept in the domain of electronics and communication engineering. An antenna forms an integral part of many commonly used devices such as wireless modems, routers, game controllers, mobile phones, bluetooth devices, and so on. In simple terms, any wireless communication makes use of antennas to serve the purpose. An antenna, also known by the term 'arial', is an electrical device that converts electrical signals into electromagnetic waves or electromagnetic waves into electrical signals. An antenna contains a transmission line usually made up of co-axial cable, it then receives the signals and converts them into electromagnetic waves, which are then transmitted via space into their required destination. A communication system essentially makes use of two antennas, a transmission antenna, which converts electrical signals into electromagnetic waves, and a receiving antenna, which receives the electromagnetic waves and converts them back into electrical signals.

Question

The Bailey unequal-split power divider uses a 90° hybrid coupler and a T-junction, as shown below.
The power division ratio is controlled by adjusting the feed position, a, along the transmission line of
length b that connects ports 1 and 4 of the hybrid. A quarter-wave transformer of impedance Zo/√2
is used to match the input of the divider. (a) For b = 2/4, show that the output power division ratio
is given by P3/P2 = tan² (ra/2b). (b) Using a branch-line hybrid with Zo = 50 22, design a power
divider with a division ratio of P3/P₂ = 0.5, and plot the resulting input return loss and transmission
coefficients versus frequency.
Zo/√2 Z
Zo
P₂

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