• March 17th, 2016

Analogue Communications and Propagation

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Part 2 (50 marks)
(i) Explain the physical meaning of the L, C, R and G parameters used to model the
behaviour of transmission lines. Sketch the circuit for this model.
(ii) Design a λ/4 transformer to match a 50 Ω coaxial cable to a 75 Ω coaxial cable,
working at a frequency of 2 GHz. You should specify all the dimensions of the matching
section. Take the phase velocity to be 3 x 108
m/s, the relative dielectric constant of the
insulator (εr) to be 2.5 and the outer diameter to be 10 mm.
(iii) Sketch your design.
(iv) What is the magnitude of the reflection coefficient at the 75 Ω cable interface with
the matching section and the corresponding VSWR?
(v) What are the inductance per unit length and the capacitance per unit length for the
matching section you have designed?
Take µ0 =4π x 10-7 H/m; µr =1 and ε0 = 8.85 x 10-12 F/m
Part 3 (30 marks)
Describe briefly the additional matching technique you would need to use if the 75 Ω cable
was replaced with a reactive load. You may use a sketch to illustrate your answer.
If the impedance of this reactive load is 75 – j40 Ω calculate:
(i) a design for a this additional matching element, specifying its dimensions and
(ii) the magnitude and phase of the reflection coefficient and the corresponding VSWR.

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