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Design of Antennas for Handheld DVB-H ... - Lunds tekniska högskola

Design of Antennas for Handheld DVB-H ... - Lunds tekniska högskola

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unloaded quality factor (Q0) and the external quality factor (Qe). The unloaded<br />

quality factor describes the internal losses, which can be further divided into<br />

radiation, conductor and dielectric losses. The unloaded and radiation (Qrad)<br />

quality factors are in an ideal case equal but in practise there are losses in<br />

dielectrics and conductors, which are included in the dielectric (Qd) and conductor<br />

(Qc) quality factors. The relation between all different quality factors is shown in<br />

equation (2.12) [26].<br />

1<br />

Q<br />

2.3.5 Bandwidth<br />

l<br />

1 1 1 1 1 1<br />

= + = + + +<br />

(2.12)<br />

Q Q Q Q Q Q<br />

0<br />

e<br />

rad<br />

c<br />

d<br />

e<br />

The useful bandwidth is limited by a number <strong>of</strong> factors, <strong>for</strong> example impedance,<br />

gain, polarization or beamwidth. The impedance matching is the main factor<br />

limiting the bandwidth <strong>of</strong> a resonator. The input impedance <strong>of</strong> a small antenna <strong>for</strong><br />

handheld devices varies quickly with frequency, which limits the frequency range<br />

over that the antenna can be matched to its feed line.<br />

The unloaded quality factor is very important because it determines the bandwidth<br />

<strong>of</strong> the antenna. The relatively Bandwidth and the unloaded has the connection<br />

shown in equation (2.13).<br />

B r<br />

=<br />

1<br />

Q<br />

0<br />

( TS −1)(<br />

S − T )<br />

S<br />

23<br />

(2.13)<br />

Where VSWR = S over the impedance bandwidth and T = Y0/G, where G is the<br />

conductance seen at the input <strong>of</strong> a resonator at the resonance frequency and Y0 is<br />

the characteristic admittance <strong>of</strong> the transmission line [26].<br />

2.3.5.1 Impedance matching<br />

A basic task in radio engineering is to match the antenna load to the characteristic<br />

impedance <strong>of</strong> the feed line to prevent voltage reflection (see figure 2.11).<br />

A matching circuit can be realized by lumped elements (capacitor and inductor),<br />

distributed elements (stub or quarter-wavelength trans<strong>for</strong>mer) or by resistive<br />

matching. It is always possible to make a matching circuit as long as the Ra(f) <strong>of</strong><br />

the input impedance is not zero. To design a matching circuit, <strong>for</strong>mulas or Smith<br />

chart can be used. Resistive matching is not recommended because <strong>of</strong> the losses it<br />

results in.<br />

Matching network by lumped elements is close to ideal as long as the physical<br />

lengths <strong>of</strong> the components are clearly smaller than the free-space length and the

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