III. Gm-C Filtering - Epublications - Université de Limoges
III. Gm-C Filtering - Epublications - Université de Limoges
III. Gm-C Filtering - Epublications - Université de Limoges
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II.2 Passive LC Second Or<strong>de</strong>r Bandpass <strong>Filtering</strong><br />
II.2.a Frequency Tunability<br />
As explained before, cable and terrestrial TV bands cover a range from 45MHz up to<br />
1002MHz. Given f0 formula, some relations and or<strong>de</strong>rs of magnitu<strong>de</strong> for L and C can be<br />
<strong>de</strong>duced. It has to be kept in mind that usual integrated capacitances in microelectronics vary<br />
between 10fF and 100pF. According to the technology, inductors may be integrated on silicon<br />
as well. However, above some tens of nano-Henrys, a spiral inductor becomes too large and<br />
so very costly in terms of silicon on-chip space. Hence, it is not efficient to integrate 50nH or<br />
more, which are values nee<strong>de</strong>d to reach the bottom of the TV bands in VHF low.<br />
To achieve a frequency sweep of the central frequency by steps smaller than a channel<br />
width of 6MHz as explained in introduction, the value either of the inductance or of the<br />
capacitance, or even both of them, has to be changed gradually.<br />
Technically, it is not optimum to switch inductors. In<strong>de</strong>ed, parallel switching of<br />
inductors, as <strong>de</strong>scribed in Figure 59.a, requires even higher inductance values since N parallel<br />
L<br />
inductances L are equivalent to a value of inductance of . The addition of inductors in<br />
N<br />
series, <strong>de</strong>picted in Figure 59.b, is efficient in terms of inductance values. However, a large<br />
difference of quality factor happens between Lmax and Lmin. Lmin is ma<strong>de</strong> of a small inductance<br />
value in series with several switches Ron in series, while Lmax is constituted of a large<br />
inductance value with no switch Ron in series.<br />
Figure 59. a) parallel inductors switching, b) series inductors switching<br />
Capacitance values can be tuned by different means. The two most popular techniques<br />
are the varactor (Figure 60.a) and the capacitor bank (Figure 61.a). The varactor, which<br />
actually is a reverse-biased varicap dio<strong>de</strong> with a voltage Vb, has a capacitance Cd which<br />
<strong>de</strong>pends on the voltage bias, as it may be seen in Figure 60.b.<br />
Figure 60. a) Varactor symbol, b) C(V) curve of a varactor<br />
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