III. Gm-C Filtering - Epublications - Université de Limoges

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