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

A possible solution is to split the whole TV band into several sub-bands. Each subband
may use a different inductor and then switch capacitors to sweep the entire frequency
range. One can imagine the use of 100nH in VHF low, 10nH in the mid-band and 1nH for the
UHF bands.
In particular, this is very interesting in terms of silicon area for the low-end of the TV
band. Indeed, capacitors get smaller when increasing the inductance value while keeping the
central frequency constant. Furthermore, for a given inductor value, the tuning range of the
filter is proportional to the ratio between the square roots of the capacitances:
f
f
max max ∝ . (II.24)
min
C
C
min
Using several inductors is a good way of keeping capacitances ratios acceptable for
integration. Nevertheless, this method requires additional pins on the chip packaging.
II.2.b Selectivity Tunability
Positioning the central frequency of the filter is one step. A second one consists in
getting the desired selectivity, i.e. the desired Q-factor. In the following a parallel RLC circuit
is considered, with a 10nH inductor and a variable capacitance.
It has been previously explained that, in an LC filter, the bandwidth and the Q-factor
are determined by either series or parallel losses. In general, series losses Rs come from the
inductor, often implemented by a long resistive spiral wire. Capacitors mainly bring parallel
losses Rp, due to a small current flowing through the non-ideal insulator. This results in an
equivalent RLC circuit, depicted in Figure 63.
I
Rs
L
C
- 51 -
Rp
V
Figure 63. Equivalent RLC circuit
Furthermore, the LC filter presents different behaviour depending on the major
contributor between Rp and Rs. To be able to compare these two contributors, the series
resistance Rs is transformed into an equivalent parallel resistance Rs// as follows:
2
Rs // Rs
( 1+ Q )
where Q is the quality factor of the resonant circuit.
= , (II.25)
Hence, the circuit is said Rp-limited if RpRs//, the circuit is said Rs-limited and series losses from
the inductor are considered as the major source of losses of the filter.