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

II. Challenges of RF Selectivity
Following chapter is dedicated to the challenges of RF selectivity. It objective is to
find which filter topology best fulfills the specified requirements of TV receivers. It also
provides a comparison of the performances of different filter topologies and structures that
may be found in the literature. Their opportunities and limitations from a technological point
of view will also be assessed.
II.1 Comparison of the Possible Topologies
II.1.a Possible Topologies
There are several ways to fit the previously described abacus and this chapter aims at
determining which one suits the best to fulfil the required specifications. From a mathematical
point of view, it consists in finding transfer function parameters (order and coefficients)
which allow achieving the desired selectivity requirements as well as an easy frequency
tuning.
Equation (II.1) shows a transfer function in Laplace domain of order { n, m}
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max ,
where m corresponds to the number of poles of H(s) and n to its number of zeros. αi and βi are
called coefficients of this transfer function.
α s
+ ... + α s
+ α s
n
1 0
n
H ( s)
= m
β ms
1 0
1 0
+ ... + β1s
+ β 0s
(II.1)
It is worth pointing out that a high order transfer function kt means a high number of
reactive elements kr to implement the circuit since k r ≥ k t . For high order filters, frequency
and selectivity tuning may become difficult to handle since several components values would
have to be tuned. That is why a low order is preferred.
In this chapter II.1, several topologies of filters are assessed in order to find which one
suits the best to fulfil the required specifications.
II.1.b Low-pass Topologies
II.1.b.i General Principle
A first order RC low-pass filter [II.1] actually consists in a resistor associated to a
capacitor as depicted in Figure 37. Another first order low-pass filter can also be obtained
using an inductor and a resistor, which is known as an RL low-pass filter. For both, high
frequencies are cut by the reactive element.