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

In the literature, negative impedance circuits (NICs) are often added to Zin to
circumvent low quality factors issues. Indeed, a negative resistance compensates for the
parallel resistance of the overall equivalent RLC circuit, leading to an enhanced quality factor.
The NIC usually intrinsically adds a capacitance to the parallel RLC circuit as well, which
results in a lowered self-resonant frequency of the Gyrator-C structure.
On Figure 78, Cnic and Rnic are the capacitance and the negative impedance created by
the NIC. Another capacitor Ctune can be used in parallel to tune the central frequency, which
gives the following formulas.
ω0
Figure 78. Gyrator-C and NIC
=
C = C
p
L
1
eff
C
+ C
nic
+ C
- 64 -
tune
This gives the following filter quality factor:
(III.59)
(III.60)
R p Rnic
C
Q = (III.61)
R + R L
p
nic
The cancellation of the parallel equivalent resistance leads to a pure LC circuit with a
ideally infinite Q-factor. The negative impedance circuit can make the structure oscillate if
Rnic cancels exactly for Rp. However, a partial cancellation of Rp and an accurate control of
Rnic value may lead to very high Q-factor (Rp+Rnic close to zero). In the literature, quality
factors superior to 100 and up to 2000 have been published [II.10 to II.14]. Though it may be
very attractive for VCOs, stability can then become a critical issue when dealing with an RF
filter.
In the literature, self resonant frequencies of Gyrator-C circuits goes from 400MHz up
to 2.5GHz and are mainly used for GSM applications. The main issue of these structures is
the poor linearity versus noise trade-off. IIP3 of -5dBm downto -30dBm are reported while,