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

Figure 46 illustrates the transfer function gain versus frequency for given parameters.
As expected, the transfer function presents a bandpass characteristic.
Figure 46. Bandpass Filter Transfer Function
From the RC and the LR first low-pass filters, two main second order bandpass filters
are derived. First one, derived from the RC low-pass, is a parallel resonator made of an
inductor L with its series losses Rs, in parallel of a capacitor C, as shown in Figure 47. The
equivalent admittance of such a circuit is minimal at the resonance frequency. Hence, the
output voltage gets higher at the resonant frequency. It is called a voltage resonance.
Figure 47. RLC resonator with parallel capacitor
Derived from an LR low-pass, the circuit depicted in Figure 48 is composed of a series
resonator. Indeed, the resonance is reached when the equivalent impedance is minimal. The
resonance happens when the output voltage gets minimal, and so, when the current get
maximal. This is called a current resonance.
Figure 48. Series LC resonator assuming series loss
II.1.c.ii Quality Factor
From the formula of Q previously given, it may be observed that the higher the Q, the
more selective the filter. Indeed, if a non-lossy filter is assumed, such as an ideal LC
resonator, this leads to an infinite Q-factor, meaning a zero bandwidth.
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Q = 20
fc = 1GHz