IEEE Circuits and Systems Magazine - Q2 2023 - 40

Figure 15. (a) Transistor-level schematic, (b) half-circuit representation of the schematic, (c) gmC equivalent circuit, and (d) smallsignal
diagram of the cross-coupled source-follower-based BPF [35].
Hs
−
XSFBPF ()=⋅
C
C
IN
F ++
ss
2 11 2
2
g
C
mm m
IN
gg
C
IN
s
g
C
m1
IN
ω0 =
gg
C
mm Q =
IN
12
g
g
m
m
2
1
(22)
where iZ represents a small-signal current in
Fig. 15(c), CL is a load capacitance of the CCIA. We
assume CC
LF and sg C
CC CFF
/2 IN
 mF3 /
() from the original OTA bandwidth
as also described in [31]. The second apfor
the first apHs
Hs
X
Hs
proximation in (25). We can see that the bandwidth
of CCIA is reduced by the amount of feedback factor
β=+
gCm3 /,L
proximation used in (25) is valid when the bandwidth
of CCIA is sufficiently higher than ω0 in the BPF. The
transfer function of the XSF-based BPF Hs
rived in (22) using the equations as below. Hs
== IN.
BPF () is deLPF
()
can be found in (18) but with an additional condition
of CC C12
40
IEEE CIRCUITS AND SYSTEMS MAGAZINE
() =
LPF
Loss
= s Hs IN
mF2
C
g
LPF ()⋅
C
C
BPF () =() ()CCIA
IN
X () Hs HsLPF ()
−
(26)
A clear advantage of the SF-based filters over the
OTA-based design is its minimal number of parasitic
poles. As shown in Fig. 12(a), the XSF filter exploits every
node within the circuit as a source for pole synthesis
while the OTA-based circuit does not. For instance,
the mirror pole in the OTA acts as a non-dominant pole
thereby necessitating additional power dissipation to
SECOND QUARTER 2023
()
Hs
Hs
=Hs s
y ()
LPF
() +



1
C
g
IN
m2




IEEE Circuits and Systems Magazine - Q2 2023

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