IEEE Circuits and Systems Magazine - Q2 2023 - 41

Figure 16. (a) Transistor-level schematic, (b) gmC equivalent, and (c) small-signal diagram of type-I SSF [36] and (d) transistorlevel
schematic, (e) gmC equivalent, and (f) small-signal diagram of type-II SSF [14].
Hs
SSF LPFI
−− () =
gg
CC
ss
2
++
C2
g 2
mm m
12
mm
12
gg
CC
12
12
−s
Hs
SSF-BPF-II () =
ss
gm1
C1
2 mm m
++
g 1
C2
gg
CC
uphold the same bandwidth as in the SF filter. A parallel
filter array adopting the XSF-based BPF was implemented
in [35]; and was used in an environmental sound
classification task [37] and a 2-class speech versus
noise task [38] with an FPGA environment.
D. Super Source-Follower (Second-Order LPF/BPF)
Fig. 16 shows a schematic, gCm equivalent, and block
diagram of the super source-follower (SSF)-based filter
circuits. As Fig. 16(a) and (d) show, the SSF filter can
be categorized into two different types depending on
how the C1 capacitor is connected: (1) C1 bootstraps
VBPF and VLPF in type-I; (2) C1 is connected to VBPF
but its other plate is shunted to GND in type-II. In both
types, the basic structure follows the lossless-first twointegrator-loop
topology as discussed in Fig. 5(a). However,
the type-II SSF incorporates a feedforward gm1
path. The transfer functions and filter parameters of
type-I and type-II SSF filters are summarized in 27 28
()
SECOND QUARTER 2023
,.
12
12
−s
Hs
SSF-BPF-I () =
ss
gm1
C1
2 mm m
++
g 2
C2
gg
CC
ω0==
gg
CC
mm
12
12
Q
12
12
ω0==
gg
CC
mm
12
12
Q
gC
gC
m
m
12
21
(27)
g
gC
m
m
22
11
C
(28)
Interestingly, both SSF types can be deployed as a BPF
without requiring any external subtractor in contrast to
the OTA-based (see Fig. 9) and XSF-based (see Fig. 15)
BPFs. For the type-I SSF, this is because C1 bootstraps
VLPF and VBPF within the lossless integral operation.
In other words, the resulting small-signal voltage difference,
i.e., −−
gv vsC , is generated on top of
m11
()
IN
LPF
the VLPF node. In effect, the VBPF is located after the
second subtractor which receives VLPF as an operand,
thereby VBPF corresponds to VY in Fig. 5(a). Note that
the small-signal current generated from the gm2 transconductor
does not contribute to the voltage difference
over the C1 capacitor since the source and sink ports of
the gm1 transconductor are all tied to both plates of the
C1 capacitor. Assuming sufficiently large output impedance
ro of the transistors, the small-signal current generated
from the M1 transistor flows entirely into the C1
capacitor, resulting that the generated small-signal current
is trapped within the MC
11−
loop (used in (30)).
IEEE CIRCUITS AND SYSTEMS MAGAZINE
41

IEEE Circuits and Systems Magazine - Q2 2023

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