IEEE Circuits and Systems Magazine - Q3 2018 - 20

VDD
MM

VB3

V1

M1

Vcm
+

MN

Vin+

MBP

MBP

MBP
VB1

iR

VSGMR

MR

MC1
-

V2

MR

MN

MM
Vin-

M1
i0

VB2

V0

MC2

MBN

Figure 23. Low g m oTA for low-frequency applications [86].

VDD
M3B

IBias
M2D

N2

M2B

+

Vin

-

Vin

M1A
1:

5) Small transconductance OTA
The LPF can be designed using a
Gm-C technique. A reduced transconductance (g m) OTA suitable
for low-frequency applications is
required. Several techniques have
been proposed to implement small
g m for designing these filters with low cutoff frequencies
[75]. The current division technique has been proposed
to reduce the small signal transconductances in voltageto-current converters [85]. The currents of two MOSFETs
are partially canceled at the output. The small signal
transconductance of the OTA can be reduced to 10 - 8 A/V.
The current division method is insufficient to implement
transconductances at the nV/A level. To achieve an even
smaller transconductance, the above methods can be
combined [86], refer to Fig. 23. The transconductance of
the OTA can be reduced to 10 - 9 A/V. The drain currents
of M 1 and M N are partially canceled at the output of the
OTA, leading to very large transconductance reductions.
It can be shown that the resulting small signal transconductance becomes the following:
MBN

VSS

M3A

M1B
M2A N 2 : 1

M2C

Mu

Mu
N
Figure 24. PMos-input symmetrical oTA with series-parallel current division to reduce transconductance without loss
in a linear range [87].

Gm =
dotted line [73]. Here, the virtual ground at the negative
input of the opamp has been extended to node X since
the a -block is enclosed within a loop. For PPG sensing
application, a single-ended version is sufficient. The
new transfer function is given by the following:
A (s) =

- R F /R i
,
1 + SR F C

(10)

a

a11

f=

a

2 rR f C

,

(11)

With this technique, CS-LPF is implemented using a
38 pF capacitor to achieve a cutoff frequency from 62 to
1.8 Hz (and even lower). The effective capacitive reduction is from 500 to 12500 times [73].
The a -block consists of two transistors, with M 1 operating at the triode region and acting as a linear resistor
20

and M 2 in the saturation region.
Both of them have identical aspect
ratios but different gate voltages
to steer current (shown in Fig. 22),
where a is given by Id1/Id2. In
[84], a low cutoff frequency control
block is used, which consists of a
transconductance block gm 2 and
a current-to-voltage block 1/gm 1,
where a is given by gm 2 /gm 1 1 1.

IEEE CIrCUITs AND sYsTEMs MAGAzINE

i0
N- 1 g
=
mMR
M+ N+ 1
v1 - v2

(12)

In equation (12), M is defined as the ratio of transconductances of M M and M 1, while N is the ratio of transconductances of M N and M 1 .
Another technique to reduce the OTA g m is the series-parallel (SP) current division structure, which reduces the transconductance based on a SP current mirror. The transconductance of the OTA can be reduced to
10 - 12 A/V [87], indicated in Fig. 24. For the NMOS current
mirrors in Fig. 24, N unit transistors are placed in series
and in parallel to achieve an effective output transconductance G m = g m1 /N 2, where g m1 is the gate transconductance of the transistors M 1 .
D. Modulation
Sources of additive noise to the PPG signal include systematic circuit offsets, flicker noise, external light sources interference, and 50 Hz power line noise. As PPG signals have a
ThIrD qUArTEr 2018



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