IEEE Circuits and Systems Magazine - Q1 2020 - 23

transistor M n2 by a factor equals to the gain of the amplifier A rg and enhances the GBW of the TIA. This comes
at the cost of the noise and power consumption increase
due to the added regulating amplifier.
The transimpedance gain of the CR-RGC-TIA is described by:
(R CS - A CS R F ) A RGC
SC PD (R CS + R F ) + A CS + 1
Z TIA (0) - - R F A RGC

Z TIA (S ) =

(44a)
(44b)

where C PD is the photodiode junction capacitance, R CS
is the resistance seen by the drain of M n1 which is described by:
(45)
R CS = ron1 //ron2 // 1
G mn2
G mn2 is the effective transconductance of M n2 given by:
G mn2 = g mn2 ; A rg ; = g mn2 g mnrg (R rg //ronrg)

(46)

where A rg is the gain of the regulating amplifier, A CS
and R RGC are the gain of the open loop common source
amplifier and the gain of the regulated cascode respectively which are given by:
A CS = - g mn1 R CS

(47)

A RGC = G mn2 (rop1 //ron2)

(48)

Using the feedback theory the input resistance of the
TIA at zero frequency is described by:
R + RF
Z (0) in = CS
(49)
; A CS ; + 1
Hence, the BW can be approximated by:
BW -

; A CS ; + 1
1
=
2r Z in (0) C PD 2r (R CS + R F ) C PD

(50)

Equation (46) shows that the transconductance of
the transistor M n2 is increased by an ; A rg ; factor compared to the ordinary CR-TIA. Therefore, the gain can be
increased at the same BW and a higher GBW is obtained
according to equations (44b) and (48). However, CR-RGCTIA would experience more power consumption due to
the added regulating amplifier. Also, since the topology
achieves higher transimpedance gain than CR-TIA, the
dynamic range is expected to be less which is confirmed
by the simulation results.

The total input referred noise current of the CR-RGCTIA is described by equation (51a) in which the first term
is produced by M n2 . The second term is due to the noise
contribution of R F and the third term is the noise contribution of M n1 . The fourth term is resulted from M p1
while the fifth term is the noise contribution of Mnrg and
R rg. Compared to the CR-TIA, the CR-RGC-TIA exhibits
higher input referred noise current because of the extra
noise sources of the regulating amplifier. Furthermore,
since CR-RGC-TIA can achieve higher transimpedance
gain but with larger input noise, its dynamic range is
expected to be less than CR-TIA. Simulation parameter
used for CR-RGC-TIA are listed in table VIII.
I n2, in = 4K B T ==

2
(2rf C PD R F ) 2 + 1
1
- 1m
c
( g mn1 R F - 1) 2 Dx R CS
2
r
1
1
+c
+ on2 mm E g mn2 c n
c
A RGC + 1 (1 - g mn1 R F )
RF
2
(2rf C PD)2 + g mn
(2rf C PD R F )2 + 1
1
RF +
g mn1 c n
+
( g mn1 R F - 1)2
( g mn1 R F - 1)2
(2rf C PD R F )2 + (A CS + 1)2
G g mp c p1
+=
(Dx A CS R F )2
2
2
2
(ronrg //R rg)2 g mn
2 r on2 (1 + (2r f C PD R F ) )
WG
+
(51a)
2 2
(1 - g m1 R F ) R CS

Dx = g mn2 ; A rg ; + 1
ron2

(51b)

W = c g mnrg c n + 1 m
R rg

(51c)

III. Simulation Results and Comparisons
In this section, the simulation results obtained at the
previously mentioned four cases are introduced for
all of the investigated topologies. Comparisons between those simulation results in all cases are listed and discussed. Both Figure of Merits (FoM 1) and
(FoM 2) [58] are used to compare the investigated topologies where:
FoM 1 = Gain . BW .C in
I noise . Power
FoM 2 = FoM 1 I Ovl
p-p

(52a)
(52b)

where I noise is the total integrated input referred noise
current, I Ovl
p - p is the maximum overloading sinusoidal

Table VIII.
Simulation parameters of the CR-RGC-TIA.
Case

WMn1

WMn2

WMp1

RF

WMnrg

Rrg

5 KHz Minimum Noise

32 μm

12 μm

5.2 μm

5 MΩ

5 μm

4.2 KΩ

5 KHz Minimum Power

2.5 μm

12 μm

1.2 μm

4.7 MΩ

1 μm

10 KΩ

100 MHz Minimum Noise

38 μm

30 μm

15 μm

6 KΩ

1 μm

6 KΩ

100 MHz Minimum Power

12 μm

7 μm

4 μm

3.8 KΩ

1 μm

6 KΩ

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