IEEE Circuits and Systems Magazine - Q1 2020 - 22

Using the small signal model of the CR-TIA, the transimpedance gain is deduced and is described by: [33]
(R CS - ; A CS ; R F ) A CG
SC PD (R F + R CS) + ; A CS ; + 1
Z (0) TIA - - R F A CG

Z (S ) TIA =

(38a)
(38b)

where R CS is the total resistance seen by the drain of
M n1, A CS and A CG are the open loop gains of the common source and the common gate stages respectively
which are given by:
A CS = - g mn1 R CS
R CS =

(39a)

1 // r // r
on1
on2

(39b)

g mn2

A CG = g mn2 (rop //ron2)

(40)

The zero frequency input impedance is described by:
Z (0) in =

R CS + R F
; A CS ; + 1

(41)

assuming that (C PD, Z (0) in) forms the dominant pole of
the circuit, then the BW is expressed by:
Table VII.
Simulation parameters of the CR-TIA.
Case

WMn1

WMn2

WMp

RF

5 KHz
Minimum
Noise

60 μm

12 μm

6 μm

9 MΩ

5 KHz
Minimum
Power

1 μm

12 μm

1 μm

6.6 MΩ

100 MHz
Minimum
Noise

33 μm

10 μm

33 μm

5.4 KΩ

100 MHz
Minimum
Power

11 μm

3.7 μm

11 μm

4 KΩ

Regulating
Amp. (Arg)

VDD

VDD
VB

Mp1

Common
Gate

Vout
Mn2

Mnrg
RF
CPD

Shunt
FB
TIA
Mn1

Figure 11. Schematic diagram of the CR-RGC-TIA.
22

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

(42)

Equation (38 b) shows that the input signal is amplified two times, one time using the CS-TIA (-R F ) and the
other time with the common gate stage (A CG). Accordingly, higher transimpedance gain can be obtained at
almost the same BW compared to the CS-TIA. Also, the
effect of the miller capacitance due to C gd mn1 is greatly reduced since the source of M mn2 provides a low resistance
node approximated by 1/g mn2 . Viewed from another perspective, CR-TIA can achieve the same transimpedance
gain as the CS-TIA at a relatively lower power consumption. However, due to the high attainable transimpedance
gain, the maximum overloading input current is limited
resulting in a lower dynamic range compared to CS-TIA.
The noise equivalent circuit of the CR-TIA is used to
deduce the total input referred noise current described
by equation (43). The first term of equation (43) is the
noise contribution of M n2 (first two lines), the second
term is the noise generated by R F . The third term is the
noise contribution of M n1 and the forth term is due to
M p . Careful inspection of equation (43) reveals that R F
noise dominates at low frequencies while the cascode
transistor M n2 noise dominates at higher frequencies.
It is clear that the noise of the CR-TIA is higher than
the CS-TIA because of the extra noise sources generated
by M n2 and M p . In addition, the gain is determined not
only by R F but also by A CG . Thus, the value of R F in the
CR-TIA is much lower than in CS-TIA for the same transimpedance gain. Accordingly, the noise generated by R F
in the CR-TIA is greater than in CS-TIA which deteriorates
the noise of the CR-TIA even further. This observation
is clear in the upcoming simulation results. Simulation
parameters used in the four cases are listed in table VII.
2
(2rf C PD R F ) 2 + 1
1
>> (g mn1 R F - 1) 2 f c g mn2 + 1 mR CS - 1 p
ron2
2
r
1
+c 1 c
+ on2 mm E g mn2 c n
A CG + 1 (1 - g mn1 R F ) R F
(2rf C PD)2 + g 2mn1
(2rf C PD R F )2 + 1
oR F +
+e
g mn1c n
2
(g mn1 R F - 1)
(g mn1 R F - 1)2
2
(2rf C PD)2
1 + ACS
+
> cc g mn2 + 1 mACS m2 + f c g mn2 + 1 mACS R F p H g mpcpH
ron2
ron2

I 2n, in = 4K B T

Rrg

IPD

BW -

IEEE CIRCUITS AND SYSTEMS MAGAZINE

(43)
H. Current Reuse with RGC TIA (CR-RGC-TIA)
The CR-RGC-TIA is shown in Fig. 11 [34]. It is a modified
version of the CR-TIA topology shown in Fig. 10. The
enhancement of this topology over the CR-TIA is the
regulating amplifier A rg which regulates M n2 . This regulation increases the effective transconductance of the
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