IEEE Circuits and Systems Magazine - Q1 2020 - 19

additional biasing circuitry. The transimpedance gain of
the RIC-TIA is described by:
Z (S ) TIA =

R out - ; A RIC ; R F
H (S 2 ) + H (S ) + ; A RIC ; + 1

Z TIA (0) - - R F
2

2

H (S ) = S C PD C out R F R out
H (S ) = S [(R F + R out) C PD + R out C out]

I 2n, in = 4K B T =

(G m)2 + (2rf C PD)2
RF
(1 - G m R F ) 2
1 + (2rf C PD R F )2
+
( g mn1 c n + g mp1 c p)
(1 - G m R F )2
1 + (2rf C PD R F )2
g mn2 c n
+
1 r 2
c (1 - G m R F )c g mn2 ( ; A 2 ; + 1) +
m
m
ron2 on1
1 + (2rf C PD R F )2
g mp2 c p
+
1 r 2
c (1 - G m R F )c g mp2 ( ; A 1 ; + 1) +
m op1 m
rop2
2
2
2
r
f
C
+
(rop3 //R 1) 2 g mp
(
(
1
2
r
PD R F ) )
2 op2
B1
+
2
(1 - G m R F )2 R out
2
2
2
(ron3 /R 2)2 g mn
2 r on2 (1 + (2r f C PD R F ) )
B 2G
+
(27a)
2 2
(1 - G m R F ) R out

(21a)
(21b)
(21c)
(21d)

where A RIC and R out are the open loop gain and the open
loop output resistance of the voltage amplifier respectively given by:
A RIC = -G m R out = -(g mn1 + g mp1) R out
R out = c g mn2 ( ; A 2 ; + 1) + 1 + 1 m ron1 ron2
ron1 ron2
// c g mp2 ( ; A 1 ; + 1) + 1 + 1 m rop1 rop2
rop1 rop2

(22)

(23)

where G m = g mn1 + g mp1 is the transconductance of the
open loop inverter cascode voltage amplifier, R F is
the shunt-shunt feedback resistor, C PD is the photodiode junction capacitance, A 1, and A 2 are the gains of
the regulating amplifier Amp1. and Amp2. respectively
which are described by:
A 1 = - g mp3 (R 1 //rop3)

(24a)

A 2 = - g mn3 (R 2 //ron3)

(24b)

Using the feedback theory, the input impedance is
obtained and it is described by:
Z in (0) = R out + R F
; A RIC ; + 1

(25)

The BW can be approximated by:
BW -

; A RIC ; + 1
1
=
2rZ in (0) C PD 2r (R out + R F ) C PD

(27b)

B 2 = c g mn3 c n + 1 m
R2

(27c)

where the first term is the input referred noise current
contribution of R F . The second term is the input referred
noise due to M n1 and M p1 . The third and fourth terms are
due to the cascode transistors M n2 and M p2 respectively.
The fifth and the sixth terms are the noise contribution
of Amp1. and Amp2. respectively. Since R out is very large,
the noise contribution due to the regulating amplifier is
sufficiently small compared to the noise contribution of
M n1, M p1 and R F .
Also, due to the regulation of the cascode transistors,
their transconductance (g mn2 and g mp2) are multiplied
by ( ; A 2 ; + 1) and ( ; A 1 ; + 1) respectively which decreases
the noise contribution of the cascode transistors. Consequently, the noise increase due to the added regulating amplifiers is expected to be compensated by the
enhancement of the effective transconductance. Simulation parameters are listed in table IV.

(26)

It is clear from equation (23) that the transconductance of M n2 and M p2 are multiplied by the factors
(A 1 + 1) and (A 2 + 1) respectively. Accordingly, an increase in the open loop output resistance and the open
loop gain are obtained. Therefore, the input impedance
is reduced and higher transimpedance gain is achievable at the same BW compared to the InvCas-TIA. Looking from another perspective, the RIC-TIA provides the
same open loop gain and the same GBW at a smaller
g mn1 and g mp1 compared to the InvCas-TIA. Conse quently, lower DC biasing current and power consumption are achievable for the same GBW compared to the
InvCas-TIA.
Input referred noise current of the RIC-TIA is presented by:
FIRST QUARTER 2020

B 1 = c g mp3 c n + 1 m
R1

Table IV.
Simulation parameters of the RIC-TIA.
5 KHz,
Min Noise

5 KHz,
Min Power

100 MHz,
Min Noise

100 MHz,
Min Power

WMn1

10 μm

4.5 μm

8.5 μm

2.5 μm

WMn2

10 μm

4.5 μm

23 μm

2.5 μm

WMp1

7.5 μm

0.6 μm

22 μm

2.6 μm

WMp2

10 μm

0.6 μm

12 μm

2.2 μm

RF

18 MΩ

18 MΩ

66 KΩ

10 KΩ

WMp3

2 μm

2 μm

1 μm

1 μm

WMn3

5 μm

5 μm

1 μm

1 μm

R1

100 KΩ

100 KΩ

9 KΩ

9 KΩ

R2

300 KΩ

300 KΩ

9 KΩ

9 KΩ

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IEEE Circuits and Systems Magazine - Q1 2020

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