1. A novel transimpedance amplifier with variable gain
Pietro Monsurrò, Alessandro Trifiletti Trond Ytterdal
Dipartimento di Ingegneria dell’Informazione, Elettronica e Department of Electronics and Telecommunications
Telecomunicazioni Norwegian University of Science and Technology
Università di Roma “Sapienza” Trondheim, Norway
Roma, Italy trond.ytterdal@iet.ntnu.no
monsurro@die.uniroma1.it; trifiletti@die.uniroma1.it
Abstract—In this paper we propose a variable-gain Transistor M1 is biased in the triode region, whereas the other
transimpedance amplifier suitable for low-power applications. Its two are biased in saturation. VCTRL controls the transimpedance
noise, bandwidth and input impedance performance are similar gain, and VBIAS determines the bias current.
to a more conventional regulated-cascode common-gate
transimpedance with resistive load, with the same power
consumption and gain performance. The proposed amplifier has,
however, variable gain, which can be easily changed by setting a
control voltage. Besides, it uses no passive components and can Vbias M3
thus occupy less space in the layout, a feature of interest in
applications which require the use of many sensors. With 30µW
dissipation, it achieves 800MHz performance with 50fF input and Vout
output loads, in a 65nm CMOS technology. The transimpedance
gain is 68dB, and the input impedance is 180Ω. Vctrl M2
Keywords-transimpedance, variable gain, front-end
Iin
I. INTRODUCTION M1
Transimpedance amplifiers are widely used in applications
where the signal from a current-mode sensor needs to be turned
into a voltage. Transimpedance amplifiers are used in optical
communications [1], because the photodiode sensor can be
Figure 1. Proposed transimpedance topology.
modeled as a current source, and in ultrasound imaging [2]. In
this last kind of application, it is important to have variable
gain in order to equalize the amplitude of the echoes. Besides, B. Frequency response
in a beam forming network with thousands of sensors, it is Under the hypotheses that each transistor has infinite output
preferable to use very simple topologies with just a few active impedance (except M1, which works in the triode region, and
devices and no passives. whose output conductance is Go1), that the gate-to-drain
In this paper we propose a novel transimpedance topology capacitance is negligible, and that the input and output load
with variable gain, good linearity, noise and bandwidth capacitors Ci and Co (not shown in Fig. 1) are much larger than
performance. It only uses three active devices and no resistors the gate-to-source capacitors of the devices, the
are required. Simulations have been performed using the transimpedance gain of the stage is given by:
STMicroelectronics CMOS 65nm low-power process,
employing 1.2V devices.
gm2
Zm = (1)
II. THE PROPOSED TRANSIMPEDANCE g m1 g m 2 + sCo ( g m 2 + Go1 ) + s 2 Ci Co
A. Topology
Fig. 1 shows the proposed transimpedance amplifier. where gm1 and gm2 are the transconductance gain of M1 and
The circuit has only one current branch, it is based on the M2, respectively.
flipped voltage follower (FVF) topology [3], and it exploits The low-frequency transimpedance is thus equal to the
feedback to reduce both its input and output impedances. inverse transconductance of M1, and a flat frequency response
978-1-4244-8971-8/10$26.00 c 2010 IEEE

2. can be easily achieved by increasing Co, Go1 or g2 with respect Assuming ideal MOS devices, the output voltage is related
to Ci or g1. to the input current by these equations:
On the other hand, the input impedance is:
VI
VO + vO = Z m I B + + VT + Z m iS (4)
sCo 2
Z in = (2) 1
g m1 g m 2 + sCo ( g m 2 + Go1 ) + s 2 Ci Co Zm = (5)
2 K1VI
IB
Due to the assumption of infinite open-loop gain, the input VI = VCTRL − VT − (6)
K2
impedance at low frequencies is zero, although in reality finite
gain effects increase the minimum achievable impedance. In
the 65nm process, the loop gain is about 20dB, and thus the where K1 and K2 are the non-linear transconductance of M1
low-frequency input impedance is about one tenth of the and M2, respectively, and iS is the input signal. VO is the bias
inverse of the transconductance of g2. point at the output and vO is the output signal around the bias
point. It can be noted that the output voltage vO and the input
C. Signal-to-noise ratio current iS are linearly related through the transimpedance gain
The transimpedance amplifier is often used to sense very Zm, and that this gain can be varied by changing the voltage on
small currents arising from sensors such as photodiodes. The the drain of M1 (VI), by changing VCTRL. With ideal MOS
signal-to-noise ratio is thus a key specification for a devices, the transimpedance should be linear.
transimpedance amplifier.
Assuming ideal MOS devices, with white drain noise III. SIMULATIONS
current equal to in1, in2, in3, respectively, and an input current
source iS, we have that the signal-to-noise ratio (SNR) is: A. Benchmark
The proposed transimpedance has been compared with a
more standard solution, a common-gate amplifier with resistive
load RO, and regulated cascode feedback to improve the input
is2, rms impedance [4], as shown in Fig. 2. The same power
SNR = (3)
2 2
in1 + in 3 consumption, supply voltage, and transimpedance gain have
been used to design this amplifier, so as to make the
comparison as significant as possible. However, the proposed
amplifier has also gain control, whereas the benchmark
where the noise due to devices M1 and M3 needs to be transimpedance has fixed gain, being it equal to RO (although
integrated over the relevant signal bandwidth. Noise due to M2 this resistor could be realized using active devices to create a
gives no contribution because of the infinite gain of the variable resistor, this would impact linearity).
cascode structure M1–M2. Under realistic conditions, its noise
contribution is divided by the voltage gain of a MOS device, The topology in Fig. 2 uses one resistor, and thus it is likely
i.e., by a factor of about 10. to occupy a larger space in the layout than the proposed
topology, which only uses active devices.
D. Linearity and gain control Calculations show that the two topologies have roughly
If M1 is biased in the saturation region, the circuit is heavily similar input impedance, noise and bandwidth, for the same
non-linear because the transconductance of M1 changes with transimpedance and power consumption.
the output voltage. On the other hand, at least with ideal MOS
devices, when M1 is in the triode region there are two
important consequences: the transimpedance becomes roughly
linear and the voltage VCTRL determines the transimpedance Ro
gain (although it also affects the output bias point), which
moreover depends linearly on the control voltage.
Vbp M4 Vout
Linearity is due to the constancy of the input voltage, which
causes the non-linear term in the triode current equation to be M1
constant. This is the result of assuming infinite loop gain, and
thus zero input impedance. The non-linear behavior in the M2 Iin
triode region depends on the square of the input voltage,
whereas in the saturation region it is due to the square of the Vbn M3
output voltage, thus linearity improves in the triode region even
with finite gain.
Figure 2. Conventional transimpedance amplifier.

3. B. Simulation results
-120
Total power consumption is 30µW for both amplifiers, and
the supply voltage is 1.5V. With a bias current of 20µA, the -125
input current swing of 10µA used in the simulations represents -130
Noise power density spectrum (dB)
about one half of the dynamic range. The input and output
-135
nodes are loaded with 50fF capacitors.
-140
Fig. 3 shows the transimpedance gain of the proposed
(solid) and conventional (dashed) amplifiers, Fig. 4 shows the -145
input impedance, and Fig. 5 the output noise spectrum. -150
-155
74
-160
72 -165
-170
70 -3 -2 -1 0 1 2 3
Transimpedance (dBOhm)
10 10 10 10 10 10 10
Freq (MHz)
68
Figure 5. Output noise spectrum (solid: proposed, dashed: conventional)
66
Fig. 6 shows the transimpedance of the amplifier for
64 varying values of the control voltage VCTRL. At very low values
for this voltage, the transimpedance increases, but the
62 bandwidth is reduced. Beyond a certain value, M1 goes in the
saturation region and the transimpedance becomes independent
60 on the control voltage. Fig. 7 shows the transimpedance and the
bandwidth of the proposed transimpedance amplifier as a
-3 -2 -1 0 1 2 3
10 10 10 10 10 10 10
Freq (MHz)
function of the control voltage. The transimpedance gain can
be varied by about 10dB by changing VCTRL. A higher range of
Figure 3. Transimpedance gain (solid: proposed, dashed: conventional)
programmability can be achieved for higher current densities
(higher gate-to-source voltages) because M1 remains in the
75 triode region for a wider range of VCTRL values. The maximum
transimpedance gain is set by bandwidth requirements, because
70 g2 and GO1 shrinks with VCTRL, limiting the bandwidth of the
complex poles (or even creating two real separated poles). The
65 minimum gain, on the other hand, is set by linearity
Input Impedance (dBOhm)
requirements, because linearity quickly worsens when M1
60 moves toward its saturation region.
55 84
50 82
80
45
Transimpedance (dBOhm)
78
40
-3 -2 -1 0 1 2 3
10 10 10 10 10 10 10
76
Freq (MHz)
74
Figure 4. Input impedance (solid: proposed, dashed: conventional)
72
The two amplifiers have roughly the same performance in
terms of noise, bandwidth and input impedance. The cascode 70
amplifier, however, has higher overshoot. This overshoot can
be compensated by increasing the load capacitor on the output 68
-3 -2 -1 0 1 2 3
of the auxiliary amplifier M2–M4, but at the expense of 10 10 10 10
Frequency (MHz)
10 10 10
bandwidth. The proposed amplifier also has a lower input
impedance at high frequencies. The frequency response of the Figure 6. Frequency response for varying VCTRL.
benchmark transimpedance amplifiers is more complicated
because it has one more pole, and one zero.

4. impedance, whereas it has some limitations in terms of
Transimpedance (dBOhm) 84
linearity with respect to a regulated cascode common-gate
82 amplifier. The transimpedance can be varied in a range of
80 about 10dB by setting a control voltage, and a wider range of
78 variability can be achieved at higher current densities.
76 The proposed amplifier doesn’t use any resistor and so it is
74
0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9
suitable for very high-density integration: this may be
important for applications such as ultrasound imaging, in
1000
which many ultrasound sensors are used to create sensor arrays
with beam forming ability.
Bandwidth (MHz)
800
600
70
400
200 65
0 60
0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9
Vctrl (mV)
55
HD2 & HD3 (dB)
Figure 7. Transimpedance and bandwidth vs VCTRL. 50
Fig. 8 shows the second and third harmonic distortion for 45
several values of VCTRL. Although HD3 is heavily dependent on 40
the control voltage, the improvement in terms of HD2 is
reduced. The amplifier has a worse HD2 performance with 35
respect to the benchmark case (50dB), whereas it achieves a 30
comparable HD3 only in deep triode region, for low values of
VCTRL. The HD3 performance for the benchmark amplifier is 25
0.45 0.5 0.55 0.6 0.65 0.7
68dB. Tab. I summarizes the results. Vctrl (V)
TABLE I. SIMULATED PERFORMANCE Figure 8. HD2 and HD3 vs VCTRL.
Proposed TZA Benchmark TZA Unit
Noise Power Density 4.7 4.3 pA/√Hz
REFERENCES
[1] Hasan, S.M.R., “Design of a low-power 3.5-GHz broad-band CMOS
Bandwidth 850 830 MHz transimpedance amplifier for optical transceivers”, Circuits and Systems
I: Regular Papers, IEEE Transactions on, Volume: 52 , Issue: 6, 2005,
Transimpedance 68 69 dBΩ Page(s): 1061 – 1072.
Overshoot 0.2 3.0 dB [2] Cenkeramaddi, L.R.; Ytterdal, T., "1V transimpedance amplifier in
90nm CMOS for medical ultrasound imaging", NORCHIP, 2009,
Input impedance 45 45 dBΩ Page(s): 1 – 4.
[3] Carvajal, R.G.; Ramirez-Angulo, J.; Lopez-Martin, A.J.; Torralba, A.;
Second harmonic distortion 28 50 dB
Galan, J.A.G.; Carlosena, A.; Chavero, F.M., "The flipped voltage
Third hardmonic distortion 51 68 dB follower: a useful cell for low-voltage low-power circuit design",
Circuits and Systems I: Regular Papers, IEEE Transactions on, 2005,
Volume: 52 Issue: 7, page(s): 1276 - 1291.
[4] Sackinger, E., “The Transimpedance Limit”, Circuits and Systems I:
IV. CONCLUSIONS Regular Papers, IEEE Transactions on, Volume: 57 , Issue: 8, 2010,
Page(s): 1848 – 1856.
A novel transimpedance amplifier with variable gain,
suitable for low-power applications, has been proposed. It has
good performance in terms of noise, bandwidth and input