I. INTRODUCTION

Recently, LiDAR(Light Detection And Ranging) systems have been paid a great deal of attention in the applications of range measurements, object recognition, near-field image processing, unmanned autonomous vehicles, etc. Especially, it is expected that they would be utilized in more various fields in near future, because of a number of advantages such as fast lock-on time, small beam spread, and decelerating vehicle detection ability when compared to conventional RF radar systems ⁽¹⁾.

Fig. 1 shows a typical LiDAR system that transmits a short optical pulse from the laser source and receives the reflected optical pulses from a target onto the input optical detector(typ. Avalanche photodiodes and PIN photodiodes). Then, the front-end CMOS integrated circuit successfully processes the incoming weak signals, thereby enabling to recognize the position and the shape of a target located in few tens of meter range ⁽²⁾.

Fig. 1. Block diagram of a typical LiDAR system.

In general, optical detectors yield very small output currents. Therefore, it mandates a transimpedance amplifier(TIA) that converts the weak photocurrents into voltage signals of sufficient magnitude for the following signal processing. Also, the optimization of high transimpedance gain and low noise characteristics is required at the receiving end. However, the bandwidth and sensitivity performance of an optical receiver is significantly deteriorated owing to the notorious photodiode capacitance. In addition, a single-ended circuit configuration is typically vulnerable to common-mode noises including power supply noise and crosstalk noise generated from silicon substrate. Hence, a fully differential structure even is desirable from the input stage to improve common-mode rejection ratio, e.g., power supply rejection ratio(PSRR) ⁽³⁾.

This paper presents a novel fully differential TIA by exploiting a mirrored-cascode circuit to a conventional voltage-mode cascode TIA for better sensitivity than a current-mode TIA. Besides, bootstrapping circuit technique is applied to reduce the significant direct effect of the photodiode capacitance on bandwidth and noise characteristics.

II. Proposed BFD-TIA

Fig. 2 shows the block diagram of the proposed bootstrapped fully differential TIA(BFD-TIA), where the mirrored-cascode(MC) input stage incorporates a voltage-mode cascode configuration with its mirrored cascode circuit to provide differential outputs, hence leading to less susceptibility to common-mode noises. Then, it is followed by a differential post-amplifier(PA) and a current-mode logic output buffer(OB) to obtain fully differential outputs.

Fig. 2. Schematic diagram of the proposed BFD-TIA.

Also, bootstrapping circuit technique is exploited in the MC input stage to reduce the direct effect of the photodiode capacitance(C$_{\mathrm{pd}}$) on the degradation of bandwidth and noise performance. In addition, DC offset current cancellation(DCC) is employed at the input node to remove DC offset currents.

1. Mirrored-cascode Input Stage

Fig. 3 shows the schematic diagram of the MC input stage. First, the incoming current signals from the photodiode generates the negative output(OUT$_{\mathrm{N}}$) through the cascode circuit with a feedback resistor(R$_{\mathrm{F1}}$). Therein, the drain node of M$_{1}$ provides the 180$^{\mathrm{o}}$ inverted voltage signal(v$_{1}$) with the same magnitude as that of the input node voltage(v$_{\mathrm{in}}$). Then, this inverted voltage(v$_{1}$) passes through an AC-coupling capacitor(C$_{\mathrm{c}}$), appears as the input signal of the MC differential stage, and finally generates the positive output(OUT$_{\mathrm{P}}$) ⁽³⁾. Another capacitor(C$_{1}$) is added to the gate of M$_{2}$ for symmetry at high frequencies to acquire fully differential signaling.

Fig. 3. Schematic diagram of the proposed MC input stage.

According to small signal analysis, the inverted voltage(v$_{1}$) is given by,

(1)

$\begin{align} \mathrm{\text{v}}_{1}&\cong - g_{m1}\times \left(\left.r_{o1}\right\| \frac{1}{g_{m3}}\right)v_{in}\\ &\cong - \left(g_{m1}\times \frac{1}{g_{m3}}\right)v_{in}\cong ~ - v_{in} \end{align}$

The input resistance(R$_{\mathrm{in}}$) and the differential transimpedance gain of the MC input stage are given by,

(2)

$\begin{align} R_{in}&=~ \frac{v_{in}}{i_{pd}}=\frac{R_{F1}}{1+g_{m1}R_{D1}} \end{align}$

(3)

$\begin{align} \frac{v_{OU{T_{N}}}}{i_{pd}}&=\left(\frac{v_{in}}{i_{pd}}\right)\left(\frac{v_{OU{T_{N}}}}{v_{in}}\right)=- \frac{g_{m1}R_{D1}R_{F1}}{1+g_{m1}R_{D1}}\cong - R_{F1}\\ \frac{v_{OU{T_{P}}}}{i_{pd}}&=\left(\frac{v_{1}}{i_{pd}}\right)\left(\frac{v_{OU{T_{P}}}}{v_{1}}\right)=\frac{g_{m2}R_{D2}R_{F1}}{1+g_{m1}R_{D1}}\cong ~ R_{F1} \end{align}$

where it is assumed that g$_{\mathrm{m1}}$ = g$_{\mathrm{m2}}$ and R$_{\mathrm{D1}}$ = R$_{\mathrm{D2}}$.

Therefore, it is clearly seen that the proposed MC input stage provides the same differential transimpedance gain, resulting in a potential to be less sensitive to common-mode noises.

Meanwhile, the equivalent noise current spectral density is given by,

(4)

$\begin{align} \overline{i_{eq}^{2}}&=\frac{4kT}{R_{F1}}+\omega ^{2}\left(C_{pd}+C_{in1}\right)^{2}\times \left[\frac{4kT}{g_{m1}}+\frac{4kT}{g_{m1}^{2}R_{D1}}\\ ~ ~ ~ ~ ~ ~ ~ ~ +\frac{4kT}{g_{m1}^{2}R_{F2}}+~ ~ \frac{4kT}{g_{m1}^{2}g_{m1}R_{F2}^{2}}+\frac{4kT}{g_{m1}^{2}g_{m2}^{2}R_{F2}^{2}R_{2}}\right]\\ &\cong \frac{4kT}{R_{F1}}+\frac{4kT}{g_{m1}}\times \omega ^{2}\left(C_{pd}+C_{gs1}\right)^{2} \end{align}$

Hence, the transconductance(g$_{\mathrm{m1}}$) of M1 should be increased to reduce the noise. Yet, it is noted that either the increase of bias current may lead to large power consumption, or the increase of aspect ratio may enlarge chip area.

Also, the bandwidth of the proposed MC input stage is given by,

(5)

$\begin{align} f_{3dB}\cong \frac{1+g_{m1}R_{D1}}{R_{f1}\left(C_{pd}+C_{in1}\right)} \end{align}$

where it is clearly seen that the bandwidth is inversely proportional to the photodiode capacitance.

Fig. 4(a) depicts the simulated frequency response of the proposed BFD-TIA, showing 86-dB${Ω}$ trans-impedance gain, 373-MHz bandwidth, 7.9-pA/sqrt(Hz) noise current spectral density, -23-dB common-mode noise rejection ratio, and 20-mW power consumption. With the bootstrapping circuit, the BFD-TIA achieves 1.38 times wider bandwidth of 516 MHz and lower noise current spectral density of 7.5 pA/sqrt(Hz). Fig. 4(b) also depicts the simulated eye-diagrams of the BFD-TIA for 2$^{31}$-1 PRBS, where it is clearly seen that two identical eyes are obtained by using the MC input stage.

Fig. 4. Simulation results of the BFD-TIA: (a) frequency response, (b) differential eye-diagrams for 20 ${μ}$A$_{\mathrm{pp}}$ 2$^{31}$-1 PRBS.

2. Bootstrapping Stage

Typically, the bandwidth and noise performance of a voltage-mode TIA is greatly deteriorated because of the photodiode capacitance. In this work, we apply the bootstrapping technique in the MC input stage, thereby significantly reducing the effect of the notorious photodiode capacitance.

Fig. 5 shows the schematic diagram of the proposed bootstrapping stage(BS), where the drain-node voltage(v$_{1}$ = -v$_{\mathrm{in}}$) of M$_{1}$ in the MC input stage is utilized as the input signal of the bootstrapping circuit. The BS generates the output signal(v$_{\mathrm{pd}}$) which is equal to v$_{\mathrm{in}}$ by cascading a PMOS source-follower and an NMOS common-source amplifier to provide the voltage gain of -1. Therefore, the AC voltage at the cathode of the photodiode is equal to the input voltage(v$_{\mathrm{in}}$) of the BFD-TIA. Certainly, a slight delay mismatch occurs across the photodiode. Yet, the AC voltage signals across the photodiode are applied with the same magnitude, so that the influence of the photodiode capacitance upon the bandwidth and the noise performance can be greatly reduced.

Fig. 5. Schematic diagram of the bootstrapping stage.

Fig. 6 shows the transient simulation results of the BS circuit, where it is clearly seen that the input voltage(v$_{\mathrm{in}}$ = 12 mV$_{\mathrm{pp}}$) of the BFD-TIA is almost the same as that of the BS with a slight delay mismatch of less than 0.345 fs.

Fig. 6. Transient simulations of the bootstrapping stage.

III. Measurement Results

Test chips of the proposed BFD-TIA were implemented by using a 0.13-${μ}$m CMOS process. Fig. 7 shows the chip microphotograph, where the chip core occupies the area of 0.022 mm$^{2}$. A PIN-photodiode, as an optical detector, was emulated by its electrical lumped-model with a 25-${Ω}$ resistor and a 500-fF parasitic capacitance.

Fig. 7. Chip photo of the proposed BFD-TIA.

Fig. 8 shows the test setup and its PCB module for measurements.

Fig. 8. Test setup and its PCB module.

Fig. 9 demonstrates the measured output eye-diagrams of the BFD-TIA, where the output signals provide clean eye-openings for both 20 ${μ}$A$_{\mathrm{pp}}$ and 110~${μ}$A$_{\mathrm{pp}}$ input currents at different data rates.

Fig. 9. Measured eye-diagrams of the BFD-TIA for (a) 20~${μ}$A$_{\mathrm{pp}}$, (b) 110 ${μ}$A$_{\mathrm{pp}}$ 2$^{31}$-1 PRBS inputs.

Fig. 10 depicts the measured differential output eye-diagrams for 50 ${μ}$A$_{\mathrm{pp}}$ 2$^{31}$-1 PRBS inputs, demonstrating less than 3% mismatch of the differential eye-openings at two different data rates of 125 Mb/s and 300 Mb/s.

Fig. 10. Measured differential output eye-diagrams of the BFD-TIA with 50 ${μ}$A$_{\mathrm{pp}}$ 2$^{31}$-1 PRBS inputs at different data rates of (a) 125 Mb/s, (b) 300 Mb/s.

Fig. 11 shows the test setup for pulse measurements.

Fig. 11. Test setup for pulse response.

Fig. 12 demonstrates the output pulses of the BS circuit and the BFD-TIA for 20~${μ}$A$_{\mathrm{pp}}$ input pulses, indicating that the input voltage(v$_{\mathrm{in}}$) of the BFD-TIA is estimated to 21.2~mV$_{\mathrm{pp}}$ by dividing the output voltage(OUT$_{\mathrm{P}}$ = 336~mV$_{\mathrm{pp}}$) by the voltage gain(= 24 dB). Then, it is very similar to the BS output voltage of 20.4 mV$_{\mathrm{pp}}$, leading to 3.8-% mismatch.

Fig. 12. Measured output pulses of both the BS and the BFD-TIA with 20 ${μ}$A$_{\mathrm{pp}}$ input pulses.

Therefore, it confirms that the photodiode capacitance(C$_{\mathrm{pd}}$) can be effectively eliminated by rendering the voltage across the photodiode equal, hence reducing the deterioration of the overall performance such as bandwidth and noise.

Table 1 compares the performance of the proposed BFD-TIA with the previously reported prior arts. When compared to the BiCMOS inverter TIA in ⁽⁴⁾, the BFD-TIA provides 39% larger transimpedance gain, 14% less noise, and 89% less power consumption. Comparison with the single-ended VCF TIA in ⁽⁵⁾ reveals that the BFD-TIA provides 11.3% higher transimpedance gain and 19.5% lower power consumption for a little higher noise current spectral density. Although the capacitive feedback TIA in ⁽⁶⁾ shows much better noise performance with variable transimpedance gain than our BFD-TIA, it dissipates 70% larger power. When compared to the CMOS inverter TIA in ⁽⁷⁾, the BFD-TIA yields 9.3% higher transimpedance gain and 79% lower power dissipation. In particular, the TIAs reported in ^(5,6) were pseudo-differential because their single-ended input signals passed through either a low-pass filter(LPF) or a replica circuit to form differential outputs.

However, the proposed BFD-TIA provides differential structure from the input stage by exploiting the MC input stage with no need of either a low-pass filter or a replica, hence showing good PSRR performance and smaller chip area. Finally, we have utilized the well-known figure-of-merit(FoM) that is defined by the ratio of the power dissipation over the operation speed, demonstrating that the BFD-TIA provides superior FoM characteristics among the TIAs together with ⁽⁵⁾.

IV. CONCLUSIONS

In this paper, we have realized a fully differential TIA in a 0.13-${μ}$m CMOS process that exploits a novel mirrored-cascode input configuration to generate differential signaling even from the input stage. Also, bootstrapping circuit technique is applied in the input stage and enables to isolate the photodiode capacitance from the noise and bandwidth determination by generating the same AC voltage as the input-node voltage and then connecting it onto the cathode of the photodiode. Hence, it can be concluded that the proposed BFD-TIA provides a potential for low-power and low-noise solutions in LiDAR systems for the applications of unmanned autonomous vehicles as well as in the area of near-field image processing systems.