I. INTRODUCTION

Light detection and ranging (LiDAR) sensors have received a great deal of attention, especially for the applications of three-dimensional imaging systems such as unmanned autonomous vehicles. They can facilely detect the target’s location and recover three-dimensional (3-D) images. Typically, LiDAR sensors are based upon the time-of-flight (ToF) mechanism to measure the range between its optical source and targets located within the feasible detection range. They measure the time interval between the light-pulse emission and the reflected pulses from the targets with the speed of light, hence estimating the distance. The detection range may vary from a few mili-meters up to a few kilometers, depending upon their specific applications ⁽¹⁾.

Fig. 1 illustrates the block diagram of a pulsed ToF-based LiDAR sensor, where the optical transmitter emits a focused optical pulse to a distant target. Simultaneously, the laser driver initializes the range measurements by sending a START pulse to the time-to-digital converter (TDC). Thereafter, the target reflects the transmitted optical pulse with a few percent reflection rate which is detected by the sensitive analog-front-end circuit. In particular, the optical receiver converts the optical signal into an electrical current via an input optical detector, i.e., a photodiode, and amplifies the incoming current to an output voltage through a transimpedance amplifier (TIA). Then, the TDC measures the time interval between the START pulse and the received STOP pulse, generating a corresponding digital output code. These pulsed ToF-based LiDAR sensors can detect targets precisely within its detection range, and therefore they can be applied for various fields such as the refinement of object recognition, navigation, collision avoidance, etc.

However, conventional LiDAR sensors can hardly identify the primary return pulse from the secondary pulses caused by multiple objects due to the nature of the reflected narrow pulses. Besides, timing accuracy can be severely deteriorated owing not only to the walk-error caused by the limited slew rates of the return pulses, but also to the slow response time of comparators. Therefore, several novel circuits have been introduced to compensate the notorious walk errors ^(2-5).

In ⁽²⁾, timing discrimination scheme by the differential voltage shift was exploited to mitigate the walk errors. The differential output voltages of TIA were split and shifted before being fed to comparators so that no external threshold voltage circuitry was needed. In ⁽³⁾, walk errors were compensated by the compensation curve representing the relationship between walk error and pulse length. This method not only compensated walk error successfully, but also achieved a wide dynamic range. However, these two methods needed complicated comparators and exploited two-channel TDCs for walk error compensation, thus leading to large chip area and power dissipation. In ⁽⁴⁾, a constant-delay detection method utilizing dual-threshold circuitry was introduced to enable the use of a single-channel TDC. Yet, it mandated careful design to achieve robustness against common-mode noises. In ⁽⁵⁾, high-precision TDCs were employed to obtain better detection of multiple targets in practice, thus resolving issues like echo, ambiguity, and walk error effectively. However, good linearity and high-resolution characteristics demanded additional intricate circuitry for high-precision measurements, which also raised design difficulties. In addition, the ring-type TDCs described in ^(5,6) degraded phase noise severely owing to the parallel-output-misalignment error that was caused by the delay mismatch of the loop counter and the arbiter set. Hence, we propose a novel 3-dimensional (3-D) modified Vernier TDC (MV-TDC) in this paper that can be exploited in a pulsed ToF-based LiDAR sensor to detect targets within the range between several centimeters to a few tens of meters.

Section II presents the architecture and operations of the proposed 3-D MV-TDC. Section III demonstrates the measured results. Then, conclusion is followed in Section IV.

II. Proposed 3-D Modified Vernier TDC

Fig. 2 illustrates the block diagram of the proposed three-dimensional modified Vernier TDC (3-D MV-TDC) that combines a 2-D modified Vernier TDC utilizing a resettable T-latch (RTL) as input circuitry as described in ⁽⁷⁾, and a delay-lock loop (DLL) preceded by an XOR gate (XOR) and an edge-detector with a few inverters. Here, the total time interval between the START and the STOP pulses can be represented by an 8-bit output digital code, i.e., a 4-bit coarse-control digital code and a 4-bit fine-control code. Both simulations and measurements confirm simultaneously that the maximum detection range of this proposed 3-D MV-TDC can reach 28.8 meters, which corresponds to 96-ns time interval with the resolution of 6 ns, i.e., (τ1-τ2) = 6 ns, and also that the minimum detection distance can be as short as 18.8 centi-meters that corresponds to 0.625-ns time interval.

III. Measurement Results

Test chips of the proposed 3-D MV-TDC were implemented in a 0.13-μm CMOS technology.

Fig. 5 shows the test setup and the chip microphotograph, where the chip core occupies the area of 0.37 x 0.89 mm$^{2}$. DC measurements reveal that the 3-D MV-TDC chip dissipates 2.9 mW from a single 1.2-V supply. For range measurements, a waveform generator (Keysight, 33660A) was exploited to provide two pulses, i.e., the START and the STOP pulses with their phase shifted. Then, the parallel outputs of the 3-D MV-TDC were measured by using a logic analyzer (Saleae Logic Pro16).

Fig. 6 - 8 demonstrate the measured output digital codes of the 3-D MV-TDC for short-range, medium-range, and long-range targets, respectively. Fig. 6(a) shows the case with no time interval between the START and the STOP pulses, which corresponds to less than 18.8-cm distance to a target. Therefore, the coarse-control loop generates the output code of 0000, and also the fine-control loop provides 0000. Fig. 6(b) shows the measured results with 0.6-ns time interval between two pulses, which corresponds to 18.8-cm distance to a target. The coarse-control loop generates the output code of 0000, while the fine-control loop provides 0001.

Fig. 7 depicts the measured output digital codes for medium-range targets. Fig. 7(a) demonstrates the case of 40-ns time interval between the START and the STOP pulses, which corresponds to 12-meter distance to a target. The coarse-control loop generates the output code of 0110, while the fine-control loop provides 1111. Fig. 7(b) shows the measured results for 60-ns time interval, which corresponds to 18-meter distance to a target. The coarse-control loop generates the output code of 1001, while the fine-control loop provides 1111.

Fig. 8 demonstrates the measured output digital codes for long-range targets. With 90-ns time interval that corresponds to 27-meter distance to a target, the coarse-control loop generates the output code of 1110, while the fine-control loop provides 1111, as shown in Fig. 8(a). With 100-ns time interval corresponding to 30-meter distance, the coarse-control loop generates the output code of 1111, while the fine-control loop provides 1111, as shown in Fig. 8(b).

Table 1 summarizes the performance of the proposed 3-D MV-TDC together with the previously reported prior arts. In ⁽¹⁰⁾, a pseudo-differential delay line architecture was utilized. However, it dissipated a large power of 6.9 mW from a 1.3-V supply and the detection range was limited to 19.2 cm only. In ⁽¹¹⁾, a time amplifier was exploited to achieve 9-bit output codes. Yet, the detection range was still limited to 19.2 cm only. In ⁽¹²⁾, a gated ring oscillator configuration was introduced. Yet, it required a 1.5-V supply, thus resulting in rather large power consumption with the detection range up to 3.7 meters. In ⁽¹³⁾, the Vernier ring configuration was presented. It consumed a large power of 7.5 mW, even though the detection range was extended to 9.83 meters. Lower power dissipation and smaller chip area were demonstrated in ⁽¹⁴⁾. Still, the detection range was significantly limited to 18 centi-meters. Recently, a 3-D Vernier TDC was demonstrated in ⁽¹⁵⁾ with the detection range from 5 centi-meters up to 1.27 meters. But, it consumed a comparatively large power of 4.5 mW. Another 3-D Vernier TDC with very low power dissipation was introduced in ⁽¹⁶⁾. However, its detection range was limited to 4.3 meters only. For comparison purposes, we utilize a figure-of-merit (FoM) that is defined as the ratio of power dissipation by the three multiplied factors (i.e., the maximum detection range, the conversion rate, and 2$^{\mathrm{N}}$), where the number of bits (N) is utilized to facilitate the performance comparison, instead of the effective value (N$_{\mathrm{eff}}$).

Hence, it can be concluded that the proposed 3-D MV-TDC provides a potential to realize a low-power low-cost solution with comparatively long-range detection capability, which is particularly suitable for the applications of LiDAR sensors.

IV. CONCLUSIONS

We have realized a 3-D modified Vernier TDC in 0.13-μm CMOS for LiDAR sensor applications, where the 2-D MV-TDC shows the resolution of 6 ns for detecting the distance from 1.8 meters up to 28.8 meters, whereas the DLL preceded by an XOR and an edge-detector provides the resolution of 0.625 ns to detect the distance from 18.8 centimeters up to 3 meters. It can be concluded that the proposed 3-D MV-TDC provides a low-power long-range solution for LiDAR sensors.