I. Introduction

Recently, a low-power, low-cost CMOS LiDAR sensor has been very attractive because it can provide strong immunity against ambient RF interferences ^(1,2). Most of the state-of-the-art LiDAR sensors utilize the time-of-flight (ToF) method to measure the distance to targets by emitting optical pulses and recovering the reflective pulses.

Fig. 1 depicts a simplified block diagram of a linear-mode LiDAR sensor, in which a transmitter (Tx) consists of a laser diode and its driver to emit optical pulses, whereas a receiver (Rx) comprises a photodiode, a transimpedance amplifier (TIA) and a post-amplifier (PA). A time-to-digital converter (TDC) receives START signals from Tx for the initialization of range detection, and then detects STOP signals from Rx for the determination of target distance.

Among these blocks, the TIA is the most critical circuit to optimize the performance, thus requiring a number of characteristics, including a variable transimpedance gain with automatic gain-control (AGC) to accommodate the input currents from a few micro-amperes to a few milli-amperes, a wide bandwidth for narrow pulse recovery, a low noise current spectral density for weak reflected signal detection, and a low power dissipation per channel for chip reliability ⁽²⁾. In particular, wide bandwidth is necessary to maintain the narrow pulse-width of the reflected pulses. Otherwise, severe pulse spreading cannot be avoided especially when the reflected optical power is strong, (i.e., with large input photocurrents), thus deteriorating precise target detection. Simultaneously, a narrow bandwidth of TIA is required to reduce noise particularly when weak optical signals are detected. Therefore, a variable bandwidth depending upon the amplitudes of incoming input photocurrents is mandatory to optimize the noise performance.

Fig. 1. Block diagram of a typical LiDAR system ⁽⁶⁾.

Fig. 2. Schematic diagram of the proposed mirrored current-conveyor transimpedance amplifier (MCC-TIA).

Hence, AGC function is mandatory to change the feedback resistance, and thus to accommodate a wide range of incoming photocurrents ^(1-5). Many previous researches have realized AGC circuits either by utilizing an off-chip external control, or by using a negative feedback control.

However, these conventional methods cannot be directly applied to LiDAR sensors because a single narrow pulse should be detected. Not to mention the off-chip manual control, the negative feedback gain-control cannot fulfil the variation of transimpedance gain within a narrow single pulse, thereby occurring detection errors. In this paper, we realize a fast AGC function by exploiting a novel feedforward control-voltage generator.

II. Circuit Description

Fig. 2 depicts the block diagram of the proposed mirrored current-conveyor transimpedance amplifier (MCC-TIA), consisting of the MCC input stage followed by an inverter transimpedance stage (INV-TIS) with a feedback resistor array (FRA), a feedforward control-voltage generator (FCG), and an output buffer (OB).

1. Mirrored Current-conveyor (MCC) Input Stage

The MCC input stage comprises a parallel combination of five symmetric current-conveyor input buffers (SCC-IBs) that are located right after the photodiode, thereby functioning as a current-buffer and enabling to isolate a rather large parasitic capacitance of the photodiode from the following INV-TIS. The five SCC-IB blocks are simultaneously turned-on in parallel. Namely, the input impedance of the MCC input stage can be reduced significantly, thus accommodating the large input currents up to 2.24 mA$_{\mathrm{pp}}$. On the contrary, the output resistance of the MCC input stage can be approximately enlarged to $\sim \frac{1}{2}\left(\mathrm{g}_{\mathrm{m}}\mathrm{r}_{\mathrm{o}}^{2}\right)$ owing to the cascode configuration, where g$_{\mathrm{m}}$ and r$_{\mathrm{o}}$ represent the transconductance and the output resistance of transistors, respectively. Thereby, the output voltage (IB_O) of the MCC input stage depends linearly upon the amplitude of the incoming input currents. Then, the increased output voltages turn on the following FCG circuitry and hence the NMOS switches in the feedback resistor array (FRA).

Fig. 3 shows the schematic diagram of a SCC-IB in which a modified NMOS cascode circuit (M$_{1}$~M$_{4}$) is merged to its symmetric PMOS counterpart (M$_{5}$~M$_{8}$). Therefore, the input currents (i$_{\mathrm{PD}}$) delivered from the photodiode can be symmetrically divided into two paths. In other words, i$_{\mathrm{PD,n}}$ flows through the NMOS cascode circuit (i.e., M$_{1}$&M$_{3}$), whereas i$_{\mathrm{PD,p}}$ flows into the PMOS cascode circuit (i.e., M$_{5}$&M$_{7}$). These two currents are mirrored onto the cascode circuits (i.e., M$_{2}$&M$_{4}$ and M$_{6}$&M$_{8}$), respectively. Due to the large output resistance of the cascode circuit, it becomes possible that almost no loss of the input currents occurs in this SCC-IB scheme.

Thereafter, the mirrored currents are summed together and flow out of the feedback resistor (R$_{\mathrm{F}}$) of the INV-TIS. Hence, a positive transimpedance gain can be generated which is different from the case of a conventional voltage-mode inverter TIA.

Fig. 3. Schematic diagram of the proposed SCC-IB block.

Fig. 4. Schematic diagram of the INV-TIS with FRA.

Fig. 5. Schematic diagram of the feedforward control-voltage generator.

According to small signal analysis, the input resistance of the MCC input stage depends upon how many SCC-IB blocks are turned on. With only SCC-IB#3 switched on, the input resistance is given by,

(1)

$$ R_{i n, 3}=\frac{1}{g m 1} \| \frac{1}{g m 7} \cong \frac{1}{2 g n} $$

, where g$_{\mathrm{mi(i=1,7)}}$ is the transconductance of M$_{\mathrm{i(i=1,7)}}$. Provided that g$_{\mathrm{m1 }}$= g$_{\mathrm{m7 }}$= g$_{\mathrm{m}}$, the input resistance becomes equal to 1/2g$_{\mathrm{m}}$.

With other two SCC-IB blocks (#2 & #4) added, the input resistance of the MCC input stage is given by,

(2)

$R_{in,2}=R_{in,3}\left| \left| R_{in,\textit{parallel}}\cong \frac{1}{2gm}\right| \right| \left(\frac{1}{2gm}||\frac{1}{2gm}\right)=\frac{1}{6gm}$.

Then, all the SCC-IB blocks (#1~#5) are turned-on simultaneously, the input resistance is given by,

(3)

$R_{in}=R_{in,2}\left| \left| R_{in,\textit{parallel}}\cong \frac{1}{6gm}\right| \right| \left(\frac{1}{2gm}||\frac{1}{2gm}\right)=\frac{1}{10gm}$.

2. INV-TIS with FRA & FCG

Fig. 4 shows the schematic diagram of the INV-TIA with the FRA that includes five feedback resistors, i.e., R$_{\mathrm{Fi (i=1~5)}}$ which can be turned-on by utilizing thick-gate NMOS switches. These pairs of thick-gate NMOS switches are controlled by the proposed feedforward control-voltage generator (FCG) that consists of two-stage cascode amplifiers and an MIM capacitor (C$_{\mathrm{MIM}}$ = 5 pF) as a low-pass filter (R$_{1}$ = 2.3 kΩ shown in Fig. 5). In particular, the second-stage cascode amplifier utilizes thick-gate NMOS transistors with R$_{2}$ (= 3.3 kΩ.), thereby generating a 2.5-V to the NMOS switches in the INV-TIS.

The mechanism of the FCG can be simply described as below. First, the FCG takes the positive output voltage (IB_O) of the preceded MCC input stage. Then, it provides the final 2.5-V DC voltage (FCG_O) to the NMOS switches in the FRA. Thus, the transimpedance gain of the INV-TIS can vary automatically according to the magnitude of the incoming input currents from the photodiode. With the input currents larger than 1.12 mA$_{\mathrm{pp}}$, the FCG turns on all the NMOS switches of the FRA. Thereby, the INV-TIS yields the lowest transimpedance gain and enables to accommodate the larger input currents.

With the input currents of 80 $\mu$A$_{\mathrm{pp}}$ ~ 1.12 mA$_{\mathrm{pp}}$, the FCG cuts off the pair of R$_{\mathrm{F3}}$. Therefore, the INV-TIS can boost the transimpedance gain 3x higher.

Fig. 6. Layout of the MCC-TIA.

With the small currents less than 80 $\mu$A$_{\mathrm{pp}}$, the FCG cannot generate a 2.5-V DC voltage. Thus, only a feedback resistor R$_{\mathrm{F1}}$ can be activated and the INV-TIS amplifies the input currents with the highest transimpedance gain.

Small signal analysis indicates that the transimpedance gain of the INV-TIS is given by,

(4)

$$ Z_{T, i n v} \approx\left(\frac{A_{i n v}}{1+2 A_{i n v}}\right) R_{F, E Q} \cong R_{F, E Q} $$

, where $\textit{A}$$_{inv}$ is the voltage gain of the INV-TIS and $\textit{R}$$_{F,EQ}$ represents the equivalent feedback resistance of the FRA.

The bandwidth ($\textit{f}$$_{\mathrm{-3dB}}$) of the proposed MCC-TIA is determined at the input node of the MCC input stage, and is given by,

(5)

$$ f_{-3 d B} \cong \frac{1}{10 \pi R_{i n}\left(C_{p d}+2 C_{g s, n}+2 C_{g s, p}\right)} $$

, where $\textit{R}$$_{in}$ represents the input resistance of the MCC input stage as described in (3), $\textit{C}$$_{pd}$ is the photodiode capacitance, $\textit{C}$$_{gs,n}$ is the gate-source capacitance of NMOS transistors (i.e., M$_{1}$&M$_{2}$), and $\textit{C}$$_{gs,p}$ is the gate-source capacitance of PMOS transistors (i.e., M$_{7}$&M$_{8}$), respectively.

Meanwhile, the input-referred equivalent noise current spectral density of the MCC-TIA including five SCC-IB blocks is approximately given by,

(6)

$$ \overline{{i^{2}}_{e q}} \cong 40 K T \Gamma\left[g_{m 1}+\frac{\omega^{2} C_{t o t}^{2}}{g_{m 2}}\right] $$

, where $C_{tot}(=5C_{in}+C_{pd}$) represents the total capacitance at the input node of the SCC-IB that comprises the input capacitance$\left(C_{in}=C_{gs1}+C_{gs2}+C_{gs7}+C_{gs8}\right)$of the SCC-IB and the photodiode capacitance ($\textit{C}$$_{pd}$).

Eq. (6) clearly indicates that the noise contribution of the MCC input stage becomes the dominant factor, and also that the noise current spectral density of the MCC-TIA can be minimized under the condition that the input capacitance ($C_{in}$) is almost equal to ($\frac{C_{pd}}{5}$), provided that g$_{\mathrm{m1}}$ = g$_{\mathrm{m2}}$ is assumed.

III. Simulation Results

Post-layout simulations were conducted for the MCC-TIA by utilizing the model parameters of a 65-nm CMOS technology, where the photodiode was emulated by its electrical lumped-model with a 25 Ω series resistor and a 500-fF parasitic capacitance. Fig. 6 shows the chip layout, in which the core occupies the area of 0.035 mm$^{2}$. Fig. 7 depicts the frequency response of the MCC input stage, which confirm that a single SCC-IB block provides the input resistance of 140 Ω, the three combined SCC-IB blocks yield 46 Ω, and the total five SCC-IB blocks generate 25 Ω input resistance, respectively. It is noted that the peak and dip may be attributed to the parasitic inductance and capacitance at the input node.

Fig. 8 reveals the transimpedance gain of 58 dBΩ, and the bandwidth of 2.5 GHz with the equivalent feedback resistance 333 Ω in the INV-TIS that enables to accommodate the input currents larger than 1.12 mA$_{\mathrm{pp}}$. For the input currents of 80 $\mu$A$_{\mathrm{pp}}$ ~ 1.12 mA$_{\mathrm{pp}}$, the FCG cuts off the pair of R$_{\mathrm{F3}}$ by switching off M$_{17}$ & M$_{20}$, and thus the transimpedance gain increases up to 68 dBΩ while the bandwidth shrinks down to 892 MHz. Similarly, the FCG cutoffs the pairs of R$_{\mathrm{F2}}$ and R$_{\mathrm{F3}}$ for the smaller input currents than 80 $\mu$A$_{\mathrm{pp}}$. Thereby, the feedback resistance increases further to provide the transimpedance gain of 77 dBΩ with the bandwidth of 92~MHz. This shrunk bandwidth with enlarged transimpedance helps to reduce the noise performance of the MCC-TIA.

Also, the simulated minimum equivalent noise current spectral density is 16.8 pA/sqrt(Hz) which leads to 0.16~$\mu$A$_{\mathrm{RMS}}$ input noise current and hence -29.5 dBm optical sensitivity for bit-error-rate (BER) of 10$^{-12}$, which certainly satisfy the SNR of 14. Fig. 9 presents the simulated pulse responses of the MCC-TIA which vividly show the narrow pulse recovery resulting from the FCG circuitry. Fig. 9(a) clearly illustrates the pulse-width variation for the case of 1.12 mA$_{\mathrm{pp}}$ input current, where the output pulse spreads 3x wider without the FCG circuit.

Fig. 7. Simulated input impedance of the MCC input stage.

Fig. 8. Simulated frequency response of the MCC-TIA.

Fig. 9(b) depicts the pulse-width variation for the case of the largest input current of 2.24 mA$_{\mathrm{pp}}$, in which it is clearly seen that the output pulse spreads 3x wider unless the FCG circuit is equipped. It is also noted that a delay occurred in the FCG is less than 80 ps and thus can be neglected (~2.7 %) in a 3-ns pulse width.

Fig. 9. Simulated pulse responses of the MCC-TIA with different input currents of (a) 1.12 mA$_{\mathrm{pp}}$, (b) 2.24 mA$_{\mathrm{pp}}$, respectively, and their corresponding output voltage signals comparing the pulse spreading effect with and without the FCG circuitry.

Fig. 10 shows the simulated eye-diagrams of the proposed MCC-TIA at 200 Mb/s with different input currents of 18 $\mu$A$_{\mathrm{pp}}$ and 200 $\mu$A$_{\mathrm{pp}}$, respectively. Each output amplitude corresponds to 79 dBΩ and 66 dBΩ transimpedance gain, indicating that there exist slight mismatches (~ 2 dB) from the pulse simulations.

Fig. 10. Simulated eye-diagrams of the MCC-TIA for 2$^{31}$-1 PRBS input currents at 200-Mb/s data rates (a) 18 $\mu$A$_{\mathrm{pp}}$, (b) 200~$\mu$A$_{\mathrm{pp}}$, respectively.

Table 1 summarizes the performance of the proposed MCC-TIA with the previously reported CMOS TIAs. Ref. ⁽²⁾ demonstrated a voltage-mode CMOS feedforward (VCF) input configuration to double the transimpedance gain. Despite the AGC circuit, it could not avoid the pulse spreading. Also, the maximum detectable current was limited to 1.1 mA$_{\mathrm{pp}}$. Ref. ⁽³⁾ merged a current-mirror (CM) input configuration with a shunt-feedback (SF) topology to achieve high transimpedance gain and wide dynamic range. Here, the AGC function was conducted by using an external field programmable gate array (FPGA). Ref. ⁽⁴⁾ utilized a capacitive feedback (CF) topology to obtain low noise currents of nano-ampere levels. Yet, the gain-control function was conducted manually to provide both low-gain and high-gain modes, in which the maximum detectable current was limited to 250 $\mu$A$_{\mathrm{pp}}$. Also, pulse spreading was still present. Ref. ⁽⁵⁾ incorporated a shunt-feedback TIA with an external gain-control, where the maximum detectable current was limited to 25 $\mu$A$_{\mathrm{pp}}$, and the pulse spreading existed. In this work, we have demonstrated a feedforward gain-control mechanism to render the AGC function within the narrow pulse-width of a single-shot optical pulse, thus enabling to remove the undesired pulse spreading. The maximum and minimum detectable currents are 2.24 mA$_{\mathrm{pp}}$, and 18 $\mu$A$_{\mathrm{pp}}$, respectively.

IV. CONCLUSIONS

We have presented a current-mode MCC-TIA which achieved narrow pulse recovery and automatic gain-control within a narrow single pulse. The MCC-TIA can provide a low-cost LiDAR sensor solution.