A high sensitive 66 dB linear dynamic range receiver for 3-D laser radar

    Corresponding author: Zhangming Zhu, zmyh@263.net
  • School of Microelectronics, Xidian University, Xi'an 710071, China

Key words: laser radarlinear dynamic rangetransimpedance amplifiertiming comparatorwalk error

Abstract: This study presents a CMOS receiver chip realized in 0.18 μm standard CMOS technology and intended for high precision 3-D laser radar. The chip includes an adjustable gain transimpedance pre-amplifier, a post-amplifier and two timing comparators. An additional feedback is employed in the regulated cascode transimpedance amplifier to decrease the input impedance, and a variable gain transimpedance amplifier controlled by digital switches and analog multiplexer is utilized to realize four gain modes, extending the input dynamic range. The measurement shows that the highest transimpedance of the channel is 50 kΩ, the uncompensated walk error is 1.44 ns in a wide linear dynamic range of 66 dB (1:2000), and the input referred noise current is 2.3 pA/$\sqrt {{\rm{Hz}}} $ (rms), resulting in a very low detectable input current of 1 μ A with SNR=5.

    HTML

1.   Introduction
  • By directly measuring the flight time of the laser pulse, the distance of a target can be accurately calculated. The pulsed time-of-flight (TOF) laser range finding principle is a basic distant detection method. At present, this kind of laser radar is widely used in the commercial sweeping robot and automatic driving vehicle because of its technical maturity and high precision.

    In the TOF technique, the input pulse of the receiver is not necessarily increased in linearity, and even the saturation input is allowed, so the dynamic range of these receivers is always very wide[2-12], leading to a large detection range. However, with the development of 3D laser imaging technology, the target detection is not limited to distance detection, but needs to distinguish the target pattern in detail. The reflection coefficient of different materials is variable, so the echo intensity of different targets at the same distance may be different, and the TOF technology may not distinguish the difference as well. In order to detect the echo intensity, the receiver must be able to amplify the echo linearly. Ngo et al.[1] proposed a receiver based on a resistive feedback transimpedance amplifier (TIA), but this method cannot maintain a high bandwidth when the transimpedance gain is increased. Furthermore, its output swing is also limited.

    In order to acquire the time of flight and the intensity of the echo pulse simultaneously, this work presents an integrated CMOS laser radar receiver combined with leading-edge detection technique and linear amplification technique: (1) an additional feedback is employed in a regulated cascode transimpedance amplifier to decrease the input impedance; and (2) a variable gain transimpedance amplifier controlled by digital switches and analog multiplexer is utilized to realize four gain modes to extend the input dynamic range.

2.   Design issue

    2.1.   Walk error

  • Since the distance, angle and reflectivity of the irradiated target are different, the amplitude of the echo is therefore quite different. When the leading edge of the echo is identified by the timing comparator, the timing of different pulses crossing the comparator threshold are always variable, which is called walk error [10], and this error can be interpreted as the comparator output jitter. Timing jitter and single-shot accuracy can be expressed as:

    where $\sigma_{\rm t}$ and $\sigma_{\rm N} $ are the standard deviation of timing jitter and noise respectively, $v$ is the input signal, $t_{\rm r}$ stands for the rising time of the input signal, and SNR represents the ratio of the peak voltage to the rms noise. As shown in Fig. 1, walk errors arise from the pulses with different width and rise time. Apparently, increasing SNR or decreasing $t_{\rm r}$, the detection accuracy can be improved. In order to ensure the effectiveness of detection, the minimum SNR should be greater than 5. Therefore, the timing walk error is greatly related to the slew rate of the echo pulse. Note that the shorter the pulse is, the smaller the walk error is.

  • 2.2.   Noise and BW

  • The input referred noise current has a significant effect on the receiver sensitivity, which is obtained by dividing the total output rms noise by the low frequency gain of the transimpedance amplifier (TIA) and the square root of the TIA bandwidth[17]:

    where $\overline {v{ }_{\rm n,out,rms}} $ is the output rms noise, $\overline {v{ }_{\rm n,out,\text{avg}}} $ represents the output noise current density, and $R_{\rm {T\thinspace }}$stands for the low frequency transimpedance gain of the TIA. When increasing the bandwidth, the noise only increases by the square root. Therefore, the narrow pulse helps to improve SNR. Considering the driving ability of the laser transmitter and the power consumption growth caused by the increase of the bandwidth, a 3-ns-width laser pulse is used in this work. The relationship between the pulse rise time and the required bandwidth (BW) of the receiver can be expressed as [10]:

    In this work, the rise time of the pulse is 1 ns, so the bandwidth of the receiver needs to be larger than 350 MHz. The total parasitic capacitance of the receiver input is about 2 pF, including 1.5 pF among the APD and others among the chip input PAD and ESD. The input pole of the pre-amplifier greatly limits the bandwidth, so the input impedance of the TIA should be as small as possible.

3.   Proposed receiver
  • From the above analysis, it can be seen that the walk error of the output pulse can be reduced by shortening the detection pulse width (or increasing the bandwidth), thereby improving the detection precision. However, the large parasitic capacitance induced by the front-end photodiode introduces a low-frequency pole, which reduces the receiver bandwidth. Therefore, this work presents an additional feedback loop on the traditional regulated cascode (RGC) circuit, which further reduces the input impedance of the receiver, thus increasing the input pole frequency. In addition, in order to improve the three-dimensional imaging distance of the laser radar, the detectable linear dynamic range of the receiver should be wide enough. However, the traditional scheme cannot guarantee the linear output in a wide dynamic range. Therefore, a simple analog multiplex is utilized in this receiver to adjust the gain, so that the linear dynamic range is extended.

    Fig. 2 shows a simplified receiver chip block diagram of this work. An APD operating in linear mode converts a laser pulse into a current pulse, and then the current pulse is amplified by a transimpedance pre-amplifier and a post-amplifier to a suitable amplitude. Two timing comparators are used to detect the slew rate and pulse width of the echo, which can be used to compensate the walk error[13, 14]. For this receiver, a wide dynamic range and large output swing are required to linearly convert the echo signal, so a variable gain amplifier is employed.

  • 3.1.   Adjustable transimpedance pre-amplifier with auxiliary feedback

  • Regulated cascode (RGC) is a kind of widely used broadband TIAs, as depicted in Fig. 3(a). With an auxiliary feedback amplifier, the input impedance of a common gate amplifier is reduced by ($1+ g_{\rm {mA}}R_{\rm {A}})$, where $g_{\rm {mA}}R_{\rm {A\thinspace }}$is the gain of the auxiliary amplifier. Therefore, the transimpedance gain of the RGC is expressed as follows[7]:

    where $C_{\rm {in}}$ and $C_{\rm {o}}$ are the total capacitor of the input node and the output node, respectively. $1{{\text{g}}_{\text{m1}}}\left( \text{1+}{{\text{g}}_{\text{mA}}}{{R}_{\text{A}}} \right)$ is the input impedance of the RGC. Eq. (4) demonstrates that small input impedance can improve the bandwidth of the RGC. If the input impedance is low enough, the input pole will be pushed to a very high frequency. Thus, the output pole turns into the dominant pole.

    The input referred noise current spectral density in RGC is derived as:

    where $C_{\rm {gs1}}$ is the gate-source parasitic capacitance of M1, and $C_{\rm {gdA\thinspace }}$is the gate-drain parasitic capacitance of M$_{\rm {A}}$. Eq. (5) shows that the parasitic capacitance is one of the main factors that increases the input referred noise, so it is necessary to reduce the aspect ratios of the input transistor and the auxiliary amplifier to minimize the parasitic capacitance. However, a small input transistor leads to low transconductance, thereby reducing the circuit bandwidth. In general, the input noise and the bandwidth need to be compromised.

    In order to further reduce the input impedance of TIA, an additional feedback is introduced on the traditional RGC, as depicted in Fig. 3(b). The additional shunt-shunt feedback consists of M$_{\rm {B}}$, M$_{\rm {C}}$, and R$_{\rm {B}}$, which further improves the loop gain. Thus the input impedance of the proposed structure is approximated to:

    where $g_{\rm mA} g_{\rm mB} R_{\rm A} R_{\rm B} $ is the gain of the cascade feedback stage. If the second term increases, the input pole will be pushed to a higher frequency, thus the bandwidth is increased. Note that M$_{\rm {C}}$ directly introduces noise current into the input node, so it is necessary to reduce the aspect ratio of M$_{\rm {C}}$, which reduces the additional noise current, but also decreases the parasitic capacitance of the input node.

    To adjust the transimpedance gain, the digital controlled transistor K1/K2 is used to switch the load resistance. There are two points that should be noticed: firstly, the size of the switch transistors needs to be large enough to prevent the on-resistance impacting the load resistance; secondly, the load resistance is too large to reduce the output swing and bandwidth, therefore, the value of the load resistance should be selected carefully.

  • 3.2.   Variable gain post-amplifier with analog multiplexer

  • In order to make the timing comparator and the post-stage ADC obtain the pulse efficiently, the post-amplifier needs to amplify the output of the pre-amplifier to a sufficiently large amplitude (larger than 1 V), thus a variable gain amplifier with analog multiplexer is proposed in this work.

    If a single ended structure is employed, the post-amplifier can hardly meet the requirements of the high bandwidth, the wide dynamic range, and the large output swing at the same time. So a single to differential buffer is utilized to improve the headroom of the output swing. Note that if the output amplitude of the pre-amplifier is too large, the input transistor of the post-amplifier will be forced into the nonlinear region. Therefore, the maximum output amplitude of the pre-amplifier is set to 200 mV.

    The post-amplifier consists of three diode-loaded differential amplifiers and an analog multiplexer, as shown in Fig. 4. The number of cascade amplifiers is selected by the digital control switches (K3/K4/K5) being 1, 2, or 3, and the high-pass filters are employed to achieve AC coupling between the stages. When K3/K4/K5 separately turns on, the gain of the post-amplifier is adjusted to 14, 28, and 42 dB in turn. Note that the gain of the single stage amplifier cannot be too large to guarantee the bandwidth, and too many cascaded amplifiers will make the design more complicated, so the bandwidth and the complexity of the circuit should be taken into account to select the number of cascaded stages. In this work, the gain of each amplifier is set to 14 dB, and the diode load is used to ensure that the gain of each stage is not affected by process variations. The analog multiplexer can flexibly adjust the overall gain to 94, 80, 66, and 54 dB, which meets the requirement of the linear output.

    In order to ensure the bandwidth of the receiver in different gain mode, considering the cascade effect, the overall bandwidth of the post-amplifier can be expressed as:

    where $f_{\rm t}$ and $f_{\rm s}$ are the overall bandwidth of the post-amplifier and the single stage amplifier, respectively. Eq. (7) depicts that the bandwidth of the single amplifier must be greater than the cascade amplifier, if the number of cascaded stages is 3, the bandwidth of each stage should be greater than 686 MHz; if the number of cascaded stages is 2, the bandwidth of each stage should be greater than 543 MHz. For satisfying all the bandwidth requirements in every gain mode, the bandwidth of each stage is expected to be at least 700 MHz for there to be enough of a margin. The last stage needs to drive the output buffer and two timing comparators, thus its bias current should be increased to improve its drive capability.

    The AC performance curves of the cascade of the transimpedance pre-amplifier and post-amplifier in different gain modes are shown in Fig. 5. The bandwidth of 54 dB gain mode is quite different from the other gain modes. This is because the load resistance of the pre-amplifier is 100 $\Omega $ in the 54 dB gain mode, while it is 400 $\Omega $ in the other gain modes. It also suggests that the transimpedance pre-amplifier is the main factor limiting the overall bandwidth, and its output pole is the dominant pole.

  • 3.3.   Timing comparator

  • The timing comparator showed in Fig. 6 is a cascade of one Gilbert amplifier, five amplifiers and one latch. In order to ensure sufficient bandwidth, the gain of each amplifier should be small (about 6 dB). The cascaded amplifiers can amplify echo pulses with very small amplitudes, reducing the deviation in comparator delay at different amplitudes, so the error introduced by the comparator delay is less than the walk error of the pulse [15, 16]. The comparator threshold can be flexibly changed by an external voltage to match the output common mode voltage of the post-amplifier. The latch with a reset switch can increase the frequency of the comparator while reducing the risk of false triggering.

4.   Measurement result
  • This work was fabricated in 0.18 $\mu $m standard CMOS technology, and the active area occupies around 0.85×0.67 mm$^{\mathrm{2}}$ (Fig. 7). Fig. 8 shows the transient response test fixture, an InGaAs APD is irradiated by a 3 ns-half-width and 1 ns-rise-time laser pulse through an optical attenuator. The responsivity of the APD is set to 5 A/W, and the attenuator adjusts the laser pulse to the desired power. A trigger pulse synchronized with the laser pulse and the differential analog outputs are measured by using a Tektronix TDS5104B oscilloscope, and the digital outputs are captured by an Altera EP3SL150F1152 FPGA. Note that the analog outputs are measured by a differential probe.

    Since the maximum gain mode represents the minimum noise level which the receiver can achieved, the measured output peak-peak noise of the highest gain mode after turning off the light source is 12 mV$_{\rm {p-p}}$, as shown in Fig. 9, and the correct output noise should be 9.7 mV$_{\rm {p-p\thinspace }}$when the oscilloscope background noise of 2.3 mV$_{\rm {p-p}}$ is subtracted. Considering the receiver bandwidth is approximately 350 MHz, the input referred noise current is calculated as 2.3 pA/$\sqrt {\text{Hz}} $(rms)[17]. If SNR $=$ 5, a minimum detectable output signal of 48.5 mV, or a minimum detectable input current of almost 1 $\mu $A, can be achieved.

    Fig. 10 shows the transients of the minimum and maximum input signals that can be detected by this receiver. The output of 1 $\mu$A input in the 94 dB gain mode is 51.3 mV, and the output of 2 mA input in the 54 dB gain mode is 1.08 V. Due to process deviations, the measured values are slightly larger than the simulation values. As can be seen from Fig. 11, the transient response of each gain mode is well linear. The linear dynamic ranges of each gain mode are 20, 14, 20, and 12 dB, respectively, so that the overall linear dynamic range of the receiver achieves 66 dB, or $1:2000$.

    In order to visually measure the walk error, the propagation delay between the synchronous trigger pulse and the receiver analog output is measured. This delay, which includes the jitter of the sync pulse, the total input-to-output delay of the receiver, and the nonlinearity of the receiver, is consistent with the non-ideal factors used in practice. The synchronization pulse and the analog output waveform are shown in Fig. 12(a). Cursor 1 is placed at the point where the sync pulse rises to 30% V$_{\rm {P-P}}$, and cursor 2 is set to the time when the output pulse rises to SNR = 3. Note that the comparator threshold is placed at the level of SNR = 3. Fig. 12(b) shows the walk error of the receiver is 1.44 ns. Thanks to the adjustable gain design, the output amplitudes in each gain mode are large enough, as shown in Fig. 11, which greatly reduces the walk error introduced by the small amplitudes.

    Table 1 summarizes the performance of each gain mode. The total power consumption of the highest gain mode is 105 mW with a 3.3 V supply. In order to drive the off-chip test instrument, the output driver occupies a large part of the total power consumption (about 60 mW), so the power consumption of each gain mode is similar.

    The proposed work uses the simple digital gain switches, while guaranteeing the TOF detection precision, to reach a wide linear dynamic range. Since the TIAs in optical communication are more concerned about the bandwidth, rather than the linear dynamic range of the analog output, they should be excluded from the performance comparison. The main performance of the proposed receiver is summarized and compared with several wide dynamic range TIAs for the laser radar presented in other references in Table 2. Although Refs. [2-4] show a very wide dynamic range, it is not suitable for linear laser 3-D imaging because of the lack of linear amplification. Ngo et al.[1] can linearly amplify the input current over a wide dynamic range, but its output swing is too small, limiting the resolution of further processing. In contrast, this work has the advantage of good noise performance, low walk error, and high transimpedance gain.

5.   Conclusion
  • To meet the requirements of 3-D laser radar, a low noise, large output swing and high linear dynamic range TIA with adjustable gain has been implemented in the 0.18 $\mu $m CMOS process. The experimental results confirm that the TIA has four configurable gain modes, and the highest gain is 94 dB. The uncompensated walk error is 1.44 ns in a wide dynamic range of $1:2000$, and the input referred equivalent noise current is 2.3 pA/$\sqrt {\text{Hz}} $ (rms) or the minimum detectable input current is low to 1 $\mu $A when SNR $=$ 5 with a 3.3 V supply.

Figure (12)  Table (2) Reference (17) Relative (20)

Journal of Semiconductors © 2017 All Rights Reserved