An Eight-Channel Switching-Linear Hybrid Dynamic Regulator with Dual-Supply LDOs for Thermo-Optical Tuning

—A novel switching-linear hybrid dynamic regulator with dual-supply LDOs for thermo-optical tuning is presented in this brief. Compared with conventional designs, the proposed design leverages the intrinsic dual supplies to extend the operating range of the LDOs, and increases the thermo-optical tuning efﬁciency by reducing the dropout of the LDOs through dynamic voltage tracking. It can simultaneously regulate eight output channels and track 0.8 V pp sinusoidal waveforms at different frequencies. Signiﬁcant efﬁciency improvement of the proposed design is achieved for envelope signals with a small difference, which is common in thermo-optical tuning. Implemented in 130 nm CMOS process, the proposed design has a total chip area of 0.675 mm 2 . The proposed design achieves a conversion efﬁciency of 88% at 1 V output driving a 200 Ω load. Its dynamic efﬁciency is about 80% when tracking 50 kHz sinusoidal signals.


I. INTRODUCTION
T HERMO-optic tuning is the core dynamic control technology for photonic devices, and has been widely used in micro-ring resonator (MRR) [1], Mach-Zehnder interferometer (MZI) [2], silicon quantum photonic circuits [3], optical neural network (ONN) [4], and optical phased array (OPA) [5], etc. The thermo-optic tuning dynamically adjusts the effective refractive index of photonic devices by changing the device temperature and its general model is shown in Fig. 1. An on-chip resistor with a few hundred ohms is usually used as the heater [6]. By changing the power supply voltage of the resistor, the device temperature is easily adjusted. Most recent designs on thermo-optic tuning [1]- [4] apply PCB or benchtop power supplies, which are not practical for large-scale integrated systems. Few designs [5], [7] achieve the integration of the power supply, but the area of the power management circuit (PMC) is relatively large. Furthermore, there is still a lot of room for improving the system efficiency as well. For large-scale and energy-efficient thermo-optic tuning, a highperformance PMC with small chip area is required.
In traditional thermo-optical tuning, a linear power supply with fixed input voltage is widely used. However, this approach has a low tuning efficiency and causes additional Siyuan   heat dissipation problem. As shown in Fig. 2, we use an MRR to illustrate this problem. When the external environment temperature is unstable, the thermal regulator in Fig. 2 (a)(b) changes the output power by dynamically adjusting the V TH to maintain the MRR's temperature, and stabilize the wavelength of MRR. For linear power supplies, the efficiency is inversely proportional to the dropout. When the V TH decreases, the power efficiency with fixed inputs will significantly drop. Alternatively, using a dynamic power supply in Fig. 2 (b) can reduce the dropout voltage, therefore improving the power conversion efficiency of the power supply. Dynamic power supplies have traditionally been used in radio-frequency power amplifiers [8]- [11] and audiofrequency power amplifiers [12]. However, the dynamic power supply for thermo-optic tuning is quite different from the above applications in terms of power range, envelope tracking (ET) speed, and the number of channels. For general thermooptic tuning, the required output power is only about tens of mW [6], and the typical bandwidth is around tens of kHz [6]. Meanwhile, multi-channel thermo-optic tuning is used in many applications, which requires multi-channel dynamic regulators. TABLE I compares the differences between these two types of dynamic power supplies. Furthermore, most existing schemes are board-level designs, and cannot meet the large-scale electronic-photonic integration requirements.
In this brief, we present a novel eight-channel switchinglinear hybrid dynamic regulator with dual-supply LDOs supporting both high conversion efficiency and wide tuning range. The remainder of this brief is organized as follows. Section II presents the structure and operating principles. Section III shows the simulation results. Section IV draws the conclusion.

II. EIGHT-CHANNEL HYBRID DYNAMIC REGULATOR
The architecture of the proposed eight-channel switchinglinear hybrid dynamic regulator with dual-supply LDOs is shown in Fig. 3. The architecture has intrinsic dual supplies, i.e., the global supply V DD and the intermediate supply V A . It is mainly composed of an envelope processor, a buck converter with fully-integrated current-mode Type-III compensator, lightweight local generated supplies (LLGS), and eight parallel dual-supply LDOs with NMOS power stage. V Env is the envelope of all input signals, which is generated by the envelope processor. The envelope processor assists the buck converter to generate a suitable first-stage output voltage V A , which should be as low as possible but ensure the normal operations of the second power stage. The LLGS and the switching converter share the global supply voltage V DD . The function of the LLGS is to provide an appropriate local voltage for the controllers of the dual-supply LDOs. Meanwhile, the power stages of the LDOs are connected to the output of the switching converter and supplied by V A . This design can alleviate the restriction on the minimum V A by the controller of the second-stage LDO without adding additional complexity. In addition, according to the changes of the input control signals V Env1 to V Env8 , the architecture can dynamically adjust the output V A of the first-stage switching converter, thereby reducing the dropout of the second-stage converter. This will improve conversion efficiency and reduce the thermal crosstalk.

A. Envelope Processing Module
The envelope processing module is used to generate a suitable V A for the second stage. Fig. 4 shows the structure of the envelope processing module. It consists of a maximum voltage selection module, a low-pass filter (LPF), and a non-inverting adder. Fig. 5 shows a simple dual-input maximum selector and the LPF used in this brief. Cascading multiple dualinput maximum voltage selectors can achieve the maximum selection of multiple signals. The first-order butterworth active LPF with 500 kHz cut-off frequency is designed to filter out the high-frequency components of the envelope signal which are outside the bandwidth of the buck converter. V Env AC is the envelope signal of all input signals. With the non-inverting adder, V Env equals to the superposition of the V Env AC and a DC offset. As V A = 2V Env while V THi = 2V Envi (i = 1, 2, . . . , 8), the dropout between V A and the max {V TH1 , V TH2 , . . . , V TH8 } equals to 2V Offset . By adjusting the value of V Offset , the minimum dropout can be guaranteed in most operating situations, thereby improving the conversion efficiency and minimizing the thermal crosstalk. In this brief, the DC offset is around 20 mV.

B. Buck Converter
Compared with the LDO, the switching converter has a high conversion efficiency. However, due to its relatively large chip area and output power, as well as its large off-chip inductors and capacitors, it is not suitable for directly supplying the resistive heaters in large-scale thermo-optic tuning. In this design, the switching converter is used to supply multiple power stages of the LDOs. As the dropout between V A and the max {V TH1 , V TH2 , . . . , V THn } can be compressed to within tens of mV, the overall efficiency of the system will be greatly improved.
The buck converter in this design is based on [13], it has been demonstrated in [13] that the buck converter with monolithic current-mode dual-path Type-III compensator has an excellent transient response and a high f ugb /f sw ratio compared with most recent works in the literature. It can track 180kHz SC-FDMA waveforms, which is adequate for our application. Fig. 6 shows the structure of this current-mode dual-path Type-III compensated buck converter.

C. Dual-Supply LDO with LLGS
The LDO for thermo-optical tuning has different requirements compared with the design for other applications. To support the high-speed and wide-range thermo-optic tuning, the LDO with wide bandwidth and large output range is required. As the load of the LDO for thermo-optic tuning can be regarded as a fixed purely resistive load, there is no need to consider the transient response caused by the load changes. The dropout of the LDO is the main factor affecting the efficiency of the LDO. By separately supplying the controller and the power stage of the LDO, the dual-supply configuration expands the operating range of V A , which allows us to reduce the minimum dropout of the LDOs. By reducing the dropout, the system efficiency is thus significantly improved. Fig. 7 shows the schematic of the dual-supply LDO. The control stage of the LDO is a two-stage amplifier with currentmirror miller (CMM) compensation proposed in [14]. To suppress the interference of the V A 's changes and the ripples on the output of each channel, we select NMOS as the LDO's power stage. The simulation result shows that the PSR of the LDO has a 25 dB improvement compared to using PMOS as the power stage in this design. The LDO with NMOS power stage conventionally has a relatively large dropout and a narrow dynamic range, which is undesirable for thermo-optic tuning. To solve this problem, we introduce the lightweight local generated supply (LLGS) structure in [15] to supply the control stage. The LLGS provides a sufficiently high local voltage V LLGS for the controller to have enough gain and a wide dynamic range. As shown in Fig. 8, the LLGS includes an error amplifier, a relatively small power transistor, and a two-stage charge pump. For the LLGS, the output voltage V LLGS is mainly determined by V SET and has nothing to do with V DD .

D. Evaluation of Efficiency
As the power consumption of the envelope processing module is negligible, the overall conversion efficiency of the system for channel i (i = 1, 2, . . . , 8) can be written as where η con and η ldo i are the efficiency of the switching converter, and the channel i of the dual-supply LDOs, respectively; I load and V THi are the load current and the output voltage of the same channel; I q is the quiescent current of the LDO and LLGS.
The efficiency of the multi-channel dynamic regulator is related to the dynamic changes of the multi-channel envelope as well. Since the multiple channels share the same intermediate voltage V A , it is impossible for the architecture to individually adjust the dropout of each linear power stage. As shown in Fig. 9, the dynamics of the envelope can be divided into two typical situations. The improvement of the system efficiency is relatively limited for V TH2 when the voltage difference between V TH1 and V TH2 is comparatively large in Fig. 9 (a). Fortunately, in thermo-optic tuning, it is common that the voltage difference between each channel is small, which has been shown in Fig. 9 (b). The proposed architecture exactly has an obvious efficiency improvement for this case.

III. POST-LAYOUT SIMULATION RESULTS
The proposed hybrid dynamic regulator structure has been implemented in 130 nm CMOS technology, and Fig. 10 shows the layout of the proposed design with a total area of 0.675 mm 2 . Fig. 11 verifies that the proposed design not only extends the operating range of the LDOs, but also greatly improves the efficiency under the same dropout between V DD and V TH . The efficiency is simulated when the load current of each channel is 5 mA. The conventional design cannot work when the dropout is less than 0.37 V while the proposed design can still keep the efficiency of around 88%. Fig. 12 shows the key waveforms in the steady state when V Env1 to V Env4 , and V Env5 to V Env8 are 50 kHz 0.4 V pp , 40 kHz 0.3 V pp , 30 kHz 0.2 V pp , and 20 kHz 0.1 V pp sinusoidal waveforms respectively.
The static efficiency of the proposed design when each channel loads the same current is shown in Fig. 13   power conversion efficiency is 94.66% when the output voltage is 1 V, and the load current of each channel is around 40 mA. When driving a 200 Ω load, the proposed design achieves the conversion efficiency of 88.6% at 1 V output. The dynamic efficiency of the proposed design when each channel tracks the same sinusoidal waveforms is shown in Fig. 14. The proposed design achieves a dynamic efficiency of around 80% tracking 50 kHz sinusoidal waveforms and driving a 200 Ω load, while the ideal efficiency of the conventional design under the same situation is at most 61.1%. The dropout between V A and V TH is both 40 mV when testing the static and dynamic efficiency. The performance of this design is summarized and compared in TABLE II.

IV. CONCLUSION
In this brief, we have proposed a novel eight-channel switching-linear hybrid dynamic regulator with dual-supply LDOs, whose architecture has great potential for large-scale thermo-optical tuning. Compared with the fixed power supply, this design reduces the dropout and significantly improves the conversion efficiency, especially for the envelope signals with a small difference. Higher system efficiency is expected by further improving the efficiency of the switching converter. A prototype with post-layout simulation results has been used to verify the advantages of the proposed architecture. Nevertheless, the operating principle is general and can be implemented with other switching converters and LDOs.