Impact of the passive component structure for high efficiency and fast response POL using Power Supply on Chip

Power-SoC, which integrates MCU, power device, control circuits and passive devices on the same chip has been attracted attention. In this paper, we discuss the impact of passive component structure for high efficiency and fast response POL using 3D Power-SoC (Supply on Chip). We propose the optimal structure according to the switching frequency based on simulations.


Introduction
In recent years, LSIs like MCU (Micro Controller Unit) face the problems such as voltage drop, voltage fluctuation and loss cause by line impedance at lower voltage and high current operations. Therefore, a POL (Point of Load) plays an important role in LSIs and it becomes main stream to implement the POL near the load (LSIs) [1]. Power supply on chip (Power-SoC), which integrates MCU, power device, control circuits and passive devices on the same chip is shown in Fig. 1, has been attracted attentions [2]∼ [4] because it can realize ultimate miniaturization of the POL.
The passive components such as inductors and capacitors occupy large part of power supplies. Increase the switching frequency is one of the most effective ways to miniaturize the passive components. Thus, the switching frequency of more than multi tens MHz is required for Power-SoC and the traditional PWM control faces the problem that cannot follow feedback control.
In addition, Power-SoC can miniaturize the POLs, however it cannot handle larger power.
In such a scheme, we previously proposed a control technique suitable for Power-SoC[5]∼ [7], which is based on parallel connected POLs. The proposed control technique changes the number of working POLs (Fig. 2).
The key applications of Power-SoC are DVFS (Dynamic Voltage and Frequency Scaling) and envelope tracking. These applications are required high efficiency and fast response. We previously reported design guideline for high efficiency Power-SoC based on 3D Power-SoC [8]. However, it has not been considered design guideline for fast response.
In this paper, we report design consideration of high efficiency and fast response POL using 3D Power-SoC. * Corresponding: kajihara.kenji653@mail.kyutech.jp † Kyushu Institute of Technology 1-1 Sensui-cho, Tobata-ku, Kitakyushu-shi, Fukuoka, Japan   Figure 3 illustrates the block diagram of experimental system for evaluations. We use buck converters. Fig. 4 shows the picture of experimental circuits. Table 1(a) and Table  1(b) show the circuit parameters and system specifications for evaluations respectively.

Simulations 3.1 Inductor
We simulated the performance of spiral and solenoid inductors using HFSS (High Frequency Structure Simulator) [9]. Chip size is 2∼3 mm × 2∼3 mm and number of turns are from 3 to 6 ( Fig. 5).

Capacitor
We calculated the capacitance and equivalent resistance (ESR) of trench capacitor using analytical model [10]. Trench capacitor is shown in Fig. 6. We decide to trench depth (H) is 20 µm, thickness of silicon oxide layer is 10 nm, and space between trenches is 0.5 µm. We changes radius of trench capacitor.

Buck converter
We use LT-spice [11] for circuit simulations and calculated efficiency and output power of  buck converter which use inductor simulated in "A" and capacitor calculated in "B". Circuit diagram is shown in Fig. 7. Switching device is GaN power device (EPC8004). The input voltage is 5 V and the duty ratio is 50% (output voltage: 2.5 V). The switching frequency are 30 MHz, 100 MHz and 140 MHz, respectively. 30 MHz is the lowest frequency which can use air core spiral inductor at high efficiency. In addition, we have already developed 30 MHz gate driver IC for GaN power devices [12]. 100 MHz is a frequency where solenoid inductors are more efficient than spiral inductors. 140 MHz is a previously reported silicon based converter [13].

Transient response
We use MATLAB/Simulink [14] to calculate transient response using the inductor simulated in "A"and the capacitor calculated in "B". The calculated transient response is sudden load change and sudden duty change. Fig. 8 and Fig. 9 show the circuit diagram of sudden load change and that sudden duty change, respectively. Figure 10 shows the transient response of output voltage at sudden load change. The output voltage stabilized in 60 µs at both increase and decrease output current. We changed it from 0.5 A to 2.5 A, and from 2.5 A to 0.5 A at the same time. Figure 11 shows at sudden duty change. The number of working POL is 1 and duty ratio changes from 50% to 33% . The output voltage stabilized in 56 µs.

Passive components
The performance of spiral and solenoid inductors at 30 MHz, 100 MHz and 140 MHz is shown in Fig. 12 [8]. The resistance and inductance increases as the number of turns increases. Figure. 13 shows the performance of trench capacitor whose trench radius is changed to 0.5∼5 µm [8]. We choose capacitance and ESR is 91.98 nF, 0.220 µΩ, (chip size: 2 mm sq.), and 207 nF and 0.099 µΩ (chip size: 3 mm sq.) when the trench depth is 20 µm.

Simulated transient response
Simulated transient response of sudden load changes of buck converter at 1 MHz is shown in Fig. 14. Simulated transient response of sudden duty change of buck converter at 1 MHz is also shown in Fig. 15. The circuit parameters and specifications used in the simulations are listed in Table 1(a) and Table  1    perimental results.
Relationship between efficiency and response time of sudden load changes is shown in Fig. 16. Relationship between efficiency and response time of sudden duty changes is shown in Fig. 17.
At switching frequency of 30 MHz, fast response time and high efficiency are obtained at chip size of 2 mm sq.   2mm sq. and 3 turns of solenoid inductor. The effect of the chip size is small, and there is no difference between spiral inductor and solenoid inductor. At over 100 MHz, for the same size, the efficiency and the response time decreases as the number of turns increases.
Also, this Eq. 1 and Eq. 2 are transfer function of sudden load change and sudden duty change.
The Eq. 3 is the transient response of sudden load change using the Eq. 1. The Eq. 4 is that response of sudden duty change using the Eq. 2 .   and Eq. 3 and Eq. 4, the response time is almost the same when the same inductance. The solenoid inductor can be use over 100 MHz because smaller inductance can be used as the frequency increases. Figure 18 shows the result of simulating when 30 MHz, chip size of 2 mm sq. and 6 turns of spiral inductor sudden load changes and sudden duty change at the same time. Form the result of Fig. 18, confirmed that sudden load changes and sudden duty change can be performed simultaneously. Figure 19 shows the relationship between response time of sudden load changes and power density at fast response time and high efficiency (>80%). From the results of Fig. 19, inductors which are suitable for fast response, high efficiency, and power density are chip size of 2 mm sq. and 5turns of spiral inductor and chip size of 3 mm sq. and 5 turns of spiral inductor at 30 MHz. At 100 MHz, chip size of 2 mm sq. and 3 turns of solenoid inductor are suitable for fast response time, high efficiency, and power density. At 140 MHz, chip size of 2 mm sq. and 3 turns of solenoid inductor are suitable for fast response time, high efficiency, and power density.

Conclusions
We clarify design guideline for high efficiency and first response POL. At 30 MHz, spiral inductor meets fast response time, high efficiency, and high power density. At 100 MHz, solenoid inductor is better than spiral inductor because power density of solenoid inductor is higher than spiral inductor. At 140 MHz, the solenoid inductor can realize fast response time, high efficiency, and high power density. Therefore, when switching frequency is 30 MHz, the spiral inductor is suitable. The solenoid inductor is suitable over 100 MHz.