Light-Powered Starter for Micro-Power Boost DC–DC Converter for CMOS Image Sensors

The design of a starter for a low-voltage, micro-power boost DC–DC converter intended for powering CMOS image sensors is presented. A unique feature of the starter is extremely low current, below 1 nA, supplying its control circuit. Therefore, a high-voltage (1.3 V) configuration of series-connected photovoltaic diodes available in a standard CMOS process or a small external LED working in photovoltaic mode can be used as an auxiliary supply for the control circuit. With this auxiliary supply, the starter can generate a starting voltage from 1 to 2.7 V using 50–200 mV supply voltage. The starter was verified by simulations and measurements of a prototype chip fabricated in a standard 180-nm CMOS technology. The results of simulations and tests showed correct operation of the starter in the temperature from 0 to 50 °C and under process parameters variation.


Introduction
Energy available in the environment in the form of light, temperature gradient, electromagnetic waves or vibration can be converted into electric power [11, 13-15, 19, 20] and used to supply micro-sensors. The miniature energy harvesters can generate voltage in the range of 50-400 mV [11,[13][14][15]19], which is not sufficient for proper operation of CMOS circuits. For this reason, the voltage generated by the harvesters is boosted to 1 V or more by step-up DC-DC converters. In recent years a number of micro-power step-up switching converters have been developed and implemented B Waldemar Jendernalik waldemar.jendernalik@pg.edu.pl 1 Faculty of Electronics Telecommunications and Informatics, Gdańsk University of Technology, Narutowicza 11/12, 80-233 Gdańsk, Poland [1-3, 5, 7, 16-18]. The main limitation of such converters is their inability to self-start at supply voltages as low as 50-400 mV. After starting, the converters can continue operation even at the input voltage reduced to 20 mV [1,17], because they can generate a proper supply voltage for themselves and for other supplied circuits. The frequently applied solution to the self-start problem is to use an auxiliary starter. In the simplest form, the starter can be a battery [1], but this solution occupies large volume and has a limited life span. The starter can also be a special switching converter designed for operation at extremely low voltage. Such starter provides boosted voltage for the main converter. Unfortunately, the demand for the starter to work at very low voltage results in decreasing its power efficiency and precision of output voltage regulation. For this reason, the starter is only run for a short time to start the main converter. The starter of this type can be based on a JFET [2] or a native MOS [5] transistor with an offchip transformer. Because JFET and the native MOS transistors can operate at zero gate-source voltage, the start-up is possible even at 20 mV. Because of the need for the off-chip transformer and because JFET is not compatible with CMOS technology, these approaches are limited in application. Another solutions [4,12,18] use an LC oscillator based on very-low-threshold-voltage MOS transistors and a Dickson charge pump to generate a sufficiently high start-up voltage.
In the known starter solutions, a voltage source was used as a power source and the main research was focused on reduction of the self-start voltage. In this study, a different approach is applied. Instead of a low-voltage source, a current source with very low current, below 1 nA and voltage of 1.1-1.3 V, is used to power the starter control circuit. Such approach is particularly suitable for sensors exposed to light, because the required current source can be realized as a set of photovoltaic diodes connected in series, which are available in a standard CMOS process [10]. Therefore, the proposed starter can be integrated with a CMOS image sensor.

Basic Assumptions and Working Conditions
The concept diagram of the proposed starter is shown in Fig. 1. In this starter, a single period of power conversion consists of two cycles. During the first one, the equivalent input capacitance C IN is charged by means of the auxiliary current source I aux . In the next cycle, the transistor M 1 is switched off, by quick discharge of C IN , to generate a boosted voltage at the drain. To initiate operation of the starter, the gate-source voltage V GS1 must be increased to where V th , (W /L) 1 , K PN and R ON1 are the threshold voltage, the aspect ratio, the transconductance parameter and the required switch-on resistance of M 1 , respectively. Due to a low supply voltage (V DD < V GS1 − V T ), the MOS transistor model [9] for the triode region is used in (1). When V GS1 increases to the value (1), the current i L (t) flowing through the inductor L 1 reaches its maximum value equal to where R ESR and R DD are the inductor equivalent series resistance and the supply source internal resistance. The current accumulates in the inductor the energy E L When the switch M 1 opens, the energy (3) is released through the diode and is mainly consumed to charge the output capacitor C O and the parasitic capacitance C P . Part of this energy is dissipated in the diode, due to the voltage drop V D , and is also dissipated in M 1 because of a limited switching-off time and other parasitic effects. Therefore, the energy balance is where V O is the output voltage, V off is the amplitude of the drain voltage pulse after switching off the transistor, and E D and E M1 are the energy dissipated in the diode and in the transistor, respectively. Typical waveforms of the inductor current i L (t), the voltage drop v D (t) across the diode and the voltage V off (t) at the drain of M 1 are depicted in Fig. 2. Figure 2 shows that while the diode is conducting current, the voltage drop v D (t) on it and as a consequence voltage on the inductor are almost constant, and therefore, the inductor current i L (t) decreases linearly in time. Taking this into account, the energy E D can be estimated as where t is the duration of the drain voltage pulse V off (t) and V D is the maximum voltage drop across the diode. The energy E M1 is difficult to calculate, because it It is assumed that the auxiliary current I aux is used only to initiate the first switch-on of M 1 , and the next cycles of charging C IN are supplied using the output voltage V O . This assumption allows for a reliable start when the starter control circuit is powered from a source with very low current efficiency and accumulated energy, such as a set of serial-connected photovoltaic diodes integrated on a chip. However, the prerequisite for this mode of operation is to meet the following two conditions. First, the maximum inductor current (2) should be greater than (6) to generate the V O high enough (greater than (1)) to sustain the operation of the starter. Second, the switching period should be greater than the time constant L 1 /(R ON1 + R ESR + R DD ); otherwise, the i L (t) will not reach the required value (6). Thus, the minimum energy for the starter initialization is where V GS1 is such that the current (2) is greater than (6), and C IN ∼ C GS1 + C GD1 because the parasitic capacitances of the transistor M 1 are dominant.

Relaxation Oscillator
The starter in Fig. 1 needs a control circuit that periodically switches the M 1 . To minimize the starting energy, the control circuit should consume as small power as possible.
A circuit proposal with such characteristics is shown in Fig. 3. In this configuration, the equivalent capacitance C IN serves as a temporary voltage source supplying the control circuit. Therefore, in ideal conditions, to discharge C IN , no additional energy is required in addition to the energy previously stored in it.
The reuse of energy stored in C IN for the discharging is mainly limited by the static power consumed by the control circuit, because the energy dissipated exactly at the switching transition is desirable since it accelerates the discharging of C IN .
When the circuit is idle, the static power is dissipated as a result of the leakage currents flowing through all the transistors connected between the gate of M 1 and ground. This power can be minimized by using long channel transistors (L > 1 µm) and transistors M4 and M5 with high threshold voltage (HVT) having small leakage current. As a result, the total static current in the proposed circuit is 190 pA at room temperature. The circuit in Fig. 3 together with C IN and I aux acts as a relaxation oscillator. The transistors M 3 , M 5 and M 4 , M 6 form two cross-coupled inverters functioning as an RS latch. Each inverter is composed of M 4 (M 5 ) transistor loaded by a very large resistance resulting from M 3 (M 6 ) leakage current. The transistors sizes are chosen in such a way that M 4 and M 5 are always switched off when the latch is idle. Two transistors M 9 and M 7 are used to set, respectively, high or low voltage levels at the latch output V y . The circuit composed of M 10 , M 11A , M 11B defines the threshold level V TH1 of the voltage V x at which the latch is triggered. Although the threshold V TH1 is dependent on temperature and process variation, this solution was chosen because of the very low bias current, which in this case is of utmost important. The influence of the threshold V TH1 variation on the operation of the starter will be discussed in Sect. 4. When the V x reaches the threshold level V TH1 , the drain current of M 9 increases and sets the latch output to high. At the same time, M 8 switches on and discharges C IN . It should be noted that without M 2 and C 1 , the capacitance C IN could not be discharged completely. The incomplete discharge occurs, because after switching on M 4 (assum- ing that M 2 is shorted) the transistor M 8 forms the diode-connected configuration. As a result, the final minimal voltage V y can only reach the M 8 threshold voltage and therefore cannot be zeroed. As a consequence, the boosting level of the output voltage is significantly reduced. To avoid such a situation, the temporary voltage source in the form of C 1 is used to provide the gate-source voltage for M 8 high enough to discharge C IN completely. Therefore, M 2 plays two roles: It disconnects C 1 from V x during the discharge transition, preventing C 1 from complete discharging, and it recharges C 1 to full voltage V x after discharging C IN . The relaxation oscillator needs periodic resetting of the latch after each state change, which is done by means of M 7 and the signal RST .

Starter Realization
The proposed starter is only intended for generating the start-up voltage sufficient for a main boost converter. Therefore, after the converter initialization the starter is disabled. The complete schematic of the starter is depicted in Fig. 4. The circuit consists of the following functional blocks: the relaxation oscillator (M 2 -M 12 , C 1 ), the feedback supplying circuit (C 2 , M 16  When the relaxation oscillator switches off M 1 for the first time, a positive pulse voltage V z at the drain is generated. This pulse switches on the rectifiers M 20 and M 25 (initially the signal SW is low). During the first switching, M 30 is turned off because its gate is connected to source by M 28 . M 30 is switched on after the delay resulting from charging C 3 by means of M 23A . Therefore, the large capacitor C 5 and the other supplied circuits are disconnected during this period. As a result, most of the energy accumulated in the inductor L 1 is released through M 20 and M 35 to the capacitor C 2 . Since C 2 has relatively small capacitance, the voltage across C 2 quickly rises above the latch threshold. From this moment, the starter is able to power itself using C 2 as an auxiliary voltage source for I aux generation. The transistors M 21 , M 22 , M 24 form a current source which takes over the role of the source I aux . M 16 -M 18 are used to prevent a feedforward flow of the I aux during the first switching of M 1 . In this period, M 18 is switched off, because its gate is connected to the source by the leakage current of M 17 . When the starter switches to the auxiliary source C 2 , M 18 is turned on by M 16 , which connects the gate of M 18 to ground. At the same time, the source I aux is disconnected, by turning off M 33 , to prevent energy losses.
For a proper operation, the relaxation oscillator needs cyclic resetting. This task is accomplished by M 7 , M 13 -M 15 and M 19 . When the voltage V aux on C 2 reaches a sufficient level, M 7 switches on and resets the latch output V y to zero. From this moment, the voltage V x may increase and C IN may be charged again. M 13 is used to disable M 7 and cancel the resetting of the latch to enable next switching of the relaxation oscillator.
To minimize the starting energy, the threshold level of the latch is modulated. During the first switching on of M 1 , the threshold voltage of the latch is set to the minimum, defined by M 11A , M 11B , since M 12D is switched on (V aux 0). This voltage is such that the starter generates energy to charge the capacitor C 2 to the required minimal level (1). Such small energy is not sufficient to charge a much larger capacitor C 5 to the level required by a boost converter. Therefore, during next cycles of oscillation the latch threshold voltage is increased, by switching off M 12D , to the level defined by M 11A , M 11B and M 12A -M 12C .
During the initial oscillations, it is not possible to precisely control voltages V aux and V out which may result in exceeding permissible voltage limits. To protect the circuit from damage by too high voltage, the voltage limiter composed of M 31 -M 32 is applied. When the amplitude of V z pulse exceeds the permissible value, M 12E and M 32 are switched on to reduce the latch threshold voltage, V aux , and V out .
After several cycles of oscillation, when V out reaches the required start-up voltage for a proper operation of the boost converter, the starter is disabled by pulling the signal ENB to high. At the same time, the transistor M 25 changes its role from the rectifier to a switch controlled by the pulse-width-modulated signal SW, which is generated by a circuit controlling the boost converter.
The exemplary waveforms illustrating the starter operation are presented in Fig. 5. The bottom waveform shows voltage V x across C IN . During the initialization period, the voltage gradually increases until it reaches, at about 420 µs, the latch threshold level of 0.81 V. After the first switching, the threshold is increased to about 1.2 V. From this moment, relaxation oscillations begin. As shown in the top and middle plots, the first switching charges C 2 to about V aux 2.55 V and C 5 to V out 20 mV. After about 1.7 ms, both voltages reach the final values V aux 2.3 V and V out 2 V. It should also be noted that after 1.7 ms, the latch threshold voltage is reduced to about 1 V to limit the output voltage. In most working conditions, the first switching is sufficient to charge C 2 to a high enough level, but if this action fails, the switching will resume automatically.

Design Procedure
The design procedure is explained based on two variants of the starter: (1) with the minimal starting energy and (2) with the lowest start-up voltage. The starter is designed for a boost converter that requires the start-up voltage V out ≥ 1 V. The AMS 180-nm standard CMOS technology was selected for both variants of the project. To make the preliminary calculations, the following parameters were assumed: V DD 50 mV, R DD 5 , L 1 800 µH, R ESR 0.35 . The remaining parameters were estimated as follows. The capacitance C 5 10 nF was selected to achieve V out voltage ripple less than 20 mV pp . The C 2 equal to 120 pF was chosen to obtain V aux voltage ripple less than 100 mV which guarantees correct operation of the relaxation oscillator. The capacitance C 1 0.6 pF is ten times larger than the input capacitance of M 8 , to keep the M 8 gate-source voltage high enough to discharge C IN completely. The efficiency factor η 1 − E M1 /E L 0.7 was determined based on the energy dissipated in the transistor E M1 and the energy stored in the inductor E L , where both energies were calculated by simulation for a single switching period. The determined maximum voltage drop on the rectifier M 25 was V D 0.9 V.
As explained in the previous section, two threshold levels are used in the latch. The first threshold level V TH1 should guarantee generation of enough energy to charge C 2 to voltage greater than (1), while the second threshold level V TH2 should be sufficient to charge C 2 + C 5 and provide enough power for the load R L . After the first switching, the required gate-source voltage (1) is generated by the feedback supplying circuit (M 16 -M 18 , M 21 , M 22 , M 24 ), which needs at least 50 mV voltage drop for proper operation. Therefore, the minimal initial voltage (1) must be greater by this value. The first variant of the starter, with the minimal starting energy, was design using (1), (2), (6) and finding dimensions W 1 and L 1 of the transistor M 1 for which the energy (7) is minimal. It is assumed that C IN ∼ W 1 L 1 C ox + C 1 , C P 2W 1 C ov + C x where C ox is the capacitance per unit area of M 1 gate oxide, C ov is the overlap In this case, for the worst technology corner (V T ∼ 520 mV, K PN ∼ 100 µA/V 2 , C ox ∼ 2.5 fF/µm 2 , C ov ∼ 0.5 fF/µm 2 ) the required first threshold voltage is V TH1 ∼ 800 mV, and the transistor dimensions are W 1 ∼ 500 µm and L 1 0.7 µm. The second variant of the starter, with the lowest start-up voltage, was calculated using the same set of equations, but finding the transistor dimensions for which the gate-source voltage (1) is minimal. In this case, the optimal parameters are as follows: V TH1 ∼ 650 mV, W 1 ∼ 1500 µm and L 1 0.7 µm.
The second threshold level V TH2 depends on the required charging rate of C 5 and the load resistance R L . The greater the V TH2 is, the faster the output voltage V out reaches its final value. Since the maximum value of V TH2 is limited by V aux , which is in the range of 1.6-2.4 V, with a small margin of safety it was assumed that V TH2 1.5V TH1 . The effects of V TH1 and V TH2 changes due to temperature and process variations are discussed in Sect. 4.1. The complete set of circuit parameters is listed in Table 1 4

Technology Corners and Temperature Variation
Due to the use of leakage currents for biasing of devices, the influence of technology corners and temperature variation on the starter operation is examined. Five corners are specified for AMS (austriamicrosystems AG) 180-nm CMOS technology: TM, WP, WS, WO and WZ, meaning, respectively, the typical mean values, worst-case power, worst-case speed, worst-case one and worst-case zero.
For a proper operation of the starter, both transistors M 4 and M 5 must always be switched off when the latch is idle. To meet such a condition, M 3 leakage current must always be greater than M 5 leakage current. Similarly, the sum of M 4 and M 9 leakages should be greater than the sum of M 6 and M 7 leakages. Such conditions are satisfied by using HVT transistors M 4 and M 5 and proper sizing of the other devices. It is also required that the threshold voltages V TH1 and V TH2 of the latch were as constant as possible and greater than (1). These voltages, in the circuit in Fig. 4, can be approximated as where I O10 and n are technology parameters, V T is the thermal voltage, and T O is a reference temperature. On the other hand, the drain-source voltage of each transistor M 11A , M 12A -M 12C working in the subthreshold region is Taking into account the leakage current (9), the drain-source voltage can be determined as The expressions (11), (8a) and (8b) show that the latch thresholds depend mainly on the difference between the threshold voltages V thN and V th10 of the n-channel (M 11A , M 12A -M 12C ) and p-channel (M 10 ) transistors. Because the temperature coefficients of both voltages V thN and V th10 are similar, the change of voltage (11) with temperature is reduced. Figure 6 shows the simulations results of V TH1 and V TH2 changes with temperature and corners. For TM corner, V TH1 varies from 920 mV to 860 mV for the temperature from 0 to 70°C. The total variation of V TH1 , including all the corners and temperature change, is 820-946 mV. As explained in Sect. 3.1, the first threshold level V TH1 is used during the start-up of the relaxation oscillator, when it is powered from the photovoltaic diodes. The starter is designed to be powered from the photovoltaic diodes in the configuration described in [10] or a small external LED working in photovoltaic mode. In both cases, the generated voltage is in the range of 1.1-1.3 V, which guarantees proper start-up of the relaxation oscillator.   Figure 6 shows that under the same conditions, the second threshold voltage V TH2 changes from 1.386 to 1.394 V for TM corner and from 1.2 to 1.544 V for all the corners and temperature range 0-70°C. The V TH2 is used to reduce the charging time of the capacitor C 5 , and therefore, its relatively large variation has less impact on the starter operation. Because after starting, the oscillator is powered from the auxiliary source V aux higher than 1.6 V, the operation of the oscillator is sustained regardless of changes in V TH2 . The changes in V TH1 and V TH2 caused by mismatch of the transistors dimensions and variation of technology parameters achieved with 200 runs of the Monte Carlo simulations are illustrated in Fig. 7 for TM corner and temperature 27°C. The complete set of simulation results for all the corners and temperatures 0, 27, 70°C is presented in Table 2. Both threshold voltages are within the range of acceptable values (0.8 V < V TH1 < 1.1 V and V TH2 < 1.6 V).

Output Voltage Variation
As the proposed starter is to be used only for a short initialization period to start a boost converter, a simple mechanism for controlling the output voltage V out is applied.  To determine the V out changes caused by devices mismatch and process variation, 200 iterations of Monte Carlo simulations were performed. The results for TM corner and V DD 50 mV are illustrated in Fig. 9 for 0°C and 70°C, whereas a summary of  the results for all the corners at 0°C, 27°C and 50°C is given in Table 3. The output voltage varies from 1.08 to 2.37 V, and therefore, a reliable start of the converter is possible. The main reasons for the output voltage changes are the changes in the threshold voltages V TH1 , V TH2 and the switch-on resistance of M 1 (R ON1 in (1)). The V out variation could be reduced by means of negative feedback; however, in such a case it would not be possible to achieve very low auxiliary current I aux < 1 nA due to the complexity of the feedback circuit.

Auxiliary Current Variation
The auxiliary current I aux is mainly used for charging the input equivalent capacitance C IN . Only a relatively small fraction of this current is consumed by the leakage current of the control circuit. The plots of the minimum I aux necessary to initiate the starter as a function of temperature and corners are presented in Fig. 10. For the V DD equal to 50 mV and all the corners, the current is below 1 nA if temperature is lower than 57°C, while for TM corner and room temperature the current is 190 pA. Such a low current value allows the use of on-chip photovoltaic diodes or small external LED diode in photovoltaic mode.

Measurement of a Prototype Starter
The starter from Fig. 4 in the version with minimal starting energy was selected for fabrication in a standard AMS 180-nm CMOS technology. The designed starter's layout and the micro-photograph of the chip portion containing the starter are shown in Fig. 11. The complete starter without bonding pads occupies 2325 µm 2 of the chip area. The L 1 , C 2 , C 5 and R L were implemented as external components with values 820 µH, 120 pF, 10 nF and 1 M , respectively. In the test setup (Fig. 12), the main power source V DD was a photodiode BPW20RF (manufactured by Vishay) shunted by the capacitor C D with 3.3 µF value. The auxiliary current I aux was generated by a light-emitting diode (LED) working in photovoltaic mode. We used a small green   Fig. 12, the relation between V DD , V out and V aux was measured.
The V DD was changed by increasing illuminance of incident light. The results of measurements taken for V DD changed from 50 mV to 200 mV are presented in Table 4. The value of the auxiliary current I aux supplying the starter ranges from 120 pA at 0°C to 0.8 nA at 50°C. The current measured at room temperature (27°C) is 240 pA. Figure 13 shows captured waveforms of V out , V aux and V Z for V DD 50 mV. It is seen that the first pulse of V Z charges C 2 to V aux > 1.9 V, which ensures correct operation of the relaxation oscillator. At the same time, as shown in Fig. 13b, the voltage V out is delayed and limited in amplitude to 400 mV. During the successive switching of M 1 , the V out increases gradually to the final value of 1.39 V.

Comparison
Most of the starters described in the literature are designed to achieve the lowest possible start-up voltage, and therefore, comparison of the starter proposed in this paper is difficult. Two groups of the starters are compared: the starters using an auxiliary voltage source [1,3,7] and the starter using a single low-voltage source shared with the boost converter [17]. A summary of the most important parameters of the selected starters is given in Table 5. The solution in [1] requires at least 600 mV to start-up and consumes 1.1 µW of quiescent power, which means 1.8 µA inrush current. The starter [3] at the same voltage needs at least 2 µW, which results in 3.3 µA inrush Fig. 13 Oscilloscope measurements of waveforms: V out , V aux and V Z : a start-up after applying V DD 50 mV, b enlarged initial part of V out , V aux and V Z waveforms current. The control circuit used in the starter [7] requires at least 1 V and consumes 160 nW of power, and therefore, it requires 160 nA of inrush current. The converter in [17] can start up by itself due to the application of a MOS transistor with a low threshold voltage. During the start-up period, 1.3 µW of power is consumed at 35 mV (37 µA inrush current). The proposed starter consumes auxiliary current in the range from 120 pA (0°C) to 0.8 nA (50°C) at the starting voltage in the range from 970 mV to 850 mV, and therefore, the static power consumed varies from 0.117 nW to 0.68 nW.

Conclusion
In this paper, the starter able to generate a starting voltage in the range from 1 to 2.7 V at a supply voltage from 50 to 200 mV is presented. The starter is designed for a low-voltage, micro-power boost DC-DC converter intended for powering CMOS image sensors. A special feature of the proposed starter is extremely low current, below 1 nA, supplying its controller. Due to this, the controller can be powered from a high-voltage (1.3 V) configuration of series-connected photovoltaic diodes available in a standard CMOS process [10]. Therefore, the proposed solution is suitable for all kinds of image sensors, e.g., imagers, vision chips [6,8] implemented in CMOS technologies. The very low current supplying the controller was achieved by using a simple relaxation oscillator biased by the leakage current of MOS transistors. The performed simulations have shown that despite the use of such a simple solution, the starter works correctly. It was demonstrated that the starter can be designed in such a way to operate properly under temperature changes in the range of 0-50°C and process variation. The starter was verified using a prototype chip fabricated in 180-nm CMOS technology. The starter output voltage measured at 0°C, 27°C and 50°C is in the range of 1.1-2.7 V, whereas the controller supply current is within the range of 0.12-0.8 nA.