1 Introduction

Energy available in the environment in the form of light, temperature gradient, electromagnetic waves or vibration can be converted into electric power [11, 13,14,15, 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 [1,2,3, 5, 7, 16,17,18]. 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 off-chip 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.

2 Principle of Operation

2.1 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 CIN is charged by means of the auxiliary current source Iaux. In the next cycle, the transistor M1 is switched off, by quick discharge of CIN, to generate a boosted voltage at the drain. To initiate operation of the starter, the gate–source voltage VGS1 must be increased to

Fig. 1
figure 1

Schematic diagram showing the principle of operation of the starter

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$$ V_{{{\text{GS}}1}} \cong V_{\text{th}} + \frac{1}{{R_{{{\text{ON}}1}} }}\frac{1}{{K_{\text{PN}} \left( {W/L} \right)_{1} }} $$
(1)

where Vth, (W/L)1, KPN and RON1 are the threshold voltage, the aspect ratio, the transconductance parameter and the required switch-on resistance of M1, respectively.

Due to a low supply voltage (VDD < VGS1 − VT), the MOS transistor model [9] for the triode region is used in (1). When VGS1 increases to the value (1), the current iL(t) flowing through the inductor L1 reaches its maximum value equal to

$$ I_{\hbox{max} } = \frac{{V_{\text{DD}} }}{{R_{{{\text{ON}}1}} + R_{\text{ESR}} + R_{\text{DD}} }} $$
(2)

where RESR and RDD are the inductor equivalent series resistance and the supply source internal resistance. The current accumulates in the inductor the energy EL

$$ E_{L} = \frac{1}{2}L_{1} I_{\hbox{max} }^{2} = \frac{{L_{1} V_{\text{DD}}^{2} }}{{2\left( {R_{{{\text{ON}}1}} + R_{\text{ESR}} + R_{\text{DD}} } \right)^{2} }} $$
(3)

When the switch M1 opens, the energy (3) is released through the diode and is mainly consumed to charge the output capacitor CO and the parasitic capacitance CP. Part of this energy is dissipated in the diode, due to the voltage drop VD, and is also dissipated in M1 because of a limited switching-off time and other parasitic effects. Therefore, the energy balance is

$$ E_{\text{L}} = E_{\text{O}} + E_{\text{P}} + E_{\text{D}} + E_{{{\text{M}}1}} = \frac{1}{2}C_{\text{O}} V_{\text{O}}^{2} + \frac{1}{2}C_{\text{P}} V_{\text{off}}^{2} + E_{\text{D}} + E_{{{\text{M}}1}} $$
(4)

where VO is the output voltage, Voff is the amplitude of the drain voltage pulse after switching off the transistor, and ED and EM1 are the energy dissipated in the diode and in the transistor, respectively. Typical waveforms of the inductor current iL(t), the voltage drop vD(t) across the diode and the voltage Voff(t) at the drain of M1 are depicted in Fig. 2.

Fig. 2
figure 2

Waveforms of the inductor current iL(t), voltage Voff(t) at M1 drain and voltage drop vD(t) across the diode after switching off M1 transistor

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Figure 2 shows that while the diode is conducting current, the voltage drop vD(t) on it and as a consequence voltage on the inductor are almost constant, and therefore, the inductor current iL(t) decreases linearly in time. Taking this into account, the energy ED can be estimated as

$$ E_{\text{D}} = \mathop \smallint \limits_{0}^{{\Delta t}} v_{\text{D}} i_{\text{L}} {\text{d}}t \cong \frac{{V_{\text{D}} I_{\hbox{max} } }}{2}\Delta t \cong \frac{{V_{\text{D}} I_{\hbox{max} } }}{2}\frac{{L_{1} I_{\hbox{max} } }}{{V_{\text{off}} }} $$
(5)

where Δt is the duration of the drain voltage pulse Voff(t) and VD is the maximum voltage drop across the diode. The energy EM1 is difficult to calculate, because it depends on many factors such as M1 switching-off time, the ratio of VGS1 to Vth before M1 switching-off, RON1, amplitude of Voff(t), oscillations. For this reason, the efficiency factor η is introduced which models the energy loss in the transistor. Using this factor, the loss can be expressed as EM1 = (1 − η)EL, where the value of η is determined during preliminary simulations based on the energy stored in the inductor and the energy dissipated in the transistor in a single switching cycle, as explained in Sect. 3.2. Based on (3)–(5), and taking into account that Voff = VO + VD, the required inductor current can be estimated as

$$ I_{\hbox{max} } \cong \sqrt {\frac{{\left( {V_{\text{D}} + V_{\text{O}} } \right)\left[ {C_{\text{O}} V_{\text{O}}^{2} + C_{\text{P}} \left( {V_{\text{D}} + V_{\text{O}} } \right)^{2} } \right]}}{{L_{1} \left[ {\eta V_{\text{O}} - \left( {1 - \eta } \right)V_{\text{D}} } \right]}}} $$
(6)

It is assumed that the auxiliary current Iaux is used only to initiate the first switch-on of M1, and the next cycles of charging CIN are supplied using the output voltage VO. 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 VO high enough (greater than (1)) to sustain the operation of the starter. Second, the switching period should be greater than the time constant L1/(RON1 + RESR + RDD); otherwise, the iL(t) will not reach the required value (6). Thus, the minimum energy for the starter initialization is

$$ E_{\text{start}} = \frac{1}{2}C_{\text{IN}} V_{{{\text{GS}}1}}^{2} $$
(7)

where VGS1 is such that the current (2) is greater than (6), and CIN ≅ CGS1 + CGD1 because the parasitic capacitances of the transistor M1 are dominant.

2.2 Relaxation Oscillator

The starter in Fig. 1 needs a control circuit that periodically switches the M1. 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 CIN serves as a temporary voltage source supplying the control circuit. Therefore, in ideal conditions, to discharge CIN, no additional energy is required in addition to the energy previously stored in it.

Fig. 3
figure 3

Relaxation oscillator as a control circuit (HVT devices are 1.8-V transistors with high threshold voltage)

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The reuse of energy stored in CIN 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 CIN.

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 M1 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 CIN and Iaux acts as a relaxation oscillator. The transistors M3, M5 and M4, M6 form two cross-coupled inverters functioning as an RS latch. Each inverter is composed of M4 (M5) transistor loaded by a very large resistance resulting from M3 (M6) leakage current. The transistors sizes are chosen in such a way that M4 and M5 are always switched off when the latch is idle. Two transistors M9 and M7 are used to set, respectively, high or low voltage levels at the latch output Vy. The circuit composed of M10, M11A, M11B defines the threshold level VTH1 of the voltage Vx at which the latch is triggered. Although the threshold VTH1 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 VTH1 variation on the operation of the starter will be discussed in Sect. 4. When the Vx reaches the threshold level VTH1, the drain current of M9 increases and sets the latch output to high. At the same time, M8 switches on and discharges CIN. It should be noted that without M2 and C1, the capacitance CIN could not be discharged completely. The incomplete discharge occurs, because after switching on M4 (assuming that M2 is shorted) the transistor M8 forms the diode-connected configuration. As a result, the final minimal voltage Vy can only reach the M8 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 C1 is used to provide the gate–source voltage for M8 high enough to discharge CIN completely. Therefore, M2 plays two roles: It disconnects C1 from Vx during the discharge transition, preventing C1 from complete discharging, and it recharges C1 to full voltage Vx after discharging CIN. The relaxation oscillator needs periodic resetting of the latch after each state change, which is done by means of M7 and the signal RST.

3 Starter for a Boost DC–DC Converter

3.1 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 (M2–M12, C1), the feedback supplying circuit (C2, M16–M18, M21, M22, M24), the MOS rectifiers (M20, M25), the voltage limiter (M31A–M31D, M32) and the disabling circuit (M34, M35) which switches off the starter after the boost converter initialization. To limit the number of off-chip components, the starter shares L1 with the boost converter.

Fig. 4
figure 4

Complete schematic diagram of the proposed starter (HV are high-voltage 5-V transistors, HVT are 1.8-V transistors with high threshold voltage)

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When the relaxation oscillator switches off M1 for the first time, a positive pulse voltage Vz at the drain is generated. This pulse switches on the rectifiers M20 and M25 (initially the signal SW is low). During the first switching, M30 is turned off because its gate is connected to source by M28. M30 is switched on after the delay resulting from charging C3 by means of M23A. Therefore, the large capacitor C5 and the other supplied circuits are disconnected during this period. As a result, most of the energy accumulated in the inductor L1 is released through M20 and M35 to the capacitor C2. Since C2 has relatively small capacitance, the voltage across C2 quickly rises above the latch threshold. From this moment, the starter is able to power itself using C2 as an auxiliary voltage source for Iaux generation. The transistors M21, M22, M24 form a current source which takes over the role of the source Iaux. M16–M18 are used to prevent a feedforward flow of the Iaux during the first switching of M1. In this period, M18 is switched off, because its gate is connected to the source by the leakage current of M17. When the starter switches to the auxiliary source C2, M18 is turned on by M16, which connects the gate of M18 to ground. At the same time, the source Iaux is disconnected, by turning off M33, to prevent energy losses.

For a proper operation, the relaxation oscillator needs cyclic resetting. This task is accomplished by M7, M13–M15 and M19. When the voltage Vaux on C2 reaches a sufficient level, M7 switches on and resets the latch output Vy to zero. From this moment, the voltage Vx may increase and CIN may be charged again. M13 is used to disable M7 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 M1, the threshold voltage of the latch is set to the minimum, defined by M11A, M11B, since M12D is switched on (Vaux = 0). This voltage is such that the starter generates energy to charge the capacitor C2 to the required minimal level (1). Such small energy is not sufficient to charge a much larger capacitor C5 to the level required by a boost converter. Therefore, during next cycles of oscillation the latch threshold voltage is increased, by switching off M12D, to the level defined by M11A, M11B and M12A–M12C.

During the initial oscillations, it is not possible to precisely control voltages Vaux and Vout which may result in exceeding permissible voltage limits. To protect the circuit from damage by too high voltage, the voltage limiter composed of M31–M32 is applied. When the amplitude of Vz pulse exceeds the permissible value, M12E and M32 are switched on to reduce the latch threshold voltage, Vaux, and Vout.

After several cycles of oscillation, when Vout 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 M25 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 Vx across CIN. 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 C2 to about Vaux = 2.55 V and C5 to Vout = 20 mV. After about 1.7 ms, both voltages reach the final values Vaux = 2.3 V and Vout = 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 C2 to a high enough level, but if this action fails, the switching will resume automatically.

Fig. 5
figure 5

Exemplary waveforms of the starter voltages: Vaux, Vout and Vx

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3.2 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 Vout ≥ 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: VDD = 50 mV, RDD = 5 Ω, L1 = 800 μH, RESR = 0.35 Ω. The remaining parameters were estimated as follows. The capacitance C5 = 10 nF was selected to achieve Vout voltage ripple less than 20 mVpp. The C2 equal to 120 pF was chosen to obtain Vaux voltage ripple less than 100 mV which guarantees correct operation of the relaxation oscillator. The capacitance C1 = 0.6 pF is ten times larger than the input capacitance of M8, to keep the M8 gate–source voltage high enough to discharge CIN completely. The efficiency factor η = 1 − EM1/EL = 0.7 was determined based on the energy dissipated in the transistor EM1 and the energy stored in the inductor EL, where both energies were calculated by simulation for a single switching period. The determined maximum voltage drop on the rectifier M25 was VD = 0.9 V.

As explained in the previous section, two threshold levels are used in the latch. The first threshold level VTH1 should guarantee generation of enough energy to charge C2 to voltage greater than (1), while the second threshold level VTH2 should be sufficient to charge C2 + C5 and provide enough power for the load RL. After the first switching, the required gate–source voltage (1) is generated by the feedback supplying circuit (M16–M18, M21, M22, M24), 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 W1 and L1 of the transistor M1 for which the energy (7) is minimal. It is assumed that CIN ≅ W1L1Cox + C1, CP = 2W1Cov + Cx where Cox is the capacitance per unit area of M1 gate oxide, Cov is the overlap capacitance per channel unit width, and Cx is the capacitance resulting from M20, M25 (Cx ≅ 0.4 pF). In this case, for the worst technology corner (VT ≅ 520 mV, KPN ≅ 100 μA/V2, Cox ≅ 2.5 fF/μm2, Cov ≅ 0.5 fF/μm2) the required first threshold voltage is VTH1 ≅ 800 mV, and the transistor dimensions are W1 ≅ 500 μm and L1 = 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: VTH1 ≅ 650 mV, W1 ≅ 1500 μm and L1 = 0.7 μm.

The second threshold level VTH2 depends on the required charging rate of C5 and the load resistance RL. The greater the VTH2 is, the faster the output voltage Vout reaches its final value. Since the maximum value of VTH2 is limited by Vaux, which is in the range of 1.6–2.4 V, with a small margin of safety it was assumed that VTH2 = 1.5VTH1. The effects of VTH1 and VTH2 changes due to temperature and process variations are discussed in Sect. 4.1. The complete set of circuit parameters is listed in Table 1

Table 1 Parameters of the starter in Fig. 4
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4 Analysis of Working Conditions and Technology Nonidealities

4.1 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 M4 and M5 must always be switched off when the latch is idle. To meet such a condition, M3 leakage current must always be greater than M5 leakage current. Similarly, the sum of M4 and M9 leakages should be greater than the sum of M6 and M7 leakages. Such conditions are satisfied by using HVT transistors M4 and M5 and proper sizing of the other devices. It is also required that the threshold voltages VTH1 and VTH2 of the latch were as constant as possible and greater than (1). These voltages, in the circuit in Fig. 4, can be approximated as

$$ V_{{{\text{TH}}1}} = V_{{{\text{DS1}}1{\text{A}}}} + V_{{{\text{SB}}11{\text{B}}}} + V_{{{\text{th}}9}} $$
(8a)
$$ V_{{{\text{TH}}2}} = V_{{{\text{DS}}11{\text{A}}}} + V_{{{\text{SB}}11{\text{B}}}} + V_{{{\text{DS}}12{\text{A}}}} + V_{{{\text{DS}}12{\text{B}}}} + V_{{{\text{DS}}12{\text{C}}}} + V_{{{\text{th}}9}} $$
(8b)

where VDS11A, VDS12A–VDS12C, are the drain–source voltages of M11A and M12A–M12C, respectively, VSB11B is the source–body voltage of M11B, whereas Vth9 is the threshold voltage of M9. The transistors M11A and M11B (M12A–M12C) are biased by the leakage current of the p-channel transistor M10, which can be approximated by [9]

$$ I_{{{\text{leak}}10}} \cong \left( {\frac{W}{L}} \right)_{10} I_{{{\text{O}}10}} \left( {\frac{T}{{T_{0} }}} \right)^{2} e^{{ - \frac{{V_{{{\text{th}}10}} }}{{nV_{\text{T}} }}}} $$
(9)

where IO10 and n are technology parameters, VT is the thermal voltage, and TO is a reference temperature. On the other hand, the drain–source voltage of each transistor M11A, M12A–M12C working in the subthreshold region is

$$ V_{\text{DSN}} \cong V_{{{\text{th}}N}} + nV_{\text{T}} \ln \left( {I_{{{\text{leak}}10}} } \right) - nV_{\text{T}} \ln \left[ {\left( {\frac{W}{L}} \right)_{\text{N}} I_{\text{ON}} \left( {\frac{T}{{T_{\text{O}} }}} \right)^{2} } \right] $$
(10)

Taking into account the leakage current (9), the drain–source voltage can be determined as

$$ V_{\text{DSN}} \cong V_{{{\text{th}}N}} - V_{{{\text{th}}10}} + nV_{\text{T}} \ln \left[ {\left( {\frac{W}{L}} \right)_{10} I_{{{\text{O}}10}} \mathord{\left/ {\vphantom {{as} {bs}}} \right. \kern-\nulldelimiterspace} \left\{ {\left( {\frac{W}{L}} \right)_{\text{N}} I_{\text{ON}} } \right\}} \right] $$
(11)

The expressions (11), (8a) and (8b) show that the latch thresholds depend mainly on the difference between the threshold voltages VthN and Vth10 of the n-channel (M11A, M12A–M12C) and p-channel (M10) transistors. Because the temperature coefficients of both voltages VthN and Vth10 are similar, the change of voltage (11) with temperature is reduced.

Figure 6 shows the simulations results of VTH1 and VTH2 changes with temperature and corners. For TM corner, VTH1 varies from 920 mV to 860 mV for the temperature from 0 to 70 °C. The total variation of VTH1, including all the corners and temperature change, is 820–946 mV. As explained in Sect. 3.1, the first threshold level VTH1 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.

Fig. 6
figure 6

VTH1 and VTH2 variation with temperature and corners

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Figure 6 shows that under the same conditions, the second threshold voltage VTH2 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 VTH2 is used to reduce the charging time of the capacitor C5, and therefore, its relatively large variation has less impact on the starter operation. Because after starting, the oscillator is powered from the auxiliary source Vaux higher than 1.6 V, the operation of the oscillator is sustained regardless of changes in VTH2. The changes in VTH1 and VTH2 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 < VTH1 < 1.1 V and VTH2 < 1.6 V).

Fig. 7
figure 7

Monte Carlo simulation results of VTH1 and VTH2 for TM corner at 27 °C

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Table 2 Summary of the Monte Carlo simulation of VTH1 and VTH2
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4.2 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 Vout is applied. For relatively small supply voltages VDD < 50 mV, the output voltage is unregulated, whereas for higher voltages the output is limited by the circuit composed of M31A–M31D, M32 and M12E. The characteristics of the output voltage are shown in Fig. 8. The curves shown refer to all combinations of the five corners TM, WP, WS, WO and WZ and three temperatures 0 °C, 27 °C and 70 °C. The output voltage Vout ranges from 1.12 to 2.7 V for VDD from 50 to 200 mV, which guarantees a reliable start of the converter.

Fig. 8
figure 8

Vout as a function of VDD for all combinations of temperatures 0 °C, 27 °C and 70 °C and corners TM, WP, WS, WO and WZ

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To determine the Vout changes caused by devices mismatch and process variation, 200 iterations of Monte Carlo simulations were performed. The results for TM corner and VDD = 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 VTH1, VTH2 and the switch-on resistance of M1 (RON1 in (1)). The Vout 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 Iaux < 1 nA due to the complexity of the feedback circuit.

Fig. 9
figure 9

Monte Carlo simulation results of Vout for TM corner at 0 °C and 70 °C

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Table 3 Summary of the Monte Carlo simulation of Vout at VDD = 50 mV
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4.3 Auxiliary Current Variation

The auxiliary current Iaux is mainly used for charging the input equivalent capacitance CIN. Only a relatively small fraction of this current is consumed by the leakage current of the control circuit. The plots of the minimum Iaux necessary to initiate the starter as a function of temperature and corners are presented in Fig. 10. For the VDD 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.

Fig. 10
figure 10

The minimum Iaux necessary to initiate the starter as a function of temperature and corners

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5 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 μm2 of the chip area. The L1, C2, C5 and RL were implemented as external components with values 820 μH, 120 pF, 10 nF and 1 MΩ, respectively. In the test setup (Fig. 12), the main power source VDD was a photodiode BPW20RF (manufactured by Vishay) shunted by the capacitor CD with 3.3 μF value. The auxiliary current Iaux was generated by a light-emitting diode (LED) working in photovoltaic mode. We used a small green LED with 1.1 V open circuit voltage and 1 nA short-circuit current at 1 klux. Using the configuration in Fig. 12, the relation between VDD, Vout and Vaux was measured. The VDD was changed by increasing illuminance of incident light. The results of measurements taken for VDD changed from 50 mV to 200 mV are presented in Table 4. The value of the auxiliary current Iaux 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.

Fig. 11
figure 11

a Micro-photograph of the chip portion containing the starter. b Design of the starter layout (21 µm × 110.7 µm)

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Fig. 12
figure 12

The test setup

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Table 4 Measured Vout and Vaux as a function of VDD
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Figure 13 shows captured waveforms of Vout, Vaux and VZ for VDD = 50 mV. It is seen that the first pulse of VZ charges C2 to Vaux > 1.9 V, which ensures correct operation of the relaxation oscillator. At the same time, as shown in Fig. 13b, the voltage Vout is delayed and limited in amplitude to 400 mV. During the successive switching of M1, the Vout increases gradually to the final value of 1.39 V.

Fig. 13
figure 13

Oscilloscope measurements of waveforms: Vout, Vaux and VZ: a start-up after applying VDD = 50 mV, b enlarged initial part of Vout, Vaux and VZ waveforms

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6 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 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.

Table 5 Performance comparison of selected starters
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7 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.