5. Transformation and amplification electronics without external supply of a periodic signal of a few millivolts in a continuous voltage of a few volts

Consider the diagram in Figure 5 which shows the location and configuration of the electronic circuits for collecting the current generated during a small fraction of the period of hypothetically inductance-sustaining vibrations of the structure. The mobile charges Q mn at the terminals of the electrode SS2 are variable over time since they vary cyclically from null to Q mn/2. A part of these electrical charges, in the ratio of the input impedance between the inductor LIN and that of the transformer electronics of this signal, generate during the short durations of their homogenization time, a peak of current which go inside this inductor and create between the two terminals of this solenoid, a voltage peak.

In Figure 5, the gray and red surfaces are stationary, the others are free to move. The green metallic connector connects face n°1 (Sp1) of the piezoelectric bridge to the return electrode. The red metallic connector connects face n°2 (Sp2) of the piezoelectric bridge to the MOS gates. For circuit n°1: The MOSEN and MOSEP sources in // are connected to the metallic electrode of face n°1 of the piezoelectric bridge. The MOSE drains are connected in parallel to the electronics without external power supply for transforming the AC signal, and to a terminal of the LIN solenoid. The other terminal of the inductance LIN is connected to the return electrode if circuit 2 is open or to ground via circuits n°2 if it is conductive.

When, the enriched MOSNE and MOSPE of circuit n°1, connect face 1 to the return electrode via the inductance LIN, as already seen, during this period the circuit composed of MOSND and MOSPD of circuit n°2 is then blocked. This connection occurs when their gates have a voltage making one of them ON.

When circuit n°1 is blocked, circuit n°2 is conducting and connects the return electrode to ground, which eliminates the charges present on this electrode and then prevents any electrostatic attraction.

Perspective Chapter: Device, Electronic,Technology for a M.E.M.S. Which Allow… DOI: http://dx.doi.org/10.5772/intechopen.105197

We will describe these electronics designed and successfully tested at ESIEE with SPICE when I was studying abandoned sensors. This electronic without external energy gave very encouraging SPICE simulation results and delivers in its output an exploitable direct voltage when it have in its input an alternating and small signals!

In these SPICE simulations, the micro transformer was assimilated to a voltage source delivering a power U \* I limited to a few nW (voltages of a few mV and current much lower than the microampere).

Now retired and no longer having sufficient means of simulations, I am simply describing the results of the SPICE simulations obtained in 2008.

The principle used to amplify and transform a weak signal without power supply derives from that of the diode bridge rectifier of Graetz or the doubler of Schenkel and Marius Latour.

The crippling problem is that the diodes of these rectifiers are conductive only with a minimum voltage of around 0.6 V at their terminals. As the alternating signal from the vacuum energy extraction device can be weaker, it is necessary to have switches that are triggered with a lower control voltage.

The principal diagram of this electronics is presented in Figures 43–45.

#### Figure 43.

Elementary stage for obtaining a negative voltage from the alternative signal of the transformer (inductance). Start interface = 200 A °.

#### Figure 44.

Elementary stage for obtaining a positive voltage from of the alternative signal of the transformer (inductance) Start interface = 200 A °.

#### Figure 45.

SPICE simulations of voltages, current, power of the transformation electronics into a direct voltage (5.4 V) of an alternating input signal of 50 mV, frequency= 150 kHz, number of stage =14, coupling capacities = 20 pF, stocking capacity = 10 nF.

The MOSE N and P transistors of this rectifier circuit must have a technologically defined threshold voltage as close as possible to zero. The precision of nullity of these threshold voltages will depend on the values of alternating voltages at the terminals of the inductor LIN, therefore on the second derivative of the temporal variations of the charges appearing on Sp2 during the time of their homogenization which is of the order of: te ¼ Rm:Cs:Log 2ð Þ In the circuit of Figure 8, a micro transformer replaced the inductance LIN. But this inductance plays the same role as this micro transformer since it delivers a limited power U.I.

The left part of the micro-transformer takes care of the negative voltages of the input signal, while the right part takes care of the positive voltages. The circuit is composed of several stages without no power supply which rectify and amplify, on the one hand the negative parts of the weak input signal and on the other hand the positive parts.

The number of elementary stages depends on the desired DC voltage, but this Dc voltage saturates with the number of stages in series (Figure 46). The results obtained from SPICE simulation are shown in Figure 8.

We observe an important point in Figures 8 and 47, the very low power and current consumption on the source since:

1. In Figure 48 the power delivered by the source begin at the start with 60 nW and ends at 2.97 pW for an input current starting at 7 pA and finishing at 1pA.

#### Figure 46.

SPICE simulations of the currents drawn by the transformer and the power consumed by this transformer. Input signal = 100 mV, frequency = 150kHz, number of stage = 30, coupling capacities = 20 pF, stocking capacity = 10 nF.

#### Figure 47.

DC output voltages as a function of the number of elementary stages for AC input voltages of 20 mV and the other of 100 mV. Start interface = 200 A °.

Perspective Chapter: Device, Electronic,Technology for a M.E.M.S. Which Allow… DOI: http://dx.doi.org/10.5772/intechopen.105197

#### Figure 48.

Influence of the coupling capacitance on the amplification of the input signal. Start interface = 200 A °.

The negative component of the alternating signal is transformed in 10 ns into a negative direct voltage of Vn <sup>¼</sup> ‐2:7 V. Likewise the positive component the positive alternating part is transformed into a positive direct voltage of Vp ¼ <sup>2</sup>:7 V We obtain therefore a direct voltage Vp‐Vn <sup>¼</sup> Vt <sup>¼</sup> <sup>5</sup>:4 V.

2. In Figure 47 the power delivered by the source begin at the start with 65 nW and ends at 4.2 nW for an input current starting at 700 nA and finishing at 90 nA. The negative component of the alternating signal is transformed in 10 ns into a negative direct voltage of Vn <sup>¼</sup> ‐3:9 V. Likewise the positive component the positive alternating part is transformed into a positive direct voltage of Vp <sup>¼</sup> <sup>3</sup>:9V. We obtain therefore a direct voltage Vp‐Vn <sup>¼</sup> Vt <sup>¼</sup> <sup>7</sup>:8 V.

An important point is the need to have a high circuit output impedance of several 10<sup>7</sup> ohms, so typically the input impedance of an operational amplifier.

The DC voltage obtained depends on the number of stages constituting these electronics without electrical power for transforming an AC signal of a few millivolts into a DC signal of a few volts. However, this transformation saturates with the number of floors, as shown in Figure 49 Note in Figure 49 that the DC output

#### Figure 49.

Evolution of the DC output voltage as a function of the amplitude of the AC input signal for a frequency of 150 kHz. Start interface = 200 A °

Figure 50.

voltage saturates with the number of elementary stages and that the optimal number of stages is of the order of 40. We also looked at the influence of the coupling capacitance on the amplification of an input signal of 100 mV with a storage capacity of 10 nF. This amplification saturates and a coupling capacity of 20 pF which seems to be optimal signal (Figure 48).

The following Figure 50 shows the influence of the value of the input AC voltage, with a frequency of 150 kHz, on the DC voltage obtained at the output of a 2 \* 14 stage device.

Figure 46 shows the power in nW delivered by the source at the start of the amplification and at the end of this amplification.

A summary of the performance of this low "voltage doubler" device is shown in Figure 51 below.

The interesting points for the presented electronics' device are:

1. the low alternative input voltages required to obtain a continuous voltage of several volts at the output


#### Figure 51.

Summary of transformations from low alternating voltages to direct voltage frequency of 150 kHz. Start interface = 200 A °.

Perspective Chapter: Device, Electronic,Technology for a M.E.M.S. Which Allow… DOI: http://dx.doi.org/10.5772/intechopen.105197

Figure 52.

S.O.I technology for making the elements of the "doubler".

2. the low power and current consumed by this conversion and amplification circuit on the source which in this case is only an inductor supplied by the current peaks generated by the autonomous vibrations.

3. the rapid time to reach the DC voltage (a few tens of milliseconds)

The technology used to fabricate the MOSNE and MOSPE transistors with the lowest possible threshold voltages is CMOS on intrinsic S.O.I. and the elements are isolated from each other on independent islands. This technology, represented in the following Figure 52, strongly limits the leakage currents.

We note that, the coupling capacities of 20 pF this electronic, like that of storage of the order of 10 nF, have relatively high values witch will require a square surface of:


But if we use titanium dioxide as insulator, it has a relative permittivity of the order of 100 and is one of the most important for a metal oxide then the size of the capacity passes to 23 mm for a thickness of TiO2 = 500 A°, which is more reasonable!
