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A 20 Mv Colpitts Oscillator Powered by a Thermoelectric Generator

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A 20 Mv Colpitts Oscillator Powered by a Thermoelectric Generator A 20 mV Colpitts Oscillator powered by a thermoelectric generator Fernando Rangel de Sousa∗, Marcio Bender Machado∗†, Carlos Galup-Montoro ∗ ∗Integrated Circuits Laboratory-LCI Federal University of Santa Catarina-UFSC Florianopolis-SC, Brazil, Tel.: +55-48-3721-7640 Email:[email protected] † Sul-Rio-Grandense Federal Institute Charqueadas-RS, Brazil Email:[email protected] Abstract—In this paper, we present a MOSFET-based Colpitts of around 13 mV , only seven milivolts far from the voltage oscillator based on a “zero-threshold” transistor operating at a supply value for which the circuit sustained oscillations at 130 supply voltage below 20 mV. The circuit was carefully analyzed mV(peak-to-peak)/97 kHz. Moreover, the circuit was powered and expressions relating the start-up conditions and the voltage supply, as well as the oscillation frequency were developed. by a thermoelectric generator which supplied a DC voltage of Measurement results obtained on a discrete prototype confirmed around 22 mV when it was installed on the arm of a person the low-voltage operation of the oscillator, which sustained in a 24oC room. oscillations of 130 mV (peak-to-peak) at 97 kHz when the voltage supply was 19.8 mV. The circuit was also powered from a II. COLPITTS OSCILLATOR thermoelectric generator (TEG) connected to a persons arm in a room with temperature of 24oC room. Under these conditions, A Colpitts oscillator can be broken in two main blocks : i) the TEG supplied 22 mV and the circuit operated as expected. a potentially unstable one-port and ii) a load network, as it is shown in Fig. 1. The one-port circuit is an amplifier which can I. INTRODUCTION include explicit positive feedback for providing the necessary Energy harvesting applications require efficient circuits op- instability. The load network must be chosen in order to satisfy erating at very low voltages. One emblematic example is the the Barkhausen criterion, that is to say, the real part of the use of a thermoelectric generator (TEG) as the energy source terminating load must be smaller than the magnitude of the for self-powered wearable medical applications. Bismuth tel- one-port negative conductance, as well as the load susceptance luride thermoelectric modules provide open-circuit voltages must cancel the one-port imaginary part at the oscillation of around 25 mV/K [1]. The small temperature difference frequency. Moreover, an amplitude limiting mechanism must between the body and the surroundings, usually of 1 to 2 K, be provided so that the amplitude of the oscillations stabilizes limits the output voltage of TEGs to 50 mV [2], which is a at a given point. This mechanism is often obtained from the very low voltage level for running conventional electronics. nonlinear characteristic of the amplifier. Some recent publications have reported TEG-based applica- tions operating at supply voltages as low as 20 mV or 35 mV; however, they use DC-DC converters that require special start- ONE−PORT up solutions such as pre-charged capacitors or batteries [3] or Load NETWORK mechanical switches [2]. The ignition of a DC-DC converter is a time-varying signal commonly obtained from an electronic Yout Y oscillator. Current state-of-the-art low-voltage oscillators op- L erate at one hundred mV or more [4], [5], imposing a severe Fig. 1. Conceptual high-level model of a Colpitts Oscillator limitation to energy scavenging applications. In this paper, we present results obtained from a Colpitts In a typical Colpitts implementation, a current source is oscillator powered by a 19.8 mV voltage supply. The circuit used to determine the amplifier operating point, however, uses a “zero threshold“ MOS transistor [6] as active element for extreme low-voltage implementation, the circuit DC path so that the necessary power gain for compensating circuit should have only the transistor. losses can be obtained from an amplifier powered from a A low-voltage realization of the Colpitts oscillator is pre- very low voltage supply. In addition to experimental results, sented in Fig 2. The circuit contains a common-gate amplifier, we provide an accurate theoretical analysis which allows us including a tapped capacitor network composed of C1 and C2 to predict the minimum necessary voltage for establishing in order to provide positive feedback. The inductor L1 is the oscillations as well as the oscillating frequency. The analysis amplifier load and resonates with the capacitive admittance at predicts that the oscillator should start-up at a voltage supply the amplifier output. At resonance, the combination of load VDD C1 gms gmd 1 + 1 C2 − gmd L1 Yout = 2 2 h C1 gms i 1 + C2 + ωC2 C1 gms C1 ωC1 1 + C2 + gmd ωC2 +j 2 2 (3) C1 gms M1 1 + C2 + ωC2 C2 LRF C A. Start-up condition COMMON-GATE AMPLIFIER If we consider all the circuit losses due to passive devices (a) embedded in a conductance GP parallel to L1, as it is shown in Fig. 4, the oscillator starts up when Re Yout < GP : Fig. 2. Schematic diagram of the ultra-low-voltage Colpitts oscillator. { } − C1 gms gmd 1 + 1 C2 − gmd and amplifier admittance is real and when its sign becomes 2 2 < GP (4) ω(Ch1+C2) gms i − negative, the oscillations at the transistor drain increase, up ωC2 + ωC2 to the point at which the nonlinearity of the amplifier alters h i its bias point, thus stabilizing the signal amplitude. To attain Assuming that gms << ω(C1 + C2), where ω is the a sufficient level of negative resistance, the amplifier should oscillator frequency in rad/s, (4) can rewritten as: provide the necessary power gain to compensate for the ohmic 2 losses of all devices. For ultra-low-voltage operation, the C2 C1 C2 terminals of the transistor are connected to the voltage supply gms > gmd 1 + + GP 1 + (5) C1 C2 C1 (VDD) and to the ground (GND) via inductors L1 and LRF C. B. Minimum voltage supply III. ANALYSIS In [8] we find an expression relating VDS to the transistor forward and reverse inversion levels, which can be written in In this paper, we are concerned with the minimum voltage terms of the drain and source transconductances as: necessary to start up the oscillator. Classic analysis of the Colpitts oscillator assumes that the transistor is operating 2 gms φt under the saturation condition and disregards the transistor VDD = φt ln + (gms gmd) (6) g 2I − output conductance. Under these conditions, the minimum md S where φt is the thermal voltage and IS is the specific current amplifier voltage gain required for oscillation is found to be 2 ′ φt W 4, when the feedback network capacitors have identical values of the transistor given by IS = µCoxn L , µ is the effective ′ 2 [7]. mobility, Cox is the oxide capacitance per unit area, n is the For an ultra low-voltage oscillator, a more careful analysis slope factor and W/L is the aspect ratio of the transistor. should be conducted, since the transistor operates mainly in In order to establish a relationship with the supply voltage, the triode region, where its output conductance is considerably we should observe in Fig. 1 that VDD is also the drain- higher than in saturation. Considering the AC model of the to-source DC voltage (VDS) of M1. So, by combining (5) oscillator shown in Fig. 3.a, we calculated the amplifier output and (6), we obtain an expression for the minimum supply admittance after replacing M1 with its linear model, as shown in Fig. 3.b. In the model, gmd is the drain conductance given by gmd = id/vd and gms is the source transconductance given C1 by gms = id/vs, where id is the small-signal drain current and M1 gmdvout vd and vs are the drain and source voltages, respectively [8]. C1 Applying the Kirchoff law of currents in the model of g v ms s i Fig.3(b), we have: L1 out + + LRF C v C2 vs out − − C2 Yout iout = vout(jωC1 + gmd) vs(jωC1 + gms) (1) − (a) (b) (2) iout = vsjωC2 Yout By replacing (2) in (1) and making some algebraic manip- Fig. 3. AC equivalent circuit of the ultra-low-voltage Colpitts oscillator. (a) ulations, we find that the amplifier output admittance is: Schematic (b) Linear model TABLE I voltage necessary to start up the MOSFET Colpitts oscillator TRANSISTOR CHARACTERISTICS MEASURED FOR VDD = 20 mV AT as follows: T = 23 oC. Parameter Value C2 GP C1 VDD crt = φt ln 1 + + φt ln 1 + 1 + | C g C IS (Specific Current) 11.18 µA 1 md 2 2 2 (Threshold Voltage) φt C2 GP C1 VTH 59 mV +gmd 1 + 1 + (7) 2IS C1 gmd C2 g (Source Transconductance) 520 µA/V " # ms gmd (Drain Transconductance) 325 µA/V The above expression allows us to recognize the importance of the relationship between passive device losses and transistor n (Slope factor) 1.6 output conductance. Initially, for a limited supply voltage, increasing the transistor aspect ratio may appear to compensate G for the ohmic dissipation in the circuit due to the P ratio. where CT is the equivalent capacitor parallel to L1, which can gmd By making GP << gmd, a limit for VDD can be given by: be reasonably approximated by CT = C1C2/(C1 + C2). IV. DESIGN C V = φ ln 1 + 2 DD GP <<gmd t For the design of the oscillator, we used a wide MOSFET | C1 2 with very low threshold voltage and high quality passive φt C2 +gmd (8) devices. The transistor used was a parallel combination of 24 2IS C1 ALD110800 unities [6].
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