## 3 Signal Conditioning Circuit
### Sensor Biasing and Heat Pulse Circuit  
The simplified schematic of the bias and heat pulse circuit used to drive the sensor (an NPNtransistor) is presented in Figure 3. The base is maintained at a fixed voltage, derived from a temperature-stable voltage reference \(V_{REF1}=1.25\) V (REF3312 from Texas Instruments). The emitter is connected to a current source, which has its value switched between two values (\(100\,\mathrm{\SIUnitSymbolMicro A}\) and \(10\,\mathrm{mA}\)), by the action of a single pole dual throw switch \(SW_{1}\) (SPDT) on a resistor. The current source is defined by the voltage reference \(V_{REF2}=1.25\) V (also an REF3312 from Texas Instruments), op-amp \(A_{1}\) (LTC6003, a rail-to-rail ultra-low supply current, low off-set and low-bias current op-amp from Analog Devices), an NMOS transistor \(M_{1}\) (VN2222), and resistors \(R_{1},R_{2}\). Transistor \(M_{1}\) is inside the negative feedback loop, and op-amp \(A_{1}\) forces \(V_{S}=V_{REF2}\). Therefore, the drain current in \(M_{1}\), which is equal to the emitter current of \(Q_{1}\), is given by:  
\[I_{E1}=\frac{V_{REF2}}{R_{eq}} \tag{5}\]  
where \(R_{eq}=R_{1}\) when \(S_{W1}\) is opened and \(R_{eq}=R_{1}//R_{2}\) when \(S_{W1}\) is closed. The values of \(V_{REF2}\), \(R_{1}\), and \(R_{2}\) are calculated to furnish the desired currents of \(100\,\mathrm{\SIUnitSymbolMicro A}\) and \(10\,\mathrm{mA}\). During the heat pulse, both the voltage \(V_{CB}\) and the emitter current are kept constant, but the variation of temperature in the transistor causes some changes in the value of \(V_{CE}\). Since during the heat pulse, the maximum temperature variation in an SHPP is usually in the order of \(5\,\mathrm{\SIUnitSymbolCelsius}\), the variation of \(V_{BE}\) with temperature (which changes the value of \(V_{CE}\)) will be only in the order of 9 mV (only 1.2 ppm  
Figure 2: Basic diagram of the power management circuit. LDO, low drop-out voltage regulator. of variation in \(V_{CE}\)). Furthermore, the typical variation of \(\beta_{F}\) with temperature (which changes the base current) is only 0.35%/\({}^{\circ}\)C/ [15], so we can assume that the power dissipated in the transistor is constant during the heat pulse. To measure the \(V_{BE}\) of the sensor transistor, two unity gain amplifies \(A_{3}\), \(A_{4}\), implemented with an LTC6004 (a dual version of the LTC6003 op-amp), are connected to the emitter and base terminals of the sensor. The outputs of the op-amps are sent to a differential analogue-to-digital (A/D) converter available in the MSP430F6736 microcontroller (from Texas Instruments), which operates with a supply current of only 1.25 uA in low-power mode, with the real-time clock (RTC) running. Although the MSP430F6736 A/D converter has 24 bits, we used only 16 bits (15 bits plus one sign bit), which was enough to measure \(V_{BE}\) with a \(\approx\) 36.6-uV resolution. In this initial phase of measurement (which lasted only 50 ms), the measured value of \(V_{BE}\) was used to calculate the equilibrium temperature between the sensor and the soil before the heat pulse was applied. Measuring the soil's temperature is very important because a calibration curve (deviation of the measured value as a function of the soil temperature) has to be obtained experimentally, before using the sensor in the soil [21]. The \(V_{CB}\) voltage in the transistor was kept constant (\(V_{CB}=6.75\) V), and since the transistor's emitter current during this measurement phase was 100 uA, the power applied to the transistor was very low (\(P=I_{E}V_{CE}\approx 730\) uW); thus, the sensor's temperature was practically not affected. During the heat pulse phase, which in our prototype lasted 10 s, the collector voltage was kept unchanged (\(V_{C}=8\) V, so \(V_{CE}\approx 7.45\) V), while the current was increased from 100 uA-10 mA (with switch \(S_{W1}\)), generating a heat pulse with approximately \(E=0.745\) J (74.5 mW during 10 s).