1 Introduction

Howland current pump based on operational amplifiers [1] is a widely used circuit for the implementation of accurate voltage-to-current (V-to-I) converters, mostly used: (1) for circuit biasing and stabilization; (2) as a reference or linearizing system for sensor conditioning; (3) as a current source for setting a test condition, regulating a signal for actuation, or injecting a known current for material characterization in measurement systems [2,3,4,5].

Figure 1 shows the schematic of a simple V-to-I converter based on Howland current pump. The load sees the equivalent Norton circuit with an ideal current source IL = (V2 − V1)/R1, supposing that the well-known balanced bridge condition R4/R3 = R2/R1 is respected, in parallel to a resistor RO the value of which is given by:

Fig. 1
figure 1

Howland current pump scheme. IL = (V2 − V1)/R1 if R2/R1 = R4/R3

Full size image
$$R_{O} = \frac{{R_{2} }}{{R_{2} /R_{1} - R_{4} /R_{3} }}$$
(1)

which, indeed, tends to be ideally infinite if the balancing condition is met. The balanced bridge condition can be obtained by using highly-matched thin film resistors.

It’s worth noting that the schematic illustrated in Fig. 1 reflects the topology of a classic difference amplifier where, however, both negative and positive feedbacks have to be implemented. In addition, unlike the difference amplifier, in Howland circuit the op-amp non-inverting input represents the output terminal for load connection. Nevertheless, solutions based on difference amplifiers require at least an external high-precision resistor [6] to set the desired V-to-I conversion factor.

In this work, we propose a new solution for Howland current pump-based current sources, exploiting single-chip (LT199x, Linear Technology) selectable-gain-amplifiers, which does not require any additional external component [7]. The designed circuit shows outstanding performance in terms of linearity, output resistance, and temperature dependence, due to the internal thin film resistors excellent matching ratio and the low temperature coefficient, enabling the implementation of high-precision current sources operating in the µA–mA range. In particular, the circuit is here proposed as a current supply and signal conditioning system for resistive temperature sensors, with the possibility of applying a ratiometric method for the implementation of highly accurate resistance measurement stages.

2 Selectable-gain amplifier-based solutions for Howland current pump

As for any other difference amplifier, pins of selectable-gain amplifiers LT199x enable positive feedback, due to the availability of the reference terminal. But, unlike traditional difference amplifiers ICs, current can be sourced with LT199x chips through the available additional internal resistors connected to the op-amp non-inverting input, so that no external component is required for V-to-I conversion.

Figure 2 shows the scheme of the proposed circuit using LT1991/5/6 gain-selectable amplifiers. The V-to-I conversion factor can be expressed as:

Fig. 2
figure 2

Connections example for a Howland circuit based on gain-selectable single-chip amplifiers LT1991/5/6

Full size image
$$\frac{1}{{R_{CONV} }} = \frac{{I_{L} }}{{V_{2} - V_{1} }} = \frac{1}{{R_{p1} }}\left( { = \frac{1}{{R_{n1} }}} \right)$$
(2)

As can be seen, different conversion factors can be obtained by parallel connections between the resistances Rpx and Rnx used as inputs, whereas parallel connections between the feedback resistors RF and RF′ allow the system output dynamics to be extended (before op-amp saturation occurs). Also, note that a voltage drop |ΔVL| = ILRp3 on the maximum allowable load voltage is introduced by the presence of the Rp3 resistor in series to the load itself, limiting the VL voltage compliance; this limitation was not present in the scheme of Fig. 1, which allows for a wider voltage compliance.

Figure 3 reports the measured output current signal IL as a function of the input voltage difference V2 − V1, for different values of the conversion factor 1/RCONV, for LT11991/5/6 based Howland circuits. Note that a very good linearity is obtained in the investigated input voltage range. Non-linearity is indeed lower than ± 0.02%, approaching ± 0.01% for LT1991 and LT1995 ICs, as expected for the resistors high matching ratio declared for the LT199x chips [8]. As expected, the maximum input control voltage amplitude (before op-amp saturation) decreases with decreasing values of RCONV. Moreover, for data shown in Fig. 3, the resistor used for load connection towards the op-amp non-inverting input was the lowest allowed by the chip type (50 kΩ, 1 kΩ, and 5.56 kΩ for LT1991, LT1995, and LT1996, respectively [8]); higher resistance values would have indeed limited the maximum output current before op-amp saturation. It’s worth mentioning here that, in the LT1996 case, the unused resistors were connected in parallel to the feedback ones (RF and RF′) to avoid op-amp saturation at very low load voltages.

Fig. 3
figure 3

Output current as a function of the input voltage difference for the circuit of Fig. 2 based on LT1991, LT1995, and LT1996 chips for different values of the conversion factor 1/RCONV

Full size image

3 Resistive sensor biasing and conditioning

The circuit of Fig. 2 was implemented for Resistive Temperature Devices (RTD) biasing and conditioning. A preliminary characterization was performed to evaluate its feasibility as a precision transducer for a resistive sensor connected as load, by using a fixed reference voltage VREF = 4.096 V obtained by means of a REF3040 followed by an OPA350 acting as a buffer. For this purpose, an LT1995 based circuit, with RCONV = RF = 4 kΩ, was assembled (IL ≈ 1 mA). A wide range of load resistance values (10−2–103 Ω) was used for the test measurements; for obtaining values as low as tens of mΩ, a 0.8 m long, 0.6 mm diameter copper wire was used to obtain five different resistance values, by shifting each time the position of the second terminal to 0.2, 0.4, 0.6, 0.7, and 0.8 m (corresponding to the full length of the wire). Figure 4 shows the measured output voltage change with respect to the output value acquired at a zero load resistance RL = 0 Ω. It is worth noting the very good linearity obtained over 5-decades of RL values.

Fig. 4
figure 4

Output voltage change versus load resistance for a Howland current pump based on LT1995 gain-selectable amplifier

Full size image

A Pt100 sensor was then connected as load and inserted in a thermostatic bath to regulate the device temperature up to T = 350 °C. A first characterization was performed in the 24–155 °C range. The measured linear temperature slope was ΔVo/ΔT = 0.764 mV/ °C, very close to the nominal one (0.770 mV/ °C) calculated by considering the temperature coefficient of a Pt100 (0.00385 Ω/Ω/ °C). The evaluated maximum relative error was ± 0.4 °C, mostly attributed to the Pt100 sensor non-linearity. Indeed, best fit of data returned a second order polynomial curve, with a linear coefficient 3.9062 × 10−3 °C−1 and a quadratic coefficient − 6.4141 × 10−7 °C−2, in good agreement with those reported in the literature for platinum resistance sensors [9].

The major drawback of the solution depicted in Fig. 2 for RTD biasing and conditioning is the voltage drop |ΔVL| = ILRp3 at the resistor in series to the load itself, which limits the sensor output dynamics. A Pt100 resistor can indeed span a resistance value from 18.5 Ω (T = − 200 °C) to 390.5 Ω (T = 850 °C), corresponding in our case to an output voltage range Vo = 2.04–2.79 V. To enhance the sensitivity of the overall system, a second prototype was implemented (Fig. 5): note that, in order to reduce the voltage drop across the load, Rp3 was connected in parallel to Rp1, decreasing the overall value from Rp3 = 1 kΩ to Rp3//Rp1 = 800 Ω. Moreover, the source current was doubled by using RCONV = 2 kΩ, and the LT1995 op-amp inverting-configuration gain was set to 3, increasing the nominal circuit sensitivity to 2.3 mV/ °C. Finally, a LT1991-based second stage was added to limit the maximum output voltage, and a single-pole RC filter was inserted to suppress any high-frequency noise contribution. By considering the full Pt100 temperature range (− 200–850 °C), the output voltage of the circuit of Fig. 5 is Vo = 3.28–1.05 V (output voltage vs. temperature curve has indeed a negative slope), thus exploiting more than 50% of the full-scale range of an A/D converter referenced to the same VREF = 4.096 V voltage.

Fig. 5
figure 5

Schematic of the prototype implemented to enhance the sensitivity of the system

Full size image

Figure 6 reports the output voltage Vo of the circuit of Fig. 5 measured as a function of the Pt100 temperature in the extended range 24–350 °C. First of all, note the excellent linearity obtained. A slight non-linearity, due again to the sensor characteristics, was observed only for T > 300 °C, underlining the necessity to consider also the quadratic term of the sensor response at high temperatures. However, the maximum relative error, estimated to be in this case as low as ± 0.06%, highlights the possibility to resolve 1 °C in the whole investigated temperature range.

Fig. 6
figure 6

Output voltage of the circuit of Fig. 5 in the 24 ÷ 350 °C temperature range for a Pt100 sensor connected as load

Full size image

To better highlight the benefits of the proposed solution, which adopts a so-called “ratiometric” measurement method [10], let us consider a n-bit A/D converter, referenced to the same VREF = 4.096 V voltage. If perfectly matched resistors are considered for the LT1995 and LT1991 ICs of the circuit of Fig. 5, the output code related to the RL value can be simply expressed by:

$$N = \frac{{2^{n + 2} }}{5} - 3 \times 2^{2n} \frac{{R_{L} }}{{R_{CONV} }},$$
(3)

so that the system accuracy is equal, as expected for a ratiometric method, to that of the RCONV factor. In this way, errors caused by a limited absolute accuracy of the voltage reference (and then of the load excitation current), as well as those induced by the excitation drift, are virtually eliminated. Moreover, any noise superimposed to the excitation source is added to reference terminal of the A/D converter, improving significantly the signal-to-noise ratio.

4 Conclusions

A new application of commercially available single-chip selectable-gain amplifiers as low-power Howland current pump circuits, was introduced and discussed. The tested circuits, based on LT1991, LT1995, and LT1996 ICs, were able to generate current signals in the 0.1–10 μA, 1–100 μA, and 10–1000 μA range, respectively, exhibiting a V-to-I non-linearity lower than ± 0.01%, as well as an excellent performance in the 0.01–1000 Ω range in terms of sensitivity and accuracy. Dedicated prototypes were also designed and implemented for biasing and conditioning of platinum resistor-based temperature sensors, demonstrating their suitability to act as extremely compact and high-precision current sources.