Device for measuring impedance of biologic tissues including an alternating current (AC) coupled voltage-to-current converter

Abstract

A device for measuring impedance of biological tissue may include electrodes and a voltage-to-current converter coupled to the electrodes to drive an alternating current (AC) through the tissue and sense an AC voltage. The converter may include an amplifier having first and second inputs and an output, a first voltage divider coupled to the first input, a second voltage divider coupled to the second input, a filter capacitor coupled between the output and the second voltage divider, a current limiting resistor coupled between the second input the second voltage divider, and a bypass capacitor coupled to the second input of the amplifier and in parallel with the resistor. A single-ended amplitude modulation (AM) demodulator may demodulate the AC voltage and generate a corresponding baseband voltage representing the impedance. The device may also include an output circuit to generate output signals representative of DC and AC components of the baseband voltage.

Claims

1. A voltage-to-current converter for a device for measuring impedance of biological tissue, the device comprising a pair of electrodes for contacting the biological tissue, at least one single-ended amplitude modulation (AM) demodulator configured to demodulate an AC voltage and to generate a corresponding output voltage representing the impedance, the voltage-to-current converter comprising: an amplifier to be coupled to the pair of electrodes and configured to drive an alternating current (AC) through the biological tissue and to sense an AC voltage, said amplifier having a first input, a second input, and an output; a current limiting resistor coupled to said second input; and a bypass capacitor coupled to the second input of said amplifier and in parallel with said current limiting resistor.

2. The voltage-to-current converter of claim 1, further comprising: an output node; an input node configured to receive an AC drive voltage; a first resistive voltage divider having a middle terminal and coupled between the output node and the input node; and a second resistive voltage divider having a middle terminal and a same voltage ratio as said first resistive voltage divider, and coupled between a common terminal with one of said pair of electrodes and to the output node, and another one of said pair of electrodes being coupled to the middle terminal; said first input of said amplifier coupled to the middle node of said first resistive voltage divider, and said second input of said amplifier coupled to the middle terminal of the second resistive voltage divider through said current limiting resistor.

3. A voltage-to-current converter for a device for measuring impedance of biological tissue, the device comprising a pair of electrodes for contacting the biological tissue, at least one single-ended amplitude modulation (AM) demodulator configured to demodulate an AC voltage and to generate a corresponding output voltage representing the impedance, the voltage-to-current converter comprising: an amplifier to be coupled to the pair of electrodes and configured to drive an alternating current (AC) through the biological tissue and to sense an AC voltage, said amplifier having a first input, a second input, and an output; a first resistive voltage divider coupled to the first input; a second resistive voltage divider coupled to the second input; and a direct current (DC) filter capacitor coupled between the output of said amplifier and said second resistive voltage divider; wherein for a given working frequency of said amplifier, values of said first and second resistive voltage dividers and said DC filter capacitor are chosen according to:
_o=(_p/(k_2R_3C))=(_GBP/(k_1k_2R_3C)) wherein o is the given working frequency, R.sub.3 is a resistive value of a first resistor of said second resistive voltage divider, C is a value of said DC filter capacitor, k2=1+((R.sub.4a+R.sub.4b)/R.sub.3) wherein R.sub.4a and R.sub.4b are respective resistive values of second and third resistors of said second resistive voltage divider, and GBP=pk1 is a gain-bandwidth product of said amplifier, wherein k1=1+(R2/R1), and wherein R1 and R2 are respective resistive values of first and second resistors of said first resistive voltage divider.

4. The voltage-to-current converter of claim 3, wherein k1 is equal to k2.

5. The voltage-to-current converter of claim 3, wherein values of said first and second resistive voltage dividers and said DC filter capacitor are chosen according to: wherein Cp is a parasitic capacitance.

6. The voltage-to-current converter of claim 3, further comprising: an output node; and an input node configured to receive an AC drive voltage; said first resistive voltage divider having a middle terminal and being coupled between the output node and the input node; and said second resistive voltage divider having a middle terminal and a same voltage ratio as said first resistive voltage divider, and being coupled between a common terminal with one of said pair of electrodes and to the output node, and another one of said pair of electrodes coupled to the middle terminal; said first input of said amplifier coupled to the middle node of said first resistive voltage divider, and said second input of said amplifier coupled to the middle terminal of the second resistive voltage divider.

7. The voltage-to-current converter of claim 3, further comprising: a current limiting resistor coupled between the second input of said amplifier and said second resistive voltage divider; and a bypass capacitor coupled to the second input of said amplifier and in parallel with said current limiting resistor.

8. A method of making a voltage-to-current converter for a device for measuring impedance of biological tissue, the device comprising a pair of electrodes for contacting the biological tissue, at least one single-ended amplitude modulation (AM) demodulator configured to demodulate an AC voltage and to generate a corresponding output voltage representing the impedance, the method comprising: coupling an amplifier to the pair of electrodes to drive an alternating current (AC) through the biological tissue and to sense an AC voltage, the amplifier having a first input, a second input, and an output; coupling a first resistive voltage divider to the first input; coupling a second resistive voltage divider to the second input; and coupling a direct current (DC) filter capacitor between the output of amplifier and second resistive voltage divider; wherein for a given working frequency of the amplifier, values of the first and second resistive voltage dividers and the DC filter capacitor are chosen according to: wherein o is the given working frequency, R.sub.3 is a resistive value of a first resistor of the second resistive voltage divider, C is a value of the DC filter capacitor, k2=1+((R4a+R4b)/R3) wherein R.sub.4a and R.sub.4b are respective resistive values of second and third resistors of the second resistive voltage divider, and GBP=pk1 is a gain-bandwidth product of said amplifier, wherein k1=1+(R2/R1), and wherein R1 and R2 are respective resistive values of first and second resistors of the first resistive voltage divider.

9. The method of claim 8, wherein k1 is equal to k2.

10. The method of claim 8, wherein values of the first and second resistive voltage dividers and the DC filter capacitor are chosen according to: wherein Cp is a parasitic capacitance.

11. The method of claim 8, further comprising: coupling a middle terminal of the first resistive voltage divider between an output node and an input node for receiving an AC drive voltage; coupling a middle terminal of the second resistive voltage divider between a common terminal with one of the pair of electrodes and to the output node, and coupling another one of the pair of electrodes to the middle terminal, the second resistive voltage divider having a same voltage ratio as the first resistive voltage divider; and coupling first input of the amplifier to the middle node of the first resistive voltage divider and coupling the second input of the amplifier to the middle terminal of the second resistive voltage divider.

12. The method of claim 8, further comprising: coupling a current limiting resistor between the second input of the amplifier and the second resistive voltage divider; and coupling a bypass capacitor to the second input of the amplifier in parallel with the current limiting resistor.

13. A voltage-to-current converter for a device for measuring impedance of biological tissue, the device comprising a pair of electrodes for contacting the biological tissue, at least one single-ended amplitude modulation (AM) demodulator configured to demodulate an AC voltage and to generate a corresponding output voltage representing the impedance, the voltage-to-current converter comprising: an amplifier to be coupled to the pair of electrodes and configured to drive an alternating current (AC) through the biological tissue and to sense an AC voltage, said amplifier having a first input, a second input, and an output; a first resistive voltage divider coupled to the first input; a second resistive voltage divider coupled to the second input; a direct current (DC) filter capacitor coupled between the output of said amplifier and said second resistive voltage divider; a current limiting resistor coupled between the second input of said amplifier and said second resistive voltage divider; and a bypass capacitor coupled to the second input of said amplifier and in parallel with said current limiting resistor.

14. The voltage-to-current converter of claim 13, further comprising: an output node; and an input node configured to receive an AC drive voltage; said first resistive voltage divider having a middle terminal and being coupled between the output node and the input node; said second resistive voltage divider having a middle terminal and being coupled between a common terminal with one of the pair of electrodes and to the output node, and another one of the pair of electrodes coupled to the middle terminal.

15. The voltage-to-current converter of claim 14, wherein said first input of said amplifier is coupled to the middle node of said first resistive voltage divider, and said second input of said amplifier coupled to the middle terminal of the second resistive voltage divider.

16. The voltage-to-current converter of claim 14, wherein the second resistive voltage divider has a same voltage ratio as said first resistive voltage divider.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 schematically illustrates two architectures for measuring the impedance of a biological tissue in accordance with the prior art.

(2) FIG. 2 schematically illustrates another architecture for measuring the impedance of a biological tissue in accordance with the prior art.

(3) FIG. 3 schematically illustrates yet another architecture for measuring impedance of biological tissues in accordance with the prior art.

(4) FIG. 4 schematically illustrates an embodiment of a device for measuring impedance of biological tissues in accordance with the present invention.

(5) FIG. 5a schematically illustrates a Howland voltage-to-current converter.

(6) FIG. 5b schematically illustrates a Howland voltage-to-current converter having a DC-blocking capacitor and a fault protection resistor.

(7) FIG. 6 schematically illustrates an exemplary voltage-to-current converter alternative to the Howland converter.

(8) FIG. 7 schematically illustrates yet another embodiment of a device for measuring impedance of biological tissues that does not include an INA in accordance with the present invention.

(9) FIG. 8 schematically illustrates yet another embodiment of a device for measuring impedance of biological tissues having DC-blocking capacitors and being connected to an ECG device in accordance with the present invention.

(10) FIG. 9 schematically illustrates an AM demodulator configured to be used in the device for measuring impedance of biological tissues in accordance with the present invention.

(11) FIG. 10 schematically illustrates a voltage to current converter known as improved Howland circuit.

(12) FIG. 11 schematically illustrates a voltage to current converter.

(13) FIG. 12 is a graph of frequency versus output impedance illustrating the decreasing of the output impedance of a Howland circuit with the increasing of the frequency and output impedance significantly increasing at the working frequency.

(14) FIG. 13 schematically illustrates a circuit for obtaining a relatively high output impedance at the working frequency and the cancellation of a parasitic capacitance effect according to an embodiment of the present invention.

(15) FIG. 14 schematically illustrates another circuit for obtaining a relatively high output impedance at the working frequency and the cancellation of parasitic capacitance effect according to an embodiment of the present invention.

(16) FIG. 15 schematically illustrates another circuit for operation at different selectable working frequencies in accordance with an embodiment of the present invention.

(17) FIG. 16 is a schematic diagram of a voltage-to-current converter to which dimensioning criterion according to the present invention may be applied.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

(18) An embodiment of a device for measuring the impedance of biological tissue is illustrated in FIG. 4. The circuit blocks in common with the prior devices of FIGS. 2 and 3 are identified by the same labels.

(19) The device has two single-end AM demodulators. Each demodulates the voltage towards ground of a respective electrode and generates a respective baseband signal. The demodulated baseband signals are supplied in input to an INA that generates an amplified copy of their difference.

(20) Differently from the known device of FIG. 2, the INA amplifies a baseband signal, thus, it has a relatively large gain and a good CMRR in the baseband range of frequencies. Therefore it may be possible to use a low cost and low power consumption INA.

(21) Differently from the prior device of FIG. 3 disclosed in Rafael Gonzalez-Landaeta, Oscar Casas, and Ramon Pallas-Areny, Heart rate detection from plantar bioimpedance measurements. IEEE Transactions on Biomedical Engineering, 55) 3):1163-1167, 2008, the device may not need a differential amplifier of the voltage drop sensed on the electrodes because, in the device, the AM demodulation is carried out in a single-end fashion. In a coupled amplifiers architecture, the bandwidth is reduced the more the gain is greater than one.

(22) Preferably, the voltages towards ground of the two electrodes are read by two single ended AC coupled buffers, thus rejecting electrode offset rejection and high input impedance before being AM demodulated. This approach is preferred because unitary gain buffers have the largest bandwidth for a given operational amplifier, and, at the same time, the very good match of the unitary gain provides a good CMRR. Noise, that is a reason for which a gain in the first stages is usually preferred, is generally not an issue in this case because the first stage works on a relatively high frequency signal in a bandwidth in which the noise of common operational amplifiers is relatively low.

(23) Any skilled person will be capable of identifying AC buffer architectures configured to be used in the device, and for this reason, they are not illustrated in detail. In a four electrode configuration, as the architecture shown in FIG. 4, an ECG front-end may optionally be coupled to measure also the electrocardiogram of a patient.

(24) The voltage-to-current converter may be a Howland voltage-to-current converter or, more generally, any voltage-to-current converter. An exemplary voltage-to-current converter may be the converter illustrated in FIG. 6. The functioning of this exemplary converter is relatively straightforward and will not be explained in detail.

(25) Another voltage-to-current converter is the classic Howland converter illustrated in FIG. 5a. This architecture may be considered unsafe for applications on the human body because it generally does not protect the body against overcurrents due to eventual fault conditions and DC currents eventually injected throughout the body.

(26) The load current is

(27) $I_Z=\frac{-\frac{R_2}{R_1}\left(V_{\mathrm{in}}-V_{\mathrm{ref}}\right)}{R_4+\left(\frac{R_4}{R_3}-\frac{R_2}{R_1}\right)Z_{\mathrm{load}}}$
in which Vin is the driving voltage. If

(28) $\begin{array}{cc}\frac{R_4}{R_3}=\frac{R_2}{R_1}& \left(1\right)\end{array}$
the current Iz is independent on the load impedance Zload. If the driving voltage Vin of the Howland circuit is an AC signal centered around the reference voltage Vref, then no DC current flows through the load. Unfortunately, this condition may not be guaranteed, for example, in the case of a single fault on the operational amplifier (i.e. one of the pins of the amplifier shorted to ground or to the supply).

(29) A Howland converter with protections against overcurrents and DC currents, thus configured to be used for applications on the human body, is illustrated in FIG. 5b. The capacitor blocks a DC current flowing through the load from the output of the operational amplifier, in case of a fault on the output of the amplifier or of the generator. This capacitor may not impact the normal functionality if the working frequency is much greater than 1/(Cdc.Math.R4). The resistor R5 works as a current limiter in case of a fault on the positive input of the operational amplifier.

(30) The architecture of FIG. 4 may be further simplified by using the Howland voltage-to-current converter or the voltage-to-current converter of FIG. 6, or more generally, any voltage-to-current converter including an operational amplifier coupled to the electrodes and configured to generate, on an output node, a signal representative of the voltage drop on the biological tissue, in the scheme of FIG. 7. In these configurations the INA may no longer be desired because the Howland voltage-to-current converter has a relatively small output impedance. The output voltage Vout and the single-end baseband demodulated signal have an amplitude sufficient for being processed.

(31) Even if the architecture of FIG. 7 is less precise in measuring the impedance Zload because it uses only two electrodes, it is relatively less complex, has a relatively smaller size, reduced power consumption, and reduced costs. In some applications a refined precision may not be required, for example, for sensing the breathing rate from thoracic impedance, and thus, the above architectures may conveniently be used.

(32) The device of FIG. 7, or of FIG. 4, may not be suitable for being connected with a two lead ECG front-end as in the prior device of FIG. 3 if only two electrodes are used. This may be a limitation because, in many applications, as for measures on the human thorax, for example, the simultaneous bioimpedance and ECG recording may be useful or even desired.

(33) This eventual limitation may be overcome in the device of FIG. 8. Two capacitors have been added to decouple, at low frequencies, the electrodes from the voltage-to-current converter. The impedance of capacitors sums up to the impedance of electrodes and to the bioimpedance, and may alter measurements. For this reason, it is desirable that the value of the capacitors be large enough to give an acceptably small impedance at the working frequency. On the other hand, it is desirable that the capacitors not be too large, otherwise this may cause an attenuation of the ECG.

(34) Moreover, the frequency of the pole associated with the capacitors depends on unknown parameters, such as, for example, electrode to skin contact impedance and body impedance. For this reason, the choice of the value of capacitors may be of a particular importance.

(35) Appropriate values of these capacitors may range from 1 nF to 100 nF, if the thoracic impedance is to be measured. Different values may be chosen depending on the particular application for which the device is designed.

(36) The AM demodulator used in the device may be of any kind. According to a preferred embodiment, the AM demodulator is as illustrated in FIG. 9. It includes an envelope demodulator D1-Cinv-Rinv and a comparator XU1 that generates a logic comparison signal OUTCOMP as the result of the comparison between the input signal INP to be AM demodulated and the output signal OUT.

(37) Differently from commonly used AM demodulators, the demodulator of FIG. 9 has a feedback comparator instead of an operational amplifier. This causes the output of the comparator to oscillate as long as the input signal attains its peak value. Then the diode becomes reversely biased, and the output of the comparator switches low. This may not significantly alter the demodulated voltage because the output low-pass filter cut-off frequency is much lower than the bandwidth of these spikes. When the input voltage INP increases, the output of the comparator almost immediately switches high.

(38) By contrast, if an operational amplifier were used instead of the comparator XU1, the output recovery time after saturation and the slew-rate of the amplifier would limit the speed with which the signal OUTCOMP switches high. As a consequence, it may not be possible to demodulate AM signals at relatively high frequencies unless a relatively expensive and power consuming high frequency operational amplifier is used.

(39) The AM demodulator of FIG. 9 thus may be conveniently employed in many applications where demodulation of high frequency AM signals is desired. The devices may be integrated in small packages and may operate in a range of frequencies up to 100 kHz with a relatively small power consumption (about 2.5 mW). However, this is just an example, since higher working frequencies may be obtained using faster components in the voltage to current converter and demodulator stages.

(40) These characteristics make the devices suitable for a vast range of bioimpedance measures and applications. The flexibility and reduced dimensions may make it ideal for wearable applications, both in a clinical environment or in home monitoring tasks, such as, a band-aid, a T-shirt, or a bangle. Examples of measurements that may be carried out with the devices are the monitoring of breath rate, heart rate, and other heart related parameters in thoracic bioimpedance, body composition analysis, or local impedance measures in limbs. When relatively high precision measures are desired, the four electrode architecture may be preferred.

(41) Referring now to FIGS. 10 and 11, the voltage to current converter may be a relatively important block of such a device for measuring impedance of biologic tissues, and it is present in FIGS. 4, 7 and 8. A possible implementation is illustrated in FIG. 5A. As noted above, to achieve a higher level of safety, the circuit of FIG. 5B was suggested.

(42) An improved version of the circuit illustrated in FIG. 5A is illustrated in FIG. 10. The same concept illustrated in FIG. 5B may be applied to the circuit of FIG. 10 obtaining the circuit of FIG. 11 which presents a higher level of safety.

(43) For these circuits the Howland condition becomes:

(44) $\begin{array}{cc}\frac{R_2}{R_1}=\frac{R_{4a}+R_{4b}}{R_3}& \left(2\right)`\end{array}$
while the condition described above requiring the working frequency f.sub.0 to be much higher than

(45) $\frac{1}{2R_{4}C}$
is translated for the circuit of FIG. 11 into:

(46) $\begin{array}{cc}{f}_0>>\frac{1}{2R_{4b}C}& \left(3\right)\end{array}$

(47) A relatively important parameter for the voltage to current converter is the output impedance. Since the frequency of the exciting current is usually greater than 10 kHz, and may be, for example, some MHz, it may not be relatively easy to achieve relatively good output impedance for the V/I converter.

(48) The limited gain-bandwidth product (GBP) of the operational amplifier constitutes a main problem for determining the decreasing of the output impedance with frequency (See, for example, LL in FIG. 12). The use of a wide bandwidth amplifier is usually desired. In general, circuits with higher bandwidth generally require, with the same technologies and topologies, a higher current consumption.

(49) This is not the only issue: parasitic capacitances in parallel with the output of the V/I converter often become the bottleneck, and it happens to reach excellent theoretical impedances which are not met in practical implementations. For this reason, the cancellation of parasitic capacitance through a negative impedance converter (NIC) has been also proposed (See A. S. Ross, G. J. Saulnier, J. C. Newell1, and D. Isaacson, Current source design for electrical impedance tomography, Physiological Measurements, vol. 24, pp. 509-516, 2003). However, this still requires GBP that is relatively higher than the working frequency and an increased number of operational amplifiers.

(50) In some applications, like the emerging one related to wearable sensors for healthcare monitoring, the additional power consumption may be relatively important. Even limiting the working frequency in the range of tens of kHz, the approaches proposed in literature usually use op-amps with a gain-bandwidth product (GBP) of, at least, tens of MHz up to GHz and, since the GBP of an op-amp is generally proportional to current consumption, this is translated in supply currents in the range of some mA. Furthermore, many approaches require more than one op-amp to work, increasing the overall supply current for the circuit.

(51) It may be relatively important to highlight that circuits of FIG. 5B and of FIG. 11, dimensioned as described above and in equations (2) and (3) respectively, generally suffer from the same issues described above.

(52) A person having ordinary skill in the art may readily recognize based upon the description herein and the circuit of FIG. 10, the circuit of FIG. 11. In general, this circuit suffers from the limitations described above. Nevertheless, a particular configuration has been determined which enables a very high output impedance to be reached at the working frequency.

(53) The particular configuration which is described below is applied to the general circuit of FIG. 16. The protection resistor R.sub.p in FIG. 11 (and in FIG. 5B) can disturb the effect obtained by the particular configuration that is described below. Of course it would be possible to protect the load in a different way to maintain the protection resistor R.sub.p. For example, a bypass capacitor is added in parallel to R.sub.p as illustrated in FIG. 13. Such a bypass capacitor is to be chosen according to:

(54) $\begin{array}{cc}{f}_0>>\frac{1}{2R_p{C}_{\mathrm{bp}}}& \left(4\right)\end{array}$
in which f.sub.0 indicates the working frequency and C.sub.bp is a value of the bypass capacitor. In this way, at the working frequency, circuits of FIG. 16 and of FIG. 13 become equivalent with excellent approximation, and all the following considerations apply in the same way to both the circuits.

(55) The Howland condition expressed by EQ. 2 is still satisfied. The capacitor C, instead, is used in a different way. Its function was typically DC-blocking in the previous circuit(s), and its value was chosen according to EQ. 3, which means that the pole of the capacitor must generally be much lower than then the working frequency. In the embodiments described herein, instead, the pole of the capacitor is used to obtain a resonance effect with the first pole of the op-amp in order to have a couple of complex and conjugate poles at the working frequency, as illustrated by the line DL in FIG. 12. The synthesis of the right circuit parameters is not simple, since it involves the modeling of the amplifier as non-ideal, and the first pole must be considered in the calculations. Referring to FIG. 13, the output impedance Z.sub.out is the impedance seen by a test generator connected in place of the load Z.sub.load and its expression results:

(56) $\begin{array}{cc}{Z}_{\mathrm{out}}=\left(R_3+R_{4a}\right)\frac{\left(1+R_{4b}\mathrm{Cs}\right)\left(1+\frac{s}{{}_p}\right)}{1+\left[\frac{1}{{}_p}-\left(k_1-k_2\right)R_{3}C\right]s+\frac{k_2{R}_{3}C}{{}_p}{s}^2}& \left(5\right)\end{array}$
in which

(57) $k_1=1+\frac{R_2}{R_1},k_2=1+\frac{R_{4a}+R_{4b}}{3}$$\mathrm{and}$${}_p=\frac{{}_{\mathrm{GBP}}}{k_1}$
is the pole of the non-inverting amplifier with feedback R.sub.2 and R.sub.1. The poles of Z.sub.out can be made complex and conjugate. The pulsation of the complex conjugate poles is:

(58) $\begin{array}{cc}{}_0=\sqrt{\frac{{}_p}{k_2{R}_{3}C}}=\sqrt{\frac{{}_{\mathrm{GBP}}}{k_1{k}_2{R}_{3}C}}& \left(6\right)\end{array}$

(59) For example with the typical assumption of the Howland circuit expressed by EQ. 2, it is k.sub.1=k.sub.2, and complex and conjugate poles are obtained satisfying the condition

(60) 0$\begin{array}{cc}Q=\frac{{}_p}{{}_0}=\sqrt{{}_{\mathrm{GBP}}{R}_{3}C}& \left(7\right)\end{array}$
which result in a quality factor:

(61) ${}_{\mathrm{GBP}}>\frac{1}{4R_{3}C}$

(62) The GBP still plays a role: the DC impedance is determined by R.sub.3+R.sub.4a, while, once that .sub.0 has been fixed, the quality factor may generally only depend on the value of .sub.p which is influenced by the GBP. For small values of k.sub.1 and k.sub.2 (they are always greater than one), .sub.p.sub.GBP and a relatively good Q, (and so a good increase of the impedance at working frequency) can be obtained also with an op-amp with bandwidth between 10 and 100 times of the working frequency.

(63) The Z.sub.out expression also presents a couple of zeros, and they act at frequency higher than .sub.0, otherwise they would mitigate or cancel the effect of the poles. This condition is expressed by EQ. 7 for the zero located at .sub.p and, for the other one, by:

(64) $\begin{array}{cc}\frac{1}{R_{4b}C}{}_0& \left(8\right)\end{array}$

(65) EQ. 8 becomes

(66) $\frac{1}{R_{4}C}{}_0$
for the circuit of FIG. 14. It may be important to highlight that this condition is reversed with respect to the one expressed by EQ. 3 which was related to the embodiments described above. This is because in those embodiments, at the working frequency, the circuit was made equivalent to the Howland one. In this embodiment, instead, the capacitance C is used to change the properties of the circuit and to obtain higher output impedance than the previous versions.

(67) In FIG. 12 the output impedance obtained by the standard Howland circuit is illustrated by the line LL. The output impedance quickly falls down and, if a low power narrow bandwidth op-amp is chosen, the impedance at the working frequency (for example, 50 kHz is selected as illustrated) is relatively low. The same effect is present in the circuit in the embodiments described above: since EQ. 2 is valid, the impedance behavior at the working frequency is the same. The capacitance, used according to EQ. 6, instead, allows the reaching of significantly higher output impedance at the working frequency as illustrated by the line DL.

(68) The complete frequency response

(69) $H\left(j\right)=\frac{I_l}{V_{in}}$
is, for this circuit, different from the one described with respect to the embodiments above. The results are complex and involve all the parameters of the circuit. In general, since the output impedance is very high only at the working frequency, the frequency response also depends on Z.sub.load. Nevertheless, to dimension the circuit, it is generally enough to calculate it at the working frequency .sub.0, for which the impedance is very high. With this assumption the frequency response can be considered independent on the load and can be calculated in the particular case Z.sub.load=0 for which the circuit results simplified:

(70) $\begin{array}{cc}H\left(j_0\right)=\frac{\left(1-k_1\right)C{j}_0}{\left(1+j{R}_{4b}C{}_0\right)\left(1+j\frac{{}_0}{{}_p}\right)}\left(1-k_1\right)\mathrm{Cj}{}_0& \left(9\right)\end{array}$
in which the approximation is the same already discussed about the zeros of Z.sub.out.

(71) Since all the parameter results are correlated, the proper design of the circuit is not obvious. Anyway there are enough degrees of freedom to satisfy, at the same time, equations 6, 7, 8 and 9. A first consideration to properly define the circuit parameters is that resistors R.sub.3 and R.sub.4a should be large to increase Z.sub.out, improve the output swing and reduce power consumption. On the other side if they are too large a very small C may be desired to properly design .sub.0, and this would impact current amplitude (EQ. 9). Thus, a compromise about their order of magnitude is desirable. Once an op-amp with a gain-bandwidth produce is given, a proper design can be obtained following these steps: once the working frequency is defined, Q can be obtained fixing k.sub.1 (and k.sub.2); Q defines the amplitude of the peak in the expression of the output impedance and it can be increased only reducing k.sub.1 and k.sub.2 (which in any case are greater than one) or selecting a different op-amp with a higher gain-bandwidth product; .sub.0 can be placed at the desired value adjusting R.sub.3 and C; and the proper amplitude for the current can be chosen adjusting the amplitude of V.sub.in.

(72) The presence of a parasitic capacitance in parallel with the output is an effect typical of practical realization of a voltage to current converter. At least a few pico-Farads can be quite common in standard PCB technology, and this can strongly decrease the output impedance of the converter. The approach allows the compensation of the effect of a parasitic capacitance.

(73) With a parasitic capacitor C.sub.p in parallel to the output, the overall output admittance becomes

(74) $\frac{1}{z_{\mathrm{out}}}+C_{p}s$
in which Z.sub.out is reported in EQ. 5. An approximated analysis can be done, remembering that the zeros must be at high frequency (EQ. 8). In this way C.sub.p adds a first order term (R.sub.3+R.sub.4a)C.sub.ps and the new Q becomes:

(75) $\begin{array}{cc}Q\frac{1}{{}_0\left[\frac{1}{{}_p}-\left(k_1-k_2\right)R_{3}C+\left(R_3+R_{4a}\right)C_p\right]}& \left(10\right)\end{array}$
so making:

(76) $\begin{array}{cc}\left(k_1-k_2\right)\frac{\left(R_3+R_{4a}\right)C_p}{R_{3}C}& \left(11\right)\end{array}$
it is possible to restore the original quality factor of EQ. 7 and the circuit still provides relatively high output impedance.

(77) It may be particularly important to highlight that it is generally not necessary that the relations above are exactly satisfied: it is enough to reduce the residual term added to

(78) $\frac{1}{{}_p}$
as much as possible. This makes the use of a mismatch between k.sub.1 and k.sub.2 a viable approach, since the exact value of C.sub.p may be unknown, but an estimation is enough.

(79) All the considerations done can be extended to the circuit of FIG. 14 assuming R.sub.4a=0 and R.sub.4=R.sub.4b.

(80) The working principle of the circuit intrinsically makes it suitable to work with a fixed frequency. A multi-frequency extension, anyway, can be obtained with the circuit showed in FIG. 15. The switches S11-S1n and S21-S2n allow adjusting C and R.sub.4b to tune the frequency, and R.sub.2 to tune the resistor ratio accordingly to EQ. 5 or EQ. 11, in case a parasitic capacitance is to be cancelled.

(81) Each terminal of the switch is connected to ground through a parasitic capacitance which is desirable to be kept as small as possible to avoid interferences with the circuit working principle.

(82) The shown distribution of switches, anyway, is chosen to reduce or minimize the effect of parasitic capacitance associated to them. With the choice shown in the picture, the branches connected to the open circuit path results in a ground connection through parasitic capacitance. They did not interfere with the circuit since they are driven directly by the amplifier output. Parasitic capacitance is present in parallel to Z.sub.out, but its effect can be cancelled if desired, as already discussed.

(83) Many modifications and other embodiments of the invention will come to the mind of one skilled in the art having the benefit of the teachings presented in the foregoing descriptions and the associated drawings. Therefore, it is understood that the invention is not to be limited to the specific embodiments disclosed, and that modifications and embodiments are intended to be included within the scope of the appended claims.