Low power current sources for bioimpedance measurements: a comparison between Howland and OTA-based CMOS circuits

Multifrequency electrical bioimpedance, also called Electrical Impedance Spectroscopy (EIS), has been widely used as a non-invasive technique for measuring many passive electrical properties from biological materials, such as: cancerous tissues (1, 2, 3, 4); tumors (5,6), meningitis (7) and brain cellular oedema (8,9). It can also be used for analyzing body composition (10,11) and bovine milk quality (12,13). Also, it is considered fast, inexpensive, practical, and efficient (14,15). Its availability for emerging wearable applications (16) and for on-chip systems such as the AD5933 (17,18) have also made its popularity grow. Microelectronics systems applied to health care solutions provide the advantages of small size devices, possible wireless signal and power transmission, portability, long time implant for low power circuits, and the possibility of improving the sensing of weak signals (on the order of milivolts) by taking them out in-situ (19, 20, 21).

EIS techniques have shown good results for detecting normal and cancerous skin in superficial tissues (22, 23, 24, 25, 26). Most EIS systems consist of applying a multi-frequency sinusoidal current of constant amplitude into the tissue sample, measuring the resulting potential, and then calculating the transfer impedance (Z_t) (14,15). In order to get accurate calculated transfer impedances, it is necessary to ensure that the injecting current has a constant amplitude over a wide frequency range, which may be obtained by using a current source with high output impedance (14,15). However, stray capacitances are known reduce the current amplitude at higher frequencies (27,28). High performance current sources with wide bandwidths based on operational amplifiers have been widely developed and can be found throughout the literature (29, 30, 31) while others have used integration techniques for developing current sources (32, 33, 34, 35, 36, 37). An integrated realization of a Voltage-Controlled Current Source (VCCS) for bioimpedance applications (33,38, 39), which are based on the operational transconductance amplifier (OTA) approach. Our targeted measuring applications require an operating frequency band of 1 kHz to 1 MHz and current amplitudes of up to 500 μA_p (peak).

A VCCS for EIS may be analog or mixed-signal. In addition, it can be single-ended or differential and the system may include a single or multiple current sources (34). Single-ended systems always have large common-mode voltages since one end is tied to virtual ground (35). Although transformer coupling can reduce this effect (35), the use of a transformer is not suitable for an integrated solution. Reducing the common-mode voltage without decreasing the output impedance of the source is required. Because the digital noise appears in terms of a common mode voltage, fully differential structures are highly recommended for low-power systems as they are intrinsically immune from common mode signals. The fully differential amplifiers have the advantage of having twice the output voltage swing compared to the single-ended ones (40). Furthermore, increasing the amplifier dynamic range is significantly important for low power applications as it also reduces the even harmonic distortion of the output signal. Therefore, the use of differential current sources allows the minimization of the common mode voltage at the load, and then reducing the errors due to limited common-mode rejection ratio of the voltage measuring amplifiers (41).

The main objective of this paper is to compare the performance of the Howland circuit based on active and passive elements with circuit topologies at a transistor level. Three OTA-based CMOS (i.e., class-A, class-AB and current conveyor) VCCSs for wideband EIS instrumentation are described in the paper and are compared at a simulation level to the Mirrored Modified Howland Current Source (MMHCS) circuit. The OTA-based circuits were designed in a 0.35 μm CMOS technology and simulation results are presented.

Three types of OTA-based CMOS circuits were made: class-A, class-AB and current conveyor. The performances of these circuits were compared with the MMHCS circuit in order to obtain linearity, total harmonic distortion, output current, and impedance response in the frequency range from 10 Hz to 1 GHz. Comparisons were done by using PSPICE simulator from Orcad (2009 version). The basic OTA-based circuits were modified using linearization techniques and current mirrors at the output stages to improve the output impedance.

Mirrored Modified Howland Current Source (MMHCS)

An MMHCS circuit was implemented using two wide bandwidth operational amplifiers OPA657 (Burr Brown, Inc.), as shown in Figure 1. The OPA657 has an open-loop gain of 70 dB, a bandwidth of 10 MHz for voltage gain of 160 V/V with 1.6 GHz for unit gain, a power supply of ±5 V, and a bias current of 16 mA. The MMHCS is a voltage controlled current source with a floating load R_L and consists of two symmetrical modified Howland structures (28,29). It is set to supply an output current I_O of 1 mApp (peak to peak) over the frequency range 10 Hz to 1 GHz, which is ideally controlled by the ratio between the input voltage V_in (= 1 V_pp) and the resistor “r” (= 1 kΩ).

Fig.1

The differential output impedance of this structure depends on the open-loop gain A, which is frequency dependent, as shown in Equation 1. The input impedance of the operational amplifier was not taken into account.

(1)Zout=(2⋅R+z)⋅[(2R+z)Z0+z⋅R⋅(A+2)]Z0⋅(2⋅R+z)+2⋅R⋅(R+z)$${{Z}_{out}}=\frac{\left( 2\cdot R+z \right)\cdot \left[ \left( 2R+z \right){{Z}_{0}}+z\cdot R\cdot \left( A+2 \right) \right]}{{{Z}_{0}}\cdot \left( 2\cdot R+z \right)+2\cdot R\cdot \left( R+z \right)}$$

where z is the series impedance of the resistor r with capacitance C, Z₀ is the output impedance of the operational amplifier, and R is the resistor of the current source (see Figure 1) in order to make a mirrored structure by considering ideal operational amplifiers.

The circuit linearity (I_O versus V_in) was investigated by DC sweeping the input voltage signal V_in from -0.6 to +0.6 volts with the frequency response of the output current measured directly across a 1 kΩ load.

Class-A OTA

This is an Operational Transconductance Amplifier (OTA) implemented to operate as a class-A amplifier. It uses a semiconductor based on a CMOS structural width down to 0.35 μm, which is manufactured by Austria Microsystems. The circuit was implemented to have a common mode control through the transistors M6 and M7 operating in the triode region (see Figure 2). It has a modified cascode output structure using the transistors M12 and M13 to increase output impedance. The source degeneration is done by using the MOS transistors MA and MB operating in the triode region. The class-A OTA circuit was projected to have a transconductance of 1 mS (see Equation 2) and an output current of 1 mA_pp (peak to peak) over the frequency range from 1 Hz to 1 MHz. The circuit is supplied by a voltage source of ±1.5V (VSS=-VDD), where Ib is a external bias current set to 500 μA, V1,2 are voltage input signals, Vcas1,2 and Vbias are DC voltages of the cascode pairs and Vout+ and Vout- can be considered as a fully-differential output, where the load is connected between these nodes.

Fig.2

(2)Gm=gds1+2⋅gdsgml$${{G}_{m}}=\frac{{{g}_{ds}}}{1+\frac{2\cdot {{g}_{ds}}}{{{g}_{ml}}}}$$

where g_m1 is the transconductance of transistor M1, g_ds is the conductance of transistor MA. The output resistance of each output nodes (Vout+ and Vout-) of the class-A OTA is approximately equal to the product of g_m9, r_o9 and r_o11, where r_o11 is the output resistance of transistor M11 and r_o9 and g_m9 are the output resistance and conductance of the transistor M9, respectively.

Current Conveyor

The Current Conveyor Current Source (CCCS) can be implemented by using translinear structures (44, 45, 46) or differential pairs (47,48). Figure 4 shows a current conveyor circuit based on two differential pairs of transistors M1-M2 and M3-M4, which allows a rail-to-rail input stage (49). This type of current source is called current conveyor second generation (CCII) due to the its input and output characteristics (39). The transistors M13 and M14 are source followers used to keep a low resistance in the X terminal and to stabilize the bias current through the transistors M8 and M12. The transconductance of the current conveyor current source is given by Equation 5, considering the transistors M1, M2, M3 and M4 from the differential pairs well matched, where g_m1=g_m2=g_m3=g_m4=g_mdif. Also, the load transistors M5, M6, M9 and M10 are considered to have equal output resistances r₀ and the conductance of the transistors M13 and M14 are also matched, where g_m13=g_m14=g_m.

Fig.3

(5)Gm=I∘VY=gm⋅r0⋅gmdif1+gm⋅r0⋅gmdif⋅R1≅1R1$${{G}_{m}}=\frac{{{\text I}_{\circ }}}{{{\text{V}}_{\text{Y}}}}=\frac{{{g}_{m}}\cdot {{r}_{0}}\cdot {{g}_{mdif}}}{1+{{g}_{m}}\cdot {{r}_{0}}\cdot {{g}_{mdif}}\cdot {{R}_{1}}}\cong \frac{1}{{{R}_{1}}}$$

The circuit showed in Figure 4 is modified from Kumngern et al (45). It is uses low-voltage cascade current mirrors and a differential output stage. The current flowing through M13-M14 is copied to the output nodes Z1 and Z2. The phase of the output current at Z2 node is 180° phase shifted compared to the Z1 node. The differential output current (I_O) is calculated by the relationship V_Y/R1 (see Figure 4). The circuit linearity (I_O versus V_Y) was investigated by DC sweeping of the input voltage signal V_Y from -0.6 to +0.6 Volts. The frequency response of the output current was measured directly across a 1 kΩ load. The circuit is supplied by a voltage source of ±1.5 Volts.

It can be seen in Figure 5 that both mirrored modified Howland and current conveyor current sources (CCII) have a linearity error of approximately 0.5% by exhibiting a constant ratio of 1 mS from -0.5 to +0.5 Volts. On the other hand, the output current of the class-A OTA is not linear over the input voltage range -0.5 to +0.5 V by presenting a linearity errors up to 10%, but it is linear between an input voltage from -0.3 to +0.3 V.

Fig.4

Fig.5

It can be observed in Figure 5 that the class-AB OTA is more linear than the class-A with a maximum linearity error of 6.6%, in the input voltage range -0.5 to +0.5 V. From Figures 2, 3 and 4 it can be calculated that the power consumption of both class-AB and current conveyor is 1.6 mW whereas it is 4.6 mW for the class-A OTA.

In order to investigate the signal distortion generated by the current sources presented in this work, the total Harmonic Distortion (THD) was simulated and the results are show in Figure 6. The THD was investigated at 100 kHz for a load resistor of 1 kΩ. It can be seen that the Howland circuit presents a better THD and it is smaller than 0.5% over the input voltage from -0.5 to +0.5 V.

Fig.6

Figure 7 shows the frequency response of the current sources. It can be seen that the output current of the mirrored modified Howland circuit has a flat bandwidth between approximately 630 Hz to 5.5 MHz and a current peak of 1.3 mAp at approximately 43.6 MHz (which can be considered as the natural frequency oscillation of the operational amplifiers caused by the second order nonlinearities of the OPA657 circuits) can also be observed. It can also be observed that the class-A OTA can drive 1 mA_pp across 1 kΩ load in a frequency range from 10 Hz to approximately 20 MHz. It can be calculated (Figure 5) that the corner frequency in this type of current source is approximately 234 MHz. Figure 5 also shows that the calculated corner frequency in this type of current source is approximately 567 MHz with 37 and 33 MHz for the class-AB OTA and current conveyor circuits, respectively.

Fig.7

Figure 8 shows the output impedance frequency responses. It can be seen that the mirrored modified Howland circuit behaves like a bandpass filter, where the maximum output impedance is 1.63 MΩ, the lower corner frequency is 490 Hz and the upper one is 1.3 MHz. It can be observed that both current conveyor and class-AB OTA circuits are identical. Although the maximum output impedance of the class-A OTA is approximately 70.8 MΩ, it decreases to approximately 2.8 MΩ at 1 MHz and 695.5 kΩ for the class-A OTA circuit.

Fig.8

The class-AB OTA and the current conveyor circuit have been shown to have a better performance in the frequency range 10 Hz to 1 MHz than the others current sources simulated in this work. However, if linearity is required from -0.6 to +0.6 volts the class-AB OTA has showed better results. On the other hand, if low power consumption is required then the current conveyor has the lowest value (1.6 mW) compared to the others simulated circuits. Apart from power consumption, one big advantage of using the OTA-based CMOS differential VCCSs is the reduced area occupied on the printed board, which is much smaller than the MMHCS circuit based on passive and active components (i.e., resistors and operational amplifiers). The implemented MMHCS circuit with surface mount OPA657 has an area of approximately 20 mm² whereas the class-AB OTA projected in this paper has a surface area of 0.004 mm².

The results from the THD showed that the Howland circuit performed better though we must bear in mind that the power supply of the Howland circuit was ±5 V but only ±1.5 V for the OTA-based circuits. This may explain some of the differences in performance in terms of linearity and THD.

It is important to emphasize that the performance of both the original and modified Howland current sources depend on the operational amplifier characteristics used in the structure, such as the open-loop gain and the input and output impedance (41). The fact that this type of current source contains both positive and negative feedback loops, resistor mismatching can also degrade the frequency response (14). The most important characteristic of a current source is its output impedance, which is frequency dependent (see Equation 1). If we make Z₀= 0, R>>r and A>>2. Equation 1 can be simplified and then the output impedance of the MMHCS circuit can be given by

where A₀ is the DC open-loop gain of the op-amp and the ω_c0 is the open-loop gain cut off frequency. It can be seen that the output impedance of the Howland current source is highly dependent on the open-loop gain of the operational amplifier used. By choosing the OPA657, a maximum differential output impedance of approximately 4.5 MΩ is expected. A full critical review of Howland current source circuits is being submitted by the authors to the journal Reviews on Scientific Instruments.

A peak frequency response in the output current of the Howland circuit was observed from the simulations. This may be explained by the second order non-idealities of the operational amplifier, which are taken into account by the SPICE model in the simulations. In practice, this peak does not occur due to the bandwidth constraint of the instrumentation amplifier used in EIS systems. The lower frequencies’ response can be improved by increasing the output capacitor, C. of the mirrored modified Howland circuit (see Figure 1). Theoretically, this response can be made down to DC but not in practice since the capacitor works against saturation of the operational amplifier. Optimized modified Howland current sources with an output impedance 100 times greater than the results shown in this work can be found in the literature (50,51), but they suffer from instability problems due to non-idealities of the amplifiers and imbalance of both types of Howland circuits (source and sink circuits), and, therefore, cannot be controlled.

In order to implement the mirrored modified Howland current source it is necessary to match both sides of the circuit, which means that both source and sink sides should have identical output currents (magnitude and phase) (30,52). Bertemes et al. (41) showed that different effects of parasitic capacitances at each side of the mirrored modified Howland current source creates large common mode voltage at the load and degrade the output impedance. They also showed from experimental data that it is possible to balance the MMHCS circuit by trimming the resistors of both non-inverting op-amp inputs (as for example, the resistors “R+r” of Figure 1).

Although the current source structures projected in this work were only simulated in SPICE, the results are encouraging for the implementation of real life circuits. The mirrored modified Howland current source has already been implemented and the results are shown in Bertemes-Filho (53). The current conveyor and class-AB OTA current sources proposed in this paper will be designed and prototyped under a semiconductor process. In practice, it has to be emphasized that parasitic capacitances may reduce both the output current and impedance frequency response of the OTA based current sources. However, the frequency bandwidth can be increased by changing the geometry of the transistors. As a result, the cutoff frequency of the current source may be improved in order to prevent parasitic capacitances presented in the experiment.

This paper simulated the performance of the mirrored modified Howland current source and compared to three types of OTA based CMOS amplifiers. The output current and impedance of the circuits were investigated over the frequency range from 10 Hz to 1 GHz. The class-AB OTA based current source has a better frequency response and lower power consumption than the other current sources. The effects of parasitic capacitances were not simulated, but they can be taken into account when projecting the OTA based current source at a transistor level.

Therefore, even at a simulation level, these results are encouraging the authors to see these circuits created in a semiconductor process. This might be interesting for microimplants and cell impedance measurements.