Bandwidth and Common Mode Optimization for Current and Voltage Sources in Bioimpedance Spectroscopy

A typical BIS measurement system consists of a front-end, a data acquisition unit and a data processing unit. The front-end generates the excitation signal, typically by a VCCS, and measures the resulting voltage. Measurements are mainly performed in the beta-dispersion range from 1 kHz to 1 MHz and should have a measurement accuracy of 0.1% or higher [18]. The output impedance of a source determines the stability of the generated signal with respect to the connected load. To achieve a measurement accuracy of 0.1% for loads between 100 and 10 kΩ[7], a minimum output impedance of at least 1MΩin the mentioned frequency band is necessary. To obtain the same accuracy for a voltage source (VS), the output impedance should be at a maximum of 1.

For safe and continuous operation on biological tissue, the standard EN 60601-1-1 defines the following maximum allowable currents

In addition, the common mode current has to be below 10μA to prevent electrode polarisation and harm to the patient. In literature, this particular demand often is neglected. However, Pliquett et al. presented an active common mode rejection circuit for a symmetrical EHCS and achieved a common mode rejection below -80 dB [9].

As mentioned before, in BIS most commonly the EHCS is employed, along with current mirror circuits and multiple feedback operational amplifier circuitry [19]. Theoretically, an EHCS can achieve a very high output impedance Zout, In reality, this source suffers from low bandwidth, the ability to drive capacitive loads and low common mode rejection. To overcome such limitations, we chose an improved EHCS by Sirtoli et al. [8] as a basis for further modifications.

The basic functionality of the circuitry, depicted in Figure 1, is an EHCS consisting of R₁ to R₄ and Rx.

Figure 1

The resistor Rx defines and limits the output current. Assuming a perfect symmetric current injection

we can apply the traditional balancing conditions of the EHCS as given in [8] to achieve a high Zout.

We note that the advantage of the circuitry as depicted in Figure 1 is the symmetric current injection from a fully differential amplifier (OP1).

The load is driven from U_L+ to U_L-, where the signal at U_L- is a phase shifted copy of U_L+, This behavior is equivalent to two current sources working in a push-pull configuration as source or sink. As a result, each source has to generate only half of the voltage drop across the load. Theoretically, this doubles the output impedance and the maximum output voltage (compliance) of the current source [8, 20]. Additionally, the circuitry in Figure 1 drives a quasi-floating load, due to the resistor R₅ connected to ground. The connection to ground could increase the common mode voltage and reduce patient safety. This issue could be addressed by a separate monitoring circuit for I_out.

Other drawbacks of the traditional EHCS include instabilities due to the positive and negative feedback. Such oscillations may occur only at high frequencies and can be compensated by additional capacitors in parallel with R₁ and R₄ [21]. However, in this paper we used a capacitor C_c in parallel with R₃ to increase the bandwidth of the EHCS. To simplify further calculations, C_c will be neglected initially. The symmetric current injection requires an equivalent load at U_L+ and U_L-, independent of Z_load, Therefore, the resistor R₅ has to mimic the voltage drop across R₁ and R₃, Furthermore, the voltage drop over R_t has to be identical to the one over R_x, This leads to the additional balancing conditions:

Because of the connection of R₅ to ground, the symmetrical current source is quasi floating and creates a load dependency of R_t as presented in [8]. To accomplish

the identical voltage drop over both current generating resistors R_x as well as R_t, R_t has to be

According to eq. (5), large values of R_x and R₃ lead to an increased value of R₅ and thus, R_t becomes less dependent on Z_load.

Let A_OL be the open loop gain. Due to the above conditions, the output current is load-independent and calculated as follows

In case of A_OL ⨠ 2, I_out can be determined by the input voltage U_in and R_x, As a result of the balancing condition eqs. (3), (4) and (5), the output impedance is solely dependent on R₃ and R_x as well as A_OL and can be calculated as followed [8]:

The output impedance is dominated by the open loop gain value of OP1, By choosing R_x < R₃, the output impedance is determined mainly by R₃, whereas the output current is set by R_x, according to eq. (7).

The output voltage swing or the saturation voltage U_sat of the operational amplifier limits the maximum operable load Z_load,max, According to Figure 1, the output voltage U_out of OP1 is given as the voltage drop across R_x and Z_load, which is always smaller than the saturation voltage of OP1 [8]:

Thus, the theoretical maximum operable value of Z_load becomes

The maximum load increases for smaller values of R_x, Additionally, the term A from eq. (10) increases the maximum operable load for R_x < R₃, Thus, R₃ has the potential to double Z_load;max without changing I_out [8].

In our application we have chosen the fully differential amplifier THS4151 (Texas Instruments, Dallas, USA) to generate the symmetrical output signal. The THS4151 has an open-loop gain A_ol of 67 dB, which is sufficient to determine the output current by U_in and R_x, according to eq. (7).

Figure 2

The choice of R_x and R₃ determine the output impedance according to eq. (8). Figure 2 shows the asymptotic behavior of Z_out for three exemplary R_x over

R₃.

R_x limits the maximum output impedance. The smaller R_x is chosen, the faster the output impedance approaches the maximum output impedance for an increasing R₃, 80% of the maximum output impedance is achieved if R₃ ⪆ 2R_x.

The maximum operable load can be used to determine R_x, We further assume a saturation voltage of 12.7 V (THS4151) and an output current of 2.08 mA. To ensure that the current source can drive a load of up to 6.5 k, R_x can be up to 2.2 kΩaccording to eq. (10). In the following, we use R_x = R_t = 2.2 kΩand R₃ = R₂ = R₄ = 4.9 k, R₁ and R₅ are set according to the balancing eq. (3) and (5) to 7.1 kΩand 12 k, respectively. Apart from R₃ and R_x , the output impedance depends on the open-loop-gain A_ol of the THS4151, which is 67 dB. These parameters achieve a theoretical output impedance of 2.27MΩ, However, the A_ol has a low-pass characteristic, which lowers the output impedance at higher frequencies. For the THS4151, the frequency-dependency of A_ol is not specified in the datasheet. However, the operational amplifier can practically maintain gain values of 40 dB for a bandwidth of 1 MHz. Under the conservative approximation of 40 dB, the output impedance drops down to 104.5 kΩat 1 MHz.

The basis of the VS, used in this work, is a non-inverting amplifier with a current sensing resistor R_s added between the output of OP1 and the feedback path, similar to the VS presented by Qureshi et al. [17]. The single-ended VS is depicted in Figure 3.

Figure 3

At first, the capacitor C_v will be neglected to simplify the calculation of U_out given by

where Z_OA is the output impedance and A_ol is the open loop gain of OA1, Eq. (11) can be simplified to an ideal non-inverting amplifier for an infinite A_ol, Consequently, the current through the load can be calculated by

Under the approximation I₂ ! 0 and I_s I_out, the output impedance is

Due to R_s, the output impedance of the VS is higher than the output impedance of a standard non-inverting amplifier without R_s, However, the output impedance can be kept low by choosing a sufficiently high open loop gain. Consequently, only a fraction of Rs contributes to Z_out, Nevertheless, the maximum current through the load is limited by R_s and the saturation voltage of OA1, Assuming A_OL ⨠ 1, the maximum R_s is given as

to drive a minimal load Z_load,min, In addition, R_s can also be used to measure the current through the load, which is essential to perform BIS measurement.

The single-ended VS can be extended to a symmetric source shown in Figure 4, The two outputs of the single-ended VS are connected to the load. The symmetric input signal is generated by the fully differential amplifier OA2 (THS4151). The output signal and thus the dynamic range and the output impedance are doubled [17].

Figure 4

We note that the symmetric VS in Figure 4 uses two separate OAs for the generation of the symmetric output signal. A different approach from Pliquett et al. [9] uses only one differential OA for the final stage. The main advantage is that the negative output would be generated by the differential OA itself. This could lead to more

symmetric output signals. However, the design from Pliquett uses additional OA in the feedback path which results in a comparable amount of active components. Future work could focus on the reduction of components by omitting the active feedback OAs, which lead to a more miniaturized realization.

The operating point is a load current of 2.93mA across a 1 kΩresistor. Thus, the source should achieve an output voltage of 2.93 V over the entire frequency range and a preferably low output impedance. The THS4631 operational amplifier is used for OA1 and has a saturation voltage of ±13V and an open loop gain of A_OL of 80 dB. The gain of the two VS set by R₁ and R₂ should be kept as small as possible to reduce the influence of output imbalances. In addition, the current through the resistors R1 and R2 is kept as small as possible to reduce the influence on the connected load. Consequently, the resistor pair R₁ = 100kΩand R₂ = 2 kΩ results in an amplification of A = 1.02 and has a low bypass current of approx. 28.7 μA. To achieve an I_load = 2.93 mA, the VS requires an input voltage of U_in = 2.885 V. For frequencies above 100 kHz, the maximum load-current is 10 mA. Applying eq. (12) and (14), the minimum operable load is 208.8Ω with an R_s of 1 k, The connected load consists of the contact impedance and the body impedance inbetween the electrodes. The electrode skin impedance is highly dependent on the type of electrodes used for the measurement. However, the contact impedance is usually in the range of a few kΩ for low frequencies and drops down to around 200Ωfor frequencies above 100 kHz [1]. The resulting load from contact and body impedance is typically in the range of 200Ωor higher. However, the load might undercut the minimum operable load of the VS in specific applications. Future work should consider the expected load of the application in the design such that R_s or U_out do not lead to a compromising minimum operable load. This ensures that the permitted patient auxiliary current cannot be exceeded. Nevertheless, for an increased patient safety the auxiliary current can be monitored via R_s, If necessary the load current can be reduced by adjusting U_in.

The fully differential amplifier OA2 uses a resistor ratio of 1.3 with R₃ = R₅ = 3R₄ = 3 + R₆ = 1 kΩ, This results in a gain of 1.5 and the overall U_in is set to 0.963 V to satisfy a load current of 2.93 mA. Similar to the EHCS, the output impedance of the VS depends on the open-loop-gain A_ol of the THS4631, which is 80 dB. According to eq. (13), the theoretical output impedance Z_out is 204mΩ, which is 104mΩhigher than the output impedance of the THS4631, At 1 MHz, the A_ol of the THS4631 decreases to 46 dB. Thus, the output impedance increases to 10.2Ω.

As both sources are symmetrical, the output signal consists of two alternating signals (U_L+ and U_L-), which are out of phase by 180°, Their difference creates the symmetrical signal

Eq. (16) describes the common mode signal U_cm over the load Z_load , which is equally shared in both individual signals of the symmetrical signal and is their mean value.

In an ideal case ( U_L+ = −U_L-), common mode components are equally shifted in the positive and negative parts of the signal and cancel each other. Thereby asymmetric effects of electrode double layers and artefacts are partly compensated [8, 9]. Indeed, inequalities of the positive and negative output create a difference between the generated currents. Due to the finite output impedance, a high common mode signal may occur [8]. This can be compensated with the help of an active feedback circuit, as presented in [9]. The compensation method by Pliquett et al. is only applicable to EHCS topologies. Here, we propose a modified circuit suitable for both types of sources (Figure 5).

Figure 5

According to eq. (16), U_L+ and U_L- are picked up at their respective outputs. For the EHCS, this causes instabilities. Thus, the signals for the feedback loop are derived from the outputs of the differential amplifier of the EHCS. OP5 forms an inverting summing amplifier and is fed back to the offset pin of the input stage of the source. The negative feedback of the offset is an active compensation of the current common mode over Z_load, To avoid unwanted high-frequency oscillations of I_out, a first-order active low-pass filter is added to the summing stage through C_ocm = 2.2 pF. This results in a cutoff frequency of 723 kHz.

R_ocm creates a symmetric bypass from U_L+ and U_L+ to ground. R_ocm should be at least one magnitude above the

maximum load to minimize the influence on the injected current. Thus, R_ocm is set to 100 k, U_offset can be manually set to provide a frequency-independent offset voltage taking the inherit offset voltage of OP5 and slight miss-matches of R_ocm into account.

For the evaluation, different offset compensation strategies can be realized by the switch S₁ and U_offset.

The static offset compensation adds a constant offset voltage U_offset to the feedback signal. U_offset was trimmed manually, so that the common mode signal is minimized. We acknowledge that trimming values might be specific to the measurement frequency. However, for the sake of practicability we used 1 kHz to trim the constant offset voltage to a low common mode signal.

The output current, output impedance, harmonic distortions and common mode rejection were measured with the setup depicted in Figure 6, All signals were sampled by a Tektronix MSO2024 along with a passive test probe (1MΩ║ 11.5 pF) having a total bandwidth of 100 MHz. Both sources drive floating loads, which requires differential voltage measurements. Thus, an instrumentation amplifier (AD8428, not depicted in Figure 6) measured the current through R_shunt = 0.39, By Ohm’s law the

Figure 6

voltage drop of two different loads (Z₁,Z₂) is directly related to the output impedance. For the symmetrical current sources (Figure 6, left), the output impedance is

where Z₁ simulates the voltage drop across a small and Z₂ across a larger load impedance. To not invoke the probeloading effect due to the sources high output impedance, U_d of the current source was measured with an instrumentation amplifier (AD8429).

A similar principle applies for the VS (Figure 6, right), where the output voltage with open clamps U_d,open and with an applied load U_d,Z2 are measured. Therewith, the output impedance of the VS holds

Impedance measurements with a Keysight LCR meter E4980A yielded Z₁ = 100.1 Ωand Z₂ = 1012.3 Ωwithin the frequency range between 1 kHz and 1 MHz.

The conducted research is not related to either human or animal use.

First, we consider the output impedance of the current source without the influence of the capacitance C_c and ideal resistor properties, which exactly fulfill the balancing condition given in eqs. (3), (4) and (5). The simulation

achieved an output impedance of 2.15MΩ, which is 150 kΩbelow the theoretical value. Second, as this is only valid for ideal resistor conditions, we evaluated the mean output impedance for Gaussian resistor value distributions with tolerances of 0.1% (Figure 7). Here, the simulated output impedance of the EHCS is 230 k, For C_c = 0 pF, the output impedance has a low-pass character and drops to 100 kΩat 1 MHz. The phase drops from 0^° to −62.3^°, A performance loss at higher frequencies is a typical phenomenon for current sources based on Howland topologies. It occurs due to inequalities at the inputs and outputs of the operational amplifier. The f_-3dB point lies slightly above 1 MHz.

Figure 7

Lastly, adding the capacitor C_c parallel to R₃ in Figure 1 shifts the f_-3dB point to even higher frequencies. The additional capacitor is a common modification for unbalanced Howland Current Sources [22]. The output impedance has been simulated for 0 pF < C_c < 4.4 pF between 1 kHz and 1 MHz. Figure 7 reveals an overshoot of Z_out at 1 MHz with C_c = 2.1 pF. The range of C_c is on

an interval of 0.6 pF. For the evaluation in hardware, this value will be also influenced by the amplifiers input- and wire-capacitances on the PCB. Thus, a trim-capacitor will be used to optimize the behavior of the EHCS in the hardware realisation.

Qureshi et al. proposed a capacitance (here: C_v) in parallel to R_s to reduce oscillations above a few MHz [17, 23, 24]. Figure 8 shows the simulations Z_out of the symmetrical VS with common values for C_v between 0 pF and 3.3 nF. Without the additional capacitance C_v, the output impedance increases from 145mΩup to 14.5 Ωwith 20 dB per decade over the whole frequency range. By introducing C_v, the output impedance turns flat for higher frequencies, due to an additional pole in the transfer function. For a capacitance of 3.3 nF, Z_out drops down to 713.5mΩ at 1 MHz and for C_v > 2.2 nF,

Figure 8

the output impedance stays below 1.05, However, such high values of C_v reduce the resulting current limiting impedance of R_s from 1 kΩ to 67.5 Ωat 1 MHz. This results in higher maximum currents then 10mA which should be prevented. This limitation could be overcome by selecting an appropriate Z_s = R_s||C_v, which can also fulfill the current limits due to the EN 60601-1 for lower frequencies.

The output impedances were calculated from the measured voltage differences across the loads Z₁ and Z₂ by eq. (17). As the differences of the measured voltages are within a few milivolts, we ensured a higher accuracy by using a moving average over 64 values of U_d.

By the addition of C_c, a great bandwidth improvement of the symmetrical EHCS circuit was observed in the simulations. This capacitance was realised with a trim-capacitor and could be set between 1,5 pF and 5 pF. In order to demonstrate the influence of C_c on the circuit, Figure 9 shows Z_out,CS for different positions of the trimming capacitor. Below 50 kHz, for all C_c the output impedance has values between 100 kΩ and 200 k, For C_c ≈ 2.6 pF and C_c ≈ 3.2 pF, Z_out,CS drops to 83 kΩ at 5 kHz. Between 50 kHz and 100 kHz, the output impedance of all capacitance values fans out, whereupon they all drop to values below 10 kΩ at 1 MHz. The largest differences in the output impedance for the different capacitors occur at 100 kHz. Here, the impedance increases up to 400 kΩ for C_c = 1.5 pF and C_c = 2.6 pF, but decreases for the measurements with the capacitor value in between (C_c = 2.1 pF) to 92 kΩ at 100 kHz. Overall, the output impedance at 100 kHz declines for the majority of capacitor values compared to its value at 50 kHz. From 200 kHz to 1 MHz, all measurement series generate a declining output impedance, with the same characteristics and no blatant aberrations. C_c 2, 6 pF was chosen for further considerations, as this value has

Figure 9

a significant higher value for Z_out;CS;meas (f = 100 kHz) than most other capacities.

The theoretical maximum load of the proposed current source is R_{load,max,calc} = 3.5 k, To determine the maximum operable load R_{load,max,meas} at 1 MHz, four resistive loads (R_load = 2.47 k, 3 k, 3.47 kΩ and 3.74 k) were selected for current measurements. The magnitude and

phase of the output current I_{out,crit,meas}(R_load = 2.47 k) in Figure 10 are similar to the values of the previous measurements below 2 k, For higher loads, the amplitude and phase decrease further. Thus, it can be concluded that the maximum operable load of the symmetric EHCS is about 2.5 kin the frequency band of the β-dispersion.

Figure 10

In simulations, the bandwidth of the VS’s output impedance increased for higher values of C_v , However, the VS showed instabilities for C_v > 2.2 nF. This behavior might be based on imbalances of the capacitors C_v of the two VS (Figure 4). Higher values of C_v have larger absolute differences due to capacitor tolerance’s and induce different cut-off frequencies and phases of the two VSs. To avoid such instabilities, we chose C_v = 82 pF for all further measurements. Besides, with this value, the VS still fulfills the current limits of EN 60601-1 for higher frequencies.

The measured output impedance of the balanced VS was calculated using eq. (18) and is shown in Figure 11.

Figure 11

Up to 60 kHz, Z_{out;V S;meas} has a flat profile with a mean value of Z_{out;V S,meas} < 1Ω, From this point up to a frequency of 1 MHz, the output impedance fluctuates much more and has a maximum value of 15.5 at 700 kHz. Overall, the balanced VS has measured impedance values in the range of the simulated values.

In order to measure the critical lower load range for the VS, the output voltages were measured across 270 , 470Ω and 740, The measurement results are shown in Figure 12, The theoretical minimum value R_load;min is 208.8Ω(eq. (14)). Magnitude and phase of the output voltage are very similar for all values of R_load , However, the waveform of the signal slightly distorts for R_load = 470Ω at a frequency of 1 MHz, resulting in a steeper drop of the phase. For R_load = 270, the distortion already appears at 500 kHz. The actual critical load value of the VS is between 470Ω and 740Ω and more than twice the theoretical value of 208.8.

Figure 12

The common mode rejection (CMR) circuit from Figure 5 enables us to compare the resulting common mode using no compensation, static offset correction and active compensation with the proposed feedback loop. The simulated CMR of all compensation strategies, presented in Table 1, has a nearly constant value between 1 kHz and 1 MHz, due to the low variance σ.

The passive method with an U_off = 0 V produces a common mode voltage of approx. -30 dB or 29.15mV with an rms value of 648 V for both sources. The static compensation technique achieved a CMR of approx. - 80 dB for the VS and approx. -130 dB for the EHCS, respectively. In contrast, the active compensation reduces the common mode signal of approx. -40 dB for both VS and EHCS. To further improve the CMR we investigated the combined application of active and static compensation. The combination reduces the common mode voltage up to −129 dB for the VS and up to −139 dB for the current source, which is equivalent to 0.35 nA and 0.1 nA offset current, respectively.

The common mode rejection was measured at 1 kΩload impedance for the three presented compensation methods. Without any compensation method, the EHCS achieved a CMR of almost -30 dB, shown in Figure 13 (blue). The CMR of the EHCS reduces from -72 dB to -43 dB with higher frequencies for the static compensation method. In contrast, the active compensation method has a fairly low frequency-dependent behavior and achieved a mean common mode reduction of -46.5 dB. The combined compensation has a mean CMR of -57.7 dB with a slightly lower reduction value for higher frequencies.

Figure 13

The VS showed a similar behavior as the EHCS without any compensation. The static common mode reduction of the VS also has a frequency-dependency (Figure 14). In contrast to the EHCS, the highest reduction of -80 dB is achieved for 1 kHz and 1 MHz and increases to -56.5 dB at 10 kHz. The active compensation method slightly improves for higher frequencies from -65.2 dB to -72.8 dB. Both compensation methods combined achieved a mean CMR of -71.8 dB, which is slightly below the active compensation for lower frequencies and above for higher frequencies.

Figure 14

The signal quality is also dependent on the spectral components aside from the measurement frequency. The relation between the signal energy at a specific measurement frequency and the energy of the remaining frequency bandwidth is called signal-to-noise ratio (SNR). The SNR of the source limits the dynamic range of the resulting bioimpedance measurements. Thus, we evaluated the resulting SNR of both sources at 10 kHz and 100 kHz. The current was measured through a 1 kΩ load with a NI-USB 6259 DAQ board (National Instruments, Austin, USA). The EHCS and the VS achieved an SNR of approx. 47 dB and 46 dB, respectively (Table 2).

Besides, the sinusoidal shape of the current is another aspect of signal quality. Due to the finite slew rate of operational amplifier, the injected sinusoidal current is biased by higher harmonics of the base frequency, resulting in a deformation of the signal shape. This behavior is

quantified by the total harmonic distortion (THD) and the harmonic distortion (HD):

where V₁ is the base frequency and V_i with i ≥ 2 are the higher harmonics. THD and HD is a relative measure of the harmonic’s signal amplitude in relation to the injected signal amplitude. The amplitude difference is given in dBc (dB carrier).

Measurements showed that the VS had a 1.85 dBc lower THD compared to the EHCS at 10 kHz. This effect diminished at 100 kHz, where both sources achieved a THD of less then -35 dBc.

A more detailed investigation of the harmonic distortion has been measured with the Tektronix MSO2024, The second harmonic distortions (HD₂, solid lines) of the EHCS and the VS are constant at -68 dBc up to 100 kHz, which is equal to the noise floor of the oscilloscope (Figure 15). Above 100 kHz, HD₂ of the VS rises constantly with 20 dBc per decade. For the EHCS, HD₂ rises at 300 kHZ with 60 dBc per decade. Both sources reach approx. -30 dBc at 1 MHz. Typical for differential signals, the third harmonics of both sources (HD₃, dashed lines) are above the second harmonics. On average, the EHCS had a HD₃ of -50 dBc and the VS has -53 dBc. The third order harmonics shows no frequency-dependent behavior in contrast to the second order harmonics. The values of the fourth as well as the fifth harmonic distortion are below the noise floor of the used oscilloscope (-64 dB).

Figure 15

The parallel capacitors C_v and C_c have been introduced to improve the bandwidth of the sources. In simulations, the added capacitor could achieve a flat spectrum of Z_out for both sources. Moreover, the simulated output impedance of the EHCS was 230 kΩfor resistor tolerances of 0.1%. The measured output impedance achieved similar results in the range of 100 - 200 kΩ for frequencies below 100 kHz. However, C_c increased Z_out up to 400 kΩ at 100 kHz. For frequencies above 200 kHz, the output impedance dropped down to 10 k, independent of C_c, Overall, the different values of C_c have a lower influence on the measured Z_out compared to the simulated Z_out, While the output impedance of the current source obtained from Sirtoli et al. featured a small difference between simulated and measured values, our implementation of the VCCS has in this regard a greater performance loss. The difference to the simulations might be caused by typical problems of the EHCS such as tolerances of component values and stray capacitance influencing the balancing conditions. Also, a too low open loop gain could be the reason for the reduced output impedance at higher frequencies. In future studies, the usage of resistors with lower tolerances or laser trimmable resistors could achieve higher output impedances, as the theoretical value reaches 2.27MΩ, An improved version with a higher output impedance might reveal if C_c has the ability to increase the bandwidth of the VCCS in real implementations.

For the VS, Z_out matched the expected values of the simulations for frequencies above 100 kHz. In the lower frequency range, the measured output impedance is slightly higher, but still mostly below the pursued 1 output impedance. The measured output impedances were evaluated for C_v = 82 pF. In future work, also higher values for C_v should be considered to further reduce the output impedance in the frequency range above 100 kHz.

The acceptable load of the EHCS has good characteristics in the lower load range. The difficulties of the EHCS occur at loads above 2.47 kΩ at higher frequencies (above 500 kHz). Such large bioimpedances do not usually occur at these frequencies, hence this impairment is negligible. The voltage source exhibits phase shifts and distortions above 470, Yet, amplitude attenuation is not affected.

The common mode signals of voltage and current sources are influenced by offset voltages of the operational amplifiers and miss-matches of resistors. Different common mode reduction strategies were evaluated. We note that the measured common mode of the EHCS might be influenced by the probe loading effect especially for the high impedance positive output. The usage of an instrumentation amplifier, similar to the measurement setup of the output impedance, is not applicable due to the common mode measurement principle. However, the probe loading effect applies to all compensation strategies and should not compromise the comparability. We could significantly reduce the common mode of both sources in simulations as well as in experimental evaluation by the application of a static offset compensation. Additionally, an active feedback compensation could also reduce the common mode signal, but to a minor extent. However, the common mode signal increases for higher frequencies. This behavior can be reduced by the usage of active compensation and results in a more constant common mode reduction over the whole frequency range. The combination of both methods achieved a mean common mode reduction by -71.8 dB for the voltage source, which is similar to the passive compensation but shows significantly less frequency-dependency. For the EHCS, the combined usage of both methods is equivalent to the purely static compensation with -57.7 dB, but has a more constant frequency behavior. According to the EN 60601-1, a maximum current of 10 μA is tolerable. The measured absolute common mode using the combined compensation strategy achieved a mean value 1.7 μA and 0.06 μA for the EHCS and VS, respectively. Thus, the proposed compensation technique is an adequate principle to fulfill the strict patient safety requirements of bioimpedance measurements. The proposed offset compensation strategy is easy to implement and achieved a significant common mode reduction, which makes them suitable for many low-cost bioimpedance applications.

For the signals at 10 kHz and 100 kHz, the SNRs are constant and almost identical with approximately 47 dB. The THD, on the other hand, increases from -42.3 dBc by 7.1 dBc for the EHCS, and from -44.2 dBc by 8.4 dBc for the VS. Both sources show the same frequency-dependent behavior, which might be caused by the THD of the differential amplifier THS4151.

The usage of symmetric signals suppresses HDs. The measured HD₂ were below the noise floor of -68 dBc for both sources up to 100 kHz. For higher frequencies, HD₂ increased, which might be caused by higher frequency poles of the sources.