## 2 Transfer Function of Galvanic-Type IBC
### Transfer Function Frequency Response Based on Quasi-Static Field IBC Model
The numerical value of Equation (6) can be calculated using the human tissue parameters from  
Figure 1: Illustration of galvanic-type IBC geometry on the human limb. [PERSON] _et al._[25], together with typical approximate human limb tissue geometries from the individual person. For safety purposes, in our experiment we have used electrical stimulation square type electrodes with dimensions of 40 mm \(\times\) 40 mm. For simplicity, the impedance of the electrode was omitted in the later calculation as the measured impedance of the stimulating electrode excluding the tissue is about 40 \(\Omega\), which is much lower than the human limb impedance of around several hundred Ohms [26]. The input signal was biphasic waveform with limitation of peak value 1 mA in order to comply with the safety standard [27] during _in vivo_ experiments. The mathematical expression of the input signal was modeled as the following uniform normal current density:  
\[J_{*}\big{(}r_{*},\phi,z\big{)}= \begin{cases}1 mA/S_{e}&z_{*}\leq z<z_{*}+d& \text{and}&0\leq\phi<1.23\,rad\\ -1 mA/S_{e}&z_{*}\leq z<z_{*}+d&\text{and}&3.14\,rad\leq\phi<4.37\,rad\end{cases} \]  
where \(S_{e}\) is the area of the electrode; \(z_{e}=70\) mm and \(d=40\) mm (shown in Figure 1) represent the corresponding position and size of the electrodes. The calculated results were then compared with _in vivo_ experiments. A network analyzer (Agilent, 4395A Network/Spectrum/Impedance Analyzer) was used to take measurements from 100 Hz to 1 MHz. Several young healthy adult subjects were recruited for our _in vivo_ experiments. Without loss of generality, two typical sets of data were shown in this article [Subject A: male, height 1.85 m, weight 90 kg, Body Mass Index (BMI) 26.01, length of lower arm 280 mm and Subject B: female, height 1.57 m, weight 50 kg, BMI 20.2, length of lower arm 250 mm]. In the model calculation, the radius of limb for subject A was proximately 35 mm, with the skin, fat, muscle and bone thicknesses of 3 mm, 4 mm, 11 mm and 17 mm [28], respectively; while the counterparts for subject B were 30 mm, 2.5 mm, 3.4 mm, 9.4 mm and 14.7 mm. The _in vivo_ experiment set up, which was composed of a network analyzer and differential active probe (Agilent, 1141A Differential Probe), is shown in Figure 2(a) while the corresponding flow chart is displayed in Figure 2(b). Also the input impedance matching issues [29] related to changes of body electrical parameter can be ignored in Figure 1 because of our high input impedance (1 M\(\Omega\)) of differential probe and operation of sub-MHz low frequency region. Then, the high input impedance bio-amplifier is utilized to extract the conduction current for further processing. Prior to the experiments, the skins of the subjects were cleansed to make good contact with the electrodes. The sinusoidal signal of different frequencies (100 Hz-1 MHz) from the output port of calibrated network analyzer was applied to the human limb at the transmitter sites, and the received signal at receiver sites was detected via the differential active probe. Then gain _versus_ frequency was obtained in network analyzer by sweeping the frequency. For each subject, both calculation and experimental results of two separation distances (S = 6 cm and 11 cm) between transmitter and receiver are reported here. Both calculated and measured results of IBC channel gain are shown in Figure 3. In addition, their absolute errors between the calculation and measurement over the frequency range (100 Hz to 1 MHz) are shown at the top in Figure 3. One can observe that our theoretical and measured IBC channel exhibits high pass characteristics. The passband starts at around 20 kHz with their maximum error below 16 dB. At S = 6 cm, measurement gains are lower than \(-\)25 dB (and \(-\)35 dB) below 20 kHz, then sustains around \(-\)25 dB (and \(-\)35 dB) of relative-flat gain for the frequency higher than 20 kHz for subject A (and subject B), respectively.