Can wearables function as second galvanic skins?
Keywords:wearables? Galvanic Skin Response? GSR? electrodermal response? amplifier?
Test results, hardware files, and firmware source code provide complete documentation for the design. This complete wrist-worn unit is a must for designers and will help get to market quickly with a robust design.
AC impedance measurement
I felt that the following detailed explanation of AC Impedance Measurement needed to be included in this article for completeness. The material is courtesy of Maxim Integrated and is on their website, as well.
The MAXREFDES73# is set up to perform an AC impedance measurement (figure 8). The 12bit DAC generates the excitation sinusoidal signal with a 1V peak-to-peak magnitude. The microcontroller DMA engine makes the direct digital synthesis possible. The DAC0 output signal is buffered by an op amp, and a second op amp is used to construct a second-order lowpass filter (LPF1). A capacitor (not shown) blocks the DC component of the excitation signal. Four internal SPST switches dynamically reconfigure the load to either the calibration path or human skin load. An 8bit DAC (not shown) generates the common-mode bias before the ADC input. An RC combination constructs a first-order LPF and gain control in LPF2. Finally, an RC combination works as a LPF before ADC input that acts as an anti-alias filter, as well.
Figure 8: Shown here is the block diagram for the MAXREFDES73# AC impedance measurement. (Image courtesy of Maxim Integrated) |
In this case the skin on the wrist is part of the input impedance of the inverting amplifier in the input circuit of the demo. A coherent sinusoid stimulates the circuit and the response gets coherently detected with a digital base band quadrature sampling receiver to detect the amplitude and phase of the network response. A known calibration path is on board that is also measured and using both of these responses the system determines the complex impedance of the skin.
Next the complex impedance can be accurately determined from a low power observation using the ratio of the responses to the test load to the calibration path.
In order to measure the impedance at a particular frequency (FC), a sinusoid voltage is applied to the test load, so that x(t) = cos(2πx FC x t).
Then the output of the ADC is a scaled and phase shifted version of the input as y(t) = V_{L }x cos(2π x t + ?)
In order to extract the phase of the received signal we need coherent detection. Now Digital base band quadrature sampling is implemented if the ADC can be synchronised with the DAC output (AC excitation). Here, the sample rate is 4 times the excitation frequency as can be seen in figure 9.
Figure 9: MAXREFDES73# ADC quadrature sampling. (Image courtesy of Maxim Integrated) |
Digital base band quadrature sampling is typically illustrated in the frequency domain; however, for the AC impedance measurements, the time domain is more applicable. The following equations illustrate the processing from y(t) to real component I and complex component Q.
y(t) = V_{L} cos(2π Fc t + ?)
T_{S} = 1/(4 Fc)
y(k) = V_{L} cos(π/2 k + ?)
kΣ {0, 1, 2, ... N1}
y(k) = V_{L}[cos?, cos(π/2 + ?), cos(π + ?), cos(3π/2 + ?), ...]
y(k) = V_{L}[cos?,sin?,cos?, sin?, ...]
To calculate the complex impedance, we are interested in extracting the magnitude and phase information:
V_{Le}^{j?} = V_{L}cos(?) + jV_{L}sin(?) = I + JQ
By observation, the first 2 ADC samples yield I and Q:
I = V_{L}cos(?) = y(0)
Q = V_{L}sin(?) = y(1)
We can split the ADC samples (even/odd) and modulate by 1 to generate multiple observations of the real component I and the complex component Q. Because we are processing a single frequency, we can average these outputs to increase the SNR (signal-to-noise ratio) of the measurements, as illustrated below:
Where N is the number of ADC samples, it is a multiple of 4.
Phase = ? = atan2(Q,I)
Magnitude = V_{L} = (I2 + Q2)
The load complex impedance (Z(s)) is measured with the calibration load (Ycal(s)) and with the sample under test load (Ysys(s)) at a frequency of interest. Based on the ratio of the responses and the two external resistors, R_{i} and R_{cal} (figure 2), the load complex impedance can be observed at the test frequency:
(Ri + Z(s))/R_{cal} = Y_{cal}(s)/Y_{sys}(s)
The load impedance magnitude and phase can be derived:
Z(s)_{magnitude} = R_{cal } (Y_{cal}(s)_{magnitude}/Y_{sys}(s)_{magnitude})R_{i}
Z(s)_{phase} = Y_{cal}(s)_{phase}Y_{sys}(s)_{phase}
For this reference design, we are more interested in the magnitude of the skin impedance, so only the magnitude data are transmitted and displayed on the mobile application's graphic user interface. In the reference design firmware, the phase data are also computed for users to use in their specific applications.
Figure 10: The full capabilities of the Wellness Watch (Image courtesy of Maxim Integrated) |
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