Subcutaneous Transmitter (A3028)

© 2013-2017, Kevan Hashemi, Open Source Instruments Inc.

Contents

Description
Versions
Electrodes
Design
Analog Inputs
Input Noise
Power Measurement
Transmit Frequency
Transmit Antenna
Body Capacitance
Battery Life
Encapsulation
Development

Description

The Subcutaneous Transmitter (A3028) is telemetric sensor that provides one or two biopotential inputs. The A3028A is fully-implantable with volume 1.4 ml and provides two EEG channels with bandwidth 160-Hz and sample rate 512 SPS for fifteen days. The A3028E is fully-implantable, 2.8 ml, and provides one EEG channel with 160 Hz and 512 SPS for eighteen weeks. The A3028M is a head fixture with replaceable battery that provides two EEG channels with 640-Hz and 2048 SPS for four days. All versions of the A3028 operate within our Subcutaneous Transmitter System. We turn the transmitter on and off with a magnet. You will find example recordings here.


Figure: Subcutaneous Transmitter A3028A-CCC. Body 13 mm wide, 13 mm long, 8 mm deep, volume 1.4 ml. The three leads are 45 mm long. Electrodes are screws 0.5 mm in diameter and 0.6 mm long. The red lead is the X input, yellow is the Y input, and the blue is the reference voltage, C (see schematic).

The A3028A comes with three helical stainless-steel leads coated with silicone (see here for helical wires in clear silicone insulation). The three leads provide us with two biopotential inputs, X and Y, that share a common ground, C. The sensor measures the voltage difference X − C and Y − C. The electrodes at the end of the wires can be stainless steel screws, gold pins, or bare helical wire, as we discuss in Electrodes and The Source of EEG.

PropertyValue
Volume1.4 ml
Mass2.7 g
Outer Dimensions14 mm × 14 mm × 8 mm
Operating Life360 hours
Shelf Life27 months
Number of Inputs2
Type of InputDifferential
Input Impedance10 MΩ || 2 pF
Sample Rate (Each Input)512 SPS
Sample Resolution16-bit
Input Dynamic Range20 mV
Input Bandwidth0.3 Hz − 160 Hz
Input Noise≤12 μV rms
Input Mains Hum<1 μV
Table: Specifications of the A3028A. The mains hum is for an implanted sensor. The shelf life and operating life are the time it takes the off-state and on-state currents to run down a fresh battery.

The A3028D is the same circuit with the same functionality as the A3028A, but with a 255 mA-hr battery instead of the A3028A's 48 mA-hr battery. The A3028D's volume is 3.0 ml and its operating life is 1900 hours.


Figure: Subcutaneous Transmitter A3028D-AAB with 50-mm Antenna. The transmitter body is 24 mm in diameter and 7 mm deep, depending upon where we measure it. The body displaces 3.0 ml. The three leads are 150 mm long. One is equipped with one 0-80 thread, 3.2-mm long steel screw and two bare-wire electrodes.

All versions of the A3028 turn on and off with the application of a magnetic field. We like to use cow magnets. Component U2 is a micro-power hall effect switch. When it detects a magnetic field, it asserts its output. When we remove the field, the transmitter changes state. If it is inactive, it activates. If it is active, it deactivates. The state change does not occur when we bring the magnet close to the transmitter, it occurs when we move the magnet away.

Warning: Check to make sure devices are inactive upon arrival at your facility. Do not store within 10 cm of iron tools, power transformers, computers, or external hard drives. During implantation, take note that stainless steel tools and work surfaces are often magnetic, and can activate and deactivate your transmitters.

We determine the version of a transmitter during assembly, programming, and encapsulation. We might change capacitors on the board to set the filter frequencies. We might change resistors to set the gain. We program the logic chip to set the sample rate for each channel. We can equip the circuit with various sizes of battery. The larger the battery, the longer the operating life.


Figure: Subcutaneous Transmitter A3028M-AAA. Bandwidth 0.3-640 Hz, 2048 SPS each channel, replaceable battery, 100 hrs operating life per battery. The bottom side of the non-implantable head fixture devices is bare, sanded epoxy for robust bonding to dental cement.

The A3028 transmits either one or two signals. Each signal has its own channel number. Each sample of each signal is transmitter by the A3028 with a radio-frequency message. Each message contains a channel number, as we describe in Message Encoding. Channel numbers lie in the range 1-222. A two-channel transmitter transmits on channels n and n+1, where n is an odd number.

Versions

The following table presents the versions of the A3028 we have defined so far. Feel free to write to us and propose a new version, and we will see if it is practical.

Version X Y Battery
Capacity
(mA-hr)
Volume
(ml)
Width
(mm)
Height
(mm)
Expected
Operating
Life
(hours)
Expected
Shelf
Life
(months)
A3028A 20-mV, 0.3-160 Hz, 512 SPS 20-mV, 0.3-160 Hz, 512 SPS 48 (BR1225) 1.4 14 7 360 27
A3028B 20-mV, 0.3-160 Hz, 512 SPS Disabled 48 (BR1225) 1.4 14 7 600 27
A3028C Disabled 20-mV, 0.3-80 Hz, 256 SPS 48 (BR1225) 1.4 14 7 950 27
A3028D 20-mV, 0.3-160 Hz, 512 SPS 20-mV, 0.3-160 Hz, 512 SPS 255 (BR2330) 3.0 24 8 1900 140
A3028E 20-mV, 0.3-160 Hz, 512 SPS Disabled 255 (BR2330) 3.0 24 8 3200 140
A3028F 20-mV, 0.3-320 Hz, 1024 SPS 20-mV, 0.3-320 Hz, 1024 SPS 48 (BR1225) 1.4 14 7 180 27
A3028G 20-mV, 0.3-320 Hz, 1024 SPS Disabled 48 (BR1225) 1.4 14 7 360 27
A3028H 20-mV, 0.3-80 Hz, 256 SPS 20-mV, 0.3-80 Hz, 256 SPS 48 (BR1225) 1.4 14 7 600 27
A3028J 20-mV, 0.3-80 Hz, 256 SPS 20-mV, 0.3-80 Hz, 256 SPS 255 (BR2330) 3.0 24 8 3200 140
A3028K Disabled 20-mV, 0.3-80 Hz, 256 SPS 255 (BR2330) 3.0 24 8 5000 140
A3028L 20-mV, 0.3-320 Hz, 1024 SPS 20-mV, 0.3-320 Hz, 1024 SPS 1000 (BR2477) 6.5 27 14 4000 550
A3028M 20-mV, 0.3-640 Hz, 2048 SPS 20-mV, 0.3-640 Hz, 2048 SPS 48* (BR1225) 2.0 16 10 100 27
A3028N 20-mV, 0.3-160 Hz, 512 SPS Disabled 48* (BR1225) 2.0 16 10 600 300
A3028Q 20-mV, 0.3-160 Hz, 512 SPS Disabled 560 (CR2354) 5.0 24.0 12.0 7000 27
A3028S Disabled 20-mV, 0.3-40 Hz, 128 SPS 48 (BR1225) 1.4 14 7 1300 27
A3028T 20-mV, 0.3-40 Hz, 128 SPS 20-mV, 0.3-40 Hz, 128 SPS 48 (BR1225) 1.4 14 7 950 27
A3028V 20-mV, 0.3-160 Hz, 512 SPS 20-mV, 30-640 Hz, 16 SPS 48 (BR1225) 1.4 14 7 600 27
Table: Versions of the A3028. For each input we give the voltage dynamic range, the frequency dynamic range, and the sample rate. All are fully-implantable except those marked *, which are non-implantable head fixtures with replaceable batteries. The expected operating and shelf lives are the time it takes an average transmitter to run down a nominal battery in the active and inactive states respectively, see below.

Starting with transmitter batch number 111, all our transmitters provide stimulus protection on both inputs by means of three resistors and two capacitors. The resistors protect against applied voltages up to ±50 V. The capacitors attenuate radio-frequency noise that might otherwise be picked up from the antenna and demodulated in the amplifier inputs. Prior to batch 111, only the A3028R provided stimulus protection. Now that all versions provide this protection, the A3028E and A3028R are identical, and we have retired the A3028R version from our table.


Figure: Batch of Fourteen Subcutaneous Transmitters A3028B-CC with 50-mm Antennas.

The A3028 electrode leads are color-coded with colors that do not blend with the natural color of animal tissue. The X lead is red, Y is yellow, and C is blue. A dual-channel transmitter produces two radio-frequency message sequences with two separate channel numbers. The lower of the two is X and the higher is Y. A single-channel transmitter may be equipped with only X or only Y. If the single channel is X, the leads will be red and blue. If the single channel is Y, the leads will be yellow and blue.

Electrodes

Each lead of the transmitter has its own terminating electrode. Each electrode type has a one-letter name, as given in the table below. We specify these electrodes with two letters for a single-channel transmitter (X or Y, and C) and three letters for a dual-channel (X, Y, and C). Click on the letter for a data sheet or photograph.

NameElectrode
A Bare wire, length 2 mm, stainless steel helix.
B Screw, thread 0-80, length 3.2 mm.
C Screw, thread M0.5, length 0.6 mm.
D Pin, diameter 0.30 mm, length 3.1 mm, Mill-Max 4353-0-00-15-00-00-33-0
E Socket, for pin diameters 0.20-0.33 mm, Mill-Max 4428-0-43-15-04-14-10-0
F Pin, diameter 0.64 mm, length 4.1 mm, Mill-Max 5035-0-00-15-00-00-33-0.
Mates with Plastics One socket E363/0.
G Pin, diameter 0.51 mm, length 6.0 mm, Mill-Max 5063-0-00-15-00-00-33-0.
Mates with Plastics One socket MS303/6.
H Depth electrode, wire 125-μm dia Pt-Ir, insulation 200-μm dia teflon.
Locate with guide cannula, cut wire after cementing.
J Depth electrode, wire 125-μm dia 316SS, insulation 200-μm dia teflon.
Locate with guide cannula, cut wire after cementing.
Table: Electrode Letter Codes for the A3028.

The A3028A-DDC is a two-channel transmitter, sample rate 515 SPS on each channel, volume 1.4 ml, with 1.9-mm long pins on X and Y, and a 0.6-mm long screw on C. The A3028A-HFC has a depth electrode on X, a gold-plated pin on Y, and a screw on C.

We provide some on-line advice on implanting the transmitters here, but most of our advice on this subject we conduct by e-mail with our customers, with assistance between customers, including the exchange of implantation videos, being common.

Design

The following files define the A3028 design. Note that we distribute all these files under the GNU Public License.

S3028A_1.gif: 2 channels 0.3-160 Hz, A3028AAV1 and A3028AAV2.
S3028B_1.gif: 2 channels 0.3-160 Hz, A3028AAV3.
S3028C_1.gif: 2 channels with stimulus protection. A3028RV1/RV2 X and Y 0.3-160 Hz. RV3 X 0.3-160 Hz, Y 0.3-80 Hz.
S3028D_1.gif: 2 channels 0.3-160 Hz, A3028AV4.
S3028E_1.gif: 1 channel 0.3-160 Hz, 1 channel 0.3-80 Hz, A3028AV5.
A3028AV3.ods: Bill of materials for A3028AV3.
A3028AV4.ods: Bill of materials for A3028AV4.
A3028AV5.ods: Bill of materials for A3028AV5.
A3028RV1.ods: Bill of materials for A3028RV1.
A3028RV2.ods: Bill of materials for A3028RV2.
A3028RV2.zip: Assembly Files for A3028RV2.
A302801D.zip: PCB for A3028RV1.
A302801E.zip: PCB for A3028AV3, AV4, AV5.
A302801E_Panel.zip: Panel 5 × 2 of A302801E.
A302801F.zip: PCB for A3028AR2.
A302801F_Panel.zip: Panel 5 × 2 of A302801F.
A302801F_Outline.pdf: Outline of A302801F with dimensions.
A302801F_Panel_Outline.pdf: Outline of A302801F panel 5 × 2 with dimensions.
A3028AV5_Top.gif: Component map of A3028AV5, top side.
A3028AV5_Bottom.gif: Component map of A3028AV5, bottom side.
A3028RV1_Top.gif: Component map of A3028RV1, top side.
A3028RV1_Bottom.gif: Component map of A3028RV1, bottom side.
A3028RV2_Top.gif: Component map of A3028RV2, top side.
A3028RV2_Bottom.gif: Component map of A3028RV2, bottom side.
Code: Logic chip firmware library.
BR1225: Diameter 12 mm battery electrical data sheet.
BR1225AHB: Diameter 12 mm battery mechanical drawing.
BR2330: Diameter 23 mm battery electrical data sheet.
BR2330AHD: Diameter 23 mm battery mechanical drawing.

The A3028 provides two amplifiers for recording two channels of EEG, or simultaneous EEG/EMG recording.


Figure: Detail of the A3028 Circuit. Once the neck is cut off, the circuit is 12.7 mm square. Left: top side with, clockwise from top-left, the logic chip, 32.768 kHz oscillator, X amplifier, and ADC. Right: bottom side with, clockwise from top-left, power switches, Y amplifier, RF oscillator, magnetic switch, and 1.8-V regulator. For a photograph of the entire circuit with programming extension see here.

When we load the battery, it remains isolated from the circuit until we apply a jumper to the programming extension or cut the programming extension off. This allows us to load leads, antenna, and battery using water-soluble fluxes, then wash the entire board in hot water, without worrying about damage to the circuit. The cleanliness of the circuit board prior to encapsulation is essential for reliable encapsulation.

Analog Inputs

The A3028 three input leads are X, Y, and C. They are red, yellow, and blue respectively. You can see all three declared with in the circuit diagram.

NameFunctionComment
XX positive inputConnected to VC by 100 nF in series with 10 MΩ.
YY positive inputConnected to VC by 100 nF in series with 10 MΩ.
Cshared negative inputConnected directly to VC.
OUTradio-frequency antennaa flexible stranded steel transmit antenna
Table: Connections to the A3013.

The A3028 amplifies and filters X and Y to produce XA and YA. The gain of the A3028A amplifier is 100. Its high-pass filter consists of a zero at 0.16 Hz and another at 0.32 Hz. Its low-pass filter is a three-pole, 3-dB ripple Chebyshev filter with 160-Hz cut-off frequency. Both XA and YA are applied to a two-channel sixteen-bit ADC. In the A3028A, the ADC samples the two channels alternately at 512 SPS per channel, for a combined sample rate of 1024 SPS. In the A3028B, sampling from YA is disabled, and XA is sampled at 512 SPS. (We note that the A3028B will replace the A3019A single-channel transmitter.)

The ADC produces sixteen-bit values between 0 and 65535. A value of 0 for X means XA = 0V, and 65535 means XA = VBAT. With a fresh battery, VBAT = 2.7 V. In the A3028A, with its gain of 100, each ADC count represents roughly 400 nV at the X and Y inputs. In the last few days of a transmitter's life, the VBAT drops to 2.2 V, at which point the transmitter fails. During this time, the voltage represented by each ADC count drops in proportion to the battery voltage. When VBAT is 2.2 V, one count represents roughly 350 nV. In theory, the dynamic range of the A3028A is 2.7 V ÷ 100 = 27 mV. But in practice, the amplifier is not able to drive XA all the way up to VBAT or all the way down to 0 V. So we quote the dynamic range as a more conservative 20 mV, or if we want to be more specific, −13 mV to +7 mV.

At each input, the A3028 provides a DC-blocking capacitor. These are C7 and C12 in the schematic. Together with input resistors R5 and R12, they form two single-pole high-pass filters with time constant 1.0 s. There is another high-pass filter in each amplifier, consisting of R6/C8 for X and R13/C13 for Y. These have time constant 0.5 s in the all current versions of the A3028. The figure below shows the theoretical step response of the A3028 input, and compares it to that of other devices we have manufactured.


Figure: Input Step Response for Various Circuits. The A3028 plot applies to either X or Y in the A3028A/D.

The common-mode reference voltage in the amplifier is VC, and VC is derived from the battery voltage by a 1.8-V regulator. Thus VC is 1.8 V, and the average value of both XA and YA are also 1.8 V. Thus the average digital value of X and Y correspond to 1.8 V. This allows us to calculate the battery voltage from the average value of either channel. We have VBAT = 65535 / average(X) × 1.8 V. This relation applies to all versions of the A3028, and both inputs, regardless of the gain and frequency response of its amplifiers, and regardless of what battery we have installed.

The figure below shows the X signal from an un-encapsulated A3028R as we reduce VBAT from 4.2 V to 1.2 V over 300 s. Our formula for VBAT from the average value of X works down to VBAT = 1.9 V. After that, the X decreases, suggesting an increase in VBAT, when in fact the actual VBAT drops to 1.8 V and the transmitter turns off.


Figure: X versus Time. We plot the sixteen bit value of X, with each vertical division being 6553.5 counts. Time is 15 s per division. Power supply voltage is 4.2 V on the left and 1.2 V on the right, so dropping 150 mV per horizontal division. [04-MAR-15]

The analog input impedance of X and Y is 10 MΩ in series with 100 nF to C via VC (see schematic). Together these produce a high-pass filter with half-power frequency 0.16 Hz. In the amplifier, the combination of R6 and C8 for X, and R13 and C13 for Y, produce a second high-pass filter. In the A3028A, these components are 50 kΩ and 10 μF, so the half-power frequency is 0.32 Hz. Resistors R6 and R13 also set the gain of the amplifiers. With R6 = R13 = 50 kΩ, the gain is 100. With R6 = 100 kΩ, the gain is 50 and the high-pass filter frequency drops to 0.16 Hz.

We set the cut-off frequency of the A3028 three-pole, 3-dB ripple, Chebyshev, low-pass filters by our choice of filter capacitance, CF. There are three capacitors in each filter that must have the same value for the filter to function properly. They are C9, C10, and C11 for the X filter and C14, C15, and C16 for the Y filter. With CF = 1.0 nF, the cut-off frequency is 160 Hz. The following graph shows how the gain of the two inputs of an A3028A varies with frequency.


Figure: Frequency Response of the A3028A.

The frequency response in the pass-band shows a slight decrease in gain from 10 Hz to 80 Hz, followed by a bump up at 130 Hz. These two features are the 3-dB ripple of the three-pole Chebyshev filter. By tolerating this non-uniformity of gain in the pass-band, we obtain a far sharper cut-off at the top of the pass-band. Amplitude drops by a factor of ten, or 20 dB from 160 Hz to 256 Hz. Frequencies above 256 Hz when sampled at 512 SPS will produce artificial sin-waves of lower frequency, in a process called aliasing. The purpose of our low-pass filter is to prevent aliasing. It is an anti-aliasing filter. Even with the sharp cut-off of our Chebyshev filter, however, we might still see aliasing of high frequency components in EEG.


Figure: Aliasing in the A3028A for 262-Hz, 10-mV Input. Full scale vertically is 4 mV and horizontally is 1 s. We see 6 Hz of amplitude 700 counts rms as well as 60 Hz mains hum of amplitude 200 counts rms.

The plot above shows what the X and Y digitized signal looks like when we apply a powerful signal above 256 Hz to both inputs. The result is an artificial waveform of frequency 262 − 256 = 6 Hz. Its amplitude is around 700 counts rms, which is one tenth the amplitude it would produce if we reduced the frequency to 25 Hz. The mains hum in the signal is carried in by the signal source when we connect it to the transmitter.

We expect some variation between amplifiers, because the three-pole filter is sensitive to the exact component values. The plot below shows the frequency response of a batch of fourteen A3028E transmitters stimulated with a 30-mV sinusoid through a 20 MΩ resistor.


Figure: Frequency Response of Fourteen A3028Es. For similar plot of response of four dual-channel A3028Ds, see here.

At 10 Hz, the fourteen channels agree to within ±0.5 dB. At 130 Hz, where we have the bump in the Chebyshev response, they agree to within ±1 dB. These variations are well within the range we expect with 5% capacitors and 1% resistors.

The A3028V provides two channels: one running at 496 SPS and 0.3-160 Hz, and one at 16 SPS and 30-640 Hz. The first is for normal EEG recording, the second is for EMG amplitude measurement. The Neuroarchiver will reconstruct the 496 SPS signal into a 512 SPS signal by filling in the missing samples using the previous sample values, and the result will be an EEG signal almost identical to the one we would obtain with 512 SPS. The Neuroarchiver will leave the 16 SPS signal as it is, provided you enter "16 512" for the default frequency in the Neuroarchiver configuration. The figure below shows the gain versus frequency of the EEG and EMG inputs. Our measurement of the EMG gain between 200-500 Hz is erratic because of aliasing noise produced by under-sampling a non-random periodic sinusoid. With a random EMG input, we expect no such error in our measurement of amplitude.


Figure: Frequency Response of Three A3028Vs, EEG and EMG Channels.

The figure below shows how the A3028R's 160-Hz low-pass filter responds to pulses applied to the X input.


Figure: Response of A3028R to 1-ms Pulses of 10 mV Delivered Through 50 Ω. The pulse frequency is 8 Hz. The vertical range is around 12 mV. For 5-ms pulses of 30 mV and 8 Hz delivered through 20 MΩ and the same vertical range, see here.

The low-pass filter introduces the ringing after the pulse, which consists of three maxima and minima in damped harmonic oscillation after the pulse has ended. The figure below shows the response of the A3028R to perforant pathway discharge spikes of amplitude roughly 10 mV.


Figure: Perforant Pathway Discharges, as Recorded with Wire Electrode. The vertical range is around 12 mV

The ringing we see after the discharge spikes is not generated by the brain itself, but rather by our low-pass filter. The slow, positive pulse following the negative spike is, however, produced by the brain, and the ringing is overlaid on top of this pulse.

Input Noise

[20-SEP-13] Input noise on an un-encapsulated A3028A with no input leads is 20 counts rms on each channel, or 8 μV. This is lower than the 12 μV of the A3019. The decrease is a result of superior distribution of power and decoupling in the A3028.


Figure: Full-Spectrum Noise from an A3028A. Note the peak at 20 Hz, the switching noise. Total noise is 12 μV rms.

[08-OCT-13] We look for noise generated by the Hall Effect Switch. This noise existed in the A3019, as we describe here. We have a new Hall Effect Switch, the SL353LT. We find that it, too, generates noise in the 10-30 Hz range in an encapsulated transmitter.


Figure: Hall Effect Switch Noise. Spectrum obtained from 8-second interval. The transmitter has channel numbers 2 and 3, both at 160 Hz, 512 SPS.

We see the same 20.75 Hz noise in both channels. The amplitude is around 7 counts, or 7 × 0.4 μV = 2.8 μV.

[11-MAR-14] When the A3028 is encapsulated and equipped with leads, these leads pick up radio-frequency power from the antenna. If the C lead is left open-circuit and the X and Y leads are connected to some solid body, the C lead acts like an antenna. The radio-frequency power is demodulated by parasitic diodes in the circuit, and the result is noise visible on the EEG, as shown here. Its amplitude is roughly 100 μV rms. If you see such noise in an implanted transmitter, your C lead has a broken conductor.

[01-DEC-16] We take a two-channel A3028D and put it in water at 40°C. We use 8-s recording intervals to measure the amplitude and frequency of the switching noise in each of the two input channels No3 and No4 as the water cooled to 19°C.


Figure: Switching Noise Amplitude and Frequency versus Temperature. The transmitter has two channels. No3 is on the bottom side of the circuit board along with the hall effect sensor that generates the noise. No4 is on the top side of the circuit board.

The frequency of the switching noise increases with frequency. We perform the same experiment with four transmitters at once, using this processor to calculate the rms amplitude of the fundamental harmonic of the switching noise.


Figure: Switching Noise Amplitude versus Temperature. No3/4 is an A3028D, No5 is an A3028B using the X input, No10 is an A3028C using the Y input, No13/14 is an A3028A.

In No13/14 the noise is far greater in X than in Y. But in No10 the noise is as large as any we have seen, and appears on the Y input. We touch the tip of a ×1 probe to the package of the Hall Effect Switch on a battery-powered, un-encapsulated transmitter. We see no signe of 20 Hz, certainly less than 200 μV. We hope to eliminate switching noise entirely in a future design, but for now we have yet to understand why switching noise appears in some amplifiers and not in others.

Power Measurement

Suppose we want to know the root mean square amplitude of a biometric signal, or the mean square amplitude, but we do not need to know its exact shape. When we monitor electromyography (EMG), our chief interest may be the power of the signal, to determine if an animal is awake or asleep, rather than examining the fluctuations in the signal itself.

As we mention above, when we try to represent a continuous, time-varying signal as a sequence of discrete samples, we must make sure that the variation in the time-varying signal between the sample points approximates a straight line. When we plot the sampled signal, we are going to display it by drawing straight lines between the samples, so these straight lines are supposed to represent what the signal actually did between the samples. If the signal varies greatly between samples, we will not see this variation. Failing to see rapid variations between samples may not concern us, but rapid variations can, through sampling, look like much slower variations when we join the samples with lines. If we sample a 100-Hz signal at 48 SPS, for example, our straight-line reconstruction of the signal will be a 2-Hz sinusoid. This generation of slow variation from rapid variation is aliasing. To avoid aliasing, we must filter the signal we want to sample so that it contains no changes of direction between sample points. With a perfect low-pass filter, which has gain 1.0 up to frequency fc and 0.0 above fc, we can sample at 2fc and avoid aliasing. In practice, low-pass filters are not perfect, and avoiding aliasing is not quite sufficient to provide adequate representation. In the A3028, we sample at 3.2fc. Our low-pass filter gain drops by a factor of 10 from fc to 1.6fc. For example, in our 512 SPS transmitter for EEG, we filter at 160 Hz. The filter gain drops by a factor of ten from 160 Hz to 256 Hz.

But aliasing does not change the power of a signal, not unless we somehow miss all the powerful moments of a signal by a spectacularly unfortunate choice of sample instants. For an irregular signal like EMG, sampling at 16 SPS and taking the standard deviation of the samples, will give us a good measure of the EMG signal amplitude. Most EMG power is in the range 40-300 Hz, so we can high-pass filter at 30 Hz and low-pass filter at 320 Hz to separate the EMG from any artifacts that may be generated by our EMG pick-up electrodes, sample at 16 SPS and obtain EMG power at a cost of only 1.8 μA in current consumption. Thus the A3028V monitors EMG on Y and EEG on X and has the same battery life as the single-channel A3028B EEG monitor.

Transmit Frequency

[29-MAR-16] We calibrate the A3028 center frequency to lie in the range 913-918 MHz at room temperature, which is around 22°C. The MAX2624 oscillator that provides the radio-frequency signal has a temperature coefficient of −0.2 MHz/°C. In an animal body at 37°C, the center frequency will drop to 910-915 MHz. Our Octal Data Receivers (A3027) and the older Data Receiver (A3018) are designed to provide reliable message reception in for center frequencies in the range 908-918 MHz. The spectrum of the entire signal spans a ±5 MHz range about the center.

Transmit Antenna

[04-AUG-16] The 50-mm antenna makes a loop roughly 20-mm long. This loop fits easily into a rat. We compared (see here and here) 50-mm and 30-mm antennas moving in air at room temperature on a self-propelled sphere and found that the 30-mm antenna performed just as well as the 50-mm. The 30-mm antenna makes a loop only 13 mm long.

When we immerse an A3028E with 50-mm antenna in water, the radio-frequency power it emits remains constant to within a factor of two as we half-immerse it in water, completely immerse it in water, or press it up agains the wall of a water-filled beaker. The center-frequency of its transmission increases by 1 MHz from air to total immersion in water. The dielectric constant of water is ninety times greater than that of air. Water affects the propagation of radio waves along the antenna, slowig them down, so that the effective length of the antenna is greater. The water also affects the oscillator within the transmitter circuit, changing its resonant frequency.

When we immerse an A3028A with 30-mm antenna in water, the power it emits rises by a factor of ten (10 dB) and the center-frequency rises by 2 MHz. The figure below is the power spectrum we measure when we hang an A3028A by its leads in air, then surround it with a beaker of water.


Figure: Power Received from A3028A with 30-mm Antenna In Air and Water versus Frequency. When half-immersed or pressed up against the wall of a beaker of water, the spectrum lies somewhere between these two extremes.

The antenna is the loop of stranded steel wire insulated with silicone that is attached at one end to the input leads. The antenna connection is marked OUT on the schematic. The antenna transmits the values of X and Y with 7-μs bursts of 902-928 MHz radio waves. The power transmitted during these bursts is roughly 300 μW (−5 dBm). The receiving antenna, which is usually a Loop Antenna (A3015C) connected to an Octal Data Receiver (A3027), must pick up at least 25 pW (−76 dBm) to overcome noise in the receiving antenna amplifiers, and at least four times (12 dB) more than the 902-928 MHz interference power picked up by the receive antenna. In our office, interference power ranges from 100 pW to 100 nW. In order to guarantee reception outside a faraday enclosure, we must receive 1 μW (−30 dBm). Inside an FE2F faraday enclosure, which offers at least ×1000 (30 dB) isolation from interference, we must receive 1 nW (−60 dBm).

Body Capacitance

For a discusion of body capacitance, see Body Capacitance in the A3019 manual.

Battery Life

[29-SEP-16] The A3028 can run down its battery in two ways. It can sit on the shelf in its inactive state, or it can digitize and transmit its input signals in its active state. In practice, the battery will be consumed by some combination of inactive and active periods.

The inactive current of the A3028 consists of the current consumption its magnetic sensor (U2) and its logic switch (U3). The average inactive current is around 2.0 μA. The shelf life of the transmitter is the time it takes the inactive current to drain the battery. For the 48 mA-hr battery, the shelf life is over two years. For the 255 mA-hr battery, the shelf life is over ten years.

The active current of the A3028 is its current consumption in the active state. This current depends upon the number of samples the transmitter takes per second. The A3028B provides one channel with 512 SPS. The active current consists of the quiescent current of the logic chip, which is independent of sample rate, and the consumption of the sample and transmit process, which increases linearly with sample rate. The figure below shows active current versus the total sample rate. To obtain the total sample rate, we add the sample rates of both channels.


Figure: Active Current versus Total Sample Rate.

The linear trend fitted to the data provides us with the following empirical formula for expected active current, Ia, as a function of the total sample rate, R.

Ia = 21 μA + (R × 0.11 μA)

The operating life of the transmitter is the time it takes the active current to exhaust a fresh battery. As the battery is exhausted, the average value of the analog inputs increases, like this. The A3028B single-channel, mouse-sized transmitter has nominal battery capacity 48 mA-hr. According to the above formula, its expected active current is 77 μA. Its expected operating life is 620 hours. The A3028E dual-channel, rat-sized transmitter has a 255 mA-hr battery. Its expected operating life is 1900 hours.

The standard deviation of the active current is 5% of its expected value. But the standard deviation of the battery capacity is closer to 10% the nominal capacity. The operating life is, on average, equal to its expected value, but varies from one transmitter to the next with a standard deviation that is 10% of the expected operating life. Assuming a normal distribution of operating life, we can be 82% certain that the operating life will be >90% of the expected value, and 97% certain it will be >80% of the expected value. In the case of the A3028R single-channel 512 SPS transmitter, we can be 97% sure that it will operate for longer than 2560 hrs, and 18% of the time it will run for longer than 3500 hrs.

If we remove the radio-frequency oscillator from an A3028E transmitter, which runs at 512 SPS, the active current consumption drops from around 80 μA to 40 μA. The sample and transmit activity consumes 60 μA, of which 40 μA is transmission and 20 μA is the quiescent current of the logic chip, amplifiers, and regulators. During the 7-μs burst transmissions, the current drawn by the transmission circuits is 11 mA.

Encapsulation

[29-SEP-16] We encapsulate the A3028 in black epoxy, then coat the epoxy with a 1-mm layer of clear silicone. The leads are stainless steel springs coated with dyed silicone. We remove one in ten transmitters from our production line for accelerated aging. These transmitters run until they exhaust their batteries while fully immersed in water at 60°C.

Corrosion is a likely cause of failure in electronic devices in warm, humid environments. Both silicone and epoxy are permeable to water vapor, so that the implanted transmitter's encapsulation becomes saturated with water vapor. Changes in the transmitter temperature provoke condensation in any cavities within the electronic circuit, such as might exist within a cracked ceramic capacitor or beneath a small surface-mount component. Our epoxy encapsulation procedure seeks to eliminate such cavities, but if they exist within the components, the condensed water, combined with the warmth of the animal body and the electrical potential presented by the circuit, result in corrosion that leads to failure of the EEG amplifier and ultimately to premature draining of the battery. At 60°C, corrosion occurs over ten times faster than at 37°C in an animal body.

The expected operating life of the A3028 in 100% humidity at 60°C is over 100 days, with the first artifacts of corrosion appearing in the EEG signal after about 50 days. Implanted in an animal, we expect no sign of corrosion in the EEG until 500 days, and no failure through corrosion until 1000 days. None of the popular versions of the A3028A run for anywhere approaching 500 days, so we claim that our transmitters will not fail due to corrosion while implanted.

Development

We have moved our development to a separate page, Subcutaneous Transmitter Development.