## Tuesday, 27 June 2017

### The Low Power Setup

With most of TT7F's features coded and tested it was time to finalize the setup with low power routines and a self-sustaining power source.
While putting together additional trackers I used that opportunity to look more closely into the current consumption of individual parts as I was adding them to the board. Things were according to the datasheet expectations with TPS63031, the main converter, and LTC3105, the MPPC solar converter (values in micro-amps).
However, after adding the MCP1700T, which supplies the board with 3.3V when connected via USB, I discovered relatively significant consumption increase in some of the trackers (4.49mA in the example above) while in others the consumption increased only by tens of micro-amps. Much later I found a dependency between the actual voltage generated by TPS63031 and the increased consumption. More the voltage differed from 3.3V, higher the consumption was. A diagram in MCP1700T's datasheet shows a diode across a transistor which I assume leaks the current when Vin is disconnected and Vout is at the voltage supplied by TPS63031. On the plus side this additional current consumption should be eliminated when the programming piece of board is snapped off in the final configuration.

Power Modes - SAM3S
ARM_POWER_SAVE.h
ARM_POWER_SAVE.c
If the MCU is erased and the finished board is powered up, the consumption is quite high as evidenced by the second row in the table below. This is predominantly caused by the microcontroller and GPS module. The MCU, being a permanent current consumer, is the first thing to look at closely. During the active periods some power saving can be done by running the chip at minimum speeds required by the specific application. For example the only time the MCU has to run at 64MHz is when sampling an image output by the camera module. During radio transmissions, which take up the most time, it's fine to run it at the XTAL frequency (12 or 16MHz depending on the physical crystal choice). For the resting periods SAM3S offers three low power modes out of which I use the WAIT mode. As opposed to BACKUP, this mode continues after waking up where it finished executing instructions while consuming datasheet stated 20uA. The intricacies of entering WAIT mode are described in the datasheet or taken care of in PS_enter_Wait_Mode() function. One requirement is switching the main clock to fast RC oscillator before calling it. After waking up the MCU runs at this RC oscillator's 4MHz clock frequency. The PLL offers a variety of frequencies for the MCU to run at and can be set up with PS_SystemInit() function according to rules described in the library.

F3 F5 F8 F9 F10
erased chip 58.1 57.5 72.8 99.1 67.2
PLL 64MHz 30.7 29.6 37.0 43.5 32.8
XTAL 12/16MHz 8.0 7.3 12.5 16.6 7.8
PLL 1MHz 5.5 2.8 8.1 14.0 3.1
WAIT mode 2.9 0.8 5.5 11.4 0.4
12MHz 16MHz 16MHz 12MHz 16MHz
3.32V 3.33V 3.38V 3.40V 3.31V

With only the second row exception these are all results of measuring current consumption with the GPS module in backup mode, in other words, at least consumption. The MCU was put in each mode doing nothing else for 10s over which average consumption was measured. The table also contains the specific XTAL used on individual boards and the main operating voltages as supplied by TPS63031. A significant variability can be seen among the boards. Tests on a separate MCP1700T suggest that at least a portion of the excess current on some of the boards could be attributed to MCP1700T leaking current when operating voltage deviates from 3.3V. Also, F9 is equipped with a Biwin GM10 GPS module instead of a Ublox MAX-M8Q which may be partially responsible for the higher consumption. Another means of controlling the power required by the MCU lies in enabling and disabling peripheral clocks as they are needed. The datasheet states current consumption per every MHz of operating frequency for each peripheral. Once again higher the frequency, higher the total consumption. With the exception of System I/O lines all pins of the MCU are set as input with a pull-up enabled after reset. Generally I try to turn peripheral clocks off and re-enable the pull-ups on pins when I am done using the specific peripheral. Avoiding free floating pins and enabling pull-ups or pull-downs instead on pins set as input, or setting pins as output is the way to limit undesirable consumption as I come to understand.
To shed some light on the marking of TT7F boards I use here: F1 is the first board used mostly for programming and testing. F2 was lost in the August flight. F3 is an old board with ATSAM3S8 from the original batch I made. F4, F6 and F7 were equipped with three faulty ATSAM3S4 MCUs and never worked. F5 is the only ATSAM3S4 board that works. F8, F9 and F10 are the new v1.5 boards with ATSAM3S8. F3, F5, F8, F9 and F10 are being prepared for superpressure flights.

Power Modes - UBLOX
ARM_UBLOX.h
ARM_UBLOX.c
The second continuous current consumer is the GPS module. I didn't design a hardware power cutoff on the board so any power saving has to be implemented in software. According to the datasheet the Ublox module is by default configured for the 1575MHz L1 C/A signal upon which the Navigation Message is modulated at 50bit/s. By receiving these messages the module acquires GPS date and time, Ephemerides of the specific satellites it is locked on and parts of Almanac. The module is equipped with 72 channels which means it can search for all the GPS satellites (31) at the same time. The average time to receive Ephemeris from a visible satellite is stated to be 27s and is valid for no longer than 4 hours. Its purpose is to give the precise satellite orbit for the following calculations. The module requires at least four satellites for a 3D solution. That means that at ideal signal conditions it requires at least the datasheet stated 29s to output position after a cold start (no previously acquired information). The Almanac takes up to 12.5 minutes to receive and because it contains only coarse orbits and other data it is valid for up to 180 days, however its acquisition isn't essential for a navigation solution. The receiver also provides several "Dynamic Platform Models" selectable in UBX-CFG-NAV5 message. These modes differ in their limits such as maximum altitude, maximum horizontal or vertical speed. For high altitude balloon purposes it is necessary to set the module to one of the Airborne modes (max altitude 50000m, horizontal/vertical speed 100m/s for Airborne <1g) otherwise it operates in the default Portable mode which is limited by a 12000m ceiling. In the following several paragraphs, however, I'd like to address the power saving modes U-blox modules have to offer.
I wanted to make an overview of available modes and settings in terms of current consumption. Once again I used Arduino DUE to calculate current from the measured voltage drop across a 1Ω shunt resistor (250 averaged samples per every 250ms). I set up the F5 board to run at 2MHz PLL and for initial 10s switched the U-blox module to backup mode to get current consumption of the tracker itself. Subsequently I woke the U-blox up and initialized the tested power mode.
The first data come from measuring the consumption in the default Continuous mode without any power saving. The module runs a slightly more power demanding Acquisition engine to search for satellite signals either during a cold start or when it has insufficient signals for navigation. Else it runs Tracking engine that does the signal measurements to produce a positional fix. The signal acquisition is noticeable in the above consumption data during the first minute. The data points were reduced by the tracker's steady state consumption as measured during the initial 10s so they should represent 5s average consumption (the averaging doesn't hide any signifficant spikes in this case) of just the U-blox module.
Cyclic Tracking is the first Power Save Mode intended for short period fixes between 1 to 10s. The module in this setting first runs the Acquisition engine, then the Tracking engine and eventually transitions to Power Optimized Tracking with the preset position update period. I measured the whole range of periods and with the exception of 1s and 2s settings the consumption during Power Optimized Tracking seemed comparable (or below the resolution or error of this measuring approach) - about 5mA. The occasional peaks in consumption correspond to moments when the receiver exited the Power Optimized Tracking and returned to either the Tracking or Acquisition states to acquire better signals. Polling UBX-NAV-PVT and reading Fix Status Flags, specifically the psmState bits, confirms this. The data points represent 5s average consumption just like the previous chart (again the averaging doesn't hide any significant consumption spikes just makes the chart clearer to read). As for the 2s setting's noticeably lower consumption I have no explanation for that. A repeated measurement showed a similar result.
ON/OFF is the other Power Save Mode intended for fix periods longer than 10s. Once again the module first cycles through Acquisition and Tracking states to produce a positional fix after which it enters Inactive state and waits for the next time to produce a new fix. One catch with this mode is that it requires UBX-CFG-CFG message to save the current configuration immediately after entering the power save mode otherwise the module wakes up with the default configuration outputting NMEA messages and forgetting it was configured for power saving. To make the two plots above I programmed the U-blox module to produce a valid fix then transition to the Inactive state with the update period set to 0 meaning it would wait for an external event to wake up. I would then wait for 30 (blue) or 60 (red) seconds before waking it up and repeatedly polling UBX-NAV-PVT until it returned a valid positional fix. In this case the data points represent 1s average current consumption to preserve the short consumption peaks.
In long term operation the module faces an issue of expiring ephemerides for individual satellites and a need to download valid ones. For this there is updateEPH bit that can be enabled to allow the module download the data in regular intervals. The plots in the chart above show the module running the same ON/OFF setup as previously but this time with updateEPH enabled. Comparing the two consumption charts it seems the module took liberty to download additional data a few times in the 30s case and once in the 60s case. This is probably dependent on the specific satellite arrangement and signal strengths. I haven't tested how exactly the module behaves after the ephemerides expire (~4 hours) without updateEPH enabled.
The last power saving approach I tested was manually forcing the module to Software BACKUP mode with UBX-CFG-PWR message. The documentation doesn't seem to comment on whether the Software Backup and Inactive state are the same or comparable. Nevertheless upon being awakened the module outputs the default NMEA messages and so requires the UBX-CFG-CFG message to save the desired configuration as in the case of the ON/OFF mode. It seems to preserve ephemerides and thus can be used as a genuine power saving approach. The data represent 1s average consumption while the module was repeatedly polled for UBX-NAV-PVT until valid positional fix. Then forced to the Software Backup mode for 30 (purple) or 60 (yellow) seconds before being woken up to repeat the cycle.

Mode 5min avg
Mode 5min avg
Continuous 22.2 mA mA Cyclic 1s 10.6 mA
Cyclic 2s 5.1 mA
Cyclic 3s 6.2 mA
Mode 15min avg Cyclic 4s 8.0 mA
ON/OFF 30s 3.7 mA Cyclic 5s 8.5 mA
ON/OFF 60s 2.9 mA Cyclic 6s 8.0 mA
ON/OFF 30s E 5.9 mA Cyclic 7s 8.9 mA
ON/OFF 60s E 2.8 mA Cyclic 8s 10.3 mA
Backup 30s 3.7 mA Cyclic 9s 8.2 mA
Backup 60s 2.7 mA Cyclic 10s 8.6 mA

The table shows average current consumption of the whole test for the individual modes. The LiPo supplying the tracker was at 4.01V. The Cyclic Tracking is particularly influenced by how many times and for how long the module exited the Power Optimized Tracking to search for better signals. Otherwise ON/OFF and manual BACKUP modes are favourites for the final implementation.

There is a couple of intricacies in setting up the Power Save Modes. I'll outline how I do it on TT7F. First I mention the name of a specific message, then in the parentheses the names of arrays that hold the configuration messages in the library above.
UBX-CFG-PRT (setNMEAoff[], setNMEAon[]) the module by default repeatedly outputs several NMEA messages that get in the way when parsing UBX protocol responses. This message can configure the module to output only the desired protocol.
UBX-CFG-GNSS (setGPSonly[]) according to the datasheet in protocol versions less than 18 (my modules are v15) Power Save Mode is supported only for GPS. That means that the other systems such as GLONAS, SBAS, etc. have to be disabled before entering PSM.
UBX-CFG-PM2 (setCyclicOperation_1s[], setONOFFoperation_perm[], etc.) this message selects the specific PSM, the update period, and it has to be configured before enabling PSM in UBX-CFG-RXM. Aside from the previously mentioned settings I always enabled doNotEnterOff bit to force the receiver to stay in Acquisition mode until it acquires a valid fix. This is also the message to enable updateEPH if desired.
UBX-CFG-RXM (setPowerSaveMode[], setContinuousMode[]) this is the message that actually switches the module between the predefined Power Save Mode and the Continuous Mode.
UBX-CFG-CFG (saveConfiguration[]) saves the current receiver configuration to internal Battery Backed RAM so the module upon waking up from Inactive or Software Backup modes can load it. In the ON/OFF PSM case it is necessary the message immediately follows setPowerSaveMode command.
UBX-CFG-PWR (setSwBackupMode[]) used to force the module into Software Backup mode. Waking up is done by rising or falling edge on the RXD1 pin, in other words by sending the module a dummy byte and providing it 500-1000ms to ensure reception of the following commands.
UBX-RXM-PMREQ (setBackupMode[]) another message to force Backup mode. I used this on MAX7 modules that didn't respond to UBX-CFG-PWR.
UBX-NAV-PVT (request0107[]) this message polls a complete navigation solution that contains year, month, day, hour, minute, second, fix type, PSM state, number of satellites, longitude, latitude, altitude, ground speed and heading.
I found that the best way to get the UBX messages in the desired configuration (other than manually putting them together and having to calculate the checksum) was by downloading U-center, a piece of software provided by U-blox, which could construct them for me in a HEX format.

Shutdown/Standby - Si4463 & MT9D111
ARM_MT9D111.h
ARM_MT9D111.c
ARM_SI4060.h
ARM_SI4060.c
In case of the transmitter (Si4463 and Si4060 are pin and to extent software compatible) all that needs to be done in terms of power saving is shutting it down when not in use. The Shutdown state is controlled by the SDN pin and the whole process is taken care of in SI4060_deinit() function. The function enables pull-up on ATSAM3S8's PB4 pin connected to GPIO1, resets the transmitter via the SDN pin to its default state and disables output on ATSAM3S8's PA8 pin which powers the TCXO. Re-initialization is done by SI4060_init() function which reverses the process. A couple of illustratory consumption plots can be found in The TT7F v1.5 Revision blog post.
The situation with MT9D111 camera module is similar. MT9D111_init() function initializes ATSAM3S8's pins connected to the camera (disable pull-ups, enable Parallel Capture Mode control). Subsequently a clock signal is provided to the camera via a PWM pin and PWM_init() function, the camera is reset and is either set up to output an image or ordered to a Standby state using MT9D111_standby() function. Disabling the PWM clock signal again the consumption decreases to the tracker's steady state power usage. There are two ME6211 regulators supplying the camera which should in total continually consume datasheet stated 100uA. A consumption plot with the camera module in use can be found in SSDV Slow Scan Digital Video blog post.

Solar Cells
The self-sustaining power supply is provided by LTC3105, a supercapacitor or a LiPo battery, and solar cells. At float altitudes the tracker can expect clear sky throughout the whole day. The on time is dependent on the Sun rising to a sufficient angle for the panel to generate enough power and the capacity of the supercap or battery for when the Sun sets again. The Sun's angle above horizon is determined by the tracker's current latitude and season of the year - the Earth's inclination to the incoming solar radiation. For example a floater at high latitude during winter time may experience only brief windows of activity around local noon.
There is a number of different types of solar cells available ranging from Monocrystalline, Thin-film all the way to multi-junction cells all with different efficiencies and price tags. I turned to the cheapest easily available solution, the Polycrystalline cells sold in 20, 40, 100 pieces per pack in all sorts of sizes on Ebay. They are most often described as Grade B solar cells apparently meaning that they can have minor visible defects though the electrical performance should be according to specification.

Collective Specs
Thickness 200 um
Efficiency 17.6 %
Temp. Coeff. of Voc -0.241 %/k
Temp. Coeff. of Isc 0.033 %/k
Temp. Coeff. of Pmax -0.37 %/k

These are collective specs for all the different sizes of Polycrystalline cells (though they are Chinese Ebay specs, so who knows). Since the cell's efficiency is dependent on temperature the coefficients represent the percentage change in open circuit voltage, short circuit current and maximum power per one kelvin change in temperature. Reading about the test conditions there is a standardized methodology for evaluating solar cells consisting of exposing the tested cell to 1000W/m2 irradiance with AM1.5 spectral composition and cell temperature of 25°C.
This chart illustrates the solar radiation arriving at the top of Earth's atmosphere designated AM0 (orange) and the remaining radiation AM1.5 (red) that makes it through to the surface on a cloudless day at noon with the Sun at 41.8° angle above horizon. The blue and purple lines represent the power converted by a Polycrystalline and a Monocrystalline cell respectively into electric power. The irradiance data come from a defined standard of Extraterrestrial Irradiance (AM0) totaling 1348W/m2 and Global Tilt Irradiance (AM1.5) with 1000W/m2 in total. The cell data were extracted from Monocrystalline and Polycrystalline spectral response curves and applied to the AM1.5 irradiance data corresponding to 17.34% (poly) and 23.94% (mono) cell efficiency.

° zenith ° horizon AM W/m2
0 90 1.0 1053
30 60 1.2 1015
45 45 1.4 958
60 30 2.0 851
70 20 2.9 721
75 15 3.8 621
80 10 5.6 479
85 5 10.3 265
90 0 37.9 23

The Air Mass parameter represents the path length through Earth's atmosphere the incoming radiation has to travel. It is bound to the Sun's zenith angle and directly affects the final solar intensity. The table above provides several illustratory values for different Sun angles above horizon (based on Kasten and Young air mass model). For a floater purposes the eventual float altitude has to be taken into account. There is a couple of models that try to estimate AM at a given altitude, however, they produce intensity values equivalent to the Extraterrestrial Iradiance (1348W/m2) inside 9km of altitude already which is well below the expected flight levels of 11-16km. Given that and guessing the majority of attenuation in the wavelengths the cells are most sensitive to happens at lower altitudes I intend to use the 1348W/m2 intensity value in further estimates on a balloon at float altitude.

Since a superpressure balloon launched from the Czech Republic (~49°N) will most likely spend its time in the northern portion of the Northern Hemisphere, I am basing this on observations of the UBSEDS flights and flights from the northern USA and Canada, I put together these maps to quickly provide estimates of the Sun's angle above horizon and hence irradiance throughout the year. One map is the situation on the Winter Solstice (the Summer Solstice being the same in reverse) and the other on the Vernal Equinox (the Autumnal Equinox being identical). The lines designate the latitudes at which the Sun appears at 5°, 15°, 25° and 90° angle above horizon during local noon. The times then mark the moment the Sun rises above 5° angle and later sets below 5° angle as viewed from that spot. All times are GMT.
Back to the Polycrystalline cells. The terms most likely to come across in solar cell specifications are:
• Voc - the open circuit voltage measured across the solar cell's terminals.
• Isc - the short circuit current measured between the solar cell's terminals.
• Vmpp - the maximum power point voltage of a loaded cell.
• Impp - the maximum power point current of a loaded cell.
• Pm - the maximum power which equals Vmpp * Impp.
• Efficiency - the cell's electrical output divided by the incident light power. It depends on the specific solar cell technology/materials used (single-junction, multi-junction, monocrystalline, polycrystalline, GaAs, CdTe, etc.).

X (mm) Y (mm) A (mm2) Vmpp (V) Impp (A) Pmpp (W) mW/cm2
39 19 741 0.50 0.24 0.12 16.2
52 19 988 0.50 0.28 0.14 14.2
39 26 1014 0.50 0.34 0.17 16.8
52 26 1352 0.50 0.43 0.22 15.9
78 19 1482 0.50 0.50 0.25 16.9
39 39 1521 0.50 0.52 0.26 17.1
52 38 1976 0.50 0.56 0.28 14.2
52 39 2028 0.50 0.68 0.34 16.8
78 26 2028 0.50 0.68 0.34 16.8
52 52 2704 0.50 0.86 0.43 15.9
78 52 4056 0.50 1.36 0.68 16.8
156 26 4056 0.50 1.12 0.56 13.8
78 78 6084 0.50 1.87 0.94 15.4
156 39 6084 0.50 2.00 1.00 16.4
156 52 8112 0.50 2.74 1.37 16.9
156 78 12168 0.50 4.10 2.05 16.8
156 156 24336 0.50 8.60 4.30 17.7

These are specifications as provided by various Ebay sellers I collected for different cell dimensions. Allegedly these should be maximum power point measurements, however, based on my own measurements on delivered cells I'd say they are rather the open circuit voltage, short circuit current and their product. The last column then provides a comparison of the provided specs in terms of mW/cm2 for individual sizes.
I bought two different sizes for testing, one pack of 52x26mm and another of 52x38mm cells. As an initial estimate I expected to use 2-4 cell configurations which should have provided 0.44-1.12W at maximum to power the tracker. The diagram above illustrates the I-V curve of a single solar cell and the effect of wiring two cells in series or parallel. A solar cell outputs DC and the amount of current is proportional to the size of the cell and the instantaneous irradiance. The voltage is the same for all sizes, but differs from cell technology to technology. The maximum power output will always be less then the product of Voc and Isc, because if too much current is drawn from the cell, its voltage collapses. That is where the MPPT converter (LTC3105) comes in to dynamically adjust the load resistance to accommodate to the ever changing irradiance. By doing so it draws at maximum only so much current to maintain a specified level of voltage on the cells.
The first option is connecting the cells in series. This accomplishes increasing the voltage (to ~1V in case of 2 cells and ~2V in case of 4) while maintaining the same current or outputting the maximal current of the smallest cell in case of wiring cells of different sizes together.
The other option is connecting the cells in parallel. The image above shows a setup of two parallel branches with 2 cells in series each. Such setup would output ~1V and twice the current. However, the idea behind this configuration is to position each branch at an angle (45° for example) one facing towards and the other away. In contrast the series wired panels would be set up to face directly upwards, parallel to ground (90° above horizon). The reason is to try to capture enough light from the Sun while it is at a low angle. The series setup needs the Sun to by higher to receive equivalent irradiance. Facing each branch in a different direction is necessary since the rotation of the tracker cannot be controlled.
Pondering on the implications of different configurations brings up the effect of shading. In a series setup if one of the cells gets shaded, the overall current output drops to the current outputted by the shaded cell and the excess current from the illuminated cells reverse biases the shaded one. In a parallel setup if one branch is shaded, the other still supplies the load. However, depending on the load resistance a portion of the current flows into the shaded cells. In big solar panels containing tens of individual cells these effects are limited by the usage of blocking and bypass diodes. However, in 2-4 cell setups the inherent forward voltage drop of the diode represents a significant portion of the voltage provided by the cells. In the images above I measured the current flowing between two parallelly connected branches, one shaded the other illuminated, to be ~35mA in case of the 52x26 cells and ~41mA in case of the 52x38 cells.

These are circuit simulations of four serially wired solar cells in four different states to illustrate the currents and voltages. The first two simulate fully lit solar cells in basically short circuit and open circuit states. The latter two then a situation where the bottom cell is shaded. Building the circuit at Falstad gives a better, more dynamic idea of how the currents flow.

These are the same circuit simulations of two parallely connected branches with two solar cells each. It is not apparent from a still image, but the 10mA current flows from the shaded cells when the setup is short circuited, while the 25.3mA current flows into the shaded cells when the setup is open circuited. This behaviour leads to dissipation of power in the cell and its heating. Though in just 2-4 cell setup, I'd hazard a guess, it is probably not as much of a problem as in solar panels with dozens of cells.

Voc (V) Isc (A)
2x 52x38 (flux) 1.11 0.39
2x 52x26 (1) 1.14 0.40
2x 52x26 (2) 1.14 0.41
2x 52x38 (1) 1.11 0.54
2x 52x38 (2) 1.15 0.53
4x 52x26 2.31 0.40
4x 52x38 2.28 0.59
2x 2x 52x26 1.11 0.80
2x 2x 52x38 1.10 1.16

These are the values for different configurations measured around noon on a day with clear skies. The row denoted 'flux' represents a measurement on a pair of cells that ended up stained with flux after soldering them together and a following attempt to clean them with Isopropanol left them temporarily dark.

P Pmax Vout 3.3V (Vin 1V) Vout 5V (Vin 2V)
Voc*Isc 70% 1mA 72% 10mA 79% 50mA 68% 1mA 74% 10mA 78% 50mA 81%
2x 52x26 0.467 0.327 0.235 0.258 0.222
2x 52x38 0.610 0.427 0.307 0.337 0.290
4x 52x26 0.924 0.647 0.479 0.505 0.524
4x 52x38 1.345 0.942 0.697 0.734 0.763
2x 2x 52x26 0.888 0.622 0.448 0.491 0.423
2x 2x 52x38 1.276 0.893 0.643 0.706 0.607

This table provides a quick idea of the potential power at LTC3105's output (W). For this purpose Pmax was approximated to 70% of the product of Voc and Isc. LTC3105's input range of 0.25-5V suggests a possibility of using just one solar cell to up to about eight cells. The output set by a feedback voltage divider can be anywhere from 1.6V to 5.25V. The table illustrates several configurations with LTC3105's efficiencies at different conditions as found in the datasheet. The percentage values represent efficiency while the mA value the output current.

52x26 52x38
°horizon W/m2 2c W 4c W 2c W 4c W
90 1348 0.337 0.674 0.492 0.984
70 1267 0.316 0.633 0.463 0.925
50 1033 0.258 0.516 0.377 0.754
35 773 0.193 0.386 0.282 0.565
25 570 0.142 0.285 0.208 0.416
15 349 0.087 0.174 0.127 0.255
5 119 0.030 0.059 0.043 0.087
1 24 0.006 0.012 0.009 0.017

This table provides LTC3105's power output estimates (W) under different Sun angles. Since it is an attempt to estimate power at float altitude of 11-16km I am for the sake of simplicity ignoring atmospheric absorption and using the Extraterrestrial irradiance of 1348W/m2 adjusted for the angle of incidence. The calculation assumes 75% LTC3105 efficiency and provides results for 2 and 4 cell systems.
These models illustrate the different configurations of the solar cells on a tracker. In the setup on the left the cells are at 0° angle to ground and face directly upwards. This is ideal for a series connection among the individual cells. The setup on the right should be wired parallelly, because insolation of the branches will be unequal most of the time. The advantage of this setup comes up during low solar angles.
These charts provide a comparison between 4 cells wired in series at 0° angle to ground (red) and the parallel configuration with the cells at three different angles (blue). A major assumption in the calculations is that the Sun faces one of the branches directly. Any rotation or misalignment of the tracker with respect to the Sun will decrease the output power. The data suggest that especially for winter time and high latitudes the parallel setup may be advantageous.

A couple of notes on soldering the cells together. It may be their cheap Ebay origin, but I couldn't properly solder most of them, despite using plenty of flux, until I scratched the surface a little to expose the metal. After that the solder finally stuck. They are also very fragile and break easily.
For connecting the test cells I used a tabbing wire which is easy to get on Ebay. It is useful since it's already tinned. The image on the left indicates how to wire the cells. They all have the negative terminal on the top side and the positive terminal on the bottom side. For the tracker setup I'll use a combination of isolated firm and thin wires similar to what can be seen in the image on the right. This is also the flux covered pair of cells mentioned previously. The residue is quite apparent.
The flux that worked alright for me (left image) was again from Ebay and generally sold and advertised along with the cells. To minimize any potential stains I usually applied it to the tabbing wire rather than the cell. I generally use the flux on the right for SMD and ordinary soldering and then clean it with isopropanol, but in case of the solar cells it turned out to be a bad combination.
Note. The values in the last two tables above assume Pmax out of the solar cells to be 70% of Voc * Isc. In actual measurements with these types of cells and my specific setup Pmax was inferred to be about 48% of Voc * Isc.

Supercapacitors
Supercapacitors should be more tolerant than LiPo batteries to the low temperatures the tracker experiences during nighttime. Throughout the day the Sun, aside from powering the setup, heats the electronics to their operating range. The negative side of supercaps is the inherently smaller capacity which generally means the tracker shuts down at some point after sunset.
To start somewhere I bought a bunch of 2.7V 15F and 40F Electric Double-Layer Capacitors (EDLC) rated to -40°C, specifically Enycap 220 series by Vishay. Their size in comparison to the tracker can be seen in the images. In case of using two of the 40F caps the whole setup can get quite massive.

Enycap
220 series
U
(V)
U1s
(V)
C
(F)
Tol.
(%C)
ESR
(mΩ)
IL0.5h
(mA)
IL72h
(mA)
E
(Wh)
M
(g)
MAL222090003E3 2.7 2.85 15 -20/+50 40 6 0.075 0.015 5.75
MAL222091001E3 2.7 2.85 40 -20/+50 18 20 0.200 0.041 9.65

Connecting two same supercapacitors in series increases the maximum voltage (2 * 2.7V -> 5.4V), decreases the capacity (2 * 40F -> 20F), the ESR increases (2 * 0.018mΩ -> 0.036mΩ) and the total leakage current stays the same (0.2mA). Connecting them in parallel leaves the maximum voltage the same (2.7V), increases the capacity (2 * 40F -> 80F), decreases the ESR (2 * 0.018mΩ -> 0.009mΩ) and increases the total leakage current (2 * 0.2mA -> 0.4mA).
The supercapacitor connects to LTC3105's output and to TPS63031 which is the main buck-boost converter supplying the board with 3.3V. Its minimum input voltage for startup is 1.8V and maximum 5.5V, however, once running it was repeatedly seen working down to ~1.55V at input. The converter's efficiency is between 75-90% depending on Vin.
Energy (Ws) 2.70V 5.25V
1x 15F 54.7
1x 40F 145.8
2x 15F parallel 109.4
2x 40F parallel 291.6
2x 15F series 103.4
2x 40F series 275.6

All these electrical characteristics offer a number of options evaluated in the table above. It shows the energy in Ws held by the specific setup at the stated voltage. In the case of two caps in series 5.25V was chosen rather than 5.4V, because it is the maximum LTC3105 can output.
The series wiring brings about a problem with imbalance between the two caps. If the capacitors differ in capacity, which given their stated tolerance (-20%/+50%) is likely, the voltage on individual caps will differ potentially exceeding the maximum voltage tolerable by a single cap. The equation above allows to calculate the worst case scenario based on the datasheet values. There is a number of balancing solutions. However, passive balancing with bypass resistors seems to either not balance the voltages quickly enough or leak too much current. Active balancing on the other hand requires too many additional parts. For simplicity I intend to limit the charging voltage at the expense of maximum energy held to ensure even imbalanced caps stay under 2.7V individually. At charging voltage of 4.1V even the extreme case charges the supercap with less capacity to 2.65V. Not expecting the worst case scenario a charging voltage of 4.5-4.7V should be doable without additional balancing.
Runtime (min) 2.70V 4.50V
1x 15F 25
1x 40F 65
2x 15F parallel 49
2x 40F parallel 131
2x 15F series 45
2x 40F series 119

The equation above calculates the time for which an application can source constant power from the charged supercap. The power used for the table was based on a test script and totaled to 0.025W. The minimum voltage was TPS63031's 1.55V and the charge voltage was dependent on the specific setup. The durations in the table are in minutes.
Some circuits with supercapacitors require a current limiting resistor so the empty cap doesn't try to source amperes of current initially. This isn't needed on TT7F, because the current is limited by LTC3105 itself and how much current it can output momentarily.
The setups I used to test the different solar cell and supercap combinations all looked similar to what can be seen in the images above. I had the tracker transmit solar and supercap ADC readings via 300 baud RTTY collecting the data in dl-fldigi. The tracker ran even without a supercap with only the solar cells, but just a short shading meant loss of power and a restart.
For illustration the chart on the left shows the tracker running a script that continuously transmitted the ADC readings. However, the consumption was too high so the supercap got never fully charged. Instead, the tracker started once the voltage reached 1.8V and shut down again when the voltage fell below 1.55V. Then about 70s later the supercap got once more to 1.8V repeating the cycle. The chart on the right shows the same setup running a more efficient script. Transmitting only once per 12s and staying in the wait mode for the remainder of the time allowed the supercap to fully charge. I then covered the solar cells and measured the time the tracker stayed in operation which more or less matched the previous estimates.
Larger the capacitance longer can the tracker operate once the solar cells no longer receive sufficient insolation. However, the initial time to charge the supercapacitors to at least 1.8V increases as well as can be seen in the rather extreme example above. Using just two 52x38 solar cells required 38 minutes to begin the first transmissions with two 40F supercaps in parallel. And that was around noon with ideal irradiance.
The difference between two supercaps connected in series or in parallel lies in the higher charging voltage in the series case and TPS63031's higher efficiency when down-converting to 3.3V compared to boosting the output from lower voltages. Whether it's worth the trouble of dealing with balancing or accepting the lesser efficiency is up to the specific application.
Concerning the long start times with the supercaps, or rather the time it takes to charge the empty cap to at least 1.8V at which the tracker begins to operate, it may not be as bad as it seems at first glance. In reality when the supercap's voltage falls to ~1.55V the tracker stops and it also stops draining the cap. So when the solar panels receive sunlight again they have to charge the cap only from ~1.55V to 1.8V to restart the tracker. I tested this by putting the 15F supercap in a freezer (-18°C) for 3 hours after it stopped supplying the tracker. Then when I re-connected it back, the two 52x38 solar pannels restarted the tracker in about 20 seconds. This was with ideal insolation, so the conditions aren't exactly comparable to sunrise, but it makes the point.

Lithium Polymer Batteries
Lithium polymer rechargeable batteries offer higher capacity at a comparable mass potentially being able to supply the tracker throughout the night. However, they don't do well with low temperatures which are inevitable at the expected float altitudes. Based on sounding data from mid Europe and Arctic latitudes the air temperature at 11-16km fluctuates between -40°C to -70°C throughout the year. It doesn't change much day to night, but absorption of the Sun's radiation seems to, according to on-board sensors, rise the temperature of the electronics to even several degrees above zero during the day. The operating tracker also generates some amount of heat which in combination with the substantially less dense air could maintain some warmth. However, in case of the low power setups the current draw is limited and the produced heat is insufficient. The tracker most likely comes close to the temperature of the surrounding atmosphere at some point during the night.
Despite that Lithium Polymer batteries have been used on floaters in the past. Particularly Leo Bodnar eventually worked his way to some specific low temperature LiPo batteries and his last flights went on for months.

Cellevia mAh Vmax Vcut Cchrg Cdis Cycles °Cchrg °Cdis Wh g
LP601730 250 4.2 2.75 1 1 300 0/+43 -10/+55 0.925 6.0
LP403035 400 4.2 2.75 1 1 300 0/+43 -10/+55 1.480 8.4

For starters I ordered a couple of LiPos the local electronics distributor had in stock. They are by Cellevia Batteries and have integrated protection circuit module which cuts off the cell if the voltage falls below 2.75V. This is important, because TPS63031 would otherwise try to drain it to about 1.55V which would destroy the cell. Apparently under-voltage leads to the electrodes dissolving into the electrolyte potentially causing shorts.
The expected discharge while powering the tracker is a few milliamps during idle periods with several seconds in the range of 50mA when the GPS module is active or the tracker transmits. In case of using the camera the consumption can rise to about 150mA for a few seconds when the tracker takes an image followed by several minutes of continual transmission in the range of 30-50mA. Image taking should thus be restricted to day time only, because the falling temperture will decrease the battery's capacity, voltage and will increase the battery's internal resistance limiting the instantaneous power output. Batteryuniversity.com states the capacity loss of Li-ion cells to be about 17% at 0°C, 34% at –10°C and 47% at –20°C.
According to the datasheet charging should occur at 0°C to 43°C and should consist of providing constant current of 0.2C to the cell until it reaches 4.2V. Then providing constant voltage of 4.2V until the current falls below 0.05C. All this taking up 8 hours. Or quick charging the same way at 0.5C current in 2.5 hours. This is, however, unlikely to happen with solar cells and the Sun gradually rising above horizon and slowly heating the tracker from freezing temperatures.
The main danger seems to be permanent Lithium plating on the anode. If charging at very low temperatures, the ions instead of intercalating into the graphite electrode get deposited on the surface. This decreases the capacity and potentially forms dendrites which may eventually short the electrodes together. However, this article states that below freezing temperature charging is possible with most of Li-ion cells, but only at very low currents. It then mentions an example rate of 0.02C at -30°C. Arguably the current initially provided by the rising sun could be proportionally small.
With the negative electrode generally made from graphite C6 on a Copper sheet, the positive electrode made from LiCoO2 on an Aluminium sheet, it is apparently the electrolyte and its additives that provide variability in terms of performance of the resulting cell. There should be mixtures allowing the battery to operate to -40°C on the market. Though it may require some digging. The cells I have most likely aren't low temp, but I consider it worth it to test them on one or two flights.
According to What Causes Li-ion to Die charging to only 3.92V maximizes the battery's longevity, but as a result provides only about 60% capacity. It may be worth a try.
Another option to test is connecting a smaller supercapacitor in parallel with the battery. In this way the supercap could satisfy the instant current demand during TX periods while slowly recharging during idle periods relieving some of the demands on the battery overnight.

Timing the Power Modes
ARM_RTT.h
ARM_RTT.c
ARM_RTC.h
ARM_RTC.c
In principle there are more ways to schedule transmissions and low power periods. One for example is to synchronize tx to the start of every GPS minute. Another way is to simply wait a preset duration between transmissions.
The Real-time Clock (RTC) peripheral in principle offers, after initial synchronization with GPS time, means of timing the transmission and wait periods. Unfortunately, in case of TT7F the clock is driven by an internal RC oscillator which is inaccurate and temperature sensitive. As a result the clock on the tested tracker lags 12s every minute at room temperature. This would most likely further fluctuate as the tracker got colder at night and warmer in sunlight. The Real-time Timer (RTT) is driven by the same RC oscillator and hence suffers from the same downfall.
For these reasons and no actual need to synchronize transmissions to GPS time I decided for simplicity. The RC oscillator's inaccuracy and the fact that the GPS module spends the idle periods in backup mode mean the tracker can't at any moment immediately know the precise time without wasting power on additional activity of the GPS module. Hence I chose an RTT timed Wait mode period which adds to more or less one minute cycle with average GPS fix and transmission durations included. The time it takes the GPS module to acquire fix upon waking up is the most variable factor. I also added a condition which prolongs this cycle to about two minutes if the solar panel voltage falls below a defined limit.

Watchdog
ARM_WATCHDOG.h
ARM_WATCHDOG.c
Watchdog provides a safety feature in case some part of the code gets stuck. It is a timer the application periodically restarts, otherwise the timer runs out (the code got stuck somewhere), the Watchdog resets the MCU and the code execution starts from the beginning again. It uses the microcontroller's Slow Clock divided by 128 which is driven by the internal RC oscillator. That means it suffers from the same inaccuracies as RTC and RTT.

void WATCHDOG_disable(void)
{
WDT->WDT_MR = WDT_MR_WDDIS;    // disable WatchDog
}


Watchdog is enabled by default so in case the application doesn't need it, it has to be disabled at the beginning of the code.

void WATCHDOG_enable(uint16_t period, uint8_t idleHalt)
{
period &= 0x0FFF;    // WatchDog Timer is 12-bits

WDT->WDT_MR = (idleHalt << 29) | (period << 16) | WDT_MR_WDRSTEN | (period << 0);
}


In case it does use it this function sets up the timer's period (4ms - 16s). The IDLEHALT bit allows employing Watchdog in applications with long sleep periods such as this one by stopping the timer when the system is in Wait mode. Watchdog can be programmed only once in the code.

void WATCHDOG_restart(void)
{
WDT->WDT_CR = (0xA5 << 24) | WDT_CR_WDRSTT;    // restarts the WatchDog
}


This function serves to restart the timer and has to be called at logical places to allow normal operation. The calls are application specific and will depend on whether SSDV is used, or not, on how long it takes to transmit RTTY telemetry, on how long it takes to get the GPS lock, etc.
It is a question whether it is necessary to use Watchdog at all. At least in case of supercap setups there is a guaranteed MCU reset every night when the power runs out. So unless it is a frequently reoccurring failure the next day provides a fresh start.

Software
ARM_TT7F1.c
This is the main code running the first low power tracker built and described in this blog post callsigned TT7F1. The core blocks of the code are expected to be the same in the other setups as well. There will be minor differences in limits, timing, power saving schemes, etc. in the individual trackers. A couple should also have an additional SSDV block.
At Power-Up, when the voltage on supercap rises above 1.8V, the MCU initializes its main clock and the delay timer to 2MHz. This frequency is sufficient for most of the tasks and brings the consumption of the microcontroller significantly down. The code also disables the Watchdog Timer. I decided not to use it this time. Immediately after that the GPS module is commanded to software backup mode. This is because otherwise the module draws about 25mA until it acquires lock which will take at least about 30 seconds. Instead the code allows setting a minimum supercap/battery voltage level required to begin main operation. In the meantime the MCU cycles between 1 second long periods in Wait mode and ADC voltage readings. After the conditions are met the code proceeds to GPS Setup. It wakes the module up, turns off the default NMEA output, sets Dynamic Model to Airborne (necessary for high altitudes), turns off other services such as GLONASS (required for the Power Saving modes) and saves the configuration. After this the code enters the main loop. At the beginning of the loop the MCU always wakes the GPS module up and checks that the Dynamic Model is set to Airborne. It then proceeds to poll UBX-NAV-PVT until the module re-acquires fix and is locked on to at least 6 satellites. If a valid positional solution is not obtained within 90 attempts (configurable), the code resets and setups the module again, and proceeds further without a current position this time. From that point the GPS is back in software backup mode. TT7F1 specifically uses fix validity to decide whether to transmit both APRS and RTTY in case of a valid fix, or only an APRS packet without a position when the module fails to acquire fix within the defined number of tries. Next the MCU collects ADC readings for telemetry data and compares the supercap voltage to a pre-defined limit. If it is above the limit, it sets flags to transmit both APRS and RTTY in one minute cycle. If it is below, it allows only APRS transmissions in two minute cycles. In the following two blocks the MCU constructs the RTTY telemetry string and the APRS packet (chosen based on valid/invalid fix). Next it decides whether to store current data in the backlog this time. It does so every 30th (configurable) loop cycle. Assuming the tracker is operational for 12 hours per day it should be able to store backlogged telemetry data for the past 10-11 days at this rate (240 backlog pages in the flash memory and ~22 entries per day). The next block of code decides which frequency to use to transmit the APRS packet based on current position. In case of areas with no airborne amateur radio operations it disables the APRS transmission. Proceeding further the MCU at this point sets its main clock to 16MHz to be able to properly generate the APRS modulation. In case the APRS transmission is allowed it sets up the transmitter and transmits the packet. After that the MCU slows back down to 2MHz and checks whether to transmit RTTY this time or not. If so, it sets up the transmitter and starts by transmitting five 250ms long blips with 1s spacing to announce upcoming RTTY transmission. The telemetry string itself is preceded by five 0x00 bytes to help the receivers synchronize. After transmission finishes the transmitter is de-initialized and the MCU enters low consumption Wait mode for the selected period (1 minute cycle with high supercap voltage, 2 minute cycle with low voltage). Upon waking up the 2MHz main clock is setup and the loop starts from the beginning again. Data retained throughout power down is the backlogged positions and telemetries.
These and the two following charts illustrate the tracker's behaviour during sunrise and sunset as recorded by the received APRS packets. The planned and tested configuration for TT7F1 is one 15F supercap and two 52x38 solar cells. The LTC3105's output is set to 2.7V. The charts above show the first version of the code which decided whether to transmit both RTTY and APRS or just APRS, and whether to transmit in 1 minute or two minute cycles based on solar panel voltage. As can be seen this wasn't a good idea, because even at mild insolation the panel generated basically full voltage and was hence useless to manage power saving in this case. The chart on the left shows the tracker powering up and down a few times during sunrise before the sun was high enough to power it reliably. Towards the end of the dataset I manually shaded the cells completely to force the tracker employ the more restrictive operation. The chart on the right then shows the power being quickly wasted during sunset.
These two charts show the final code which uses 2.5V limit on the supercap voltage to decide whether to transmit both in the fast cycle or save power with only APRS and longer cycles (the RTTY transmission takes about 15s so it represents a significant power demand compared to just 0.7s long APRS packets).This time the tracker started smoothly during sunrise (left) and lasted much longer during sunset (right). Although the data come from two consecutive evenings its not fair to compare the two based on timestamps alone, because the second day developed clouds towards the evening and shaded the Sun earlier than the previous day.
Concerning the chosen 2.5V limit being relatively close to the maximum 2.7V potentially not providing much space. I left the supercap inside a freezer (-18°C) for a while, then powered the tracker with it and watched the voltage on a multimeter. The low temperature didn't seem to lead to any observable voltage drop.
I also tried measuring consumption with my traditional setup using Arduino Due which sampled the voltage drop across a 1Ω resistor connected between the tracker's GND and Arduino's GND. The tracker was placed in a less favourable spot for GPS fix acquisition so it took a little longer than usual. The first two active cycles were followed by a longer wait mode period as the supercap voltage was still below 2.5V. The seventh cycle was the first with successful GPS fix and hence full operation. At about 33 minutes into the test I completely shaded the solar cells. The tracker then managed three fully active cycles before transitioning to the APRS only longer cycles which slowed down the supercap voltage depletion.

TT7F1 Final Setup
In this section I'll document finalizing the TT7F1 setup to a launchable state. Most of the things and tests previously addressed in this blog post were done with this particular tracker.
I started with a 2m-band dipole antenna made of a 0.013p guitar string. The dimensions were 492mm for each of the two elements. I didn't go with a ground plane antenna, because at this length and thickness the guitar string wasn't stiff enough to preserve the desired shape of the radials.
As I understand it the antenna is resonant inside the 70cm-band as well since it is its 3rd harmonic. The difference should be in the radiation pattern which would have more lobes. Above is a graphical representation of the situation modelled in 4nec2. For these specific dimensions the frequency sweep returns an impedance of 70-j32 Ω (SWR of 1.87) at 144.5MHz. However, in the case of the higher band the reactance disappears only at about 451MHz resulting in 7.3 SWR (~58% of power gets reflected back to the transmitter) at 434.5MHz.
Since this was the older version of the board I had to solder the ground element at the bottom of the tracker and isolate it with a piece of Kapton tape. The element's proximity to the GPS antenna seemed to detune it leading to a little longer fix acquisition times. As a result I had to prolong the GPS fix timeout from 60 tries to 90. I also bent the GPS antenna a little away from the dipole. After that the fix acquisition improved.
I then drove to the traditional spot for my long range tests with the tracker placed and powered in the garden some 4.6km away. The APRS signal was strong and packets decoded without any issues. The RTTY signal, on the other hand, was noticeably weaker. In the end I managed only partial decodes. Especially since I forgot to bring my LNA. It may have been the case of simply being in a poor spot from the perspective of the radiation pattern (at a different place much closer, roughly 400m, the signal was strong). Either way, since APRS is the main tracking system I am willing to give it a go and simply evaluate the RTTY signal further once it's launched.

To verify that I wasn't the only one capable of receiving the tracker's APRS reports I headed to my other test spot with a view towards a couple of real iGates.
As the data from aprs.fi show the tracker did quite nicely with me wandering about for some 20 minutes. It was repeatedly received by an iGate 15.7km away. The GPS readings seem to be accurate to several meters which is fine given the low power nature of the tracker. Originally the GPS module kept producing much less accurate fixes with just 4 satellites after waking up from the software backup mode. Hence the requirement for at least 6 satellites in the code.
Being satisfied with all the tests I stepped forward to cutting off the programming piece of the PCB. I used a snap-off utility knife, swept across the drilled section a few times on both sides and broke it off easily. The tracker lost 0.75g in mass.
TT7F1 is supplied by two 52x38mm serially wired solar cells. They were joined by a piece of stiff wire isolated in the middle where it touches the tracker. The positive and negative leads were made with AWG30 wire and taped to the structure and later the tracker to ease off any potential bending or pulling.
The cells were placed at a 0° angle to ground. As it's clear from the images I didn't hold back with the Kapton tape to secure the solar panel. Unfortunately I hadn't prepared the board for this when I designed it and couldn't think of any better solution now when building it. Nevertheless there is nothing pulling on the panel and it holds quite well in the end.
This being the first and probably the lightest tracker it is equipped with just one 15F supercapacitor. It is soldered to the bottom ground pad and yet to be soldered to the LTC3105 out/battery in terminal. It will be probably closer to the actual launch so it doesn't power up when unintentionally illuminated. The solar+ lead isn't yet soldered either.
To better secure the supercap and tighten up the whole tracker I used a piece of a heat shrink. The downside of using a lightweight guitar string antenna is that it bends under its own mass. I had to make small loops in the string holding the tracker and slip the antenna element through them to straighten it.
All in all the finished tracker weighed 13.39g. In the upcoming weeks I plan on building four more trackers before the actual launches.

1. I really appreciate all of the documentation you are providing of your process and findings. I'm in the process of designing and building a floating pico balloon payload and this information has been very helpful to me.

Thanks!

Jared (N7SMI)

2. Hi,

This is a great rundown of your project. A query when you run UBX-CFG-CFG to save your settings prior to GPS shutdown - it talks about battery backed up RAM. Are you running a cell in your circuit to specifically do this? It looks as if the rest of your tracker just operates on solar and capacitors which would seem to be a non-permanent source of power. Or is it simply configured during daylight hours when the solar power is working , and on wake up at sunrise the full program running the shut off of the NMEA sentences runs again?

Many thanks

3. Hi Richard,

I use only the u-blox module without any backup battery or power switching on TT7F. As long as the module is powered the saved configuration stays in the RAM. You can provide separate backup power supply to the V_BCKP pin while in my setup it is wired straight to VCC. As you observed, the tracker re-initializes the GPS every time there is a loss of power (generally nighttime). In later versions, I added a reset instruction (0x06 0x04) ahead of turning of the NMEA output, because on occasions the MCU may reset or loose power while the GPS stays on. One thing to watch out for is waiting for the u-blox module to finish its power-up sequence. It won't responde to any instructions until its done. I use simple delays, another way is checking whether the module responds with an ACK message.
One thing about saving the settings. In case of entering the ON/OFF mode, you should send the UBX-CFG-CFG immediately after the UBX-CFG-RXM instruction. If you do it prior, the module won't know it is supposed to be in the power saving mode. If you do it too late, the module may already be powered down.

Tomas