A Modernized GPS-Derived 10 MHz Frequency Standard (2024) Author: Bertrand Zauhar, VE2ZAZ / VA2IW Page last updated: 03/03/2024

INDEX

INTRODUCTION ORIGINAL SYSTEM DEVELOPMENT COMPONENT PROCUREMENT BOARD DESIGN PCB ORDERING ASSEMBLY AND INTEGRATION FIRMWARE PROGRAMMING LCD DISPLAY FIELD DEFINITIONS GPS CONFIGURATION SERIAL CONSOLE FLL CONFIGURATION AND OPERATION OCXO CONFIGURATION (IN FIRMWARE) COMMENTS ON STABILITY AND ACCURACY ERRATA AND IMPROVEMENTS

This page documents an improved and modernized version of the "Simplified GPS-Derived Frequency Standard", which the author originally designed back in 2006. Being open sourced and well documented, this project can become a great learning platform for whoever would like to advance on 10 MHz reference concepts, more serious Arduino programming and board design. Moreover, owning this reference system can bring in some reference accuracy and stability approaching atomic-grade levels.

Although this modernized version brings in several improvements, the principle of operation on this system is the same as on the original design:

• A 10 MHz adjustable "ovenized" crystal oscillator (OCXO) continuously increments a hardware 16-bit counter.
  
• A one Pulse-Per-Second signal derived from GPS captures values from the counter.
  
• The difference between captured counter values is read by the firmware every 10 seconds. Knowing that the ideal count difference for a 10.0000 MHz signal is 57600, an offset is computed.
  
• At the end of the sampling cycle, the firmware adjusts the OCXO frequency via a Digital-to-Analog-Converter (DAC) to compensate for the average of the frequency offsets, thus targeting the 10.0000 MHz ideal frequency.
  
• This cycle repeats...

Block diagram of the modernized version of the VE2ZAZ GPS-Derived Frequency Standard

This modernized version of GPS-Derived Frequency Standard offers the following improvements over the previous version:

• A 32-bit micro-controller, the STM32 Black Pill (STM32F401C) or Blue Pill (STM32F103C) platform (previously an 8-bit PIC micro-controller),
• A true 12/14/16-bit Digital-To-Analog-Converter (DAC) to generate the OCXO tuning voltage (previously a PWM output and some low-pass filtering),
  
• A real clock distribution chip with 50 Ohm output impedance to fan out to the four 10 MHz references (previously a CMOS gate chip),
• A faster 10MHz signal receiver/shaper/buffer chip. This provides a sharper and more accurate 10 MHz reference into the FLL.
• A 20-character, 4-line LCD display that provides the essential system status information (previously non-existent),
• A buffered 1-PPS output available for external usage (previously non-existent)
  
• Separate digital and analog +5V rails, for a lower noise performance (previously a single +5V rail),
  
• A firmware developed in C language on the Arduino IDE environment, offering easy code change/recompile by the user (previously coded in unintuitive PIC assembly language),
• A Proportional-Integral (PI) FLL loop, yielding a much finer frequency control and faster convergence (previously a constant step FLL loop),
• A three-stage FLL acquisition process: short, medium and long sampling cycles (previously a two-stage coarse-fine process). This provides a much faster convergence towards the ideal 10 MHz frequency, and a faster recovery from short or small GPS disturbances.
  
• A PCB integrating the GPS, the DAC and even a prototyping area which can, depending on the model used, hold the OCXO,
  
• A native USB 2.0 serial port on STM32 Black Pill (the STM32 Blue Pill requires an external UART-to-USB converter),
  
• A comprehensive VT-100 text console via the USB port for easy configuration and control of the system parameters, and for complete status monitoring (replaces the very basic text console and the Windows software).

In 2022, the author developed and documented this modernized system in French language, for the benefit of the French speaking community. He created a series of six YouTube videos documenting the entire development process and testing of this system. One would benefit a lot from watching the videos with the English subtitles enabled. The video playlist is accessible by clicking on the thumbnail to the right.

The project was designed in the KiCad electronics design environment. The design files (schematics, PCB, Gerber files) are packaged in the ZIP file to the right. For easy consultation, a PDF version of the circuit schematics is also available to the right. The author is happy to share the entire design with other users. Please understand the licensing conditions before using it. See the legal note below. Legal Note This hardware design is made available under the following license: CC BY-SA 4.0 (Creative Commons Attribution-ShareAlike 4.0 International). See this link for more detail. In summary:   You are free to: Use, share and adapt the design, even commercially, You must: Give appropriate credit to the author. Distribute your contributions under the same license.

A rendered view of the PCB top side VE2ZAZ GPS-Derived Frequency Standard V1 (2024) KiCAD Design files VE2ZAZ GPS-Derived Frequency Standard (2024) V1 PCB - Circuit Schematics

Display The display is a common 4-line, 20 characters per line, monochrome, backlit HD44780-compatible LCD unit. This unit works on a +5V supply, and its signals have a 5V TTL swing. It is equipped with a PCF8574-based I2C back-pack board. The combined display and back-pack can be purchased from Chinese online stores for less than $10. GPS The GPS used must works on a +5V supply, and its signals must have a 3.3V LVTTL swing. It must have a RF connector for external antenna support, and provide a 1 Pulse-Per-Second signal at the connector. Such GPS board can be purchased from Chinese online stores for less than $10. The ublox series of GPS boards is a good choice. Although using a better timing grade GPS unit is a sound proposition, any good navigation grade GPS will do the work just fine. The reason for this is that the GPS 1 PPS signal gets integrated (averaged) over a long period by the firmware, typically a for few hours in duration. The real gain in system performance is achieved by this averaging, more than by the raw GPS performance alone. Important Note: These GPS boards typically have an on-board GPS patch antenna. That antenna is not used when the GPS is integrated into an enclosure. Thus that on-board antenna must be disconnected. More details are provided in the Assembly section. GPS Antenna A suitable external GPS antenna is amplified, and has a 3 to 6 meter long coaxial cable terminated with a male SMA connector. Such navigation-grade antenna can be purchased from Chinese online stores for less than $5. STM32 Black Pill or Blue Pill The author suggests using the STM32 Black Pill. There are several incentives in using the Black Pill platform, namely cost, availability, CPU performance, direct USB port vs. requiring an external Serial-to-USB adapter. Both the firmware and the system board can accommodate either a STM32 Black Pill or a STM32 Blue Pill board. By default, the firmware is configured to run on a Black Pill platform. When a Blue Pill is used, a compiler constant located in the header of the main C source file must be commented out (disabled). The constant to comment out is "BLACK_PILL_USED". In addition, the system board must be configured for either the Black Pill or the Blue Pill. See the STM32 board type configuration note in the "ASSEMBLY AND INTEGRATION NOTES" section for more detail.

The 4x20 LCD display with I2C board A suitable GPS board A suitable amplified GPS antenna The STM32 Black Pill Board

• It must be a quartz-based oscillator,
  
• It must be "ovenized" (OCXO type), 
• It must be stable in frequency and wave shape,
• It must have sufficient output amplitude (1 Volt RMS under load will meet most requirements),
• It must provide a monotonic output (no ripple or glitches on the rising/falling edges),
• It must have a frequency tuning input pin.
  

• Morion MV89: Very desirable (will yield high system performance). Has a double-oven. +12 VDC supply, 5 Hz tuning range. Sine wave output. Simple to integrate into the system. Its cost has gone up lately, unfortunately.
  
• Hewlett-Packard 10811 and 10544 series OCXOs: High performance, 1 Hz tuning range. However are expensive, are large, require multiple DC supplies, a negative tuning voltage, and an adapter PCB.  The units in circulation are getting old and showing some signs of failure. Note that their frequency vs. adjustment voltage response has an inverted behavior. That must be set in the firmware at compilation time.
• Isotemp OCXO131-100: Suitable (will yield slightly degraded system performance, see comment in the system performance section), 8 Hz tuning range, 5 VDC supply, 5V CMOS square wave output.
  
• Other Isotemp OCXO131, OCXO134 or OCXO143 series oscillators. Similar performance as the OCXO131-100. However some specifications (supply voltage, output shape, amplitude, tuning range, stability) may be difficult to determine. With some research, the user may find a suitable unit at a very attractive price.

The PCB has the following characteristics: A double-sided copper design, however all components mounted on the top side, 100 mm x 100 mm dimensions, qualifies for "special price" PCB manufacturing. Recommended material: FR-4, 1.6 mm (0.062") thickness. Soldermask and Silkscreen layers provided for both sides, Has a prototype area for easy circuit additions, Uses surface-mounted components, some of which have a very fine lead pitch, Uses fine traces and vias. Those who would like to build this system should have the PCB made by a reputable PCB manufacturer (JLCPCB, PCBWay and the likes). For the order, the Gerber files need to be transferred to the manufacturer. The ZIP file containing the manufacturing files (Gerber and NC Drill files) is available to the right.

GPS-Derived Frequency Standard (2024) V1 PCB - Gerber files

ASSEMBLY AND INTEGRATION

Board Assembly The system board contains many surface-mounted components, some of which have a very fine lead pitch. This project requires some SMD soldering equipment and the skills to operate it. Thus, this project cannot be put together by beginners. For them, assistance from a skilled person is required. STM32 board type configuration Prior to installing the STM32 board on the system board, four jumpers (JP5, JP6, JP7, JP8) must be configured based on the type of STM32 board used, either Black Pill or Blue Pill. These jumpers are located on the system board, inside the STM32 board footprint. See the image to the right for jumper locations. On each of the four jumper locations, the gap between the center pad and the proper adjacent pad (black or Blue) must be bridged. A solder ball between two pads is suitable. Board installation The STM32 Black Pill or Blue Pill board has two rows of 20 pins interfacing to the system board. Although one could solder the STM32 board directly to the system board, it is suggested instead to populate the system board with two 20-position single-row female header connectors that will mate with the matching standard single-row male connectors on the STM32 board. This will provide the ability to easily remove and insert the STM32 board in the future. GPS on-board antenna disconnection The recommended GPS boards have an on-board GPS patch antenna. That antenna will not be used when the GPS is integrated into an enclosure. Thus the on-board antenna must be disconnected. On the GPS board, remove the coupling capacitor (typically C2) that brings the patch antenna signal to GPS antenna input. See picture to the right.

STM32 type configuration jumper locations The capacitor to be removed on the GPS board System integration inside the author's enclosure

Power supply strategy
In such a high accuracy system, linear DC supplies should be privileged over switching supplies. The following power supply distribution was adopted by the author for this project. A clean, regulated +12 VDC, 2 Amperes analog supply feeds the entire project through a 2 Amperes fast-acting fuse. That +12 VDC is sent to the OCXO, a Morion MV89A. The +12 VDC rail is also regulated down to +8 VDC using an LT1084, TO-3 case, adjustable linear regulator. That +8 VDC is sent to the project board, which regulates down to +5 VDC (separate analog and digital regulators). Typical current of the system board is 300 milliAmperes. On his project, the +8 V regulator was already available in the enclosure, so it was wise to use it as an intermediate step-down stage to dissipate some of the heat that would otherwise have been dissipated by the small +5 V regulators on the system board. Moreover, having a hefty +8V regulator also allows to feed a separate +5 V regulator dedicated to the OCXO (in the case where a +5V OCXO is used), while keeping the power dissipation from that regulator as low as possible. Another advantage of having an additional regulator is the reduction in noise sent to the system board. The user will adapt the power distribution based on OCXO supply requirements. The chosen OCXO can typically require a +5 or +12 VDC supply at a current of up to 1.5 Ampere for a few minutes after power up.

OCXO mounting
Due to its smaller size, the Isotemp OCXO131 type oscillator can be mounted directly on the system board, in the prototyping area. Note that the hole size in that area may be too small to receive the oscillator pins directly, so some interfacing plan may have to be devised. Also note that an external supply is still required, as the on-board +5V regulators are not sized for that task.
Other brands and models of OCXOs, due to their size, may have to be mounted off-board. A separate prototyping PCB is suggested as the support for the OCXO. Short pieces of coaxial cable should be used to interconnect the oscillator output and the tuning voltage. See the picture of the author's system integration inside the enclosure.

Post-DAC Gain and Offset settings
The voltage gain and the output offset produced by the two operational amplifiers that follow the DAC output must be configured in hardware. Component U5 contains these two operational amplifiers. The Post-DAC Gain and offset values are determined by the make and model of the target OCXO. The user shall consult the OCXO datasheet to derive its tuning voltage range. The implemented gain and offset must produce a tuning voltage range that matches the OCXO tuning voltage range.

The Post-DAC gain and offset are set by configuring resistors, jumpers and capacitors on the system board during board assembly, as per the configuration table on page 4 of the circuit schematics. The configuration table is reproduced here. Notice that an external supply voltage may be required for some OCXOs.

OCXO Tuning Voltage Range	Post-DAC Gain	Post-DAC Offset (V)	R11	R12	C12	Jumper JP1 Upper Voltage Rail	Jumper JP2 Lower Voltage Rail	Jumper JP2 Offset
0 to +5V	1.0	0.0	Not Installed	0 Ohm	Not Installed	Position 1-2	Installed	Not Installed
0 to +8V #	1.6	0.0	100K	62K	Not Installed	Position 2-3	Installed	Position 1-2
0 to +10V #	2.0	0.0	100K	100K	Not Installed	Position 2-3	Installed	Position 1-2
-5V to +5V *	2.0	-5.0	100K	100K	0.1uF	Position 1-2	Not Installed	Position 2-3

* Configuration used with HP OCXOs (series 10544 and 10811). External -5VA_EXT negative supply required. Voltage must be equal to
  or lower than -5 Volts.
# External +VA_EXT positive supply required. Voltage must be equal to or greater than +8 Volts.

The author has found that a 0 to +5V tuning voltage (Post DAC gain of 1, offset of 0V) is suitable for his Morion MV89 and Isotemp OCXO131-100 OCXO units. Other OCXO makes and models may require different gain and offset settings.

10 MHz Output Wave Shape
The 10 MHz reference outputs can have the following wave shapes selected in hardware using jumper JP4:

• The same wave shape as the one produced at the OCXO output. For this, Jumper JP4 must have its positions 1 and 2 shorted together.
  
• A square wave shape, regardless of the OCXO output wave shape. For this, Jumper JP4 must have its positions 2 and 3 shorted together.

FIRMWARE PROGRAMMING

The firmware load running on the STM32 micro-controller is compiled and uploaded by the user in the Arduino IDE programming environment. The IDE must first be configured to support the STM32 family of micro-controllers. Consult the Internet to find out how to add and configure the support for the STM32 Black Pill or Blue Pill, as this is beyond the scope of this web page. The following Arduino libraries must be installed in the Library Manager prior to compiling the code: FlashStorage_STM32 LiquidCrystal_PCF8574 The latest firmware version is available on GitHub, at the link provided to the right. Legal Note This software design is made available under the following license: CC BY-SA 4.0 (Creative Commons Attribution-ShareAlike 4.0 International). See this link for more detail. In summary:   You are free to: Use, share and adapt the design, even commercially, You must: Give appropriate credit to the author. Distribute your contributions under the same license. Firmware Version History Version 2 (March 2024): Initial English firmware release.

VE2ZAZ's GPS-Derived Frequency Standard (2024) V1 Firmware on GitHub

• D - Current DAC value
  
• Range is 0 - 65535.
• ΔD - Previous cycle DAC value change
• C - Current Cycle Status: 
• Short, Medium or Long cycle.
  
• #nnn is the sample number in the current cycle.
• ΔHz - Current computed frequency difference from nominal, in Hz.
• AL - Alarm field. See types of alarm below.
  
• An uppercase character indicate an active alarm of that type. 
• A lowercase character indicate a previously active alarm of that type.
• Current GPS UTC Date, as extracted from the GPS.
• Current GPS UTC Time, as extracted from the GPS.
• P (flashing at a 1 Hz rate) - Indicates the presence of a 1 PPS pulse.

• A / a - In initial acquisition after startup.
• D / d -  The DAC has reached its minimum or maximum value.
• F / f  - The FLL is off.
• P / p - GPS PPS signal is missing.
• R / r -  In long cycle, the sample is rejected because it is too far away.
• V / v - The FLL is unlocked because it is not in a long cycle.
• O / o - The OCXO does not provide a 10 MHz reference.
• G / g - GPS provides invalid data.

GPS CONFIGURATION

The following configuration settings are recommended to extract maximum performance from the GPS:

• The GPS should be configured in fixed position mode,
• The current LAT and LONG coordinates should be entered if possible. This accelerates power up acquisitions.
  
• The 1-PPS signal should be enabled and configured to make its rising edge line up with the time reference. A 10% duty cycle on the 1-PPS high level pulse is appropriate.

The user shall refer to the GPS documentation to find out how to configure the GPS with the above settings.

SERIAL CONSOLE

The system can be monitored and configured using a serial console, which is available via a serial-USB connection sourced from the STM32 board. When using a Linux-based computer, the serial port carrying the console will typically show up as "/dev/ttyACMxx". On a Windows-based computer, the serial port will be identified as COMxx. "xx" is the port number, and will vary from computer to computer. Since this is a USB link, connection parameters (bit rate, parity, etc) are irrelevant.

Any simple TTY terminal program able to access the USB ports as serial connections is suitable for the task. However, a terminal program supporting the VT-100 protocol will provide additional benefits, such as non-scrolling status screen and character highlight. A good, simple console program for Linux platforms is Minicom, which is readily available in most distributions. In Windows, a known good VT-100 terminal emulation program is TeraTerm, which is available for free.

Status Reports
The following box shows a typical detailed status report provided by the serial console, Such report is printed on the console screen after every 10-second sample. In standard  TTY mode, a new status report will make the information scroll on the screen. In VT-100 mode, these status fields will appear static on the screen.

================================================================================ 29/02/24-14:31:04-UTC Alarms:                                           AL---r-g Cycle:                                            Medium Sample:                                           10 / 10 Current DAC value:                                34181 Oscillator counter| Nominal Count:                57599 | 57600 Offset from nominal count:                        -1 Count offset average:                             -0.600000 Offset average (ppm)                              -0.0060 Offset average (Hz):                              -0.060000 Calculated average frequency of reference (Hz):   9999999.940000 SAMPLING CYCLE COMPLETED Ajustement made to DAC:                           530 New DAC value:                                    34181 Offset calculation (Hz) of PI loop:               -0.060000 Pause for stabilization... ================================================================================ _1_2_3_4.....

In addition, there is a condensed status report available. In this mode, a one-line status report is printed after every 10-second sample. Examples of condensed lines are shown below. Also included are the field definitions, which can be printed by typing the DEFIN command (more on the commands below).

S|29/02/24_20:04:57|al___r_g|34182|L|00002|00720| 00000| 0.00000|________|______ S|29/02/24_20:05:07|al___r_g|34182|L|00003|00720| 00000| 0.00000|________|______ S|29/02/24_20:05:17|al___r_g|34182|L|00004|00720| 00000| 0.00000|________|______ S|29/02/24_20:05:27|al___r_g|34182|L|00005|00720| 00000| 0.00000|________|______ S|29/02/24_20:05:37|al___r_g|34182|L|00006|00720| 00000| 0.00000|________|______ S|29/02/24_20:05:47|al___r_g|34182|L|00007|00720| 00000| 0.00000|________|______ S|       a         |   b    |  c  |d| e   |  f  |  g   |    h   |    i   |  j   | a: UTC date and time taken from GPS. b: Alarm field. c: Current value of the DAC (from 0 to 65535) controlling the OCXO frequency. d: Current FLL cycle type (C=Short, M=Medium, L=Long). e: Sample number in the current sample cycle. f: Total number of samples to collect in the current cycle. g: Average deviation in counter pulses from the nominal value. h: Average deviation in counter pulses (g) expressed in Hertz. i: Average frequency deviation of the P-I loop in a long cycle. j: DAC change applied at the end of the current cycle.

Configuration Commands
The system can be configured using a series of console commands. Some commands require one or more parameters to be provided, otherwise they will be rejected. All commands must be followed by a LINE FEED.

The following box shows a list of the available commands and their definition. The commands can be typed in lowercase or uppercase. Notice the parameters following some of the commands. Each parameter has its range provided within the <...-...> characters. Parameters with fixed choices are provided within the <.../.../...> characters. All parameters are separated by a space character.

Commands: ---------- HELP or ?                            : This help. DEFIN                                : Help for condensed display mode fields. DAC <0-65535>                        : New forced DAC value. DACBIT <16/14/12>                    : The number of bits used by the DACx0501. CYCDUR <1-65535> <1-65535> <1-65535> : Number of samples per short/medium/long cycles. CLRALM                               : Clears previous alarms shown in lowercase. FLL <ON/OFF>                         : Enable FLL.                              NPPS <1-10000>                       : Number of PPS per sample.                PARAM                                : List of adjustable parameters and their current value. PI <0-1.0000> <0-1.0000>             : Constants Kp and Ki of the P-I loop of t. RESET                                : Restarts the micro-controller.            REACQ                                : Restarts the acquisition process.        THRES <0-100.0000> <0-100.0000>      : Thresholds (in Hz) for switching to medi. VERBOS <ON/OFF>                      : Detailed display mode.                   VT100 <ON/OFF>                       : VT100 option of detailed display mode.

The command definitions shown above can be printed on screen by typing either the "?" command or the "HELP" command.

The current system parameter values can be printed on the console with the PARAM command. Typical parameter data is shown below:

Parameter Values ---------------- Number of DAC resolution bits:              16 DAC value:                                  34182 Vtune voltage at OCXO (calculated):         2.59886 FLL operation:                              ON Number of PPS per sample:                   10 Short cycle duration (samples):             1 Medium cycle duration (samples):            10 Long cycle duration (samples):              720 Medium cycle threshold (Hz):                0.101000 Long cycle threshold (Hz):                  0.010100 Detailed display mode:                      ON VT100 detailed display mode:                ON PI Loop Index Kp:                           1.00 PI Loop Index Ki:                           0.00

Alarms
On both the console and the LCD display, the alarm field has the same appearance and function:

• There are 8 positions in the alarm field. They are:  A, L, F, P, R, V, O, G.
  
• Each position shows the status of one specific alarm.
  
• Uppercase letters indicate currently active alarms,
• Lowercase letters indicate previous alarms.
  
• An underscore or hyphen character indicates the absence of current or previous alarm.
  
• Previous alarms can be cleared with the CLRALM command, or by shorting out the alarm clearing jumper (J10 pins) on the system board.

The following box shows the alarm definitions:

Alarms:                                                                         --------                                                                        Uppercase letters indicate currently active alarms.                               Lowercase letters indicate previous alarms. Can be cleared with the CLRALM command. A / a                 : In initial acquisition after startup.    L / l                 : The DAC has reached its minimum or maximum value (limit). F / f                 : The FLL is off.                              P / p                 : The GPS PPS signal is missing.               R / r                 : In long cycle, the sample is rejected because it is too far away. V / v                 : The FLL is unlocked, because it is not in a long cycle. O / o                 : The OCXO does not provide a 10 MHz reference. G / g                 : The GPS provides invalid data.

The alarm definitions shown above can be printed on screen by typing either the "?" command or the "HELP" command.

FLL CONFIGURATION AND OPERATION

The following diagram shows the  overall FLL process flow. A description of the FLL behavior follows.

The FLL can transition between short, medium and long sampling cycles at the end of each sampling cycle, based on the calculated frequency offset from the nominal 10 MHz target. At start up, the FLL uses a short cycle (typically a single sample) to make coarse frequency corrections. As the measured OCXO frequency gets closer to the nominal 10 MHz target, the FLL transitions to a medium duration cycle, which produces finer frequency corrections. On a stable system, the FLL ultimately transitions to a long sampling cycle, which typically lasts a few hours. The firmware can also decide to transition back to a shorter sampling cycle if the latest sample deviates too much (indicating a degraded system condition), or if alarm conditions exist. Note that cycle durations and transition thresholds can be configured by the user at run time via the serial console.

The P-I Compensation Loop
The OCXO frequency adjustment process implements a Proportional-Integral (P-I) compensation loop. As a result, a frequency adjustment is calculated and applied at the end of each sampling cycle via a DAC value change. Being a P-I loop, the applied DAC value change is calculated:

• In part as a function of the latest measured frequency offset from the target nominal,
  
• And in part by a longer term trend of the frequency offsets.

Note that the "differential" action of a P-I-D loop is not implemented on this system. A sample reject algorithm is implemented instead. This algorithm has an action similar to the differential action, which is to reject grossly off-frequency samples (outliers).

Two coefficients, Kp and Ki, are used to shift the weight of each of the two actions, Proportional and Integral. These coefficients can be configured via the serial console. The author invites users to try different settings and see the resulting impact on system behavior and performance. Nonetheless, the author has found that the integral action has little effect with a stable OCXO. A purely proportional loop yields repeating, fast-converging and stable results once the OCXO is fully warmed up and stabilized.

The following equations illustrate the proportional and integral actions in the P-I loop.

Variables:
    OffsetF: Offset measured in Hz vs. the nominal target frequency 10.000000000 MHz
    OutputF: Value in Hz used to calculate the DAC adjustment.

In a P Loop: 
    OutputF = OffsetF * Kp
    This means the larger the offset is, the more the DAC value will be changed.

In a P-I Loop:
    OffsetF_accumulation = OffsetF_accumulation + (OffsetF * delta_time)        (accumulated over 10 cycles)
    OutputF = (OffsetF * Kp) + (OffsetF_accumulation * Ki) 
    This means the DAC value change will be calculated in part as a function of how far away from nominal
    the latest measured frequency is, and in part by a longer term trend of the frequency offsets.

Loop Index Conditions:
    Kp + Ki = 1 :     Recommended situation.
    Kp + Ki < 1 :     Under-compensated loop. Will requires more DAC adjustments to reach the nominal
                              frequency.
    Kp + Ki > 1 :     Over-compensated loop. Not recommended, will create a compensation oscillation (the loop 
                              will not converge towards the nominal target frequency).

Recommended values (defaults):
    Kp = 1 , Ki = 0 : Creates a purely proportional compensation loop.

Reference material on PID loops:
   PID – Helping Computers Behave More Like Humans:
    https://spin.atomicobject.com/2016/06/28/intro-pid-control/

Recommended FLL settings

The author has spent some significant time analyzing system performance using various parameter settings, with both 10MHz OCXOs discussed above. Here are some parameter recommendations for those of you who don't have the time or capability to measure frequency accuracy. Following these recommendations should allow similarly built systems to yield good performance. It must be stated here that these are only suggestions. The users shall see these as a good starting point, and may find values that better suit their system setup. It will not damage anything to play with these parameters! Worst case, just revert to these suggested parameters.

Parameter	Suggested Value	Command Used	Note
Number of DAC resolution bits	16	DACBIT 16	Must match the DAC chip resolution populated on the board. 12 and 14 bit DACs will degrade performance.
Number of PPS per sample	10	NPPS 10	No real benefit in changing this value. The internal counter keeps counting regardless of the sample duration. In the end, the samples contribute the same way to the average calculation. Fewer longer samples vs. more shorter samples.
Short cycle duration (samples)	1	CYCDUR 1 10 720	These values work well with the MV89 OCXO. *For the OCXO131-100 OCXO, a one hour sampling cycle is recommended.
Medium cycle duration (samples)	10
Long cycle duration (samples)	720 (*360)
Medium cycle threshold (Hz)	0.101	THRES 0.101 0.0101	Changing these values may lead to the FLL being stuck in shorter cycles, and not reach the Long cycle, or transitioning too fast to a longer cycle.
Long cycle threshold (Hz)	0.0101
PI Loop Index Kp	1.00	PI 1 0	With these P-I index values, the FLL applies frequency corrections in a proportional fashion, and the integral contribution is disabled. The sum of Kp and Ki should never be greater than 1.00 . See comment on P-I loop above.
PI Loop Index Ki	0.00

The following diagram shows overall FLL process flow. A description of the FLL behavior follows.

OCXO CONFIGURATION (IN FIRMWARE)

The OCXO and DAC characteristics must be captured in the source code header before compiling the source code for a given system. This is an important step to perform in order for the frequency adjustment to work properly. The 4 compiler constants of interest are:

    DAC_VOLTAGE_MIN
    DAC_VOLTAGE_MAX
    DAC_POST_GAIN 
    RESPONSE_OCXO_HZ_PER_V

These constants are located near line number 150 of the source code file.

DAC Output Voltage Limits
First, the minimum and maximum DAC output voltages must be measured and entered next to the two their respective constants. The author has already measured these voltage values and captured them next to the appropriate compiler constants in the source code. It is expected that these values will be very similar from system to system. They are:

    DAC_VOLTAGE_MIN                     0.0123
    DAC_VOLTAGE_MAX                     4.995

That said, the users may want to measure these voltages on their system. The DAC output voltage is probed on resistor R9. These measurements can be performed during the OCXO Frequency Response measurement below.

Post-DAC Gain
Next, the voltage gain configured on the operational amplifiers following the DAC output must also be captured in the source code. The Post-DAC Gain value is dependent on the make and model of OCXO used. The implemented gain (and offset) must produce a tuning voltage range that matches the OCXO tuning voltage range. That gain is set by configuring resistors and jumpers on the system board during board assembly, as per table on page 4 of the circuit schematics. A subset of that table is reproduced here:

OCXO Tuning Voltage Range	Post-DAC Gain
0 to +5V	1.0
0 to +8V #	1.6
0 to +10V #	2.0
-5V to +5V *	2.0

The compiler constant of interest is DAC_POST_GAIN.

Refer to item Post-DAC Gain and Offset Settings in the ASSEMBLY AND INTEGRATION NOTES section to find out what values to capture in the firmware source code. As a reminder, the author has found that a 0 to +5V tuning voltage is suitable for his Morion MV89 and Isotemp OCXO131-100 OCXOs. This corresponds to a Post-DAC Gain value of 1.0 . That value should be captured next to the compiler constant:

    DAC_POST_GAIN          1.0

Remember that other OCXO makes and models may require a different Post-DAC Gain value.

OCXO Frequency Response
The Frequency vs. Voltage response (slope) must be measured, and then entered in the source code. Optionally, the minimum and maximum DAC output voltages can also be measured here. The compiler constant "RESPONSE_OCXO_HZ_PER_V" must be assigned the proper slope value. The number to modify is located next to the constant. That value can be a number with decimal(s). Note that if the OCXO lowers its frequency when its tuning voltage is increased, the response value entered must be negative.

The author has measured the response values for the two suggested OCXOs. For these units, simply enter one of these numbers:

    Morion MV89A:                     1.489
    Isotemp OCXO131-100:       2.6385

For other OCXOs, the user can execute the following measurement steps

1. Ensure that the system is stable and that the GPS is receiving a valid signal.
   
2. Turn off the FLL using the "FLL OFF" console command.
   
3. Manually set the DAC voltage to its maximum using the "DAC 65535" command.
1. Measure the OCXO frequency with a good frequency counter, and to the nearest 1/10th of a Hz. If no frequency counter is available, use the "Offset average (Hz):" value provided by status report on the serial console. Note down the value. 
2. Measure the OCXO tuning voltage at the OCXO. Note down that value.
   
3. Optionally measure the DAC output voltage on resistor R9. This becomes the DAC_VOLTAGE_MAX constant value to enter in the source code.
4. Manually set the DAC voltage to its minimum using the "DAC 0" command.
1. Measure and note down the OCXO frequency.
2. Measure the OCXO tuning voltage at the OCXO. Note down that value.
3. Optionally measure the DAC output voltage on resistor R9. This becomes the DAC_VOLTAGE_MIN constant value to enter in the source code.

The RESPONSE_OCXO_HZ_PER_V value can be calculated with:
  

	(Step 3-a Frequency)	-	(Step 4-a Frequency)
RESPONSE_OCXO_HZ_PER_V   =	----------------------------------------------------------------------
	(Step 3-b Voltage)	-	(Step 4-b Voltage)

Make sure to recompile the source code with the updated compiler constants.

The following diagram shows overall FLL process flow. A description of the FLL behavior follows.

COMMENTS ON STABILITY AND ACCURACY

• Selection of a good, stable OCXO,
• Well planned DC supply distribution,
• Avoidance of DC switching converters and supplies,
• Comprehensive DC supply decoupling,
• Optimization of wire and cable lengths (shortest possible),
• Use of coaxial cable wherever noise coupling can be an issue,
• Optimum positioning of the GPS antenna,
• Proper configuration of the GPS parameters,
• Proper control loop (firmware) parameter selection.

• Using a Morion MV89 OCXO, ublox neo-8 GPS, and for a one-hour sampling period, his system consistently produced accuracy figures in the low 10^-11's.
• Using an Isotemp OCXO131-100 OCXO, ublox neo-8 GPS, and for a one-hour sampling period, his system consistently produced accuracy figures in the high 10^-11's to the low 10^-10's.
• Stability measurements made by the author over a one-hour period confirmed a better medium term stability (less drift) on the Morion MV89 OCXO than on the Isotemp OCXO131-100 OCXO.
  
• 
  

OCXO: Morion MV89 DAC resolution: 16 bits Sampling Period: 60 minutes FLL: Proportional adjustments Measurement duration: 27 hours

OCXO: Isotemp OCXO131-100 DAC resolution: 14 bits Sampling Period: 50 minutes FLL: Proportional adjustments Measurement duration: 24 hours

Off-Air Measurement Setup