Frequently Asked Questions - Performance
- How does the FireFox Synthesizer offer such wide bandwidth?
- How can spur performance be increased even further?
- Does the FireFox need calibration?
- There is a Frequency Estimate display in the menus. What is this number?
- There is a Resolution number displayed in the menus. What is this number?
- There is an option to turn Fractional-N mode on/off. What is this used for?
- 1. How does the FireFox Synthesizer offer such wide bandwidth?
The FireFox synthesizers’ internal circuitry divides the output bandwidth into four bands, with each band optimized to reduce noise, spurs, and to offer the best linearity possible. The frequency bands are: DC (0.00001Hz) to 30MHz, 30MHz to 398MHz, 398MHz to 770MHz, and 770MHz to 1.64GHz. These bands are switched seamlessly in the background. A Direct Digital Synthesizer (DDS) with a 10-bit DAC and 1GHz sample rate generates the first two bands (DC to 398MHz). Frequencies above 398MHz are generated by a very low phase noise PLL controlled VCO phase-locked to the internal DDS.
- 2. How can spur performance be increased even further?
An LC-type output filter can be used to reduce out-of-band spurs. These filters can be designed with public-domain software (see for example “Elsie”, an easy to use filter designer available at Tone Software, or these can be purchased off-the-shelf. Mini Circuits offers such filters as small inexpensive ceramic components in their LFCN and HFCN series filters.
- 3. Does the FireFox need calibration?
The FireFox system never needs frequency calibration; it is constantly being calibrated by the GPS timing signal. The FireFox RF output amplitude has been calibrated at the factory, and it is recommended that the unit is returned to Jackson Labs once a year for amplitude calibration. The user may also self-calibrate the FireFox units using an Agilent power meter; see the Hardware FAQ.
- 4. There is a Frequency Estimate display in the menus. What is this number?
The FireFox system constantly measures the internal OCXO offset to the GPS 1PPS signal. This measurement is done in 10ns steps (100MHz sampling). The firmware then adjusts the OCXO steering voltage (Electronic Frequency Control – EFC) to compensate for any drift between the OCXO and UTC. The timing differences between the OCXO and the 1PPS signal are stored in memory once per minute over a 30-minute period. The momentary difference is then compared to the difference that was measured 30 minutes ago, and a drift is calculated from these two values. Thus an estimate of the overall time base drift over the last 30 minutes can be established. This drift is typically less than +-5×10-11 over a thirty-minute period when locked to the GPSsignal.
As an example, let’s assume the Frequency Estimate display indicates 1.6 ×10-11. At 100MHz output frequency we can calculate the estimated accuracy of the output signal to be:
100MHz * 1.6 ×10-11 = 0.0016Hz
Thus the absolute frequency error of the output (to the UTC atomic reference) is estimated to be 1.6mHz, and the output frequency is thus estimated as 100,000,000.0016Hz.
- 5. There is a Resolution number displayed in the menus. What is this number?
This value shows the minimum step resolution that the DDS can generate in the particular frequency band it is operating in.
The DDS system has 32bit integer accuracy with an additional 16bit fractional component. The resolution is applied to three frequency ranges (DC-398, 398-770, 770-1640MHz). The effective frequency resolution is thus over 48bits.
This resolution determines the smallest frequency step size that can be generated by the DDS system, and thus determines the residual mathematical error of the system. The smallest fractional frequency step that can be generated in Fractional-N mode is smaller than the 10µHz step size of the FireFox system, and the value displayed in the LCD can thus be used to estimate the frequency error at any particular frequency.
See also the Fractional-N mode FAQ.
- 6. There is an option to turn Fractional-N mode on/off. What is this used for?
This setting option allows exact, cycle-accurate coarse frequencies to be generated (32bit integer mode), or frequencies with a much finer resolution (48bit fractional mode) but with a very small fractional residual uncertainty.
Consider the following explanation: the DDS has a 32bit integer component. This integer component alongside the 1Gs/s sample rate allows 232 individual frequencies to be generated without any residual error according to the following formula:
Fout = (32bit Tuning Word * 1GHz)/ 232
This formula is accurate for output signals from 2MHz to 398MHz. Use the following formulas to determine the resolution of the output signal for the remaining frequency bands:
DC to 2MHz: Fout = (32bit Tuning Word * 0.5GHz)/ 232
398 to 770MHz: Fout = (32bit Tuning Word * 2GHz)/ 232
770MHz to 1640MHz: Fout = (32bit Tuning Word * 4GHz)/ 232
The frequencies generated with fractional-N mode turned off are thus cycle-accurate without any slipped cycles or residual frequency error. As an example, consider the following example of generating a 10MHz frequency with a tuning word of 4294967296:
10.0MHz = (4294967296 * 1GHz)/ 232
The advantage of integer mode is thus that this particular tuning word generates a cycle-accurate, phase-drift-free 10MHz signal without any cycle slipping, or residual. The phase angle to the internal 10MHz OCXO is fixed, and remains drift free. The disadvantage of this mode is its granularity, which is limited by the 32bit tuning word.
The frequency granularity with fractional mode turned off, and an output frequency ranging from 2MHz to 398MHz is thus exactly 0.23283064365386962890625Hz. Keep in mind that the absolute accuracy of the output signal is limited by the accuracy of the 10MHz reference signal from the OCXO.
To improve the frequency granularity of the output signal, a fractional-N mode can be enabled that increases the frequency resolution by an additional 16bits. The disadvantage of this mode is that it is not mathematically deterministic; there is a frequency uncertainty of about 1/2LSB that prevents this mode from being cycle accurate.
By increasing the DDS resolution, the DDS residual is made very small (about 1GHz / 248 at a 10MHz output frequency). The frequency resolution with fractional-N mode turned on is thus 3.55µHz for an output ranging from 2MHz to 398MHz.
This DDS resolution is typically less than the systems’ minimum resolution of 10µHz. The system attempts to match the user selected 10µHz step setting to the closest frequency that the DDS can generate. The frequency difference between the desired setting (selectable in 10µHz steps), and the actual frequency being generated causes a very small error.