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12/28/2012

Fine Frequency Control using the Philsar PS-XX00 Fractional-N Synthesizers



Many techniques from simple to complex, currently exist for synthesizer frequency output control by manipulating the crystal oscillator to maintain a constant output frequency. All of them have associated cost and parts count considerations. This application note describes how to perform fine frequency control using the Philsar PS-XX00 series fractional-N synthesizers and a VCO. This method is a simple and low cost alternative to pulling the crystal reference frequency in order to manipulate the final output frequency.

Applications 
• Radio Calibration
• Automatic Frequency Control
• Reference Crystal Accuracy
• Reference Crystal Temperature Compensation
• Reference Crystal Aging Compensation
• Doppler Correction

Step Size
The Philsar PS-XX00 family of synthesizers (PS-1200, PS-2500 and PS-6500) has 18-bit fractionality on the main synthesizer giving 262,144 steps with respect to the internal reference frequency. The formula is for calculating the step size is:
 
R is an integer value ranging from 1 to 32 used to divide the crystal reference frequency (FXtal) to arrive at the internal reference frequency (Fref).
Example 1. Using a 20 MHz crystal and a reference division of R = 1 yields,
                
This represents the minimum step size achievable with a 20 MHz crystal oscillator and R=1.

Example 2. Using a 20 MHz crystal and a reference division of R = 32 yields,
                      
This represents the minimum step size achievable with a 20 MHz crystal oscillator and an R value of 32.

Frequency Resolution
Fine resolution can be achieved by having a very fine step size of 2 Hz (R=32) to 76 Hz (R=1) as indicated above. This step size is independent of the output frequency and applies to the PS-1200 and PS-2500. The PS-6500 will have a 4 times greater step size on the main synthesizer due to a fixed divide-by-4 to the divider input. Another way to look at the frequency resolution is in parts per million (ppm) relative to the output frequency. The formula for calculating the resolution in ppm is defined as follows:
                           
Example 3. Calculate the correction in ppm of a 1.9 GHz PLL output by using a 20 MHz crystal and R = 1.
                                  

Radio Calibration
The ability to calibrate a radio or a PLL output using a high resolution fractional-N synthesizer is much simpler than using Automatic Frequency Control (AFC) or characterizing crystal oscillators for temperature drift or aging and offers many advantages. During production, radios must be tuned to perform at expected frequencies within a predetermined tolerance.

Tuning radios can be time consuming and expensive. Frequently radios have a tunable component which is adjusted by a technician to calibrate the radio frequency output. A major reason for this requirement is due to the absolute frequency inaccuracy of the crystal. When a 10 MHz crystal oscillator is purchased there is associated with this part a frequency error. For example, a 10 MHz crystal might actually be 10.000005 MHz. If the value of N is 250, this would mean an output frequency of 2.5 GHz, this would translate to a PLL output inaccuracy of 1250 Hz. This error must be corrected prior to shipping the radio product. Further to this, once the product has been shipped the crystal frequency will also change due to temperature drift and aging.

In other words the frequency output value will constantly be changing. The amount will be dependent upon the type of oscillator being used. Temperature drift and aging of the crystal oscillator are relevant in the field, whereas the initial crystal inaccuracy is an issue in manufacturing.

A common method employed for correcting these problems is to use a Voltage Controlled Crystal Oscillator (VCXO). In this method the system determines that the crystal frequency is either high or low and therefore must be adjusted. A correction is introduced to the crystal to return the output frequency back to its original desired value. This method involves hardware components and software algorithms to perform this correction. A different method is proposed in the AFC section of this application note where the output frequency of the VCO is corrected.

A simpler method to correcting either the crystal frequency inaccuracy or the VCO output is to allow the crystal frequency to drift naturally and perform a calibration of the crystal relative to the output. The method is simple in concept. What we need to do to perform this calibration is to measure the output of the VCO and to perform a simple calculation to determine the actual crystal frequency. Correcting the output of a radio requires more calculations as the different IFs which are system dependent must be brought into the overall equation. If we program a fractional-N PLL to output a given frequency of 2.45617 GHz, then the synthesizer will perform a calculation to determine the actual Fractional-N value required to bring the output of the VCO to 2.45617 GHz based on the value of the crystal frequency using the following formula.
                                 
Example 4. Perform a calibration on a PLL operating at 2.45617 GHz using a 20 MHz crystal and a reference division of R = 2.
Therefore using formula [4]:
                                             
Therefore the required N value for the PLL to produce the desired frequency output is 245.617.

If we then ask the synthesizer to output the desired frequency, the output will be N x internal reference frequency FRef (which is the crystal frequency FXtal divided by the reference divider R) or
approximately 2.45617 GHz. At this point we need to take a measurement of the actual output frequency of the PLL. If the output is determined to be 2.45637 GHz, this tells us that the error in the output is 200 kHz. This also tells us that the crystal value that we have been using is in error. Substituting the measured output for the desired output we are able to calculate the actual crystal oscillator frequency.

                                         
Therefore the actual crystal frequency in the system is 20.001628 MHz, 1628 Hz higher than we expected. The new crystal frequency value would now be placed in non-volatile memory inside the radio to be used for future calculations.

The crystal frequency error can also be expressed in 81.4 ppm as in the following example:                                                                 
If we now use this new crystal frequency of 20.001628 MHz in the calculations using formula [4] we now determine that the new required N value.                                              
                           
Recapping, the actual crystal frequency was determined to be 20.001628 MHz which is a correction of 81.4 ppm. The new N value required in order to achieve the originally desired 2.45617 GHz output is now 245.596. Now that we know that the crystal frequency is actually 20.001628 MHz, we can use this number in all of the frequency calculations until we determine that we need to perform the calibration again. In production, this would mean automating the procedure without the need for tuning elements as all corrections are performed in software.

A key benefit is that radio manufacturers are no longer dependent upon the crystal vendors to manufacture crystals to very tight frequency tolerances as they can simply correct for these by using
a high resolution synthesizer. In fact, similar frequencies can easily be substituted with only small changes in performance due to higher N values. Using this method a 19 or 21 MHz crystal could easily be used. This type of calibration is not limited to final production test. If the radio system that is deployed in the field has a means of determining what the frequency output is, then we could periodically use this method in the radio to self calibration in the field and update the crystal frequency value in the non-volatile memory.

As was stated earlier, since the crystal frequency can be allowed to drift, all that we need to know is what the actual crystal frequency is at any given moment. The factory calibration would have previously corrected for the initial inaccuracy of the crystal oscillator therefore this is the starting point for any future drifting of the crystal frequency. Continuing to perform this calibration method in the field, the effects of aging and temperature drift can be easily corrected for in a TCXO. If the calibration is performed often enough and depending on the system requirements, then perhaps even a free running crystal could be utilized.

With this system calibration method being performed in the field, the system would be able to compensate for any temperature drift without requiring any knowledge of the system temperature.
There are several advantages offered by this method:
• Any similar crystal frequency could be substituted i.e. 24.1 or 23.9 MHz
• The absolute accuracy of the crystal frequency is no longer important as this can be corrected in
  production test
• Crystal aging now can be field corrected
• Temperature correction of the crystal can be performed real time without requiring prior knowledge
  of the temperature characteristics of the crystal or the actual operating temperature of the radio

Automatic Frequency Control
Automatic frequency control is a method of adjusting the output frequency of a PLL up or down, based on the system’s ability to measure the actual operating frequency or the ability to track a
drifting carrier frequency in a remote transmitter. In either case the correction can be performed directly by the synthesizer. If automatic frequency control is being employed, this can alleviate the need to perform any correction because of crystal inaccuracy, temperature drift or aging of either a local receiver or a remote transmitter. Typically, automatic frequency control is achieved by the use of a Voltage Controlled Crystal Oscillator (VCXO). A VCXO is a Crystal Oscillator (XO), a Temperature Compensated Crystal Oscillator (TCXO) or an Oven Controlled Crystal Oscillator (OCXO) with a varactor diode that is controlled by an external voltage. The varactor diode responds to a voltage which corrects the crystal oscillator frequency for crystal accuracy offset, temperature drift or aging effects. VCXOs are typically used in systems with 200 kHz channel spacing or less.

A VCXO has a frequency versus tuning voltage slope and also a linearity associated with this slope. The linearity is specified as the minimum and maximum slopes of the frequency vs. voltage. If a VCXO is operated with large frequency variations, this can cause a stressing which will result in degraded phase noise, aging and temperature stability, thus partially negating the very reasons for having selected a VCXO in the first place. If a system has the capability for correcting the crystal, then it is reasonable to assume that this correction could also be applied to the synthesizer output as well. This has many advantages: First, there is a cost savings as the expensive VCXO can be replaced by a less expensive crystal oscillator. Second, power can be reduced if the PS-XX00 series on-chip
crystal oscillator is used as it consumes much less power than external oscillators. Third, close in phase noise is improved as the phase noise of a crystal oscillator is lower than a typical VCXO. The actual corrections would also be smaller because the crystal is not constantly being corrected (stressed) which can cause further variations in aging, temperature sensitivity and phase noise. Fourth, there is no additional frequency versus tuning voltage slope or the associated linearity to contend with. Large variations relative to a VCXO are well within the normal operation of the PS XX00 series fractional-N synthesizer.

Crystal Characteristics
Crystals made from quartz are available in frequencies typically ranging from 10 to 150 MHz. There are various ways to cut quartz crystals which affect the performance. The “AT” cut has become
the most popular because it can operate at relatively high frequencies and gives excellent frequency versus temperature stability. The typical frequency range of a crystal based on a fundamental is about 30 MHz. Above 30 MHz the cut of the material becomes too thin for practical production. For frequencies above this point, odd integer multiples such as the 3rd, 5th, 7th or 9th overtone ofthe fundamental frequency are used.

Reference Crystal Accuracy
Crystal oscillators vary in accuracy as well. Expensive accurate crystals use a deposition technique to grow the material until crystals reach the desired frequency. These expensive crystals have the same phase noise and temperature characteristics as the inexpensive crystals but have a lower initial frequency offset error. This offset error is usually expressed in tolerance in ppm at room temperature. The actual output frequency can be anywhere within the specified range.
Example 5. Tolerance = +/- 10 ppm @ 25oC

If a low cost crystal with a possible large frequency offset is chosen in the system, then it is possible to correct for this inaccuracy in final test. By performing a measurement of the frequency output of the PLL synthesizer and comparing this with the desired output, then the error can be calibrated out of the system by storing a correction factor in non-volatile memory. The amount of frequency offset seen in a typical system does not exceed the synthesizers ability to perform the correction. The correction factor itself can be placed in a non-volatile memory in the system. This method allows a cost sensitive product such as a multi-mode handset to have an inexpensive crystal.

Reference Crystal Temperature Compensation
The output frequency of a crystal oscillator drifts with the external temperature. This drift is expressed in stability in ppm at room temperature. The frequency versus temperature curve can be seen in Figure 1 on page 4. Typical temperature drift of a crystal can be up to +/- 30 ppm over the operating temperature range.
Example 6. Stability = +/- 30 ppm (-10oC to +60oC)

Temperature compensated crystal oscillators (TCXO’s) have an added thermistor/resistor circuit that drives a varactor diode which is in series with the crystal. This circuit is designed to cancel the crystal temperature characteristics. The circuit will improve the temperature stability of the crystal, however it will never eliminate the temperature drift entirely.

Typical temperature drift of a TCXO can be 2 ppm over the operating temperature range. The Philsar PS-XX00 series of fractional-N synthesizers has an internal crystal oscillator. If a TCXO can be replaced by the internal oscillator and a basic crystal, then a cost and power savings compared with the TCXO can be achieved. Replacing the TCXO means that the crystal temperature characteristics will have to be corrected.
                                                             
 
                                     
Many radio systems now have the system temperature available in software. If we know the temperature, then all that remains is to develop the curve representative of the temperature characteristics of the crystal. The typical curves for the crystal can sometimes be obtained from the manufacturer. With this knowledge the synthesizer frequency output can be adjusted at the VCO via software in the microprocessor or DSP controlling the synthesizer.

If the radio system does not have the ability to measure temperature, then a simple circuit involving a thermistor and a low cost A/D can be utilized. The added cost of this would reduce the cost saving to be had by the elimination of a TCXO, however the designer now has the system temperature in software that can be utilized in other parts of the system. It can be pointed out that crystals do not all have the same temperature characteristics from unit to unit. This is a function more of the tolerances of the oscillator circuitry and the compensation network than of the crystal characteristics. TCXO
manufacturers will typically mark the package with an “offset” frequency either in Hz or ppm. Having the crystal oscillator circuitry in a very repeatable BiCMOS process may minimize the effect.

In any case, just as the TCXO manufacturer can tweak the offset manually, this can be performed as part of the automated test set up, where the actual output at room temperature can be measured and an offset in Hz can be fed into the system memory. Another benefit of performing crystal compensation in software is the fact that the designer is not required to state the operating temperature range when specifying the oscillator, as would be the case with a TCXO. This is because the temperature compensation circuit in a TCXO can not completely compensate for the individual characteristics of the crystal. The manufacturer will only match the thermistor/resistor network to the crystal curve
over the specified temperature range. As seen in Example 3, a 1.9 GHz system using a 20 MHz crystal
can be corrected by 0.04 ppm or by 76 Hz. This can eliminate the requirement for an expensive TCXO reducing the system cost.

Crystal Aging Compensation
Crystal output frequencies drift with time. Aging is caused by thermal effects such as temperature cycling, high ambient temperature or even high drive levels to name a few. The average drift of a crystal can be 2 to 3 ppm per year. This means that after a number of years the crystal may drift so that the VCO output frequency is not in the center of the channel. This can render the PLL and the radio inoperative. The amount of drift that can be tolerated is system dependent. The frequency error per year attributed to aging can be calculated by:
                          
Where DF is the change in the crystal frequency over the period of 1 year.

Example 7. Calculate the total frequency error after 3 years of a 1.9 GHz GSM radio using a 200 MHz high side LO and a crystal that ages 3 ppm per year. Using a 200 MHz high side LO means that the output frequency of  the PLL synthesizer would be 2.1 GHz. Therefore,
                           
Therefore, after 3 years the total drift would be 18.9 kHz. In a GSM system the channel spacing is 200 kHz. This means that after only 3 years, the actual frequency would be approximately 20% away from the center of the channel due to aging alone!

If the GSM handset in Example 7 is part of a multi-mode, multi-band handset that alternately uses (fall-back mode) the AMPS mode, then the errors in AMPS mode could also be calculated.
Example 8. Calculate the total frequency error after 3 years of a 894 MHz AMPS radio using a 45 MHz high side LO and a crystal that ages 3 ppm per year. Using a 45 MHz high side LO means that the output frequency of the PLL synthesizer would be 939 MHz. Therefore,
 
Therefore, after 3 years the total drift would be 8.4 kHz. In an AMPS system the channel spacing is only 30 kHz. Even though the total drift over 3 years is less than what it would be as in the GSM system, relative to the channel spacing, a frequency drift of over 50% has occurred in the AMPS example.

The average drift of a crystal can either be attained by the manufacturer or can be measured. Sample units can be measured over a period of time and statistical results maintained. The longer the period of time over which the tests are performed, the better the crystals can be characterized. This data can be fed into non-volatile memory aboard the system and any corrections can be performed at specific time intervals. Any corrections are performed directly at the VCO.

Doppler Correction
Many of the radio systems employed today, such as cellular phones, pagers and satellite handsets have one or both terminals mobile. This movement causes a change in frequency up or down according to the following formula:
 
Example 9. Calculate the doppler shift of a cellular phone operating at 1.9 GHz and in a vehicle travelling at a rate of 100 km/h.
The 176 Hz shift can be corrected to a resolution of 76 Hz or 2.4 Hz increments as seen in Examples 1 and 2.

In the case of a satellite handset communicating with a Low Earth Orbit (LEO) satellite the doppler shifts can be 25 kHz. Therefore, there is a significant requirement for correcting satellite handsets.
In the case of the cellular example, when the automobile is travelling away from the base station, the doppler shift is subtracted. When the automobile is travelling toward the base station it is added.
One problem associated with doppler correction is that the figure is not a constant. The automobile will often not be traveling directly towards or away from the base station but rather will be at varying angles or at rest. This means that the doppler shift can be anywhere from zero to the maximum value, as calculated above. The amount of inaccuracy that can be tolerated is dependent upon the system requirements. However, the shift in ppm can be calculated by:
 
Example 10. Calculate the doppler shift in ppm with an operating frequency of 1.9 GHz and doppler shift of 176 Hz.
 
We can look at the non-correlated effects of Doppler Shift, Temperature Drift, Crystal Accuracy and Aging. This can be calculated by:

 Example 11.  Calculate the total non-correlated  frequency error by  using the  individual error values from Examples 10, 6, 5 and 7.
                                 The resultant is a non correlated total frequency error of 32 ppm.

Crystal Temperature Characterization
A TCXO can be realized in software by characterizing crystals according to temperature. These crystals can be temperature-characterized by placing them in an oven and measuring the frequency output versus temperature curve over the desired temperature range. The number of temperature points would depend on what the final system accuracy requirement is. Typically a calibration point every one to ten degrees could be utilized. These values can then be used for correcting the output
frequency of the PLL. As seen in Figure 1, the crystal frequency versus temperature curve typically crosses the zero axis at about 25oC. Variations in the load capacitors of the crystal oscillator circuit and the manufacturing tolerances affecting the thickness of the crystal can introduce an initial frequency offset in the frequency versus temperature curve.

In order to reduce the effect of these variations, in final test performed at 25oC, an output frequency can be generated by the PLL synthesizer. The frequency can be measured and compared to the desired frequency. This error would be translated into an offset for the PLL. This value would be placed in non-volatile memory and used to permanently offset the synthesizer output. Alternatively, the correction could be performed as in the Radio Calibration section above, where the error is used to recalculate the crystal reference frequency.












































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