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.
