perf T&F re perf T&F re

A6-1PPS16One possible method of extracting frequency offset fromphase data is a quadratic least squares fit on a block of data.This is a standard method for extracting phase offset, frequencyoffset, and frequency drift from phase difference information. Havingextracted the offset frequency, we can then make a correction to thecontrolled oscillator to remove the offset. If the control constant wasknown exactly, there would be no under or overshoot. The problemwith this method is that we do not know how large to make theblock of data that we analyse. The reliability of the fit is given bythe correlation coefficient, and ideally this should be monitored ona continuous basis. What is required is a continuous least squaresprocess. This is of course, a Kalman filter, and this was the eventualmethod selected for implementing the control algorithm.The Kalman filter will be briefly described in general in a (hopefully)simple way, and then the specific implementation for our problemwill be described in more detail.A block diagram of a Kalman filter is given in figure 1. It is basicallya recursive estimation, based on noisy measurements, of the future“state” of a system . The system is defined as a “state vector” anda “state transition matrix”. The system in our case would be thecontrolled oscillator that we wish to predict, and the state vectorwould contain the phase offset, frequency offset, and frequencydrift variables. The “state transition matrix” defines the differentialeconomical design. The basic ns clock to give a basic ±200 pstiming Tel resolution +44 is (0)1803 400 ns resolution. 862062(one processor cycle at a 10MHzclock frequency). Fax +44 (0)1803A time867962interval expander mustbe calibrated as otherwise aThe time interval expander extendsthe resolution by 2000 the time error pulse rollsglitch will be produced whenoverFig. 2: Kalman filterond, the dead time is used tocalibrate the time expander. Thehardware generates exact pulsesof 100 ns and 500 ns by gatingfrom the 10 MHz clock. Theseare expanded and measured. Therelationship that exists between the state variables over one timeincrement. The concept of a system driven by noise processes isimportant here. If our Rb had absolutely constant drift, its outputphase would be known for all time once the initial drift , frequencyoffset and phase offset had been determined. Data gathered a yearago would have as much validity as data an hour old. If the Kalmanfilter is given this model of the Rb, the results are identical to theleast squares fit of all the data. Of course the quadratic least squaresfit assumes that the Rb can be modelled by three constants.A more realistic physical model would allow the drift to vary.If this varied in a deterministic way, we should add a further termto the state vector to reflect this deterministic process. However ifthe variation was random, we can tell the Kalman filter that thisis so. Note that the filter is only optimum for white gaussian noiseprocesses. However in our case we can model the noise of the Rboscillator more accurately by adding white gaussian noise to eachterm in the state vector. If we add some uncorrelated noise to eachterm in the state vector, we end up with white phase noise, whiteFM noise, and random walk FM noise due to the single and doubleintegration in the model. This is shown in figure 2.The measurements are also assumed to be contaminated withgaussian white noise. In our case we only have one measurement,that is phase offset. We do not know that the main contributer tomeasurement noise, the GPS receiver, is either white or gaussian.16 bit DACs are used, with theoutput However of the fine this tune is a DAC limitation of the simple Kalman filter that we intenddivided by 256 and added tothe to output use. of If the we coarse are sure tune of the characteristics of the measurement noise,DAC. we This can gives include effectively this 24 knowledge by adding more terms to the statebit resolution with an overlapbetween vector. the We coarse are and then fine essentially including the known aspects of thetune measurement DACs. A software in the nor-systemalisation process ensures thatmodel.the fine tune DAC is used fortuning As most well of as the the time. state Only vector, the Kalman filter maintains awhen matrix the controlled that gives oscillator the current variances (mean square error) ofhas drifted out of range of thefine the tune quantities DAC would the coarse in the state vector. These give us current estimatestune DAC need adjusting, withthe of chance the of likely a very small errors glitch in the state vector, in our case variances of phasein offset, the tuning frequency voltage. A precision,low noise, voltage referenceoffset, and frequency drift. These will be very usefulis used for to display supply the to DACs. the user. They also have another use, which will beThe demonstrated microcontroller is provided later. In effect they control the “bandwidth” of thewith an RS232 interface. A simpleset of control codes enablefilter. As more data comes in, the variances decrease, and the filtermonitoring gives more and set weight up of the to the current estimate( which represents thecontrolled oscillator parametersto complete accommodate history a wide range of the data), and less to the current measurement.of controlled The measurement oscillators. A Windowsfront end program will usevariance, which we have to tell the filter, alsothe affects control codes the to “bandwidth”. enable the If we tell the filter that the measurement isoperation of the PLL to be monitorednoisy, with it real reduces time graphs the of bandwidth.performance measures.So far we have considered the Kalman filter as a device for analysingSoftware the incoming design data in an optimum way. However we need toIn control normal operation the Rb the oscillator, auto and reduce the frequency offset tocalibration performs calibrationcycles zero. every An 20 ms. elementary The approximatetime of arrival of the nextmethod would be to write periodic corrections1PPStoinputthe Rbpulsecontrolis known,DAC,soand wait for the Kalman filter to track out thethe resulting calibration cycles discontinuity are paused in the measurements.However there is a muchwhile the 1PPS is measured. Theraw better measurement way. of If the we arrival adjust the frequency offset term in the state vectortime at is the corrected same for time the actual that we correct the Rb , the filter will ignore theexpansion ratio and is scaled tolie correction, in the range -500.000000 and no to extra settling time will be required. In effect we+499999999 ns relative to theinternal are defining clock. the model of the Rb to have a frequency discontinuity atTechnical feature 19The first valid 1PPS edge to arriveafter reset is used to zero theinternal clock. This makes thearrival time initially close to zero,and avoids problems with lackof precision in the floating pointEmail sales@quartzlock.comwww.quartzlock.com