Design and Development Considerations of Voltage Controlled Crystal Oscillator (VCXO) Networks

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1 Design and Developent Considerations of Voltage Controlled Crystal Oscillator (VCXO) Networks David Green & Tony Scalpi, Cypress Seiconductor Corporation Overview The concept of placing piezoelectric devices, or crystals, in oscillator circuits by today s standards is considered a coon, well-practiced experience. The oscillator functions norally under all stated conditions with little thought given to the science behind the technology. The purpose of this paper is not to cover the aspects of the fixed frequency syste, but rather, to explore the ipact of adjusting the crystal frequency. To this end, the VCXO, or Voltage Controlled Crystal Oscillator plays a pivotal role in serving this critical need. The VCXO introduces to the syste a echanis to adjust an oscillator output frequency that changes frequency as function of an input control signal. In ost cases, the VCXO functions as part of a larger closed-loop syste, serving as a frequency tracking echanis fro external sources often derived fro error control voltages extracted through the deodulation process. The relationship between the control input and output frequency ost often does not follow a 1:1 relationship across the full operating range of the control input. In fact, in any cases the relationship is syetrical but non-linear especially as the VCXO axiu or iniu operating range is et. Such frequency softening effects help to cushion the potential for abrupt frequency transitions to occur in the event the closed-loop response approaches rail. Well-crafted systes always exhibit sooth and clean frequency transitions as the control signal is varied over the full operational range. Real-world experience strongly hints that VCXO operation does not always turn out to be as sooth as originally presued. In fact, if iproperly designed, the intended transfer function of voltage to frequency is not always followed. About the only consolation I can offer in this regard is that experience shows a repeatable proble, and consistently wrong regardless of the direction of the control raping signal. The bigger proble, however, is that a box-to-box coparison ay show that an adjacent syste ay not exhibit a proble, supposedly with the sae circuitry. The transfer function in question generally exhibits one unique property, which is the generation of a rather sharp or abrupt frequency transition far greater than norally expected for a sall increental step size. The behavior of the VCXO iediately surrounding the transition zone ay also show isbehavior. This is often expressed as a reluctance to track the expected curve. However, in soe cases the transition unexpectedly appears without warning. 1 of 23 djg@cypress.co

2 Abrupt changes in frequency are not always catastrophic and can only best be defined by syste particulars. Clearly, a syste capable of handling the transition will ask the effects. Given the closed-loop nature of the syste, the syste designer ay never know that a potential proble ay exist, or care for that atter as long as the syste can always copensate over all operational conditions. However, there are any cases where the error signal iposed on the closed loop syste is so excessive as to cause syste loss-of-lock. It turns out that not only is the agnitude of the frequency change a factor, but the location in the frequency-voltage curve plays into the probability of syste failure. For those fortunate to have this transition occur in an area norally used by the syste, at least early syste detection is far greater. Contrast this, however, to cases where the transition is located on a portion of the VCXO transfer curve where the syste is unlikely to operate, then the ystery really deepens when unwelcoe field failures surface. Good VCXO syste design ensures that the VCXO center operating frequency is surrounded by a well-balanced pulling range, and is norally expressed in PPM fro the nor or center frequency. PPM is an expression which is a noralized ter for frequency offset expressed in Parts per Million. Generating a VCXO transfer function requires a prograable control, a stable frequency easureent instruent and soe eans whereby the output frequency is recorded over the full step resolution of the VCXO operating range. The purpose of this paper is to help the syste designer understand how VCXO frequency transient behavior can best be avoided. Much of the ensuing work up to this point covers the basics so that the fraework is properly set for a spirited discussion on this interesting but largely unwelcoe VCXO phenoenon. 2.0 Crystal Oscillator Overview Undoubtedly, during the typical electrical engineer s design career ost will work with soe sort of crystal clocking source. After all, the ubiquitous quartz crystal serves as the heartbeat of the syste quietly vibrating away without cause for concern. The successful design passes initial testing and oves to the production stage. Production easures gear up for price reduction. A coponent all too often found on the list is that of the crystal. The story is largely the sae pick a lower cost unit exhibiting the sae center frequency and loading paraeters and the production engineer s task is coplete. After all, if it worked in the original design why should there ever be a substitution proble during production? Should a postproduction failure rate begin to eerge, iproper oscillator operation is the last thing ost consider as being a potential proble because with casual observation it appears to be fully functional. Fixed frequency oscillators generally show probles during start up. During the noral course of debug activity, naely through the start-up/shut-down sequence, syste defects are ferreted out early. VCXO design, however, requires ore than startup analysis. Not only ust oscillator startup operation 2 of 23 djg@cypress.co

3 occur, but also correct tracking to the transfer function ust be tested. There is a strong tendency to excuse inor variations as being inor iperfections in the oscillator network. What ay in fact be really happening is that the network is kindly giving you a clue that a frequency transition is about to occur, or even in the ore subtle case you are just on the cusp of experiencing a transition. Being sensitive to these clues can save a lot of heartache fro occurring later on in the project cycle. Good VCXO design requires a thorough understanding of how the active gain eleent and crystal behave in the syste; first to fully understand why it will oscillate, then to ove into what happens in the oscillator circuit network as coponent reactance effects take place in the network. Finally, we need to learn what paraeters are necessary to specify when it coes to correct crystal selection. Along with this discussion, our attention will focus on the Pierce oscillator configuration as being the industry workhorse for coon digital syste applications. 2.1 The Barkhausen Criteria for Oscillation First things first, we need to understand the Barkhausen criteria for oscillation. Siply stated, in order for oscillation to occur sufficient gain and proper phase alignent ust exist in a feedback syste. It is as siply put as that, but actual experience says that this is soon forgotten when the active gain eleent oscillates when it is not suppose to, and the oscillator sees to behave like an ordinary aplifier. Oscillation ay occur anytie anywhere should these intended or unintended conditions exist in a syste. For the digital designer, the conductive path (or wire) is the only eleent that can coplete the feedback path. However, for the seasoned RF designer, a radiated path, typically ore subtle, can serve the sae eans. It akes no difference to gain eleents how the feedback signal arrives back to the input only that if present with the right phasing conditions the stable syste is ripe for oscillation to occur. Other factors that ake a great design turn ugly are the unwelcoe birdie effects of oscillation that often results fro gain eleents that break sporadically into oscillation then agically disappear when a probe is attached to the syste. The point that requires re-ephasis is that regardless of what the designer intends any syste coprising sufficient gain and the proper phasing creates the recipe for oscillation to occur. Therefore, whatever the resulting frequency or frequencies siultaneously present on the output, there should be no ystery as to why they exist since this is nothing ore than a network expressing itself in ters of the proper gain and phase that eet the Barkhausen criteria. Many designers erroneously feel that an oscillator in operation is soehow iune fro siultaneously producing other output oscillation tones. Nowhere is there a stipulation that the Barkhausen effect is liited to defining just one output frequency, or tone. Anytie a conditions exists where aple gain and proper phase exists oscillation ay occur. The fact is that noise is always present in the syste regardless whether a tone is present or not. This opens the 3 of 23 djg@cypress.co

4 door to the possibility that ore than one tone ay be siultaneously present. This does not say that an oscillation event is perfectly independent. In a siple world, such operation would be totally independent. Unfortunately, there is usually interdependence where the effects of energy being generated ay odify or excite yet other odes of operation. The net effect is that due to the presence of unwelcoe oscillation, the oscillation of interest ay be ipacted. Further, sporadic oscillations can coe and go. While the ystery of why this is happening can be difficult to resolve, understanding that the oscillation is a natural consequence of dealing with the Barkhausen effect ust be understood and accepted. The syste challenge lies in the ability to design aplifiers that provide adequate gain and bandwidth over all operating conditions desired, and that they function only for the intended ode of operation. 2.2 Building an Oscillator Network 101 Before delving into a spirited discussion on VCXO analysis, the need to understand fundaental oscillator basics and noenclature usage is necessary. We will need this knowledge base as we start to concentrate on network specifics. We start our discussion with a wide-bandwidth aplifier that theoretically inverts the phase between input and output over a relatively wide frequency bandwidth and runs in linear ode (that is, a sinusoid input produces a sinusoid output). A resistive eleent is placed to set bias to the logic input threshold region and to provide a feedback signal back into the input. -A Figure 1 Basic Gain Aplifier with Feedback Power f o Figure 2 Power vs. Frequency 4 of 23 djg@cypress.co

5 Consider the circuit network in figure 1. Two fundaental eleents exist; an inverting gain aplifier and a resistive feedback. Reeber that we discount the resistor as adding phase. What will happen if an input generator is added and frequency swept while the relative phase difference is easured between the input and output? For low frequencies or for frequencies well within the operational bandwidth of the aplifier the output will be aplified and inverted. In fact, the phase should be really close to the ideal 180 as expected. In reality, however, we know that as the generator sweeps to higher frequencies, the phase through the aplifier begins to change fro the ideal 180. Sweeping yet higher ay show a lagging phase response to the point where at a given frequency the output ay produce a frequency in phase with the input (or ultiples of 360 ).In this case, the safe harbor of 180 ends up at zero. Continuing the input frequency sweep ay reveal yet other frequencies that exhibit the exact sae zero phase crossing. The question now to ask is if a syste like this will oscillate. We know that at least one condition of the Barkhausen criteria is et: proper phase alignent. Can the condition of aple gain be satisfied? That really depends on the aplifier. If sufficient gain cannot be et then oscillation will not happen but if there is just enough gain in the syste then occasional sporadic and/or long-ter oscillation ay be possible. Can ore than one oscillation take places siultaneously? The original sweep ay provide soe clues to this, especially where zero phase crossings occur, so the possibility ay exist. Understand that this is a siplification for discussion purposes, and as such, discounts generator-loading effects, which would have to be accounted for in a real situation. Our network at this stage is therefore left to the whis of aplifier capability. Since the resister adds no phasing inforation, it siply presents to the aplifier an attenuated replica of the output, which is a function of the ratio between the feedback resistance and the ipedance seen at the input. -A Figure 3 Aplifier with a BPF in Feedback Path 5 of 23 djg@cypress.co

6 Power f filter c Figure 4 Power vs. Frequency Now consider figure 3. In this exaple, a Band-Pass filter (BPF) is added in the feedback path. The feedback resistor reains to aintain proper biasing. With the introduction of the band-pass filter, only a sall frequency spectru slice can pass through the filter while all reaining frequencies experience attenuation. A network of this architecture ight be ore prone to eet Barkhausen criteria due to the cobined effect of the phase shift introduced by the aplifier in cobination with the phase shift of the band-pass filter. This is particularly true when it coes to ajor phase changes in the filter transition region, as opposed to the filter pass band region. Owing to the nuber of poles and zeros present, the steepness of the filter roll-off curve can cause ajor phase variation with little change in frequency. This is where the Q of the filter network also coes into play. The higher the filter Q the ore selective the filter becoes and the steeper the roll-off slope. By assuing the Barkhausen criteria is et, a variable reactance introduced into the syste would require little change for oscillation, especially if operation could be convinced to operate in the roll off regions adjacent to the filter pass band. Aplifiers aplify everything they are capable of aplifying. The point being that noise energy coponents are part of this, but too often disissed as a factor of concern especially for the digital syste designers. Noise energy is always aplified and passed through the band-pass filter to the input. For any digital syste designers, noise is often translated to jitter. While ost energy is attenuated, a portion thereof that happens to correlate to the BPF filter response passes through the filter. What keeps this process fro getting out of control is that the odds for noise correlation in the network for any given period are low. However, this is how oscillation starts. Noise energy naturally present in the syste that can eet Barkhausen criteria continues to be aplified through the closed loop (it naturally correlates inside the network). As this process continues a signal is built up which begins to exhibit a large signal-to-noise (SNR) ratio as copared to the non-correlated noise in the syste. The resulting frequency spectru starts to take on the for in figure 4. An oscillator network of this nature, as copared to the original architecture is uch ore likely to behave in a predictable anner as feedback energy is ore controlled vs. that of the pure feedback resistive approach. What does this all prove? Prograable reactive eleents in the feedback path with adequate Q present allow phasing adjustent, which translates to a change in frequency if it is to continue to oscillate. Correlated energy is ephasized because as the tone 6 of 23 djg@cypress.co

7 is shifted, the old tone no longer eets Barkhausen criteria and dies, while the new tone is built up fro noise through the correlation process discussed. All of this occurs rather quickly and so it would see that there is nothing ore than one continuous variable tone. If no energy in the syste can eet Barkhausen criteria then oscillation will fade, and the network will stabilize to soe DC constant. -A Figure 5 Non-linear Aplifier Power f 0 3 f 0 5 f 0 Figure 6 Multiple Tone Generation due to Square Wave Up to this point, we are discussing discrete frequencies through a linear aplification eleent. What happens if the aplifier output is non-linear, that is, square waves are produced on the output? What can be said about the gain? You know this type of network the ubiquitous inverter found on practically every logic syste design ost likely configured as the Pierce configuration; super high gain and wide bandwidth. In fact, so uch gain is norally generated that the output saturates twice for every clock cycle. Since square waves are being generated on the output a quick review with a spectru analyzer reveals that for a perfect 50% duty cycle, odd haronic energy is generated. Obviously, the lessthan-perfect case generates even-haronic tones. In practice, however, these are attenuated enough as to not be a real eleent of concern in a syste. At this point, I need to introduce a new ter to our vocabulary called electrical haronics. Electrical haronics are defined as haronics specifically generated by the active gain eleent. The additional energy now present in the network has increased as copared to the earlier linear exaples with the presence of ultiple output tones to operate at precisely the 3 rd, 5 th, 7 th haronic respectively. With the BPF present in the feedback path, all but one tone arrives 7 of 23 djg@cypress.co

8 back at the input. If the phase is correct, then oscillation ay occur. Now suppose an additional BPF was inserted in the feedback path where it happened to be centered at the 3 rd haronic. Could both the fundaental and 3 rd siultaneously satisfy Barkhausen and oscillate? The siple answer is yes as long as the aplifier and feedback can support the necessary gain and phase for such operation. Clearly ore energy is required to support two odes of operation assuing that the fundaental is as strong as in the one-tone case. Coon non-linear aplifiers found in the ajority of digital type applications have the gain necessary to support such odes if the opportunity presents itself. Syste Q Syste Q has to do with the use and efficiency of energy storage in the network. The higher the Q the ore narrow in bandwidth we can construct a band-pass filter. Naturally, this leads to steeper skirts. Crystal eleents exhibit an incredible aount of Q or energy storage. The Q present at the oscillation points of interest creates steep phase slopes. Therefore, reactive changes in the network forces oscillation to shift in accordance along the crystal reactance curve. Syste Q also plays the role of syste stability. Owing to the high Q of the crystal, frequency stability follows which is paraount in aintaining stable clocking sources. Negative R I a not going to labor on this topic, but in oscillator design, -R (pronounced negative R) plays a role in helping to define gain in aplifiers. While I a largely skeptical of Spice in odeling crystal resonant structures, generation of R for the gain aplification section, in conjunction with the loading capacitors can prove useful and reasonably accurate for ost purposes. Successful siulation and generation of R results in a gain curve expressed as R on the negative vertical axis and +R on the vertical positive axis. Both of these eleents are referenced against a frequency sweep. Siulation setup is norally accoplished by using a swept AC current source in place of where the crystal connects into the syste and then plotting the voltage in response to the stiulus. The voltage is typically noralized against a 1-ap reference as it akes it easier for post processing. Only the real part of the coplex expression is used for this analysis. Shaping and shifting of the curve vertically is done through aplifier design and bandwidth liitations that hopefully best fits to the yriad of crystal solutions found on the arket today. Naturally, for optiu cases, where crystal selection and usage is liited, and well understood, provisions can be ade in the R network curve to optiize to these conditions. It is coon to see R plots which start at any negative hundreds of ohs on the low frequency side, only to approach the zero oh point in a negative exponential fashion. Figure 7 is such an exaple where the gain quickly peaks at around 15 MHz. Even at a 100 MHz, there is aple R for crystal startup. This is typical of devices found on the arket today and represents the bandwidth available in these solutions. 8 of 23 djg@cypress.co

9 f (MHz) -R (Oh) Figure 7 Exaple -R Plot Piezo-Electric Property Overview All of this discussion now leads to discussing a special type of filter called the crystal. The core eleents will be briefly discussed which are necessary as we ove into oscillators using piezoelectric eleents. One of the ajor sources of isunderstanding is that of series vs. parallel ode of crystal operation. This is an area where isconception abounds and I hear it repeatedly, therefore this area needs ephases. One crystal eleent is not without the other as these odes of operation are intrinsically part of the piezoelectric eleent. In light of the fact that a crystal datasheet ay indicate a parallel-ode of operation, this does not preclude the possibility of running the crystal in series ode! What the datasheet is telling you is that for a particular loading, the crystal will resonate at a particular frequency for the specified ode of operation. The key to ensure that the crystal operates in the correct ode is to place it in an environent whereby the correct ode ay be exploited while discouraging other odes of operation. Note that this stateent is not liited to fundaental series or parallel ode of operation, but for overtone odes of operation as well. Where in the crystal datasheet does it say that I cannot run the crystal in overtone operation? In the vast ajority of cases, it does not preclude this operation. It ay not guarantee specific results, but it does not stop it. A parallel-ode specified crystal ay be run in series-ode by changing the network structure such that the phase relationship causes the crystal to function as to what appears as a low-ipedance resistive ode. The secret to good crystal behavior control is to look for ways to adjust the phase of the network by using reactive eleents in the network that siultaneously encourage one ode 9 of 23 djg@cypress.co

10 of operation while discouraging other odes of operation. Naturally, a good understand of R, that ensures that aple gain is present in the syste is iportant. By definition, a series resonant ode of operation supports eleents operating in a low resistive ode with phase, or ultiples of 360. The coplete network solution is structured such that with proper gain present and the crystal, once resonant with 0 phase shift, copletes this operating condition. It is therefore up to the oscillator designer to ensure that the coponents around the crystal are designed such that this condition can happen. Now, shifting the crystal either lower or higher in frequency with-respect-to (w.r.t.) the series resonant frequency will ake the crystal appear either capacitive or inductive, respectively. Parallel ode of operation eans that the crystal will appear inductive to the network, or that the crystal is to resonate slightly higher in frequency fro that of series resonant ode operation (why we want to do this will soon becoe clear). Parallel ode of operation does not ean that the crystal is operating at the actual crystal parallel resonant frequency. Good oscillator design is about proper crystal placeent such that expected results are achieved overall operating circustances. 10 of 23 djg@cypress.co

11 Crystal Series Resonant Frequency; appears resistive Crystal appears Capacitive Typical region for Parallelode Operation Crystal appears Inductive Inharonic Spur Region Crystal Parallel Resonant Frequency; high ipedance Figure 8 Crystal Forward Gain, S21 representation for a 50-Oh Syste Figure 8 is just too good to pass by, as it will help relate this discussion about series and parallel ode operation just described. Through use of a network analyzer running in two-port ode, the crystal forward gain, or S21 ay be analyzed. The purpose is to provide a relative feel for what the forward transission looks like in a 50-oh syste close around the fundaental frequency of crystal operation. For this particular exaple, a frequency sweep is conducted over a 300Khz range with the crystal operating parallel frequency set a 13.5Mhz for a specified load (reeber that in this exaple we are not loading it exactly according to the datasheet so we can t expect it to be exactly centered on 13.5Mhz). At the start of the sweep, the crystal appears relatively lossy, going capacitive as it begins the clib to the iniu attenuation point. At the peak is where the crystal operates as series resonant. At series resonance, the crystal appears resistive, and a sith chart looking at the coplex ipedance would verify this. Transitioning through this point the response starts to grow inductive as crystal 11 of 23 djg@cypress.co

12 forward gain attenuation losses quickly build on a steep negative slope as it transitions to the parallel resonant frequency. With approxiately -75 db of attenuation, significant loss is exhibited at approxiately at MHz. This is where any ake the istake in thinking that a parallel ode crystal operates at the parallel resonant point; it siply does not. Crystal parallel ode operating is really referring to an operational region above the series resonate point that slides along the S21 curve, appearing inductive to the surrounding oscillator network. As we start to understand the Piece network, this will becoe ore obvious as to why this fits together so well. Crystal Inharonic & Overtone Discussion Continuing with the frequency sweep, past the crystal parallel resonant ode the crystal produces soe ore bups along the way. These are tered spurs, or ore exactly inharonic spurs. This is another source of confusion for any because they think that this is related, or is showing overtone operation such as the 3 rd haronic. Inharonic spurs have nothing to do with overtones. This is inherent to the crystal and represents areas of crystal operation that we want to avoid. Note that the axiu upper frequency is 13.7 MHz, which is not even close in frequency to excite 3 rd haronic operation. A piezo eleent atheatical description is a coplex ulti-diensional proble not easily resolved in detail. In discussing haronics earlier in this discussion, I entioned electrical haronics as those generated fro the nonlinearity of the aplifier. This is iportant in order to set the stage for another set of haronic excitation odes naturally present in the piezoelectric aterial. Excitation of the crystalline structure at frequency ultiples of approxiately 3, 5, 7 (etc) of the fundaental results in what we will call echanical haronic, or echanical overtone odes of operation. Crystal echanical odes are representative of how a crystal can be excited as being stiulated by electrical tones generated by the aplifier. By understanding how the haronics play into the syste, avoidance of VCXO frequency transition probles can be avoided. Referencing back to figure 8, generation of a plot of the 3 rd haronic takes on the sae pattern, only the pattern is shifted downward on the scale (ore overall attenuation) and the dynaic range is reduced. The key echanical properties of the crystal is that resonant frequencies of a vibrating structure reveals that integral frequency ultiples between the echanical fundaental and echanical 3 rd, 5 th, 7 th etc are not exact nuerical ratios. This is largely because echanical vibrating systes are not perfectly one-diensional. Finite plate size plays an iportant role as it leads to creating other odes of vibration other than the odd-integral haronics of the fundaental. The good news is that the crystal blank and electrode size can be designed so that we can specify placeent of the 3 rd haronic with respect to (w.r.t.) the fundaental. The reason the crystal norally resonates at the anufacturing fundaental frequency as opposed to naturally running at an overtone has to do with the law 12 of 23 djg@cypress.co

13 of least resistance. The resistance of the fundaental ode is uch lower than that of the higher overtones and as such like ost things in nature if left to its own erits the network will choose the path of least resistance and operate at the fundaental. In fact, at the operating point of resonance, the resistance seen at the 3 rd haronic is approxiately nine ties that of the fundaental. This square law relationship continues for the 5 th, 7 th and higher haronics. Crystal Electrical Model Crystal electrical odels can be siulated with soe degree of accuracy, but siulation where ultiode interaction takes place requires a far ore coplicated odel. Fro an electrical standpoint, figure 9 outlines a coon electrical odel. Capacitor C 0 specifies the intrinsic capacitance as generated between the crystal plates. This is often referred to as the static capacitance since this is representative of intrinsic plate capacitance. C 1, L 1 and R 1 are representative of the fundaental otional leg of the coplex intrinsic crystal internal network while two additional otional legs are represented in the exaple that cover the 3 rd and 5 th overtones. Associated with each otional capacitor is a otional inductive eleent. We use the ter otional so that it is understood that these eleents are electrical equivalents only and to distinguish the fro a real capacitor or inductive eleent that would be either too sall, or too big to represent with real coponents. C o L C 3 3 L C 2 2 L 1 R 3 R 2 C 1 R 1 C 1 = pf R = R N 2 n 1 C C n = N 1 2 = L n = L 1 Figure 9 Crystal Electrical Equivalent A careful review of the otional capacitance, inductance and resistance odels leads to soe fascinating relationships. The otional capacitance for the fundaental ranges fro approxiately 0.1 to 0.001pF, but generally favors the low side (<30fF). This is sall when you think about it, but the otional 2 capacitances for the echanical haronics are further reduced by1 N for each overtone excitation ode. Yet, the otional inductance for every otional leg is 2 always the sae. The resistance increases by N for each higher haronic so it should be obvious that the expected ode of operation is the least resistive as the 3 rd echanical haronic will produce a resistance 9 ties greater when copared with that of the fundaental. Given the above atheatical relationships, it is tie to start putting the puzzle together. 13 of 23 djg@cypress.co

14 Shunt capacitors in series or shunted off the crystal legs (we also call the loading capacitors, C L ) are doinated by the otional capacitance value for a particular ode of operation. This is because fro an AC perspective, the series capacitive equivalent is always doinated be the sallest value in the chain. The net capacitive value is less than the sallest eleent in the tank. The second point, subtle and very iportant -- when the shunt capacitors (as in the case of a Pierce configuration) change values (in an attept to shift the frequency a VCXO effect) the frequency shift, or operational range of the echanical overtone is narrower as copared to the fundaental. Reeber that the inductance is always the sae for the excitation of any otional leg, but the series otional capacitance for the 3 rd 2 overtone is1 N saller. Since the external load capacitor values are the sae for the fundaental or 3 rd overtone, the frequency swing range will be reduced as copared to the fundaental. Said another way, a delta change in the fundaental frequency (say fro a VCXO frequency shift) is not linearly atched with the sae delta shift in frequency when it coes to the third haronic. The 5 th haronic shift is even worse. Thinking further on this topic, exciting a crystal to operate in 3 rd overtone or 5 th overtone actually produces a ore stable fixed oscillator as copared to using the fundaental ode. However, VCXO operation with overtones is not practical due to the stiffness of overtone operation. 2.2 Crystal Pierce Oscillator Topology Our attention now turns to the ubiquitous Pierce oscillator. Why a Pierce configuration? My speculation is that two-pin inverting eleents are well understood by the logic designers and as such, tradition has worked its agic into the inds of designers worldwide. -A Figure 10 Ubiquitous Pierce Oscillator Network Configuration Figure 10 should start to look failiar. The filter presented earlier is replaced by a different filter structure called a crystal. Besides this, the only other difference is in the addition of the loading capacitors, C L on each crystal leg. If you reeber the discussion about the S21 characteristics, then the use and need for the shunt capacitors will soon becoe ore apparent. As a reference point, the crystal, in conjunction with the shunt capacitors fors a tank circuit ipleentation. The question is will this network oscillate? Most everyone will raise their hands and say yes because ost of us know by experience that it should oscillate. After all, 14 of 23 djg@cypress.co

15 this is not new aterial! Nevertheless, why should it oscillate? The fact is that oscillation will only occur at the frequency point where the network fully functions to eet the Barkhausen criteria; a balancing act of phase and gain that produces an output frequency. Generally, due to the abundance of gain in ost non-linear aplifiers, it ostly boils down to phasing. Our network, however, is soewhat ore coplicated since we have the equivalent of any reactive eleents sandwiched in that little echanical can called a crystal R out -A Mode of operation Figure 11 Pierce Operational Phasing Exaple Figure 11 outlines a siple restructuring of figure 10 and ay represent soething ore akin to phasing assignents during actual operation at frequency. The aplifier actually no longer behaves as an ideal generator, rather it is lagging by 10 fro the theoretical causing a net 190 phase shift. Resister R out represents the resistance generated by the aplifier output being fed into the first capacitive shunt load (in reality this is an ipedance, but we will siplify for this exaple). At the operating frequency of interest, this presents a 70 phase change while the crystal in cobination with the other shunt produces the reaining 100 of phase shift. All of this agically adds up to 360 back at the gain stage input so that the energy is correlated throughout the syste. The only agic that you have to understand is that if there is a frequency that can atch the phasing criteria with proper gain you will experience oscillation and that the frequency was built out of noise correlation naturally in the syste. There is other noise energy present (it does not just go away because soething starts to oscillate), but unless this energy can phase correlate with the necessary gain, it will reain an integral, but hopefully less significant eleent in the syste. Now that we have an understanding of the respective phasing eleents in our syste, it is tie to look carefully at how the crystal electrically appears in this diagra as we reference back to figure 8. The purpose of the shunt capacitors is to perfor two ain functions. Our first need of the shunt capacitors is to load the crystal so that it appears inductive. Our S21 plot indicates that for the crystal to appear inductive it needs to be operating above series ode. Adding shunt capacitors creates the condition where we end up creating a positive crystal phase change. We are not talking about large aount of phase, but since the curve is steep, it does not take uch to ake that frequency change. Note that we are running nowhere near the actual crystal parallel resonant frequency. As you can see fro figure 8, we can ride along the agnitude curve until either we 15 of 23 djg@cypress.co

16 run out of phase variance, or we kill the gain. Since the vertical scale is 10dB per division, our zone of operation cannot be extree as the crystal attenuation alone ay end up killing oscillation R out -A C L Mode of operation C L Figure 12 Pierce Configuration with Adjustable Shunt Capacitors Figure 12 shows a Pierce VCXO configuration, where the reactive shunt capacitors in the crystal tank can now be adjusted. Changing the values of the shunt capacitance ends up changing the phase through the network and odifying the load reactance. As the phase changes, the only way that oscillation can be sustained is that the frequency of operation ust change to naturally copensate for these effects. Figure 12 provides a feel for what ight happen, phase wise, in a VCXO over a relatively narrow pull range. Naturally, if the phasing becoes too extree, or the gain dies out, then Barkhausen requireents are no longer et and oscillation dies. Another point of consideration is what happens on the gain aplifier due to changes in the load reactance placed byc L. As the capacitive aount of CL increases, the reactance decreases. This has the effect of increasing the RF current through the crystal. As the current increases, the power dissipation increases which has the effect of exciting other unwanted odes. The key is to always run the iniu aount of power through the crystalline structure as possible, but still allow for adequate operating argin for startup and noral operating conditions across voltage and teperature variations. Non-linear aplifiers are prone to exerting this type of operating condition because a square wave output is a serious indicator that ore RF output power is available if the tank can take it. VCXO Design Considerations The objective of a VCXO is to function as the core frequency-tracking eleent in the syste. A control signal, ost likely consisting of a control voltage is presented to the VCXO device and the output frequency tracks along a predeterined curve. Tracking curves are not always linear functions and any ties are softened at the edges. Figure 13 shows such a transition. The vertical axis is presented as a noralized +/- PPM offset error while the horizontal is that of the control-voltage step range. In this exaple, the range of operation is approxiately +/- 200 PPM. As the VCXO tracking approaches the PPM offset extrees, the transition is softened. This is often a desirable trait so that 16 of 23 djg@cypress.co

17 frequency transitions are held to a iniu. Two VCXO tracking curves are presented operating across three zones consisting of a, b and c. Overlapping of the curves serves to show that incorrect operation is easily disissed, and does not becoe obvious until soething breaks. Such breakage ost likely occurs in b, but the tail end of a is certainly isbehaving. Of the two curves presented, one curve operates properly across all three zones and clearly represents an expected response. At first glance, the second curve appears to cause probles in zone b. In reality, this curve shows inconsistency in all three zones. While b is considered to be where real syste failure is prone to breakage, the surrounding area is largely frequency deviant both leading up to, and transitioning into zone c Low to High VCXO Sweep PPM f c e, a b c VCXO Step Range Figure 13 VCXO Transfer Function of Voltage vs. Noralized Output Frequency Figure 13 expresses change in frequency vs. VCXO input step range. Expressing this inforation in the context of power vs. frequency is one of the purposes of figure 14. The frequency response of figure 14 shows relative frequency relational properties of VCXO pull range between the fundaental and 3 rd overtone. Both the electrical and echanical properties are superiposed in order to visualize what is happening. This illustration is iportant to understand before discussion the ensuing illustrations. 17 of 23 djg@cypress.co

18 Electrical & Mechanical Fundaental PPM Range (VCXO Sweep Range) Electrical 3 rd PPM Range (sae as Electrical fundaental) Mechanical 3 rd PPM Range (reduced fro fundaental) Mechanical 3 rd Falls within Electrical 3 rd Range Power Electrical & Mechanical Fundaental Center f c e, f 3c e f 3c Mechanical 3 rd Center Electrical 3 rd Center Figure 14 Fundaental and 3 rd Overtone Operational Relationships Electrical and echanical overlapping is expressed with the center frequency f c e, showing the respective pull range as that of the width of the hatched box shown in figure 14. The left and right ost edges of the box region are representative of the axiu negative and positive offset ranges. This would correlate to -/+ 200 PPM when referencing back to figure 13. The actual frequency separation that would norally exist between the fundaental and 3 rd is reduced considerably in this illustration so that a side-by-side relationship can be expressed. The center frequencies for the electrical and echanical third are represented by f 3 and f 3 respectively. c There are two interesting properties that this graphs shows. First, the pull ratio between the fundaental and 3 rd overtone range is not copletely a 1:1 relationship. While the pull range between the fundaental and electrical 3 rd does aintain a 1:1 relationship the pull range ratio between the fundaental and echanical 3 rd does not. In fact, the ratio is reduced by a otional capacitive 2 factor relationship of 1 N. Another iportant point to consider in this illustration is that the placeent of f 3 which does not necessarily align to the crystal echanical 3 rd center f ce 3. As c discussed earlier, uch of this separation is due to ulti-diensional effects in the crystalline structure. ce 18 of 23 djg@cypress.co

19 Electrical 3 rd Tone & Mechanical 3 rd non-overlap Fundaental Tone f > 0 Power a f 0 f e, 3 e Figure 15 VCXO Low-side Pull with no Overlap Electrical 3 rd Tone & Mechanical 3 rd Overlap f 0 Power b f 0e, f 3e, Figure 16 Electrical and Mechanical 3 rd Overlap Electrical 3 rd Tone & Mechanical 3 rd non-overlap f > 0 Power c f 0 f e, 3 e Figure 17 VCXO High-side Pull with no Overlap Figures illustrate what happens as the VCXO is swept fro the negative PPM to axiu positive PPM. Each illustration is representative of the particular VCXO operating zone as shown in figure 13. The VCXO is swept fro low to high, starting in zone a and proceeding through zone c. During the noral course of operation through a, everything proceeds noral until f 3 begins to close the gap on f e 3, or in other words as f 0, the VCXO 19 of 23 djg@cypress.co

20 frequency response begins to deviate fro the expected ideal response. In fact, the frequency begins to lag as to what would norally be expected. As the VCXO enters zone b, an unexpected sharp frequency transition occurs. That is, as f 3 passes through the f e 3 zone, 3 rd overtone coupling takes effect between the electrical and echanical 3 rd. The crystal echanical 3 rd is accepting energy fro the non-linear aplifier output. Continuing the VCXO pull transition into zone c, f 3 breaks away fro f e 3 as the VCXO frequency response once again attepts to regain the expected response. A tie doain representation through an oscilloscope often looks as follows. Figure 18 Sinusoid Norally Present on Aplifier Input Figure 19 Large ipact due to 3rd Mechanical Excitation on Aplifier Input Figure 18 shows a well-behaved signal at the aplifier input that should always exist over the full VCXO pull range as indicative of noral and correct VCXO operation. However, in the case of f 3 transitioning through f e 3, the resulting 3 rd overtone is excited in the tie doain readily showing up as a 3 rd haronic presence in the resulting wavefor. Significant and additional energy is now being correlated in the syste. Clearly, excitation of the echanical 3 rd is to be avoided when working with VCXO designs and is largely responsible for why figure 13 iproperly transitions. Now, consider the case where range. f 3 and f ce 3 never overlaps across the VCXO pull c 20 of 23 djg@cypress.co

21 Mechanical 3 rd Operates outside Electrical 3rd f seplo PPM _ Low_ Range 3 f0 Power f c e, f 3c f 3c e Figure 20 Non-overlap, Mechanical 3 rd low-side Placeent f 3 sephi 2 PPM _ High _ Range f0 Mechanical 3 rd Operates outside Electrical 3rd Power f c e, f 3c e f 3c Figure 21 Non-overlap, Mechanical 3 rd high-side Placeent Through proper positioning of f 3 w.r.t. f e 3, the electrical 3 rd overtone will never overlap the echanical 3 rd. Because no echanical overtone coupling takes place, the result will be a sooth transition in the VCXO curve with no abrupt frequency transitions. In order to eet there operating conditions two choices exist for the VCXO designer, which is to either place the f 3 excitation range f 3 e below or above. Depending on placeent, certain rules apply as to the recoended iniu separation. In the case where f 3 is placed below f 3 e, a iniu separation of approxiately one ties the VCXO total low pull range (worse case for VCXO axiu negative pull) provides sufficient separation; this paraeter of separation is designated as f. On the flip side, if 3 f seplo 3 is placed above f 3 e, then the iniu separation (worse case for VCXO axiu positive pull) is on the order of two ties the VCXO high pull range. This paraeter of separation is designated as. f 3 sephi 21 of 23 djg@cypress.co

22 General Crystal Specification Suggestions The fundaental goal in specification and selection of a crystal for proper VCXO operation is in the ability to specify a pull range no greater than necessary in order to eet the needs of the pull range and to ensure that electrical and echanical odes never overlap. The key is in specifying the iniu aount of otional capacitance C 1 that eets the needs of a prograablec L to satisfy iniu and axiu syste specific PPM pull range. The crystal electrode size plays three pivotal roles. First, the size dictates the value of otional capacitancec 1. Second, the electrode size (deterination ofc 1) sets the position for the echanical 3 rd w.r.t. the electrical 3 rd. Third, due to the reduced or increased area, the aount of network RF energy transfer through the piezoelectric structure is affected. As previously entioned, the iniu power for guaranteed operation is a design goal, but due to a different electrode size this paraeter ight require adjustent. Use of the ter pullable crystal is generally indicative of an intrinsic otional capacitance C 1 that runs in the range of 25 to 30 ff -- greater C 1 leads to greater pullability, which also leads to a lowerc0 C1 ratio. Such a range ost typically leads to a crystal that exhibits an undesirable echanical 3 rd that appears above the electrical 3 rd. In this case, as the axiu positive PPM offset is reached the gain present in the aplifier (-R) actually increases due to lighterc L loading in the network (higher reactive loading). In such a situation with a high aplifier gain present, sall noise perturbations ay be just enough for the network to allow the start of energy injection in the region of the echanical 3 rd. In addition, since the electrode size is larger (as copared to the next exaple), ore energy that is undesirable aybe transferred into the crystalline structure further eroding the possibility for a stable syste. On the other hand, reducing C 1 to function around the range of 18fF +/- 20% generally leads to a echanical 3 rd that appears below the electrical 3 rd. The benefit of this design is to reduce network gain as the axiu negative PPM is reached. This is due to the increased loading capacitance C L. In addition, the saller electrode size contributes to less energy absorption (as copared to the earlier case) further helping to aintain a well-behaved syste. Crystal Manufacturing Specifications The crystal anufacturer can add a third overtone screening specification to the crystal specification. To ensure that no electrical and echanical 3 rd overlap will occur, a guard band is added. A specification exaple ight look like the following. Third Overtone (FL) (with CL=14pF) ust be less than MHz and greater than MHz (F0 of MHz +/- 100 PPM Min ) 22 of 23 djg@cypress.co

23 Translated is that the electrical 3 rd overtone is precisely 40.5 MHz. A crystal with a fundaental loading of 14pF (at an FO of 13.5 MHz) ust exhibit a iniu f spacing of 2700 Hz for both the low and high side operation. The 2700 Hz equates to a noralized +/- 200 PPM of iniu spacing in the region of the electrical 3 rd. Note that 1350 Hz is derived fro +/- 100 PPM offset error at 13.5 MHz. Third Overtone FL Spurs (with CL=14pF) ust be less than MHz and greater than MHz (F0 of MHz +/- 100 PPM Min) As entioned earlier in figure 8, spurs are always naturally present. The crystal anufacturer should screen for this by the exaple spur specification above. In this specification, all that is being said is that the spurs ust be greater than or less than +/- 200 PPM fro the electrical 3 rd operating region. VCXO Network Gain Considerations VCXO gain can play a role in helping to aintain sooth VCXO transitions. Once the characteristics of the crystal play out to the proper specifications, review of the oscillator gain section should be reviewed. The general rule-of-thub is that the gain should be set at the iniu setting that eets all required startup and operational conditions over all syste variables including teperature and voltage effects. Observation has indicated that with prograable gain oscillators, lowering the gain helps to itigate the effects of echanical 3 rd excitation, as it tends to roll off the gain bandwidth. This akes sense, as less electrical overtone energy is present in the syste to excite echanical odes of operation. Having an iproperly designed crystal for the application and solely relying on gain setting is dangerous, especially when production runs are in ind. While this ay appear to be a solution for prototype and early production runs, do not be too surprised to find fallout as the production run rate is increased as there is often enough variation in devices over ultiple lots to cause probles. Suary Design of a VCXO appears alost trivial until loss of syste lock occurs in the syste. Casual observation of the VCXO would indicate a fully functional response. Only until the operational curve is carefully observed over different operating paraeters to ensure proper operation can the VCXO be ruled out as a possible troubleaker. This white paper presentation should help the user understand core oscillator operating principle and the specifics on crystal operational odes. Through proper use of the concepts and principles discussed, application should lead to better crystal specification and screening guides for stable VCXO operation. The principles outlined in this paper provide the VCXO syste designer greater insight as to the potential pitfalls of VCXO design seldo understood and discussed in clocking literature. 23 of 23 djg@cypress.co

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