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The fast data rates of today's digital systems continue to demand faster and better clock signals with low jitter and phase noise attributes — not to mention smaller form factors. Crystal oscillators are typically the devices that are providing the originating timing signals for these systems.

Oscillators with internal phase-lock loops (PLLs) that generate a high-frequency output from an easily produced low-frequency crystal are often used. However, the degraded phase jitter of this approach is prohibitive for many new applications. Other techniques, such as the use of surface acoustic wave (SAW) devices, have cost, availability and frequency stability issues. We take a look at the design process, trade offs and the resultant benefits of oscillators built with pure analog circuits and no frequency multiplication for providing the clock signals for jitter-intolerant systems. Actual test results of models VF266 and VF261 oscillators are used as an example.

For the development reviewed here, dual differential, positive emitter-coupled logic signals are chosen for their high speed, noise immunity and the ability to distribute them on a backplane via 50 Ω structures.

For packaging, the small, proven 5 mm × 7 mm footprint LCC oscillator (Figure 1) is the chosen form factor. A 3.3 V supply voltage, low jitter of less than 1 ps RMS and a phase noise floor of -145 dBc/Hz is specified. A 300 MHz upper limit frequency of operation is also chosen. The important constraint of using the 5 × 7 LCC package requires that a single-stage oscillator amplifier be used (with buffer) and a small format resonator be developed to fit in the package. For dual PECL output signals, oscillators have been available at up to 160 MHz for a number of years in the 5 mm × 7 mm package. This is about the top end of availability for standard-production third overtone resonators, which are most commonly used in these devices.

The specifications laid out here required development of high efficiency amplifiers and inverted Mesa high-frequency resonators to allow the resultant VF266 and VF261 oscillators to now push the upper frequency to 300 MHz for the 5 mm × 7 mm package PECL product without the use of noise-generating PLLs or other phase noise degrading multipliers.

In oscillator design, the choice of the quartz resonator and its resultant design is most often the prime consideration. Blank geometry, electrode design and overtone modes with their attending trade offs must be evaluated. Figure 2 provides the basis for decision making.

Overall, the frequency of the resonator is determined by the thickness of the quartz wafer, with the frequency increasing as thickness decreases. This is achieved by mechanically sawing and then lapping the wafer to the desired thickness. Therefore, increasing frequency makes for fragile resonators, and processing the components becomes more difficult as they get thinner. To achieve higher-frequency operation with the same thickness blank, the crystal can be vibrated at a harmonic or overtone of its fundamental frequency. The plano-plano (flat) fundamental mode blank cannot be manufactured above 50 MHz or 60 MHz economically. The third overtone (three times fundamental frequency) resonator of the same process cannot be easily manufactured above 150 MHz to 180 MHz.

Above this, fifth, seventh, etc. overtones are available. Any of these can be used in the right design situation. However, as the overtone number goes up, the resistance of the crystal inevitably increases. In addition, the amount of problematic spurious modes increase, and these are made worse by attempts to decrease the resistance of the desired overtone mode. Therefore, for the oscillator producer desiring high yields, the lowest possible overtone available economically should be used.

It has long been a struggle to develop ways to economically produce higher frequency resonators of the lowest possible overtone. The major solution to this has been the development of the inverted Mesa-type crystal resonator. This type is effective at driving down the overtone number that can be used to hit any particular frequency. The inverted Mesa is ideal for creating fundamental mode and third overtone mode resonators up to 600 MHz or higher. This technology allows the generation of high-frequency crystal-controlled clock signals without the use of noisy PLL multipliers.

The physical characteristics of the inverted Mesa resonator are reviewed in Figure 3. The selective chemical etching of the center area of the resonator is the key to its performance. The outer thicker ring of quartz forms a strong “frame” around the thin fragile-etched central resonating portion. The center portion is etched to the desired thickness (frequency), and the strong outer ring allows for ease of handling. The fact that the transition from the thin active area of the resonator to the supporting ring is a continuous piece of interrupted quartz solves all sorts of issues with other methods for mounting electrical and mechanical contacts to a thin quartz wafer. By using inverted Mesa fundamental and third-overtone resonators, efficient, low-resistance crystals are made available with good matching characteristics to amplifiers and with troublesome spurious modes controlled.

A simplified representation of one of the circuits chosen for this oscillator family is shown in Figure 4. The amplifier is of the inverting type similar to a biased NPN RF transistor. A pi-network consisting of capacitors and the crystal resonator form a frequency-selective feedback network. Appropriate buffer drive circuits follow to shape the output wave and provide the required 50 Ω AC output impedance. This circuit can be looked at as a closed loop servo system with the amplifier as the feed forward path and the crystal and reactive components as the feedback path. The inverting amplifier is complemented by the phase inverting feedback network. At one specific frequency, the loop has zero phase shift around it and oscillations can build up.

Of course, the second criterion is that the gain of the amplifier must exceed the losses in the feedback network to sustain oscillations. One well-established way of analyzing this oscillator circuit is to open the loop at a chosen point and predict the performance via measurements or calculations of gain and phase (transfer function) across the opened network. Test evaluation of the open loop circuit is cumbersome and usually requires that the circuit be tested in a format different from its final physical condition. Hence, stray reactances may not match, and simulating the proper input and output loading impedances that would have been in place when the circuit is closed loop are problematic.

For this development, the circuit test characterization was done with a more usable form of analysis generally known as negative resistance characterization. This method has the advantage of being able to be performed on the fully configured oscillator in its actual layout and package to include all the stray impedances and proper loading. Figure 4 covers the theory of the test.

If all the components except the crystal are boxed off into an amplifier/filter network and just the crystal is removed, we can examine the input impedance to the network and characterize it as a function of frequency. The network will have some real component and imaginary component of its input impedance. In this case, much of the network is an amplifier so it will have gain. When we examine the input impedance, we will find that the real component will be negative at some frequencies, which represents the gain of the amplifier as conditioned by the other components. The imaginary component will have reactive values that reflect the other passive components and the amplifier.

Similar to the closed-loop oscillation requirement of having gain greater than 1 and a net zero phase shift around a closed loop, the crystal connected to the amplifier network is a loop that will oscillate if the sum of the resistances around the loop is zero or negative and the sum of the reactive impedances is zero. This breaks the analysis into two pieces. First, characterizing the amplifier network for its frequency response at the terminals where the crystal will connect and second, comparing this to the impedance of a manufacturable crystal design in order to determine if the circuit will oscillate and at what frequency. With this technique, circuits can be characterized and optimized to create good oscillators well into the UHF range.

Crystals have numerous resonant responses: some desired, some undesired. The fundamental mode response is the most active and will have the lowest resistance. Other things being equal, the oscillator will always choose to operate in this mode. All odd number (3, 5, 7) harmonic overtone responses of the fundamental will be active too. Even number overtone responses exist in the mechanical resonant nature of the crystal blank also-. However, they are not electrically excitable with the electrode structure used, and therefore they are electrically inactive and not usable. In the 150 MHz to 300 MHz range, third overtone resonators are desired. A method is needed to cause the circuit to operate on the third overtone (say 200 MHz) rather than the dominant fundamental (67 MHz). The negative resistance test method is ideal for optimizing for this performance.

Figure 5 adds insight to the analysis of the amplifier network. The simplified amplifier circuit shown has inverting phase and gain represented as transconductance, and a high input impedance and low output impedance allowing these two factors to be omitted from this general illustrative analysis. We can look into the input terminals where the crystal would connect to develop equations for a negative resistance analysis. From Figure 5b, if we apply test voltage Et to the input port, we can write two equations to represent the network.

Vout/X2 + gmVin + It = 0

Vin/X1 - It = 0

Solving for the input impedance (Zin) by determining Et/It (where Et = Vout - Vin), we find that:

Zin = X1 + X2 + gmX1X2

The assumption is that X1 and X2 are pure reactances and could be inductances or capacitances. The reader can look at the results of trying the four combinations of positive or negative reactances in the two positions. However, if two capacitors (C1 and C2) are used for X1 and X2, then the following input impedance will result:

Zin = 1/(jwC1) +1/(jwC2) - gm/(w²C1C2)

Parsing this into real and imaginary components yields:

Zin = -gm/(w²C1C2) {Real component}

-j/((wC1C2)/(C1 + C2))

{Imaginary component}

We find that the real part is negative (gain) and that the imaginary part is capacitive. This indicates that the network will oscillate if we connect a component that has a real portion (resistance) that is less than the negative real term of the network and if it has an imaginary term (inductive) that is opposite and equal to the imaginary term of the network. It looks like a perfect spot for a resonator. If a crystal resonator is applied that can produce at some frequency an inductive reactance that equals the capacitance reactance of the network and that has a resistive loss that is less than the negative resistance of the network, the combined network will oscillate. This network is fairly non-discriminating and will work for some broad range of frequencies with the crystal fully controlling the frequency of operation. Of course, it will operate (capture) on the lowest resistance mode that is available, which would be the crystal's fundamental mode resonance. Our need is to operate on the third overtone so we have to go back to the input impedance equations and see what can be done. If we examine one of the other options for the X1 and X2 components, such as where X1 is changed to an inductor (L1), we find:

Zin = gm(L1/C2) {real component}

+ j(wL1-1/(wC2) {imaginary component}

Now we see that the real component is always positive under all conditions. Even if the reactance conditions are satisfied, the real conditions will not allow for oscillations. Our task is to create a condition where at the third-overtone crystal frequency, the network has capacitance at both X1 and X2 positions (hence, negative resistance) and at the fundamental frequency, the network has capacitance for one X value and inductance at the other (no negative resistance). This is best performed with a tank circuit for one of the X impedances (for example, X1). By tuning the tank circuit to a resonant frequency that is between the fundamental and third-overtone frequencies, the network will have inductance for X1 at the fundamental frequency and capacitance for X1 at the third overtone frequency and only the third overtone resonance will have the potential to achieve oscillations.

For a network with the tank circuit included, the negative resistance plotted either by simulation or measurement as a function of frequency will show the capabilities of the circuit to select only the desired overtone and can be used as an analysis tool. Relative ratings of gain margin can be made to ensure the design will operate on the desired overtone. This technique and others can be used to refine a network that is selective in the impedances it presents to a crystal to reliably select only the desired overtone mode.

For our real-life development of the 150 MHz to 300 MHz oscillator product with third-overtone inverted Mesa crystals, circuits of topology similar to Figure 4 were used with BiCMOS devices. The resulting amplifier networks were analyzed via a network analyzer in their actual packages with full physical stray impedances in place. Circuits were developed to cover the overall range broken up into sections. As an example, the result for a version that is optimized for 150 MHz to 212.5 MHz frequency band is shown in Figure 6.

The task here is to prove that the oscillator cannot operate within the band of fundamental frequencies of the crystals and that it will operate well on the third overtone resonance of the crystals. Note that two plots for negative resistance are shown in Figure 6. Figure 6a is the measurement with just the network measured itself. It shows large negative resistance over the desired operating range. Figure 6b shows the measurement with a capacitor added across the amplifier input that is equal to the Co of the crystal (see equivalent circuit in Figure 2). This is a critical piece of knowledge. The “parasitic” electrode capacitance (Co) of the resonator must be included in the measurement because it is always present in the circuit even during the few milliseconds prior to the start up of the oscillator signal and excitement of the piezoelectric resonance of the resonator. The gain-degrading effect of this capacitance must be included for real-world measurements.

For this frequency band, crystals will have fundamental resonances in the 50 MHz to 71 MHz range. We see from Figure 6b that for this range, the amplifier network input impedance has only positive values of its real component. Therefore, the oscillator cannot operate on these frequencies no matter how excellent and low resistance the crystal's fundamental mode. The negative resistance curve sweeps down to a nice maximum at around 160 MHz and displays more than 150 Ω of negative resistance through the range up to 212.5 MHz and beyond. Hence, any crystal with less than a 150 Ω resistance at the third overtone will have sufficient gain to oscillate. The crystals used in this design had resistances of less than 70 Ω.

The attributes of low phase noise (and therefore low jitter) have been achieved by these designs. New levels of performance for high-speed differential outputs are achieved without noisy PLL multipliers in a smaller package footprint. Figure 7 provides real measurement results on sample product. The phase noise is generally 20 dB improved for competing PLL clock solutions. Of particular importance is the noise floor over the SONET noise bandwidth of 12 kHz to 20 MHz, which represents a typical telecom jitter intolerant application. Here, the integrated phase jitter is typically 0.3 ps RMS, which is compatible with these applications.

The development of better performing (higher-frequency, lower-noise, smaller package) oscillators continues. Developers will do well to use the methods of network analysis of the negative resistance of proposed oscillator circuits in their work. The development of the inverted Mesa resonator has produced a higher-performing alternative to SAW-based oscillators and other bulk resonator types, which use a PLL or other such parametric multiplier that also multiplies noise. Products have been developed that demonstrate the effectiveness of the design techniques for both the overtone selection and robust gain margin for the third-overtone inverted Mesa crystals used. The products meet a wide need for a small SMD 5 mm × 7 mm footprint oscillator that can generate low jitter, high frequency, differential PECL signals for critical performance applications.

Dan Nehring is vice president of engineering, Frequency Control Products, Valpey Fisher Corp., Hopkinton, Mass.