OSCILLATOR DESIGN TECHNIQUES ALLOW HIGH APPLICATIONS OF INVERTED MESA

By Kurt Wessendorf lithium niobate. The arrays are comprised of Sandia National Laboratories electrodes that alternate polarities. When an RF signal voltage of the proper frequency is Albuquerque, New Mexico applied across them, the surface of the crystal expands and contracts, generating a Tom Payne displacement wave on the surface of the President crystal. Avance Technology TmT Bulk Acoustic Wave Cedar City, Utah Model

By using inverted-mesa techniques to Bulk acoustic wave (BAW) resonators selectively thin the resonator, the practical operate on entirely different principles. The upper frequency range of bulk wave crystal displacement wave produces a resonating oscillators has risen dramatically over the past vibration which travels through the crystal. The several years. A new technology called Tab- crystallographic orientation used in mesa Technology (TmT) has paved the way for manufacturing BAW devices is crucial to their new design approaches in telecommunications performance characteristics. For applications applications including small, portable high- in the Megahertz range, the AT-cut is the most frequency equipment such as pagers, cellular common orientation because of its relatively telephones, keyless entry and other wireless low temperature coefficients. Figure 1 is the communications systems. Many designers electrical equivalent model of the AT-Cut have shied away from these new devices resonator. This model shows only the because of the lack of standardized design fundamental and the first two overtones of the practices. Fortunately, as this article will resonator. Also, not shown in this model, are demonstrate, many classic bulk wave designs the spurious modes that can exist. These can be adapted to high frequency operation modes are process driven and can be kept when the new crystals are used in the relatively lossy in a well designed and fundamental mode. fabricated resonator. C0 is the static capacitance of the resonator which is in Most existing high-frequency equipment is parallel with the motional arms (Cm, Lm and Rm) built around surface acoustic wave (SAW) which are a function of the piezoelectric resonators. The SAW resonator consists of properties of the quartz. two transducers with arrays of fine metal electrodes deposited on a highly polished piezoelectric substrate such as quartz or Using inverted mesa technology, crystals can now be produced in the fundamental frequency range of 40 MHz to 200 MHz with overtones to 600 MHz. The inverted mesa process uses chemical etching to reduce the thickness of the quartz in the center region of the blank, leaving a thicker outer ring for added crystal strength. Inverted mesa technology permits higher than were previously possible with flat AT quartz crystals. The tiny geometry of these resonators also minimizes the static capacitance (C0) of the devices which allows for higher loaded Qs at Fiigure 1. AT-Cut Resonator Modell high frequencies. However, the use of inverted mesa crystals has been limited by their high Figure 2 graphically illustrates the cost and the difficulties associated with volume resonator’s reactive impedance, X , versus e production. frequency [1]. (This graph is not drawn to scale). TmT involves batch processing crystals using photolithographic techniques similar to those used in semiconductor processing. In a process developed by Avance Technology, a SaRonix company located in Cedar City, Utah, one by two inch quartz wafers are lapped and polished to approximately 3 mil thickness. 130 individual resonators approximately 50 by 170 mil in size are formed photolithographically on each wafer with the resonating region etched down to 0.5 mil or less depending on the desired frequency. Calibration to the exact frequency is accomplished by evaporating a thin gold layer onto the resonating region. The individual resonators are attached at their Fiigure 2. Resonator Reactiive Impedance vs. Frequency supporting 3 mil end onto headers using conductive epoxy and then hermetically sealed Typically an oscillator will be using the into a cylindrical metal or rectangular ceramic resonator in the inductive region, or as a enclosure. resistive element very near fs. The fundamental resonant frequency of the AT-cut crystals This manufacturing technology makes generally specified today is 1-30 MHz. In AT- volume production of consistent quality, high cut crystals, the thickness of the crystal wafer frequency crystals possible. The thin determines the frequency–the thinner the wafer resonating region of TmT crystals is the higher the frequency. Unfortunately, thin cantilevered from a thicker base, enabling a wafers are very fragile and difficult to handle much smaller crystal design. The inherent without breakage, limiting the fundamental small size of these unique crystals makes it frequency of these devices. The AT-cut possible to package the miniature devices in 2 resonator can also be operated on odd mm by 5 mm tubular casings similar to those mechanical overtones of the fundamental used in the watch crystal industry. When frequency, generally the third and fifth. These mounted in a conventional hybrid oscillator overtones are higher Q than the fundamental circuit, the TmT crystal is hermetically sealed in and demonstrate superior aging its own enclosure. This eliminates the most characteristics. common sources of crystal failure in hybrid

SaRoniix/Sandiia Natiionall Laboratoriies/Page 2 oscillators–blank fractures and contamination. design depends on a wide range of variables, The low mass of quartz blanks mounted in typically a one-port BAW oscillator can be small, sealed metal or ceramic packages many times more efficient and run at lower results in rugged components that are much overall currents than a 2-port SAW based less susceptible to shock, vibration and design. The circuits presented here can handling damage. These devices provide an produce 0 dBm outputs with currents from 3 attractive alternative to SAW devices in many mA to 5 mA and useful outputs (-10 dBm) with applications. as little as 0.6 mA of dc current. High-power (15 dBm) low current (11 mA) designs which High-Frequency Oscillator Designs are demonstrating >60% power efficiency at frequencies to 200 MHz using these new resonators are in development*. Another Traditional 2-port SAW oscillator designs distinct difference between SAW devices and are based upon a 50W gain block, Figure 3. BAW (AT-cut) devices is the frequency versus The power efficiency and minimum operating temperature response. Figure 4 and Figure 5 power of this type of design is limited by the are the temperature response curves gain block () and the low impedance respectively for the SAW and BAW devices. splitter. Since the gain blocks typically use shunt feedback for matching, relatively large bias currents (tens of milliamps) are required to achieve the gain required to drive the low impedance SAW and splitter. In many designs milliamp or sub-milliamp currents may be desired to meet a low overall current (thus power) budget of a system.

Fiigure 4. Frequency vs. Temperature of SAW Deviice [2]

Fiigure 3. Two-Port SAW Osciillllator Ciircuiit

One-port (negative resistance) oscillators can offer greater design flexibility than 2-port designs. The chief advantage is that the circuit can be designed to optimize the current used in the oscillator for the oscillator configuration chosen. Also one can more optimally match a transistor to the load via low- bandwidth, reactive networks than via resistive shunt feedback. In a one-port design, the oscillator itself may be part of the matching structure which also simplifies the design. Fiigure 5. Frequency vs. Temperature Curves for AT-Cut Although overall efficiency (h) of any oscillator Resonator [3]

SaRoniix/Sandiia Natiionall Laboratoriies/Page 3 Fiigure 6. Fundamentall Mode Piierce Osciillllator The AT-cut resonator temperature response is approximately three times less The with fundamental than the typical SAW temperature response. mode resonator (Y1) is shown in Figure 6. This By careful selection of crystal angle one can circuit is probably the most popular oscillator obtain an AT resonator with temperature design type and operates with the resonator as variations of less than ±10 ppm over a an inductive element. It provides a relatively temperature range of -40° C to 75°. Finally, low distortion sine wave to RL if the oscillator is SAW devices can't be economically produced properly designed. The bias circuit is relatively at low volumes because of the tooling cost to stable and is easy to implement. RC is chosen produce mask sets. for the desired dc bias current and if Rf is chosen to be ~50 times RC then the transistor The ability to achieve fundamental will be biased with the collector voltage (dc) at frequencies up to 200 MHz with AT-cut BAW approximately ½ of +V. The ratio of crystals can mean dramatic reduction in power amplitude (collector to base) is approximately consumption in many applications. Volume C1/C2. C1 is usually chosen to dominate the production costs typically compare to SAW transistor input impedance and therefore will devices, while sampling is far more be relatively large. The magnitude of XC1 economical. should be in the 50 W to 200 W range. Making C2 two to five times smaller than C1 to creates Today good quality high-frequency a large amplitude of oscillation (at the collector) and passive components are readily and a good impedance match to RL. At the available in low-cost, surface-mount packages. frequency of oscillation |XC1|+|XC2|= |Xe| where When these devices are used in conjunction Xe is the inductive reactance of the resonator with high frequency TmT resonators, many Y1, and XC1 and XC2 are the capacitive classic bulk-wave oscillator designs are reactances of C1 and C2 respectively. The realizable at high frequencies. These designs resonator is designed to be resonant with CL can be easily implemented with fundamental- C1C2 mode resonator operation with no inductors in which is at the desired frequency [4]. C1 + C2 the circuit. To achieve higher frequencies For very precise designs C or C may be (>200 MHz) use of resonator overtones and or 1 2 trimmed. Also varactor can be used in frequency multiplication techniques can be combination with C and/or C to make the used. These circuits become a little more 1 2 frequency voltage controlled and allow for complex and will require at least one inductor. temperature compensation. Here are several examples.

The Pierce Oscillator using a The Pierce Oscillator using a Fundamental Mode Resonator Resonator Overtone

SaRoniix/Sandiia Natiionall Laboratoriies/Page 4 Fiigure 7. Overtone Piierce Osciillllator resonator as an inductor. The Colpitts design has one side of the resonator tied to ground An AT-cut resonator can be operated on and like the Pierce design the resonator is an odd resonator overtone (typically the third or resonant with the combination of C1 in series fifth) to achieve much higher frequencies. with C2 [5]. The series combination of C1 and These overtones can be used if the C1C2 fundamental at the desired frequency is difficult C2, defined as CL, is equal to . At to produce or a higher Q resonator structure at C1 + C2 the desired frequency is required for greater circuit resonance, assuming the reactive frequency stability. To convert the Pierce elements dominate the circuit impedances, the oscillator to resonator overtone operation, one base to emitter voltage gain provided by the must add a tank circuit to the basic design to tank (Y1, C1 and C2), is 1+C2/C1. The reactance select the desired overtone, Figure 7. This tank of C2 is usually chosen to be less than R3 and circuit is C1 in parallel with L1. C4 is a high greater than RL. C1 is usually chosen to be less value dc blocking capacitor. L1 and C1 are than or equal to C2. The transistor, used in an chosen to be net capacitive at the desired emitter follower configuration, must supply less overtone, usually the third. If this is true and the than unity gain to sustain oscillation. The tank is inductive at the fundamental then this output can be taken directly off C2. The load oscillator will run at the third overtone of the (RL) could also be placed in series with the resonator. Select L1 and C1 such that: resonator as long as the resonator impedance 1 is significantly larger than the load, RL. > F1, where F1 is the resonator 2p L1C1 The Colpitts design can be designed to XL1XC1 operate the resonator on an overtone. C1 or C2 fundamental, Also should be made must be replaced with an LC tank circuit using XL1 + XC1 the same techniques described for the Pierce -j50W to -j150W at 3F1 where XL1 = jwL1 and oscillator above. XC1 = 1/(jwC). The Pierce and Colpitts designs are the two most popular oscillator designs. They require few parts, are easy to design and are capable of high performance. VCXO (voltage The using a controlled ) designs are Fundamental Mode Resonator commonly implemented with the Colpitts configuration. To achieve a broad tuning range it is desirable to have the varactor in series with the resonator. This is because this arrangement keeps the oscillator gain requirements and thus amplitude of oscillation constant over wide range of varactor capacitance. This is easily achieved in the Colpitts oscillator since one side of the resonator is normally connected to ground; where as the Pierce oscillator has the resonator placed in-between the load capacitors.

The Butler Oscillator

Fiigure 8. Fundamentall Mode Collpiitts Osciillllator At very high frequencies, or overtone operation, it may be difficult to operate the The Colpitts oscillator, Figure 8, is another resonator as a good, high Q, inductor. popular oscillator circuit which operates the Therefore it becomes necessary to operate the

SaRoniix/Sandiia Natiionall Laboratoriies/Page 5 resonator near Fs where the resonator is will generally lose approximately 10 dB of approximately resistive and near its minimum output power per successive harmonic. impedance. Figure 9 is a Butler oscillator Therefore one should chose lower harmonics if design. It is a series resonant design that also power efficiency is a design issue. operates the resonator at low power levels. The Butler oscillator design can be used as a frequency multiplying oscillator by matching the collector of the transistor to the load at a harmonic of the oscillator frequency, Figure 10.

Fiigure 9. Butller Osciillllator

This design uses a Colpitts structure (L1, C1, C2) with the resonator completing the connection of C2, and C1 to the emitter. C3 is a Fiigure 10. Frequency Mulltiipllyiing Butller Osciillllator dc blocking capacitor and has no real effect on To eliminate the primary oscillator the oscillation properties. In this case, at the frequency from the output , L2 is designed to oscillation frequency, the resonator will be resonate with C7, L3 is a choke and will look approximately resistive and therefore near Fs. like a small capacitor at high frequencies in The LC tank, ( L1, C2 and C1 ), also selects the parallel with C7. Since the collector of the desired fundamental or overtone mode of the transistor is shorted to ground at the oscillator resonator. For this example, the output is taken frequency there will be no output power off of the collector through an impedance contribution at this frequency. An added benefit matching network which could be a narrow- of having little or no primary frequency on the tuned tank circuit or transformer. collector of the transistor is that this minimizes the Miller effect. The Miller impedance would Frequency-Multiplying Oscillator effectively shunt L1 with an impedance Design proportional to Ccb and the gain from base to collector. Minimizing Miller effects also helps decouple the oscillator from the load. Incorporating TmT crystals and simple multiplication techniques crystal controlled To make a frequency multiplier one must frequencies to 1 GHz can be achieved. For the simultaneously design a tank circuit to shunt self-limiting oscillators described here the the oscillator current (primary) to ground and circuit nonlinearities will drive the loop-gain to impedance match the desired harmonic to the one. These nonlinearities result in the one. These nonlinearities result in the load. At the desired harmonic L2 and C7 generation of significant harmonic currents. If generation of significant harmonic currents. If resonate with the combination of C4, C5 and RL. one designs a matching network to supply a The matching network therefore has a series poor match at the oscillator frequency and a resonant and a parallel resonant frequency. very good match at some desired harmonic of The higher order harmonics will be attenuated the oscillator then frequency multiplication is because successive harmonics naturally achieved. It is desirable for maximum power decrease in amplitude and the matching efficiency to choose the harmonic with the network will provide filtering. Thus the output 2 network will provide filtering. Thus the output greatest current since power goes with I . One will primarily be a single harmonic of the

SaRoniix/Sandiia Natiionall Laboratoriies/Page 6 oscillator frequency. Depending on the R3 and R4. The differential amplifier oscillator harmonics generated by the oscillator, the design will produce predominately odd- complexity of the matching network, the harmonics when driven heavily into desired level of distortion, and overall efficiency compression. Therefore from a power of the circuit, one can pick any harmonic of the efficiency standpoint this circuit can be an primary frequency. It may be necessary to excellent tripler and a good quintupler. The odd shunt L3 (choke) with a high value resistor (~5 harmonic generation also helps ease the kW) to damp a possible low frequency mode of design constraints on the multiplier tank oscillation caused by L3 parallel resonating with because the adjacent harmonics are already C4 at the collector node. suppressed.

For simplicity, the oscillators presented Q2 is the Pierce oscillator transistor which here are not necessarily the most power drives Q1 via the emitter. To maximize the efficient possible. Applying the following rules- output power of this design, one must have a of-thumb can dramatically improve the relatively large signal at the base of Q2 to drive efficiency of any oscillator (or amplifier) design: the differential amplifier into compression and 1) share bias currents by putting transistors in generate the desired harmonics. To series; 2) design each transistor to perform accomplish this C1 and C2 should be more than one function; 3) switch transistors by approximately equal in value. The multiplier using Class B or C configurations; 4) exploit tank will shunt the primary oscillator current to the nonlinearities of the design or 5) ground and impedance match the desired third combinations of the above. or fifth harmonic to the load. Using a 200 MHz resonator with a tripler design for a 600 MHz The Differential-Amplifier Oscillator- output can produce approximately 0 dBm of Multiplier output power with 5 mA dc current off a 3 to 5v Multiplier supply. This design is capable of providing low harmonic distortion by suppressing all An example of exploiting a nonlinearity for harmonics to at least 23 dB below the desired best efficiency or function can be demonstrated output. in a Pierce oscillator using a differential amplifier multiplier Figure 11. When using transistors in this circuit it may be necessary to place a small capacitor (~ 1 pF) from the emitters of Q1-Q2 to ground, via a short trace. This will limit the bandwidth of the circuit and thus dramatically reduce the possibility of undesired oscillation conditions that may exist near the cut-off frequency of the transistors.

The combination of miniature size, low power consumption and temperature stability afforded by oscillators using TmT resonators opens the door to new design approaches in small, portable, high frequency equipment. As more designers realize how simple it can be to Fiigure 11. Diifferentiiall-Amplliifiier Piierce Osciillllator-Mulltiiplliier convert low frequency bulk wave oscillators to high frequency designs incorporating these This circuit is rather unique in that it has new devices, their use can be expected to only one LC tank circuit (multiplier) but can increase at a rapid rate. provide frequencies to 1 GHz. This is because provide frequencies to 1 GHz. This is because * of the excellent multiplying properties offered Sandia National Laboratories has a by the differential amplifier (emitter-coupled proprietary design for high-efficiency, high- output power oscillators for frequencies to pair). Q1 , Q2 and R7 are dc biased via R1, R2,

SaRoniix/Sandiia Natiionall Laboratoriies/Page 7 approximately 200 MHz using BAW resonators. For more information call Kurt Wessendorf at 505-845-8817 or email at [email protected]; or for license agreement information contact Art Verardo at 505-843-4172 or email at [email protected].

References

[1] M. E. Frerking, Crystal Oscillator Design and Temperature Compensation, Van Nostrand Reinhold 1978 pp. 20-30. [2] Used by permission of Mark Stevenson, Sawtek Inc., Orlando, Florida. [3] Used by permission Carl Maddalone, Chapman & Hill, Inc, New York, New York. [4] M. E. Frerking, Crystal Oscillator Design and Temperature Compensation, Van Nostrand Reinhold 1978 pp. 56-63. [5] M. E. Frerking, Crystal Oscillator Design and Temperature Compensation, Van Nostrand Reinhold 1978 pp. 76-79.

Additional Reading

K. O. Wessendorf, “High Efficiency UHF Oscillator for Portable Battery-Powered Applications,” 14th Piezoelectric Devices Conference and Exhibition Proceedings, 1992. K. O. Wessendorf, “High Frequency Voltage- Controlled-Oscillator for Use With Inverted- Mesa Quartz Resonators,” 1996 IEEE International Frequency Control Symposium Proceedings, 1996. R. Rhea, Oscillator Design and Computer Simulation, Prentice Hall, 1990. B. Parzen, Design of Crystal and Other Harmonic Oscillators, Wiley Interscience, 1983. V. Bottom, Introduction to Quartz Crystal Unit Design, Van Nostrand Reinhold, 1982.

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