Chapter 1 Introduction
1.5 Organization of this thesis
It is the aim to investigate the problems while applying piezoelectric resonators to build the high frequency, high quality factor, and low phase noise oscillators and provide some useful solutions.
In chapter 2, the structure and equivalent circuits for SAW resonator and FBAR are introduced. By using these resonators, we present two feedback loop oscillators:
2488 MHz voltage-controlled oscillator with STW resonator and 2488 MHz voltage-controlled oscillator with FBAR. The designs of oscillators and performances will be measured and discussed.
In chapter 3, the basic theory and measurement method for the residual phase
noise of the two-port devices will be introduced. After that, we will discuss the different measurement techniques for absolute phase noise measurement and chose the frequency discriminator method to measure the phase noise of the oscillators with piezoelectric resonators. By examining the residual phase noise of the devices, we can find the main noise contributors in the oscillator quickly and accurately. The method to predict the phase noise of the feed-back loop oscillator based on the residual phase noise of devices will be introduced. The prediction of the phase noise of the oscillator has a good agreement with the measured results.
In chapter 4, Pierce oscillator which is widely used in low-frequency crystal oscillators is applied for 622 MHz application. For solve difficulty of the oscillation start-up in this band, an extra phase shifter is added. The oscillator design method and how to choose a proper phase shifter are discussed.
In chapter 5, the balanced oscillator with a 433 MHz one-port SAW resonator is presented. We use a commercial one-port SAW resonator which is made by ftech Co.
to demo this circuit. Based on this balanced oscillator, a push-push SAW oscillator is constructed and achieves 6dB improvement in phase noise of oscillator in comparison with one-side oscillator.
In chapter 6, there are the short conclusion of our work and the view of the future work.
Chapter 2
Feedback Loop Oscillators with Piezoelectric Resonators
2.1 Piezoelectric Resonators
2.1.1 SAW Resonators [4]
Both one-port and two-port SAW resonators are used for the tanks of oscillators in this thesis. Fig. 2-1(a) shows a typical configuration of the one-port SAW resonator where two grating reflectors are replaced at both ends of the inter-digital transducers (IDT). Very steep resonance can be detected by the IDT when the device is designed so that resonance frequencies of the IDT and reflectors coincide with each other. The width of the IDT is about quarter wavelength of the acoustic wave. The length of the gaps between the IDT and reflectors significantly influence the resonance characteristics. Fig. 2-1(b) shows the equivalent circuit near resonance, where C1 and L1 are the motional capacitance and inductance, respectively, corresponding to the contributions of elasticity and inertia. R1 is the motional resistance corresponding to the contribution of damping. C0 is the capacitance of the IDT. The capacitance ratio γ is given by:
where ωr and ωa are the resonant frequency and anti-resonant frequency, respectively.
The smaller γ enable us to control the oscillation frequency over a wider range by a capacitance parallel-connected to the resonator. This feature is preferable for use in a voltage controlled oscillator where the varactors are employed as a voltage adjustable
capacitance.
IDT Reflector Reflector
Gap Gap
(a)
R1 L1 C1
C0 (b)
Fig. 2-1 (a) Structrue, and (b) equivalent circuit model for one-port SAW resonator.
Fig. 2-2(a) shows a two-port SAW resonator where the grating reflectors are replaced at both sides of a conventional transverse filter. When the devices are designed so that the reflectors resonance at IDT resonance frequency, the transfer admittance becomes very large at resonance and a very narrow but low-pass passband is realized. Fig. 2-2(b) shows the equivalent circuit near resonance. The resonance circuit is involved as s shunt element between two IDTs because the structure is equivalent to a one-port SAW resonator when the two IDTs are parallel-connected.
The oscillator can be constructed by using two-port SAW resonator as a feedback element. This configuration is widely used for operation in the UHF range because of its insensitivity to parasitic circuit elements.
Reflector IDT IDT Reflector
Gap Gap
(a)
R1 L1 C1
C0 1:-1 C0
(b)
Fig. 2-2 (a) Structrue, and (b) equivalent circuit model for two-port SAW resonator.
2.1.2 Film Bulk Acoustic Resonators
Another high frequency bulk wave approach is to obtain a specified thickness by thin film deposition techniques rather than by thinning crystal plates. There is considerable breadth to the thin film resonator technology, both in device types and applicable frequency spectrum. Much of this is due to the fact that the technology is based upon thin films that can be fabricated, by various means, on a variety of substrates employing integrate circuit type wafer scale processing. Bulk wave resonators require that both surfaces be free to vibrate, even though vibration amplitudes are fractions of a nanometer, in order to sustain a resonance. This condition is supplied by mechanically free surfaces such air or vacuum. Resonator geometries suitable for use with piezoelectric thin film resonators are shown in Fig.
2-3. The resonators in Fig. 2-3(a) and (b) have mechanically low impedance material interfaces of air or vacuum while the one in Fig. 2-3(c) is solidly attached to the substrate. The configuration of Fig. 2-3(a) is a membrane structure supported by the edge of the substrate [17-30].
(a)
(b)
(c)
Fig. 2-3Thin film resonator configurations (a) membrane formed by etching a VIA in the substrate. (b) air gap isolated resonator. (c) solidly mounted resonator (SMR) using a reflector array to isolate the resonator from the substrate.
Typical fabrication involves deposition of a piezoelectric film on a supporting substrate followed by removal of a portion of the substrate to form the membrane and thereby define the resonator. The configuration is similar to that used in inverted mesa quartz crystals where a thin piezoelectric membrane is surrounded by a more rigid supporting structure. The difference is in the details of how the membranes are formed. The second configuration involves fabricating an air gap under the resonator [31,32]. This may be accomplished by first depositing and patterning an area of temporary support material, next depositing and patterning an overlay piezoelectric resonator with electrodes, and finally removing the temporary support. The approach in Fig. 2-3(a) has seen greater work of the two membrane configurations and is know generally as the FBAR (Film Bulk Acoustic Resonator) configuration [19].
Advances in thin film processing have allowed the fabrication of membrane devices with high width to thickness ratios. Within one membrane of AlN multiple
resonators have been fabricated and electrically interconnected to form complex ladder filters [22]. Resonators have an electrical response that is modeled quite accurately by the Butterworth Van Dyke (BVD) equivalent circuit shown in Fig. 2-4.
[23,27].
R1 L1 C1
C0
Fig. 2-4 Butterworth Van Dyke (BVD) equivalent circuit.
2.2 Voltage-Controlled Oscillator with STW Resonator
2.2.1 Design Method
In this section, a highly stable VCSO with STW resonator working directly at 2488.32 MHz is developed. The high-Q STW resonator on quartz was demonstrated in 1987 [11]. Its advantages over the conventional Rayleigh waves are the very high velocity and low propagation loss [4]. The wave velocity of STW is approximately 5000m/s, which relaxes slightly the requirement of the photolithography process. A coupled-mode resonator is carefully designed to accommodate the request of wide band tuning and low phase noise applications. The unloaded quality factor equal to 5500 was realized in this work.
It is noted that the oscillator with one-port SAW resonator suffers from large parasitic capacitance from inter-digit transducers. Here, the architecture with two-port resonator forming a feedback loop is chosen as shown in Fig. 2-5. It consists of a single loop amplifier, an electronic phase shifter, a lump element reactive Wilkinson power splitter, a lumped element reactive phase adjusting, and a two-port STW resonator. The resonator acts as a short circuit with zero phase-shift at the desired frequency. No output buffer amplifier is used because it may degrade the oscillator’s white phase noise floor. The oscillation starts as the closed loop gain satisfies Barkausen’s criteria. The total loop gain is larger than unity at the frequency of oscillation and the phase shift is equal to 2πN radians, N is an integer. The conditions are written as
where, Ga：Gain of Loop Amplifier, Gp：Loss of Phase Shifter and Loop Phase Adjust, Gs：Loss of STW Resonator, θa：Phase change in Loop Amplifier, θp：
Phase change in Phase Shifter and Loop Phase Adjust, and θs：Phase change in STW Resonator. During design phase, the open loop gain is evaluated by breaking the loop at the appropriate plane with equal input and output impedance, such as line AB noted in Fig. 2-5. Here, the impedances seen are 50ohm network analyzer measurement.
Actually the input/output impedances in each module are all set to 50ohm for convenience. This approach has the advantage that the noise characteristics of the individual component as measured in an open-loop configuration have a direct bearing on the closed-loop phase noise of the oscillator.
Fig. 2-5 Block diagram of a feedback loop oscillator.
2.2.2 STW Resonator
To achieve low insertion loss, high frequency, and high quality factor, the SAW resonator with STW is employed.[5] The picture of the resonator is shown as Fig.
2-6(a). The STW is a shear wave with very high velocity and energy trapping reduces the diffraction of the shallow bulk wave into the substrate, thus reduce in device
insertion loss and increase in resonator Q. The width of the transducer is approximately 0.5μm. The overlap aperture is about 250μm. This larger transducer width also makes it possible that the resonator could be manufactured in mass production with acceptable yield. Since STW also do not associate volume charge with propagation, its propagation loss is small. [4] To achieve the proper turnover temperature, the 90° rotated ST-cut quartz is employed to be as substrate of the resonator, which has the turnover temperature approximately at 45°C. This work simplifies the circuit design without using extra temperature compensation circuit for the real environment and lowers the cost.
The IDTs are detailed in Fig. 2-6(b) with die size of 1.8mm x 1.2mm. The input and output IDTs have 100 fingers are placed between two shorted reflectors, which has 90 fingers, and are separated by a shorted grating with 3 fingers. The resonant modes formed by input and output IDTs are coupled just as two coupled parallel LC resonators. The coupling is carefully tuned by the central grating. This results in a two-mode wideband response such as that shown in Fig. 2-6(d). Due to the grounding grating the insertion loss is reduced to 4~5dB, which is much smaller than that of 10~15dB in conventional SAW or STW delay line. [10] The approximately linear phase change with slope equal to 1.713×10-6rad/Hz is obtained within the 3dB frequency band. The up and down limits of the phase change are above ±90o. The loaded Q factor
2 is estimated equal to 1537. The group delay is about 1.713×10-6 rad/Hz. High insertion loss out of the pass band is revealed in Fig. 2-6(c).
The spurious are suppressed under 30dB. The center frequency is trimmed to 2488.32 MHz.
(a)
(b)
(c)
(d)
Fig. 2-6 (a) Picture, and (b) structure of the STW resonator, (c) insertion loss from 2468 to 2508 MHz, and (d) insertion loss and transmission phase responses 2486.32 - 2490.32 MHz.
2.2.3 Loop Amplifier
The HBT monolithic amplifier is selected as the loop amplifier because of low noise figure and high dynamic range. The P1dB is at +17dBm and the bandwidth is 4 GHz. Its bandwidth was properly selected to prevent high 2nd harmonics. The nominal gain of 17dB is much greater than that required to overcome the total loop losses to insure the stable oscillation. The magnitude of gain variation over temperature is approximately 0.005dB/°C and this feature can prevent the AM-PM noise induced with the temperature variation.
2.2.4 Power Splitter
Because resistive attenuator in the feedback loop will degrade of white phase noise floor, an unequal Wilkinson power splitter is employed to adjust the excess small signal loop gain instead of resistive attenuator. [33] The Wilkinson power splitter can be realized as lump component or transmission line designs. To save the volume, the circuit is realized by the lump reactive components instead of microstrip line as shown in Fig. 2-7.
Port 3 Port 1
Port 2
Fig. 2-7 Wilkinson power splitter.
2.2.5 Electronic Phase Shifter
The electronic phase shifter is used to tune electronically the oscillation frequency.
The electronic phase shifter is constructed with silicon tuning diodes and inductors using T-circuit as shown in Fig. 2-8. It is basically a tunable high pass filter which, except for providing variable phase shifter in the loop, suppresses the excess gain of the loop amplifier at low frequency, preventing it from spurious oscillation. The phase noise and tuning linearity will be affected by the tuning diodes. High residual phase noise of tuning diodes will degrade the phase noise of voltage-controlled oscillator.
With proper selection of varactor diodes, the high tuning linearity and low phase noise are achieved at the same time.
Fig. 2-8 Electronic phase shifter.
The phase shift of loop amplifier and power splitter is about equal to -80° and 90°, respectively. The electronic phase shifter is about 40°. Because the total phase shift around the loop must be 2πN radians, another 10° is required, which is from the loop phase adjust constructed with fixed lumped reactive components. The frequency dependences of total phase shifter and open loop gain seen from the reference plane
A-B line indicated in the Fig. 2-5 are shown in Fig. 2-9. Curve X and Curve Y are the total phase shift with Vtune = 0Volts and Vtune = 5Volts, respectively. Curve M and curve N are the respective open loop gain with Vtune = 0Volts and 5Volts, respectively.
The group delay is about 1.74×10-6rad/Hz. As compared to Fig. 2-6(d), we see that the SAW resonator dominates the phase shift. The slight increase in group delay may be from the tunable phase shifter with varactors. The oscillation frequency is predicted at the zero-crossing point with enough gain margins about 2dB. This gives us the benefit of low flicker noise from the amplifier without deep gain compression.
The tuning bandwidth is approximately equal to the resonator’s 1dB bandwidth. It is approximately from 2487.85 MHz to 2488.85 MHz. The tuning bandwidth is approximately equal to the resonator’s 1dB bandwidth.
Fig. 2-9 Total phase shifter and the open loop gain at the oscillation frequency.
2.2.6 Oscillator Performance
The performances of the oscillator with STW resonator are measured. The narrow and wide scan of output spectrum and relative levels of harmonic are shown in Fig. 2-10(a) and (b), respectively. Because the STW resonator do not have 2nd harmonic response and the bandwidth of the loop amplifier is limited at 4 GHz, the
2nd harmonics of oscillator is suppressed below 58 dB as shown in Fig. 2-10(b) without any output low pass filter. The tuning characteristic is shown in Fig. 2-11 with ±200ppm range and good linearity. The frequency dependence on temperature is illustrated in Fig. 2-12. The turnover temperature is approximately 45°C, which is mainly determined by the SAW resonator.
(a)
(b)
Fig. 2-10 (a) Measured output spectrum for the 2488.32 MHz and (b) harmonics spectrum.
Fig. 2-11 Dependence of the oscillation frequency on tuning voltage.
Fig. 2-12 Dependence of the oscillation frequency on temperature.
The phase noise of the oscillator is measured as shown in Fig. 2-13. The measured parameters of the STW oscillator and the specifications of the other commercial products are summarized in Table 2.1.
Table 2.1: Measured results for the voltage-controlled STW oscillator and comparison with the other commercial products.
Value
Item This Work Synergy M-tron SAWTEK
Supply Voltage (Volts)
+5 +5 +5 +5
Supply Current (mA) 65 60 100 55
Output Power (dBm) +13 +3 +7 +10
Tuning voltage (Volts) 0-5 1-4 0-5 N/A
Tuning Range (ppm) ±200 250 ±50 80
Sub Harmonic (dBc) -58 -30 -26 N/A
Phase Noise @ offset
100 kHz (dBc/Hz) -153 -142 -145 -145
Fig. 2-13 Measured phase noise spectrum for the oscillator with STW resonator.
2.3 Voltage Controlled Oscillator with FBAR
After the success development of 2488 MHz voltage-controlled oscillator with STW resonator, we try to use the FBAR to replace the STW resonator. Basically, the suspended FBAR device is a three-layer structure with the top and bottom electrodes sandwiching a middle layer of oriented piezoelectric material. Air interfaces are used on both outer surfaces to prevent acoustic energy leaking out of the device; as the solid membrane and air boundary form high impedance to acoustic wave, functioning as high-Q acoustic reflectors at all frequency. When RF signals are applied near the mechanical resonant frequency, the piezoelectric transducer excites the fundamental bulk compress wave traveling perpendicular to the films. Resonators for use in stable oscillators need low temperature coefficient (TC), which needs composite structures for positive and negative coefficient compensation. On the contrary, for temperature sensing, a higher degree of TC is required for sensitivity, which is achieved also though composite structure containing all positive (or negative) coefficient material.
Here, AlN is employed for the potential integration. AlN has a crystal structure of hexagonal wurtzite where aluminum and nitrogen atoms are combined. AlN film is grown along (002) direction to achieve high piezoelectric coupling to the required extensional mode. AlN lattice extends and retracts toward c-axis orientation creating vibration if an alternating field is applied cross the crystal.
In this section, a high quality factor FBAR was designed and fabricated. Using this resonator, a high frequency voltage-controlled FBAR oscillator is designed and realized with hybrid circuits.
2.3.1 FBAR Design and Fabrication
It was reported that the lower the full width at half maximum (FWHM) value of a piezoelectric material has, the better the performance characteristics of the resonators and filters has. [34] Thus, the AlN piezoelectric film needs to have highly c-axis oriented columnar structure. [35] To achieve this requirement, a SiNX thin film is added between AlN and bottom electron. [36] The SiNX layer also serves as an etching stop layer to protect bottom electron while patterning the AlN layer.
The resonant frequency of FBAR is predominantly determined by half wavelength of standing acoustic wave in the resonator. The fundamental resonant frequency is then inversely proportional to the thickness (d) of the piezoelectric material used, and is equal to Va /2d, where Va is an acoustic velocity at the resonant frequency. The Nth harmonic frequency of the FBAR can be approximated as
)
where delec_t, dpiezo, dSiN, and delec_b are the thickness of top electrode (Al), piezoelectric material (AlN), buffer layer (SiNX), and bottom electrodes (Cr/Au), respectively.
Velec_t, Vpiezo, VSiN, Velec_b are the acoustic velocities of top electrode (Al), piezoelectric material (AlN), buffer layer (SiNX), and bottom electrodes (Cr/Au) respectively.
According to equation (2.4), the thickness of each layer in the FBAR for fundamental frequency (N=1) at 2.48 GHz for unlicensed application was designed and listed in Table 2.2.
Table 2.2: Physical properties of representative materials for FBAR. [37-39]
Layer Metal Piezoelectric Buffer Metal
Layer material Al AlN SiNX Cr/Au
Density (kg/m3) 2700 3255 3270 19700
Acoustic velocity (m/s) 6420 10400 11000 3240 (Au)
Designed thickness (Å) 3500 11000 1000 1000
Thermal expansion
coefficient (ppm/oC) 23.6 4.6 0.8 14.4
It is well known that AlN films must be grown orientated in the (002) direction to achieve high piezoelectric coupling to the required extensional mode. Therefore columnar AlN grains whose c-axes are perpendicular to the substrate are needed. The four layered composite structure Al/AlN/SiNX/Au of FBAR is shown in Fig. 2-14.
Fig. 2-14 Process flow of FBAR.
AlN was fabricated on (100) crystallographic oriented epitaxial silicon wafers.
After RCA cleaning, silicon wafer was deposited with low stress silicon nitride (Si3N4) using Low Pressure Chemical Vapor Deposition (LPCVD) and the thickness is 1200Å.
The Si3N4 layer served both as a high resistivity substrate to eliminate any parasitic contributions from mobile charges or a highly boron-doped epitaxial layer and an etch obstruction layer. Temporary support (sacrificial layer: Cu) is formed by E-gun on top of Si3N4 followed by electrode and piezoelectric layer. Then, a thin layer of Cr/Au film which thickness is 1000Å was fabricated by electron beam evaporation and
The Si3N4 layer served both as a high resistivity substrate to eliminate any parasitic contributions from mobile charges or a highly boron-doped epitaxial layer and an etch obstruction layer. Temporary support (sacrificial layer: Cu) is formed by E-gun on top of Si3N4 followed by electrode and piezoelectric layer. Then, a thin layer of Cr/Au film which thickness is 1000Å was fabricated by electron beam evaporation and