Chapter 3 Measurement and Prediction of Phase Noise in Oscillator
4.2 One-port SAW Resonator
In conventional Pierce oscillator circuits, the crystal resonator is effectively inductive and forms a highly frequency selective π network with two capacitors which provides the additional phase shift necessary to sustain oscillation. But crystal resonator is hard to be available which fundamental frequency is higher than 200 MHz. For this reason, one-port SAW resonator is chosen to replace crystal resonator for high frequency application. One-port SAW resonator is good for frequency from 200 MHz to 1 GHz and the same topology with bulk crystal resonator. The typical equivalent circuit model used for one port SAW resonator is shown in Fig. 4-2. This models the motional arm as series R-L-C in parallel with a static capacitor C0. The static capacitor C0 is due to the inter-digital transducers (IDTs) of SAW resonator and the stray capacitor of package between the terminals of SAW resonator. The typical values at 622 MHz are given as L1 = 42.22 uH, C1 = 1.55 fF, R1 = 20.2 Ohm, C0 = 2.11 pF. Although the topology is similar to that in low frequency crystal resonator,
the shunt capacitance C0 has a serious bad effect on the oscillation because of high frequency operation. [49] This point is detailed in the following paragraph. The reactance characteristics with frequency are shown in Fig. 4-3. Fr is called the resonant frequency and is where L1 and C1 are in series resonance and the resonator looks like a small resistance R1. The frequency Fa is the anti-resonant frequency and is the point the where L1-C1 look inductive and resonate with C0 to form the parallel resonance frequency Fa.
R1 L1 C1
C0
Fig. 4-2 Equivalent circuit for one-port SAW resonator.
Fig. 4-3 Reactance of SAW resonator.
4.3 Oscillator Design
The Pierce oscillator is designed to look into the lowest possible impedance across the resonator terminals. The oscillation satisfies the Barkhausen criterion with
closed loop gain 1 and phase shift equal 360 degrees. [≧ 48] As shown in Fig. 4-1, the signal from the input to the output of the amplifier is phase shift 180 degrees. The resonator appears as a large inductance since it is operating in the parallel mode between Fr and Fa. In conjunction with Ca and Cb, the passive circuit forms a pi network that provides an additional 180 degrees of phase shift from output to the input. Ca in series with Cb plus any additional stray capacitance forms the load capacitance for the resonator. However, there exists some shunt capacitance in the SAW resonator itself, which is often ignored by the SAW venders. [49] The implications are illustrated in the followings. The insertion loss and the phase shift of the SAW resonator in conjunction Ca and Cb are shown in Fig. 4-4. The line A and the line C are the insertion loss and phase shift respectively obtained without Ca and Cb. The initial phase at 621 MHz is negative rather than positive as often observed in crystal resonator. With increasing Ca and Cb, the phase shift downward and reaches finally the requirement of 180 degrees as shown in the line D. Unfortunately, the minimum insertion loss also degrades from -1dB to -8 dB as shown in the line B. This implies the amplifier needs to draw more DC power to overcome the insertion loss.
Accordingly, the efficiency of the oscillator is degraded.
Fig. 4-4 Phase shift and insertion loss of open-loop simulation for conventional Pierce oscillator.
To prevent the degradation of efficiency, we modify the Pierce oscillator as shown in Fig. 4-5. An additional phase shift is inserted in series with the SAW resonator. The insertion loss and the phase shift in the π feedback network in modified circuit are shown in Fig. 4-6. In the beginning, the capacitances of Ca and Cb were trimmeduntil the phase shift of 180 degrees at 622.2 MHz as shown in the line III. In this moment, the insertion loss of π network as shown in line II is about 15dB too high to be overcome. To achieve the Barkhausen’s criterion, the resonance phase shifter is trimmed to have the minimum insertion loss coincidence with the frequency of 180 degrees as shown in line IV. We can see the minimum insertion loss before (line II) and after (line I) adding the phase shift is almost the same. No larger power amplifier is needed. The efficiency of oscillator is improved.
Fig. 4-5 Modified Pierce oscillator.
Fig. 4-6 Phase shift and insertion loss of open-loop simulation for modified Pierce oscillator.
In Fig. 4-6, we can find an extra 90 degree phase shifter is required. The phase shifter can be implemented in different types, including transmission line, and lump LC components. The 90 degree phase shifter can be implemented with a
4 λ transmission line. While applied in the frequency of 622.08 MHz, the phase shifter
constructed by lump LC circuits is the better choice because of the wave length in this frequency is about 48 cm. The size of the transmission line phase shifter is unacceptable. Here, we will discuss the method to design phase shifter with lump LC components.
The After we decide the impedance Zo and phase shift θ for the phase shifter we need, the 2 x 2 transmission (ABCD) matrix can describe the two-port phase shifter as follows:[50]
T or π circuit, as shown in Fig. 4-7 and Fig. 4-8, can achieve the requirement of the matrix. In T-circuit, Z3 is equal to –j50 and can realized with a capacitor C=5.11 pF.
For symmetric, Z1 and Z2 is the same value and equal to -Z3. Z1 and Z2 can be realized with inductors L=12.79 nH. In π-circuit, Y3 is equal to –j0.02 and can be realized with an inductor L=12.79 nH. For symmetric, Y1 and Y2 is the same value and equal to -Y3. Y1 and Y2 can be realized with capacitors C=5.11 pF. Finally, we choose the π-circuit, as shown in Fig. 4-9, for the phase shifter in the oscillator. By using π-circuit, the C2
and combined with Cb and C1 can absorb some parasitic capacitance from SAW resonator. The final modified Pierce oscillator just has one more inductor and one more capacitor than conventional Pierce oscillator.
Z1 Fig. 4-7 The ABCD matrix for T-circuit.
3 Fig. 4-8 The ABCD matrix for π-circuit.
Fig. 4-9 The 90 degree phase shifter at 622.08 MHz.
The active part of this SAW oscillator is designed with tsmc 0.18um CMOS process.
The oscillator circuit is shown in Fig. 4-10. Because of the RF signal is input from the gate and amplified after passing through the output drain terminal, the dominant noise source is from the gate input terminal. This is because the noise source in an amplifier system is due to following equation [51]:
1
Thus, the noise of the system with amplification is governed by the input stage, where Gi is the gain of each stage amplifier. In core oscillation circuit, drive power into the resonator should be kept at a safe minimum level to assure proper start up.
Excessive drive power will result in resonator fracture or long term frequency drift. If multi-stage amplifier is used, the G1 is not large enough to suppress the noise caused by 2nd or 3rd stage amplifier. To achieve the low phase noise, only one active transistor is used in the core circuit.
Fig. 4-10 Circuit diagram of active device of SAW oscillator.
Negative resistance is created by using the RF-NMOS device M2 in the common source configuration. The device size of M2 is W/L = 192/0.18 (um). PMOS M1 and
M3 are used as the current mirrors. M1 acts as the active load of M2. Rf is the feedback resistor of M2. The chosen value of Rf is sufficiently large so that the input impedance of the inverter and the resonator can be matched. The SAW resonator in series with phase shifter is used as a frequency-determining element between the drain and the gate of M2. The output power is coupled from the gate of M2 to the limiter buffer amplifier constructed by M4 and M5.
Fig. 4-11 shows the linear simulation of open-loop frequency response using the osc-port function of Agilent Advance Design System (ADS) software in order to insure that negative resistance is large enough (|S11| > 1) in the desired frequency. The open-loop point is shown in Fig. 4-5. The oscillation starts when the phase of S11
equals to zero and amplitude of S11 is larger than one. The Barkhausen criteria are also satisfied in this moment.
Fig. 4-11 Results of linear simulation using ADS.
4.4 Oscillator Performance
The photograph of chip is shown in Fig. 4-12. The chip was fabricated by tsmc 0.18um CMOS process. Chip size is 850 x 465 um2. Table 4.1 is the summary of SAW oscillator performance. The spectrums of oscillation in narrow and broadband band scan are shown in Fig. 4-13 (a) and (b), respectively. The oscillator provides 4.0dBm of output power. Agilent E5052A Signal Source Analyzer was used to measure the phase noise of the oscillator. The measured phase noise is shown in Fig.
4-14 at 622 MHz. Phase noise of -136dBc/Hz at 10 kHz offset represents the excellent phase noise of this work.
Fig. 4-12 Picture of the active part of the SAW oscillator.
Table 4.1: Measurement results for the SAW oscillator.
Output Frequency 622 MHz
Output Power 4.0dBm
Phase Noise -136 dBc/Hz @ 10 kHz offset DC Power Supply 1.2V, 15mA
(a)
(b)
Fig. 4-13 (a) Fundamental spectrum and (b) harmonics spectrum of oscillator.
The comparisons of phase noise with other works are shown in Fig. 4-14. [52]
We can see the phase noise of this work is much lower than those in Vectron VS700 and the product of TXC. The reasons may be from the low noise process of device in our work. As indicated in [53], the noise figure of the device by circuit-theory-derived equation was given as
g m t
R f g
f +
+
=1 2γ γ NFmin
Where Rg is the gate resistance, ft is the unit gain frequency, f is the oscillation frequency, and γ is the proportional constant of the drain current noise. In the above equation, we can see larger ft can reduce the NFmin.
Fig. 4-14 Phase noise comparison for different SAW oscillators.
The product of TXC is fabricated by 0.35um CMOS process and this work is fabricated by 0.18um CMOS process. The gate resistance is about 8Ω/sq at 0.18um
CMOS process and 35 Ω/sq in 0.35um CMOS process. The ft of 0.35um CMOS process is about 13 GHz and the ft of 0.18um CMOS process is about 34 GHz. The large difference of ft and gate resistance between two difference processes makes the low phase noise of this work. Another reason is only one transistor is used as active device.
Chapter 5
Balanced Oscillator with One-port SAW Resonator
5.1 Introduction
Balanced circuit topologies are widely used to enhance circuit’s performance, such as differential amplifier and balance mixer. But how to generate accurate antiphase signals is the most difficult part of circuit design. Traditionally, balanced signals are obtain by the use of passive or active baluns. Several oscillator circuits have been reported that have two identical oscillators operating in antiphase. The resonators may be in the form of dielectric resonators [12], hairpin resonator[13], microstrip patch resonators[14], or 180 degree phase shifter[15].
A technique for generating accurate antiphase signals is presented in this work. A simplified analysis of the balance oscillator and measurement results of two identical oscillators with one-port SAW resonator at 433 MHz are presented to demo this technique. Based on this balanced SAW oscillator, a push-push oscillator can be constructed. By using the feature of the accurate antiphase signals, the phase noise and the even harmonics of the push-push oscillator can be improved.
5.2 Oscillator Design
The core circuit of this balanced oscillator is a Colpitts oscillator stabilized with one-port SAW resonator and is shown as Fig. 5-1. The base-to-emitter capacitors cause each device to exhibit negative resistance, as well as some reactance. In the SAW resonator, the surface waves are trapped between the two reflectors of Fig 2-1(a), making multiple transits between them and creating a standing wave, like
electromagnetic waves in a cavity resonator. This one-port SAW resonator serves as the tank of the SAW oscillator and acts like a short-circuited
2
λ cavity, which the
zero node voltages and maximum node currents are at both of the terminals of the resonator. Some important parameters of the transistor are listed in the Table 5.1 and the equivalent circuit model of the one-port SAW resonator used in this oscillator is shown as Fig. 5-2.
Fig. 5-1 Oscillator with one-port SAW resonator.
R1 L1 C1
C0
L1 = 72μH C1 = 1.9 fF R1 = 13 Ω C0 = 2.7pF
Fig. 5-2 Equivalent circuit model for one-port SAW resonator.
Table 5.1: Parameters of the transistor.
Characteristic Typical Value
DC Current Gain (hFE) 75 to 150
Gain Bandwidth Product (fT) 12.0 GHz Feed-Back Capacitance (Cre) 0.4pF
Noise Figure (NF) 1.5dB
The oscillation condition can be expressed as:
=1 Γ
⋅ ΓA R
This equation implies amplitude and phase conditions:
=1
Based on this core circuit, the balanced oscillator is constructed by two identical SAW oscillators and shown in Fig. 5-3. The one-port SAW resonator acts as the tank of the SAW oscillator and is also applied for the coupling network between two identical oscillators. The oscillation frequency is the resonant frequency of the SAW resonator which is under fundamental vibration mode. Under fundamental vibration mode, the RF currents of the opposite plates of the resonator is out of phase, which leads to the corresponding outputs of two identical oscillators 180o out of phase. Both of the terminals of the resonator in the balanced oscillator are virtual ground because the SAW resonator acts like a short-circuited
2
λ cavity, which the node voltages are
zero. The oscillation condition for the oscillator can be expressed as:
1 1
1⋅Γ =
ΓA R and ΓA2⋅ΓR2 =1 For the balanced structure,
A A
A =Γ =Γ
Γ1 2
R R
R =Γ =Γ
Γ1 2
Where ΓA and ΓR are the same as the half-circuit shown in Fig. 5-2.
This equation implies amplitude and phase conditions as follows:
=1 Γ
⋅ ΓA R
=0 + R
A θ
θ
So, we can make sure the behavior of the half circuit of balanced SAW oscillator is the same as that of the one-side SAW oscillator.
Fig. 5-3 Balanced oscillator with one-port SAW resonator.
The outputs of the balanced oscillator possess inherently in phase in even harmonics and 180o out of phase in odd harmonics. The differential outputs are fed to a output coupling network (0o or 180o power combiner) and a push-push oscillator will be available as shown in Fig. 5-4.
Output
Q-Fig. 5-4 Principle of push-push oscillator.
Since the even harmonics responses for SAW resonator, as shown in Fig. 2-1, is very weak, the push-push SAW oscillator is not suitable for operating at the twice fundamental frequency. For fundamental frequency operation, the push-push SAW oscillator can be used to suppress the even harmonics and improve the phase noise of the oscillator when the resonators with higher quality factors are not available. The strategy is using the 180o power combiner to cancel the undesired even harmonics and add the correlated fundamental oscillation carriers. All even harmonics are in phase in the balanced outputs and can in principle be completely cancelled. When the two outputs are combined using an 180o power combiner, the balanced RF output voltages are correlated and therefore to produce a 6-dB-higher combined output power. The increase in combined output power will lead to the improvement in phase noise of push-push oscillator.
5.3 Measurement and Discussion
The balanced SAW oscillator has been fabricated on FR4 substrate and its photograph is shown in Fig. 5-5. The detail circuit is shown in Fig. 5-6. The size of the pc board is 25mm x 25mm for the convenience of measurement. The oscillation starts when the DC voltage supplies to the transistor is 3.0V and the ASK input is also set to “High” (3.0V). Table 5.2 summarizes the data measured for the oscillator.
Table 5.2: Performance of balanced SAW oscillator.
Characteristic Measured Results
Frequency 433 MHz
DC Voltage (Vcc) 3.0V
DC Current 17mA
Power Consumption 51mW
Output RF Power 3.0dBm
Fig. 5-5 Photograph of balanced SAW oscillator.
Fig. 5-6 Circuit diagram of balanced SAW oscillator with ASK switch.
Lecroy WAVE pro 954 oscilloscope is used to measure the output waveforms of the balanced oscillator. Fig. 5-7 shows the output waveforms of Q+ and Q-. We can see the two outputs are almost the same amplitude and indeed 180o out of phase.
Fig. 5-7 Measured output waveforms of the balanced SAW oscillator.
HP 8561EC spectrum analyzer is used for the measurement of the oscillation frequency and harmonic spectrum for this oscillator. Fig. 5-8~11 present measurement results for the balanced oscillator. Fig. 5-8 and Fig. 5-9 show the harmonic spectrums for the output Q+ and Q-.
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
Fig. 5-8 Harmonic spectrum of the output Q+.
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
Q-Fig. 5-9 Harmonic spectrum of the output Q-.
The harmonics spectrum of the balanced oscillator after the 180o power combiner is shown as Fig. 5-10. The suppression of even harmonics is achieved by feeding output signals to the 180o power combiner. Because even harmonics are in phase, they can in principle be totally cancelled. By replacing 180o power combiner with 0o power
combiner, Fig. 5-11 shows the suppression of odd harmonics and we can sure that the fundamental outputs of the oscillator are nearly exactly 180o out of phase.
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
Fig. 5-10 Harmonic spectrum of the subtraction (Q+, Q-).
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
Fig. 5-11 Harmonic spectrum of the sum (Q+, Q-).
Table 5.3 reveals the harmonics before and after the 0o or 180o power combiners.
The 22dB reduction factor in the second harmonic after 180o power combiners is remarkable. In the meantime, the degradation in third harmonic is negligible. It is noted that the cancellation of second harmonic is limited by the difference between these two identical oscillators, including the features of the transistors, circuit layout and other passive components.
Table 5.3: Harmonics before and after the 0o or 180o power combiner.
Harmonics 1st 2nd 3rd
Agilent E5052A Signal Source Analyzer was used to measure the phase noise of the oscillator. The measured phase noise spectrum for this circuit is shown in Fig.
5-12. At 100 kHz offset from the carrier, the phase noise is about -158 dBc/Hz for balanced outputs and -164 dBc/Hz for the output combined with 180o power combiners. Beside an increase in output power level by about 6 dB, a significant reduction in phase noise was also observed. Since the noise voltage perturbations associated with the two identical active devices are uncorrelated with each other, the noise voltage will keep the same level at the linearly combined output. Thus, a 6 dB reduction in phase noise is expected, which is in good agreement with the measurement results.
Fig. 5-12 Measured phase noise of SAW oscillator at 433 MHz.
Chapter 6 Conclusions
In this thesis, we introduce the basic structure of piezoelectric resonators, including SAW resonators and FBAR, and applied these different resonators for the oscillators in UHF band. There are four types of oscillators with piezoelectric resonators presented in this thesis: 2488 MHz voltage-controlled oscillator with STW resonator, 2488 MHz voltage-controlled oscillator with FBAR, 622 MHz modified Pierce oscillator with one-port SAW oscillator, and 433 MHz balanced oscillator with one-port SAW resonator.
The tuning ability of the 2488 MHz voltage-controlled oscillator with STW resonator achieves ±200ppm and its phase noise performance is 8dB better than the other commercial products at offset 100 kHz frequency. The white phase-noise floor is about -170dBc/Hz. In the design phase of this oscillator, we found that the lower phase noise of the oscillator can not be achieved by using the actives devices with lower noise figure. By examining the residual phase noises of the main components in the oscillator, we found that the residual phase noise of the STW resonator dominate the phase noise of the oscillator, instead of active devices and the behavior of the phase noise is shaped by the important factor of group delay.
For developing the voltage-controlled FBAR oscillator, a FBAR is designed and
For developing the voltage-controlled FBAR oscillator, a FBAR is designed and