A Novel Voltage Controlled Crystal Oscillator (VCXO) Circuits

1,2Ulrich L. Rohde, Fellow IEEE and 1Ajay K. Poddar, Senior Member IEEE 1Synergy Microwave Corp., 201 McLean Boulevard, Paterson, NJ 07504, USA

2University of Cottbus, BTU Cottbus 03046, Germany

Abstract

Reference signal source requires high quality (Q)

factor resonating element, such as micro-machined or piezoelectric crystal that acts as an electro-mechanical resonating element in VCXO circuits. Apart from the apparent advantages of these electro-mechanical resonators they suffer from multi-mode resonance and cross talks. The selection and controlling of the desired mode is critical and challenging task when the spacing between modes is relatively small. The active mode-selection techniques reported in this paper minimizes the mode-jumping and phase noise for overtone mode VCXO, even those with relative low Q factor crystal. The measured phase noise for 290 MHz 3rd order overtone VCXO is typically –128 dBc/Hz at 1kHz offset from the carrier, and to authors knowledge, this is the reasonably good phase noise performance for the inexpensive class of VCXOs so far reported. 1. Introduction

The increasing demand of wireless communication service creates a demand for broadband network and higher operating frequencies in the market place. As the operating frequency shifts higher, generation of stable power-efficient reference signal sources with low cost become challenging due to the frequency limitations of crystal resonator and device circuitry [1]-[6].

To meet the above challenge, most such effort is in direction to employ phase locked loop (PLL) using crystal resonator. The drawback of this approach is spurious oscillations in fundamental mode due to multiplying mechanism by PLL circuit, thereby, causing deterioration in jitter characteristics, and introducing bit error in the communication systems [2].

Other options for high frequency signal sources, such as VCSO (Voltage controlled SAW resonator oscillator) uses surface acoustic wave (SAW) resonators, which have cost, availability and frequency stability issues. Therefore, designing low phase noise

high frequency VCXO as a reference frequency standard is challenging for a given cost, size, stability, phase noise, and power-consumptions.

In this work, we report a 3rd overtone mode 290 MHz VCXO in SMD package that has the characteristic features of high negative resistance and low drive level, while maintaining the thermal stability and phase noise performances. The reported VCXO circuit is validated with an active mode-coupling mechanism that minimizes the mode jumping and optimizes the phase noise performance, even those with relative low Q crystal resonators, for high frequency applications. 2. Crystal Resonator

Crystal resonator is a piezo-electrical material in which mechanical deformations due to vibrations (compression/torsion/shear) cause potential differences across the distinct surfaces and vice versa. The choice of the crystal resonance frequency is trade-off between manufacturability, stability and unwanted mode suppression. The crystal wafer thickness determines the resonance frequency, which is inversely proportional of the thickness of the quartz wafer. Therefore, higher frequency pushes the limit of the wafer thickness and the processing becomes difficult, as they get thinner and makes it fragile. Figure (1) shows the mechanical and electrical characteristics of AT Cut quartz resonator [3].

Figure1. Typical crystal resonator: (a) Quartz resonator, (b) AT Cut crystal thickness at different overtones, (c) Equivalent circuit and (d) Impedance characteristics (fundamental & overtones) [3].

978-1-4244-4565-3/09/$25.00 ©2009 IEEE

One possible solution is to vibrate the crystal at overtone of its fundamental frequency. For designing high frequency VCXO, the circuit toplogy determines the crystal configuration (fundamental, overtone, parallel, and series). In other words, the oscillator circuit toplogy forces the crystal resonator into either fundamental (lowest major resonant response), overtone (major responses other than fundamental), parallel (one of the inductive regions of the crystal’s reactance curve or series mode (one of the resistive points on the crystal’s reactance curve) as shown in Figure (2).

Figure (3) describes the typical motional parameters (Lx, Cx, and Rx) that govern the natural series resonance, whereas, C0 is the parallel holder capacitor, and Cv denotes the tuning diode capacitor required for pulling up the resonant frequency. The series (fs) and parallel resonance (fp) is given by (Figure 3) [4]

xxs CL

eseriesfπ2

1)mod( = (1)

xCC

xsp C

Cfeparaellelf>

+≈

002

1)mod( (2)

As illustrated in Fig.(3b), electrode holder capacitance C0 supports the pole that implies parallel resonance (fp), can be viewed upon like a parallel resonant circuit with capacitive transformations. In addition to this, electrode capacitance C0 causing gain-degrading effect that must be compensated for high performance VCXO applications. From (1) and (2) the mode separation (fs - f0) can be expressed through the figure of merit M [4] as

0

0 )(2f

ffQM p −

= (3)

From (3), Figure of merit M describes the existence of series (fs) and parallel (fp) resonance modes, therefore due care must be taken for suppressing the unwanted resonance mode; otherwise, it leads to mode jumping. For stable oscillations, series resonance frequency fs (wanted oscillation mode) is to be tuned by series tuning diode Cv (Fig. 3), and the relative frequency shift

can be expressed as )(2 0 v

x

s CCC

ff

+=∆ (4)

Figure 2. Typical impedance characteristic of crystal resonator

RxLx Cx

C0

CpCp

Quartz

Elec

trode

s

(a) Crystal Model (b) Electrical Lumped Model

Lx: Motional InductanceCx: Holder CapacitanceRx: Series ResistanceC0: Holder CapacitanceCv: Variable Capacitor

t

xsresonance

xxs

CCCff

CLf

++≈

=

0

1

121π

Cv

Figure3. Crystal: (a) Electrode and (b) Electrical lumped model

From (4), frequency drift can be optimized as a correction factor but Cv is temperature sensitive, and induces relative change ∂f in fresonance (pulled up resonance frequency) as

≈∂

++≈

v

vC

resonancevx

xsresonance C

dCkf

fCC

Cffv

,1 (5)

where kCv is temperature coefficient that causes a relative frequency fluctuations with temperature as a penalty to pull-up the overall frequency shifted due to holder capacitance C0 and package parasitics but over all performances degrades at higher UHF/VHF ranges.

3. High Frequency Crystal Resonator

High frequency crystal resonator is critical element for building VHF/UHF VCXOs as reference frequency standards in data communications. Low phase jitter of reference signal is a key factor to provide high quality processing. And if we could establish the condition for resonance at VHF/UHF range by fundamental, we would be able to design the VHF/UHF VCXOs with excellent jitter characteristics without being influenced by the unwanted spurious characteristics.

The resonance frequency of the crystal is determined by the effective thickness of the quartz wafer, which is controlled by mechanical sawing and lapping of the quartz wafer to the desired thickness (freq∝1/thickness). But there is a physical limit to process and manufacture the thinner quartz wafer, and quartz have reached their technological limit in terms of the operating frequency under the constraints of cost and reliability (Fig.1) [3].

Reducing wafer thickness beyond certain limit makes fragile resonators and moreover, processing the component becomes more difficult as they get thinner. The conventional approach (without reducing the thickness of the quartz wafer) to obtain high frequency oscillation is to vibrate the crystal at overtone modes of its fundamental frequency. Overtone modes (3rd, 5th, 7th, 9th, 11th… 2n+1, where n is an integer) solution can translate frequency in VHF/UHF range but they are sensitive to spurious modes. And, as the overtone number goes up, the loss resistance Rx (Fig. 3b) of the

crystal increases by manifolds. Therefore, lowest overtone mode is preferred if that particular overtone number yields the desired higher resonance frequency.

It has long been a research activity to develop a mechanism to produce high frequency fundamental crystal resonators or lowest possible overtone modes at VHF/UHF ranges. The typical solution to this has been the development of the inverted Mesa-type crystal resonator (Fig.4) [3], which is effective in lowering the overtone number that can be matched to hit desired higher frequency (up to 600 MHz and higher). As depicted in Figure (4), the centre portion is chemically etched to make it thinner than the outer ring so that centre ring vibrates at higher frequency without breaking since it is supported by the thick outer ring of uninterrupted quartz. The outer thicker ring of the quartz forms a strong frame structure around the thin fragile-etched central resonating layout. The center layout is etched to known thickness corresponding to the operating frequency and the strong outer ring enables for ease of handling.

The above technique allows manufacturing very thin quartz crystals resonators, which is suited for high frequency overtone VCXOs applications. However, fundamental high frequency crystal resonator is welcome approach but need lot of effort to manufacture and processing very thin high frequency quartz crystal, therefore not economically viable solutions to date.

Recent publication describes the AT-cut quartz, which is double inverted Mesa air-gapped electrode that vibrates at 622 MHz fundamental frequency with vibrating gain between resonance frequency and anti resonance frequency is more than 35 dB [5,6].

Figure (5) shows the picture of the 622MHz fundamental crystal resonator in which blank mounting and electrode connecting are adopted direct bonding technology by metal alloy and wire bonding technology.

4. Example: Crystal Oscillator Circuits

Figure (6) shows the electrical equivalent circuit of a

quartz crystal that includes all the modes.

Figure 4. Typical inverted high frequency Mesa quartz resonator [3]

Figure 5. Photograph of 622 MHz fundamental crystal resonator [5]

Each series resonant circuit (Ri, Li, Ci; i=1,3,5,7..) as depicted in Figure (6a) represents a mechanical modes (excited by the piezo-electric effect), and the capacitor C0 is the capacitance between the electrodes. In general, crystals are optimized with respect to a particular mode based on the design constraints and operating frequencies requirements suitable for VCXO toplogy.

As shown in Figure (6a), first RLC branch (Ri, Li, Ci) models the fundamental mode of oscillation, and the other branches are odd overtones, which are odd multiple of the fundamental frequency. The overtone element values are calculated as Ln= L, Cn= C/n2, Rn= n2R; where n is the nth overtone (n =3,5,7,9…). The resistor R represents the heat dissipation due to mechanical friction in the crystal, L is the electrical equivalent of crystal mass, and the capacitor C represents the crystal stiffness or elasticity.

A. Fundamental Crystal Resonance Mode

Due to the existence of both series and parallel resonance modes in the crystal, there may be two ways of utilizing a crystal resonator in VCXO, either as low impedance devices in series resonance around f0 or as a high, inductive impedance device in parallel resonance fp. Figures (7a) and (7b) show the typical schematic and CAD simulated plot of the impedance and phase characteristics for 10 MHz crystal (Example 1).

Example 1 (Fundamental Mode): mHLpFCRpFCMHzffs 13.100.25,5.6,0.7,10 11100 =⇒=Ω====

kHzCCfffHz

Qf

RLQ p 9.17

2,05.51

2,97940

0

100

0

1

10 ==−=== ω

mWPPowerDrivef

ffQM q

p 1.0:,6.350)(2

0

0 =−=−

=

L1

C1

R1

L3

C3

R3

L5

C5

R5

Ln

Cn

Rn

C0

Li

Ci

Ri

C0

Fundamental Modes Model for certain resonance Odd Overtones

Z(s)

(a) ( b)

Figure 6. Typical distributed electrical equivalent circuit of a quartz crystal: (a) Includes all modes, (b) particular mode (I =1,3,5..n )

As depicted in Figure (7b), both series (f0) and parallel (fp) resonance sow steep phase characteristics (fast rate of change of phase), which is required for good frequency stability. Crystals operated in fundamental mode have usually high M values, therefore, for practical purpose, impedance may be narrowband approximated around either f0 or fp.

With known values of poles and zeroes, the crystal impedance is [4]

0100

01

2100

21

2)(2)(

))()(())(()(

ωωωωω

ωωωωωω

jsjjCjsj

sjsjsjCsjsjZ

p

z

ppp

zzc −

−≈−−−

−−= (6)

−=∆

∆+=

−+

≈

−=∆

∆+=−+

≈

=

pi

p

i

ii

c

jQ

CR

jQ

jC

CCj

parallel

jQR

CCC

jjQseries

Z

ωωω

ωω

ω

ωωωω

ω

ωωωω

ω

ω

ωωωω

ω

,21

)(1

)(2

2

,21

2

2)(2

)(

0

200

000

00

00

0

200

000

(7)

From (7), series resonance is independent of the electrode capacitance C0, whereas in parallel resonance capacitance C0 determines the equivalent parallel resistance Rp as

200 )(

1ωCR

Ri

p = (8)

From Ex 1, parallel resistance Rp can be calculated as Ω×=

×××××== −

326122

00

103.795]10102107[5.6

1)(

1πωCR

Ri

p(9)

Ω×=×××××

== −3

2612200

103.795]10102107[5.6

1)(

1πωCR

Ri

p (10)

(a) Typical schematic (b) CAD Simulate plot

Figure 7. (a) Schematic of crystal, (b) CAD plot of the impedance and phase versus freq: fs = f0: series resonance, fp: parallel resonance

B. Overtone Crystal Resonance Mode

Overtone crystals have commonly smaller relative distances between the series and parallel resonances; the higher the mode number, the smaller the distances. Since the series-parallel resonance frequency interval of a crystal resonator is inversely proportional to the square of the overtone order, the higher the overtone order, the more difficult the compensation techniques.

There are two possible solutions. First, the compensated fundamental frequency or low-order overtone frequency is multiplied, and second, the output frequency of a high-order crystal oscillator is directly compensated, in which series inductances are added to the crystal to widen the series-parallel resonant frequency interval. But these techniques can reduce the loaded Q of a compensation system, and degrade both the frequency-temperature and the phase noise characteristic.

This is exemplified by 9th overtone crystal data (Example 2), where the figure of merit M even falls below one, so the zero and pole separation along the imaginary axis is smaller than the distance to the imaginary axis. With M approaching zero, the contributions from all resonance pole-zero pairs to the crystal impedance through equation (6) tend to cancel each other, so all what will be left is the shunting impedance of the electrode capacitance.

Figure (8) shows the typical schematic of the 9th overtone crystal as per data given in Example 2.

Example 2 (9th Overtone Mode): mHLfFCRpFCMHzffs 876.115.0,85,0.7,300 11100 =⇒=Ω====

kHzCCfffkHz

Qf

RLQ p 214.3

2,605.3

2,41610

0

100

0

1

10 ==−=== ω

nHC

Lf

ffQM p

p 21.401,8916.0)(2

0200

0 ===−

=ω

With exception of modest deviations closely around f0 (over and below by changing the values of LP), the shunting effect of C0 dominates the patterns in Fig. (8).

According to (3), M may also be interpreted as the ratio of the electrode impedance over the series circuit impedance at f0. To get a distinct frequency response that may serve for oscillator design with a low M value crystal, the effect of the electrode capacitance must be compensated, otherwise leads to poor stability and phase noise performances. One obvious way to do so is to neutralize C0 by a parallel inductance Lp as shown in Fig. (8). If the tuning is exact, then expression for LP is

02

0241

CfLp π

= (11)

this results in to only the series resonant circuit, and may be used as an equivalent circuit around f0. Figure (9) depicts the impedance magnitude and phase plot

before inductive (Lp) compensation. Figure (10) illustrates the impedance magnitude and phase plot after inductive (Lp) compensation: 1) Lp set exactly to ideal value, 2) 10 % over, and 3) 10% below the ideal value.

C. Selection And Controlling Of Resonance Modes

Crystal exhibits both desired and undesired modes therefore selection of the desired modes is critical for designing high frequency crystal oscillators. The fundamental frequency (lowest-mode) response is the most active due to lowest value of Rx (Figure 3b).

Higher order overtone mode (3rd, 5th, 7th, 9th, 11th… 2n+1, where n is an integer) will be active too but as the overtone number increases goes up, the loss resistance Rx (Fig. 3b) of the crystal inevitably increases. For high frequency operation, a method is needed to select a particular mode corresponding to desired frequency so that other active modes fail to sustained oscillations.

The novel approach is to maximize the negative resistance generated from the active device for a given mode and must yield positive value of resistance for all the other overtone modes including fundamental [3]. Figure (11) shows a typical Colpitts VCXO circuit for analysis purpose including noise contributions.

Fig. 8. A typical schematic of the overtone crystal resonator (Ex. 2)

Fig. 9. Magnitude and phase plot before inductive compensation

Fig.10. Magnitude and phase plot after inductive Lp compensation: set exactly to ideal value, 10 % over, and 10% below the ideal value.

Cc

C1

C2

ibn

vbn

rb icn

BaseCollector

Emitter

B''

C

re1 = re||(1/Y21)

inr

Cry

stal

-Mod

elS

ymbo

l for

Qua

rtz C

ryst

al

Cv

re1

Zin(t)

Active Device Network

X1

X2Zin: Rin+jXin

Zin(t): Input Impedance

Fig.11. Typical Colpitts VCXO including noise contribution

The value of the input impedance Zin (looking into the base of the transistor in Fig. 11) can be given as [1]

imaginaryrealininin CCjCC

YjXRZ

++

−=+≅

21212

21 111ωω

(12)

From (12), we notice that real part is negative (gain) and imaginary part is capacitive. The oscillator circuit shown in Figure (11) will oscillate if we select a crystal resonator that exhibits inductive property at mode and has lower value of loss resistance than the negative real part Rin generated by the active device network (Fig.11).

Accordingly, crystal is selected, which can exhibit inductive motional reactance equals to capacitive reactance (Xin) of the network, and has a lower loss resistance than the negative real part Rin generated by the active circuit. The above arrangement of network will operate on the lowest available resistance mode associated with the crystal’s fundamental mode resonance (lowest resonance frequency).

For a higher frequency operation we have to operate on overtone mode, therefore reactive part (Xin) is to be dynamically controlled so that one of the feedback capacitor (C1, C2) can be made inductive to stop the oscillation at fundamental mode for a give frequency as

partimaginarypartrealininin C

LjCLYjXRZ

−−

−+

=+≅

12

1

221

1ω

ω (13)

From (13), we notice that even combined crystal and active device reactance conditions are satisfied, the positive real part conditions will not initiate oscillation under all conditions. Therefore, design goal is to create a condition where at the desired overtone mode crystal frequency, active device network has capacitance at both X1 and X2 position (effective negative resistance) and at the fundamental frequency, the active device network capacitance for one X value (X1 or X2) and inductor at the other (effective positive resistance).

This condition can be achieved by incorporating tuning diode CV and tuning the resonator network to a resonant frequency that lies between fundamental and overtone frequencies, therefore, network will have inductance for X1 at the fundamental frequency and capacitance for X1 at a given overtone frequency and only the target overtone resonance will have the potential to maintain stable oscillations.

5. Design Example And Validations The new approach includes selection of the desired

overtone mode and suppresses mode-jumping phenomena (especially when the crystal resonates at fundamental and other higher order overtone modes).

In addition to this, the mode-selection approach discussed in this paper (section 4) includes a methodology for optimum injection locking and to reduce or eliminate phase hits, and retaining low phase noise and low thermal drift.

To validate the design approach, a 3rd overtone 290 MHz VCXO is built as an example to apply the concept of mode-selection and mode-feedback mechanism.

Figure (12) shows the schematic of the 3rd overtone 290 MHz VCXO in which fundamental and higher order overtone mode is (5th, 7th, 9th…2n+1, where n is an integer) is suppressed by mode-feedback and evanescent mode coupling techniques. This enables steep change of phases for pre-selected 3rd overtone mode, thereby maximization of group delay. However, the drawback of this approach is mode-jumping due to mode-feedback, which can be compensated by phase-shifter for suppressing of the unwanted oscillation.

Figures (13) and (14) show the CAD simulated and measured phase noise plot (with and without mode-feedback). As shown in Figure (14), mode-feedback approach offers significant improvement in phase noise performances (-128 dBc/Hz @ 1kHz offset for 290 MHz carrier frequency). At lower offset, we notice the deviation of 3-5dB between measured and simulated phase noise, the possible reason is inaccuracy of flicker parameters of crystal resonators and active device.

The dynamic noise-feedback is an effective method to reduce the 1/f noise at lower offset (close-in). By introducing an additional low frequency negative feedback loop, the close-in noise can be reduced by 10-15 dB in the flicker region (work is in progress).

Figure12. Schematic of 290 MHz 3rd overtone mode VCXO

Figure13. CAD Simulate phase noise plot VCXO circuit (Fig. 12)

Fig.14. 290 MHz 3rd overtone mode VCXO

5. Conclusions

This work offers cost-effective solution and can be applied for a crystal resonator (both high-Q and low-Q) based VCXOs for substantial reduction in phase noise. 10. References [1] U.L. Rohde, A.K. Poddar, and G. Boeck, The Design of Modern Microwave Oscillators for Wireless Applications: Theory and Optimization, Wiley, New York, 2005. [2] N. Nomura et al., “ 1[GHz] High Frequency Colpitts Oscillator”, 2005 IEEE MTT-S Digest, pp. 526-529. [3] D. Nehring, “Novel high-frequency crystal oscillator cuts jitter and noise”, RF Design Journals, pp. 32-42, June 2005. [4] U. L. Rohde and A. K. Poddar, “Dynamic Noise-Feedback and Mode-Coupling Silences The VCXO Phase Noise” 2008 IEEE FCS, pp. 554-561. [5] M. Umeki, T. Sato, H. Uehara and M. Okazaki, “ 622 MHz High Frequency Fundamental Composite Crystal Resonator With An Air-Gapped Electrode”, 2004 IEEE International Ultrasonics, Ferroelectrics, and Frequency Control Joint 50th Anniversary Conference, pp. 365-368. [6] T. Inoue, M. Yoshimatsu, and M. Okazaki, “ Miniaturization of angular rate sensor element using bonded