Abstract:
A voltage controlled Colpitts type crystal oscillator includes a first crystal and a transistor coupled to the first crystal to provide positive feedback for generating an output oscillatory signal. A variable capacitance is coupled to the first crystal for producing a change in a frequency of the oscillatory signal when a corresponding change in the variable capacitance occurs. A first inductance is coupled in a resonant circuit that includes the variable capacitance and the first crystal having a value selected to provide a pulling range of at least 0.4% with respect to the frequency of the oscillatory signal. In one embodiment of the invention, a second crystal is coupled to the first crystal and included in the resonant circuit. An energy dissipating impedance is coupled in the resonant circuit to the first crystal for decreasing a Q characteristic of the first crystal to increase the pulling range of the oscillator. The first inductance separates the second crystal from each of the first crystal and the energy dissipating impedance to decrease an effect of the energy dissipating impedance on a Q characteristic of the second crystal.

Description:
FIELD OF THE INVENTION  
         [0001]    The present invention relates to crystal oscillators and, more particularly, to voltage controlled crystal oscillators.  
         BACKGROUND OF THE INVENTION  
         [0002]    Crystal oscillators or crystal oscillator circuits are well known in the art. One characteristic of crystal oscillators is their ability to provide extremely stable operation. As such, crystal oscillator circuits are best known for their extremely stable operation. Additionally, crystal oscillators advantageously provide low phase noise performance. Further, crystal oscillators are low cost, with high Q crystals of small size. A disadvantage, however, with respect to current crystal oscillators is their inability to provide wide band operation (i.e. they have a small pulling range).  
           [0003]    The present invention relates to a type of crystal oscillator of which the frequency may be controlled by an electrical voltage, which enables the operating frequency of the oscillator to be freely selected within a given band of frequencies. The given band of frequencies is typically defined by the oscillator and/or oscillator component(s). This type of crystal oscillator is known as a voltage controlled crystal oscillator (VCXO).  
           [0004]    The range of operating frequencies for a VCXO may be termed the band or tuning range of operating frequencies. A VCXO typically has a center frequency of operation with the upper (maximum) and lower (minimum) frequency of operation being the pulling range of the VCXO. A problem is that traditional voltage controlled crystal oscillators cannot be pulled by an amount greater than about 0.05% (e.g. ±2.5 KHz pulling on a 10 MHz crystal).  
           [0005]    What is therefore needed is a voltage controlled crystal oscillator that provides a pulling range that is greater than the prior art.  
         SUMMARY OF THE INVENTION  
         [0006]    The subject invention is a voltage controlled crystal oscillator (VCXO). Single or dual crystals are separately tuned with inductance and/or capacitance to provide a wide pulling range. The subject VCXOs provide stable frequency output over wide pulling ranges, typically better that 1.2% of the nominal resonant frequency thereof.  
           [0007]    In accordance with one form of the subject invention, there is provided a voltage controlled crystal oscillator. The voltage controlled crystal oscillator includes a first crystal, a second crystal disposed in parallel with the first crystal, a first reactance associated with the first crystal, a second reactance associated with the second crystal, and transistor circuitry in communication with the first and second crystals and operative to output an oscillatory signal.  
           [0008]    In accordance with another form of the subject invention there is provided a voltage controlled crystal oscillator. The voltage controlled crystal oscillator includes crystal resonator means having a first crystal and a second crystal disposed in parallel for providing a crystal oscillation signal, first reactance means associated with the first crystal for tuning the first crystal, second reactance means associated with the second crystal for tuning the second crystal, and transistor means in communication with the crystal resonator means for outputting an oscillatory signal in response to the crystal oscillation signal.  
           [0009]    In accordance with yet another form of the subject invention there is provided a method of generating an oscillatory signal comprising the steps of: (a) providing a crystal resonator structure having a first crystal and a second crystal disposed in parallel, (b) providing a first reactance associated with said first crystal, (c) providing a second reactance associated with said second crystal, (d) generating a crystal oscillation signal from said crystal resonator structure and said first and second reactances, and (e) providing transistor circuitry in communication with said crystal resonator structure, said transistor circuitry operative to output an oscillatory signal in response to said crystal oscillation signal.  
           [0010]    Without being limiting, the subject invention has application in spread spectrum communication systems employing impulse transmissions (e.g. time domain spread spectrum, frequency hopping spread spectrum, and direct sequence spread spectrum systems) for faster and easier tracking and acquisition of spread spectrum codes. Again, without being limiting, this technique can also be adopted/adapted for clock recovery in SONET, ATM, and/or ETHERNET based systems. Further, while the various embodiments of the subject invention are disclosed with respect to a Colpitts type oscillator, it should be appreciated that the subject invention applies to other types of oscillators such as Pierce oscillators, Clapp oscillators, Hartley oscillators, and/or the like. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0011]    The above-mentioned and other features and advantages of this invention, and the manner of attaining them, will become more apparent and the invention will be better understood by reference to the following description of an exemplary embodiment of the invention taken in conjunction with the accompanying drawings, wherein:  
         [0012]    [0012]FIG. 1 depicts an electrical model of a quartz crystal;  
         [0013]    [0013]FIG. 2 depicts a block diagram of an exemplary voltage controlled crystal oscillator in accordance with the principles of the subject invention;  
         [0014]    [0014]FIG. 3 is an electrical schematic diagram of an exemplary embodiment of a single crystal voltage controlled crystal oscillator in accordance with the principles of the subject invention;  
         [0015]    [0015]FIG. 4 is an electrical schematic diagram depicting the methodology for adding capacitance to a tank circuit portion of a single crystal voltage controlled crystal oscillator in accordance with the principles of the subject invention;  
         [0016]    [0016]FIG. 5 is an electrical schematic diagram of an exemplary embodiment of a dual or twin crystal voltage controlled crystal oscillator in accordance with the principles of the subject invention;  
         [0017]    [0017]FIG. 6 is the electrical schematic diagram of FIG. 5 showing exemplary values for the various components;  
         [0018]    [0018]FIG. 7 is a graph depicting inductance versus frequency pulling for a single crystal voltage controlled crystal oscillator;  
         [0019]    [0019]FIG. 8 is a graph depicting capacitance versus frequency pulling for a dual crystal voltage controlled crystal oscillator;  
         [0020]    [0020]FIG. 9 is a graph depicting tuning voltage versus frequency change (pulling) for a dual crystal voltage controlled crystal oscillator; and  
         [0021]    [0021]FIG. 10 is an electrical schematic diagram of another exemplary embodiment of a dual or twin crystal voltage controlled crystal oscillator in accordance with the principles of the subject invention. 
     
    
       [0022]    Corresponding reference characters indicate corresponding parts throughout the several views.  
       DETAILED DESCRIPTION  
       [0023]    An equivalent electrical circuit for a quartz crystal, generally designated  20 , is shown in FIG. 1 and reference is made thereto. The equivalent electrical circuit for a quartz crystal  20  has a first terminal  22  and a second terminal  24 .  
         [0024]    Particularly, the equivalent electrical circuit for a quartz crystal  20  has inductance (that may be termed “motional inductance”) represented by an inductor  26 , capacitance (that may be termed “motional capacitance”) represented by a capacitor  30 , and resistance represented by a resistor  28  (a mechanical loss representative by a resistor  28 ). The inductor  26 , capacitor  30 , and the resistor  28  comprise the series components. The equivalent electrical circuit for quartz crystal  20  also has a shunt capacitance represented by the capacitor  32 . The shunt capacitance  32  is defined as the sum of the electrode capacitance and the holder (i.e. the case containing the crystal) capacitance. The shunt capacitance is of importance in getting the crystal to work above the series resonant frequency. The capacitor  32  comprises a parallel component. The capacitor  32  is thus coupled in parallel with the series components.  
         [0025]    For ease of presenting various formulas and/or identities, the inductor  26  may be represented by L 1 , the motional capacitance  30  may be represented by C 1 , the resistor  28  may be represented by R 1 , and the shunt capacitor  32  may be represented by C 0 .  
         [0026]    There are two possible modes of operation of the quartz crystal (equivalent electrical circuit for a quartz crystal)  20 : a series resonance mode and a parallel resonance mode. The frequency of oscillation and related parameters for the quartz crystal  20  are given by the following equations, labeled equations (1), (2), and (3).  
         [0027]    Particularly, series resonance (i.e. the series resonant frequency) f s  of the crystal  20  is given by equation (1) as:  
           f   s  (series resonance)=1/(2π( L   1   C   1 ) 1/2 )   (1).  
         [0028]    The series resonant point is the point of minimum impedance. Stated another way, the lowest crystal impedance exists at the series resonant frequency.  
         [0029]    The parallel resonance point (i.e. the parallel resonant frequency) f p  of the crystal  20  is the point of maximum impedance. Stated another way, the largest crystal impedance exists at the parallel resonant frequency. Parallel resonance is given by equation (2) below. Equations (3) and (4) are provided as well. Particularly, the parallel resonant frequency f p  is given by equation (2) as:  
           f   p  (parallel resonance)=1/(2π( L   1   C   eq ) 1/2 )   (2),  
         where  
           C   eq =( C   1   C   0 )/( C   1   +C   0 ) ;  
         and  
           Q  (quality factor)=(2 πf   S   L   1 )/ R   1 =1/(2πf S C 0 R 1 )   (3)  
         [0030]    A crystal that may be used for parallel mode operation can be used in series mode operation by using a specified load capacitance (not shown) in series with the crystal  20  (rather then a specified load capacitance in parallel with the crystal  20 , not shown). The resonance frequency of the crystal  20  can be adjusted slightly by adding either parallel or series trimming capacitance (capacitor(s)) as appropriate.  
         [0031]    Referring now to FIG. 2, there is depicted a block diagram of a voltage controlled crystal oscillator (VCXO), generally designated  40 , in accordance with the principles of the subject invention as discussed herein. The VCXO  40  has an input  41  and an output  46 . The input  41  is representative of both a physical terminal or the like and an input signal developed at the physical terminal. The input  41  is in communication with crystal circuitry  42 . The crystal circuitry  42  is operative to provide a resonator structure. The crystal circuitry  42  is coupled to transistor circuitry  44 . The transistor circuitry  44  is operative to provide an oscillator structure. The crystal circuitry  42  provides a resonant input for the transistor circuitry  44 . In one form, the oscillator structure is a Colpitts oscillator and, more particularly, a variation of a standard Colpitts oscillator. It should be appreciated, however, that the subject invention may be utilized with other types of oscillator configurations. An output  46  is coupled to the transistor circuitry  44 . The output  46  is representative of both a physical terminal or the like and an oscillator output signal developed at the physical terminal.  
         [0032]    Referring now to FIG. 3, there is depicted an electrical schematic of an exemplary single crystal VCXO embodiment generally designated  50  in accordance with the present principles. The VCXO  50  includes transistor circuitry  52  in like manner to transistor circuitry  44 . The transistor circuitry  52  forms a modified Colpitts oscillator and has an output  60  in like manner to the output  24 . The VCXO  50  also includes crystal circuitry  54  in like manner to the crystal circuitry  42 . The crystal circuitry  54  is coupled to the transistor circuitry  52 . A voltage source  56  is coupled to the transistor circuitry  52 .  
         [0033]    Particularly, the transistor circuitry  52  includes an NPN transistor Q 1  having a feed back loop  53  that includes a voltage divider formed by capacitors C 2  and C 3  of selectable capacitance. Particularly, the capacitor C 2  is coupled between the base of the transistor Q 1  and the emitter of the transistor Q 1 , while the capacitor C 3  is coupled between the emitter of the transistor Q 1  and ground. The feedback loop  53  provides enough feedback to the transistor Q 1  to maintain oscillation. Emitter resistance R 3  is provided between ground and the junction or node between the capacitors C 2  and C 3 . The emitter resistor R 3  is also coupled to the emitter of the transistor Q 1 .  
         [0034]    The transistor circuitry  52  also includes biasing resistance for the controlling the operating point of the transistor Q 1 . In the VCXO  50  of FIG. 3, biasing resistance is in the form of resistors R 1  and R 2 . The resistor R 1  is coupled between the voltage source  56  and the base of the transistor Q 1 . The resistor R 2  is coupled between the base of the transistor Q 1  and the resistor R 1  at one junction or node, and ground. The output  60  is capacitively coupled by a capacitor C 5  that is coupled to the collector of the transistor Q 1 . Additionally, a tank circuit such as an LC circuit embodied as inductor L 2  and capacitor C 4 , is coupled to the collector of the transistor Q 1  and the output  60  (capacitor C 5 ).  
         [0035]    Particularly, the crystal circuitry  54  includes a crystal Xtal 1  (preferably a quartz crystal) that is coupled to inductor Lx (inductance) at one end thereof, and to variable capacitance  58  embodied in VCXO  50  as a parallel configuration of a first, fixed capacitance or capacitor Cx and a second, variable capacitance or capacitor Cv. The capacitors Cx and Cv are coupled to ground. The inductor or inductance Lx is provided in the crystal circuitry  54  and couples the crystal Xtal 1  to the base of the transistor Q 1 .  
         [0036]    The crystal Xtal 1 , like all crystals, has a fundamental frequency. This fundamental frequency of the crystal coupled with the inductance Lx provides tuning or pulling of the crystal. By utilizing the electrical characteristics of the crystal with a selected inductance (e.g., Lx) and capacitance (e.g. Cx and/or Cv), one of which is voltage variable, pulls the crystal. In the embodiment of FIG. 3, capacitance Cv is variable and can be implemented by using a semi-conductor junction, the semi-conductor junction effective as a variable capacitor. Such a junction can provide varying capacitance with varying input voltage. This variable capacitance operates as a varactor.  
         [0037]    Lx provides a function of providing the tuning of the crystal through resonance with the capacitor value. Value selection of the inductance is thus necessary. With respect to FIG. 7, showing a graph depicting inductance versus frequency pulling for the single crystal voltage controlled crystal oscillator of FIG. 3. It can be seen in FIG. 7, that inductor Lx (or inductance) provides a 50 kHz pulling at 10.7 MHz for values of Lx less than 7 uH, and, for example, up to approximately 300 kHz pulling at 10.7 MHz for higher values (up to 33 uH) thereof. This provides a pulling range of 2.8%. The present invention provides a pulling of a minimum of 50 kHz or 0.46% without sacrificing tuning linearity (better than 2%) and single side band (SSB) Phase noise variation over the tuning range (better than 6 dbc/hz over the entire tuning range).  
         [0038]    With respect to the VCXO  50 , if the reactance of the crystal Xtal 1  (X e ) and the reactance of the circuit (X) satisfy the following relationship, then oscillation will occur.  
           X   e   =−X  i.e.  R   e   =−R    (4)  
         [0039]    Equation (4) represents a worst case operating condition for starting up the oscillator. Under typical and preferred operating conditions, the following relationship is valid:  
         − R&gt;R   e    (5)  
         [0040]    With respect to the VCXO  50  of FIG. 3:  
         − R=−g   m /(ω 2   C   2   C   3 )   (6)  
         [0041]    where g m  is the mutual conductance of the transistor Q 1  and ω is the angular frequency of oscillation of the transistor Q 1 . The capacitance C 2  and C 3  are chosen for appropriate operation as desired and can be evaluated for known values of R, g m , and ω. The biasing resistors R 1  and R 2  are chosen for appropriate operation as desired and can be chosen to provide the desired operating point of the transistor Q 1 . The capacitors Cx and Cv in the circuit  54 , together with the motional capacitance of the crystal Xtal 1  or oscillator will control the pulling range of the circuit. If the resonance frequency with a load capacitance (i.e. C x , C v ) is f l , then the difference between f l  and f s  (frequency pulling) (neglecting inductance at the present) is given by:  
         Δ f/f   s =( f   l   −f   s )/ f   s =[½( C   0   /C   1 )] [1/(1+( C   L   /C   o ))]  (7),  
         where  
           C   L =[(1/ C   2 )+(1/ C   3 )+(1/( C   x   +C   v )] −1    (8).  
         [0042]    According to one aspect of the subject invention, the VCXO  50  thus includes inductance, represented in the crystal circuitry  54  by the inductor Lx. As indicated above, inductance (i.e. inductor Lx) can increase the pulling range of the crystal circuitry  54  and thus the VCXO  50 . In particular, the pulling range may now be represented mathematically by:  
         Δ f/f   s =( f   l   −f   s )/ f   s =[½( C   0   /C   1 )] [1/(1+( C   L   /C   o ) (1/(1−ω 2   L   x   C   L ))]  (9).  
         [0043]    Referring to FIG. 4, there is depicted an electrical schematic of an exemplary alternative embodiment of a VCXO, here generally designated  70 . The VCXO  70  includes transistor circuitry  72  in like manner to transistor circuitry  44 . The transistor circuitry  72  forms a modified Colpitts oscillator and has an output  78  in like manner to the output  24 . The VCXO  70  also includes crystal circuitry  74  in like manner to the crystal circuitry  42 . The crystal circuitry  74  is coupled to the transistor circuitry  72 . A voltage source  76  is coupled to the transistor circuitry  72 .  
         [0044]    Particularly, the transistor circuitry  72  includes an NPN transistor Q 1  having a feed back loop  73  that includes a voltage divider formed by capacitors C 2  and C 3  of selectable capacitances. Particularly, the capacitor C 2  is coupled between the base of the transistor Q 1  and the emitter of the transistor Q 1 , while the capacitor C 3  is coupled between the emitter of the transistor Q 1  and ground. The feedback loop  73  provides enough feedback to the transistor Q 1  to sustain oscillation. Emitter resistance R 3  is provided between ground and the junction or node between the capacitors C 2  and C 3 . The emitter resistor R 3  is also coupled to the emitter of the transistor Q 1 .  
         [0045]    The transistor circuitry  72  also includes biasing resistance for the controlling the operating point of the transistor Q 1 . In the VCXO  70  of FIG. 4, biasing resistance is in the form of resistors R 1  and R 2 . The resistor R 1  is coupled between the voltage source  76  and the base of the transistor Q 1 . The resistor R 2  is coupled between the base of the transistor Q 1  and the resistor R 1  at one junction or node, and ground. The output  78  is capacitively coupled by a capacitor C 5  that is coupled to the collector of the transistor Q 1 . Additionally, a tank circuit such as an LC circuit embodied as inductor L 1  and capacitor C 4 , is coupled to the collector of the transistor Q 1  and the output  78  (capacitor C 5 ).  
         [0046]    Particularly, the crystal circuitry  74  includes a crystal Xtal 1  (preferably a quartz crystal) that is coupled at one end thereof to inductance (inductor Lx) that is coupled to the base of the transistor Q 1 , and to variable capacitance  80  embodied in the crystal circuitry  74  as a series configuration of a first, fixed capacitance or capacitor Ca and a second, fixed capacitance or capacitance Cb that can be selectively switched into and out of series coupling with the capacitor Ca. The capacitor Cb is coupled to ground and between the collector and emitter of a transistor (switch) Q 2 . In this manner, the capacitor Cb can be switched on and/or off by the transistor Q 2 . When the transistor Q 2  is turned off by an input signal (e.g. modulated input) applied to the base of the transistor Q 2 , the variable capacitance becomes the series equivalent of the capacitors Ca and Cb. When the transistor Q 2  is turned on through the input signal (e.g. modulated input) applied to the base of the transistor Q 2 , the variable capacitance becomes the capacitor Ca. Modulation may then be applied at the input of the transistor Q 2 , thereby making the oscillator a Frequency Shift Keying (FSK) type modulator or low power transmitter.  
         [0047]    It should be appreciated that the inductance Lx (inductance) of FIG. 4 performs in the same or similar manner as the inductance (inductor Lx) of FIG. 3. In FIG. 4, with the values as provided, the VCXO  70  provides a maximum frequency of 10.625 MHz and a minimum frequency of 10.618 MHZ at a power output of −9 dbm .  
         [0048]    With respect to Equation (3) above and the VCXO  70  of FIG. 4, capacitance now becomes:  
           C   L =[(1/ C   2 )+(1/ C   3 )+(1/ C   x )] −1    
         [0049]    where C X  is a function of C a , C b , and the transistor Q 2  output capacitance C ce . When the transistor Q 2  is fully on, C X =C a . When the transistor Q 2  is off C X  becomes:  
           C   X =[(1/ C   a )+(1/( C   b   +C   ce )] −1 =(1/ C   a )+(1/ C   b )] −1  if  C   b   &gt;&gt;C   ce    (10).  
         [0050]    The frequency shift can be properly controlled by appropriate selection of C a , C b .  
         [0051]    Referring now to FIG. 5, there is depicted an electrical schematic of an exemplary and basic VCXO generally designated  90 . The VCXO  90  includes transistor circuitry  92  in like manner to transistor circuitry  44 . The transistor circuitry  92  forms a modified Colpitts oscillator and has an output  96  in like manner to the output  24 . The VCXO  90  also includes crystal circuitry  94  in like manner to the crystal circuitry  42 . The crystal circuitry  94  is coupled to the transistor circuitry  92 . A voltage source of five (5) volts is coupled to the transistor circuitry  92 .  
         [0052]    In one form, the transistor circuitry  92  includes an NPN transistor Q 1  and a feed back loop  93  that includes a voltage divider formed by capacitors C 11  and C 13 . Particularly, the capacitors C 11  and C 13  are coupled in series such that capacitor C 11  is coupled to the base of the transistor Q 1  and the capacitor C 13  is coupled to ground. A resistance R 7  is provided between the junction or node of the capacitors C 11  and C 13 . An emitter resistance R 5  is coupled to the resistor R 7  and to the emitter of the transistor Q 1  and is also coupled to ground. Change in values of the capacitors C 11  and/or C 13  provide different operating characteristics. The capacitors C 11  and/or C 13  may thus be used for tuning the VCXO  90 .  
         [0053]    The output  96  is capacitively coupled by a capacitor C 12  that is coupled to the collector of the transistor Q 1 . Additionally, a filter such as an RC circuit embodied as resistor R 4  and/or resistor R 6  and capacitor C 9 , is coupled to the collector of the transistor Q 1  and to the base of the transistor Q 1 .  
         [0054]    Particularly, the crystal circuitry  94  includes dual or twin crystals. More particularly, the crystal circuitry  94  includes a first resonant structure  98  having a first resonant substructure  100 , and a second resonant structure  104  having a second resonant substructure  106 . The first resonant substructure  100  includes a first crystal  102  represented by its electrical schematic equivalent. The second resonant substructure  106  includes a second crystal  108 , represented by its electrical schematic equivalent. The second resonant substructure  106  may have an additional or “de-Q&#39;ing” network or circuitry  110  (here shown as capacitor C 6  in parallel with a resistor R 3 , the whole being in series with an inductor L 5 ). The first resonant structure  100  includes an inductance (inductor) L 2  in series with the crystal  102  while the second resonant structure  104  includes an inductance (inductor) L 4  in series with the crystal  108 . The inductors L 2  and L 4  are coupled together at a node with a fixed capacitor C 7 . The capacitor C 7  is coupled in series with a variable capacitor Cv. The additional circuitry  110  provides linearization of the tuning response of the second resonant structure  104 . This is accomplished by reducing the “Q” or de-Q&#39;ing the crystal. Particularly, changes in capacitance Cv causes the resonant frequency of the second resonant structure  104  to be linear or more linear. Stated another way, a change in a voltage, not shown, that varies the value of capacitance Cv creates a proportional (linear) change in the oscillator frequency (Δf).  
         [0055]    Variation in the inductance L 2  provides tuning of the resonant structure  100 /crystal  102  while variation in the inductance L 4  provides tuning of the resonant structure  104 /crystal  108 . Additionally, variations in the fixed capacitor value and tunability of the variable capacitor, provide changes in the pulling range of the VCXO.  
         [0056]    The first and second resonant structures  98  and  104  are in parallel while the overall super resonant structure  115  is coupled at one end to the base of the transistor Q 1  and to the series capacitors C 7  and Cv.  
         [0057]    The dual crystal oscillator  90  of FIG. 5 is similar to the wideband VCXO single crystal embodiments shown above. With respect to the dual crystal oscillator  90 , both the first and second crystals are chosen to be parallel resonant crystals. Inductances L 2  and L 4  are the two series inductances that may be individually added in series to a respective crystal (i.e. L 2  with Xtal 1  and L 4  with Xtal 2 , respectively) in order to improve the pulling range of the individual crystals. The network or trimmer circuitry  110  may be inserted across the crystal  108  in order to linearize the tuning response (i.e. to make the frequency response of the resonant substructure  106  linear with respect to change in capacitor Cv). The overall tuning is accomplished by variation of capacitor Cv in a similar manner as in the single crystal VCXO.  
         [0058]    More particularly, networks  100  and  106  are resonant at different frequencies, for example 10.63 MHz and 10.76 MHz. Capacitor C 3  (capacitance) with respect to the network  106  provides a 90° phase shift between the networks  100  and  106  such that when the network  100  is at its lowest impedance, network  106  is at its highest impedance and vice versa. This ensures that both networks  100  and  106  interact at a minimum. Inductor L 2  cancels the effect of capacitor C 2 , improving the tunability of the network  100  by the variation of C 7 , Cv and L 3 . Without the network R 3 , C 6 , and L 5  (circuitry  110 ), the resonance circuits  100  and  106  tend to have sharp tuning characteristics that may impact tuning linearity. The circuitry  110  effectively reduces the “Q” of the crystal  108  by a factor of approximately 4-5. Typical crystals have a Q of 2000. Application of circuitry  110  reduces the Q of the circuit  106  to be between 400-500. This reduction of Q helps to transition from network  100  to network  106  without interruption or abruptness when Cv is varied. It is also possible with the present configuration to realize tuning linearity of better than 2-3% as shown in FIG. 9, without resorting to the use of complicated compensation circuits.  
         [0059]    With respect to an application of the subject VCXO, in order to preserve the ssb (single side band) phase noise characteristics at lower and upper ends of the tuning range, two separate series inductors L 2  and L 4  are used in both networks  100  and  106  (i.e. both “arms” of the circuitry) in order to cancel the effect of capacitors C 2  and C 5  respectively. A measured SSB phase noise for the VCXO  90  at the lower end was −145 dbc/hz, with an upper end of −139 dbc/hz, giving a difference of 6 dbc/hz.  
         [0060]    Referring to FIG. 6, there is depicted the dual crystal oscillator  90  of FIG. 5 with exemplary values shown for the various components. It should be emphasized that the values are exemplary. As such, other values may be used depending on the crystals  102  and  108  chosen, the transistor Q 1  chosen, and other components.  
         [0061]    [0061]FIG. 7 depicts a graph, generally designated  120 , of inductance Lx versus frequency pulling for the single crystal embodiment of FIG. 3. It can be seen, that the frequency can shift from approximately 50 KHz to approximately 300 KHz (a range of 250 KHz) utilizing inductances from 1 to 13 μH.  
         [0062]    [0062]FIG. 7 shows the frequency pulling characteristics with respect to the value of Lx, the external series inductor. It can be seen that by controlling the value of this inductor, the tuning range can be increased or decreased. The specific range of inductance values for Lx is dependent on crystal case capacitance C 01 , C 02 . For an HC49 crystal as used in a prototype for one of the crystals of the networks  100  or  106 , C 01  is of the order of 7 picofarad (pf), whereas for a HC18 crystal as used in the prototype for one of the crystals of the other of the networks  100  or  106 , C 02  was of the order of 5 picofarads. The frequency tuning range can be quantified as being about 25 KHz per microhenry of inductance added.  
         [0063]    [0063]FIG. 8 depicts a graph, generally designated  130 , showing the effect of the pair of capacitances C 2 , C 3  (FIGS. 3 and 4) having equal values or of the pair of capacitances C 11 , C 13  (FIGS. 5 and 6) having equal values on the frequency pulling for the single crystal or dual crystal oscillator (VCXO), respectively. It can be seen that the frequency can shift from approximately 60 KHz to 140 KHz (a range of 80 KHz) utilizing a capacitance that varies from 1 to 248 pf for each capacitance of the corresponding pair of capacitances.  
         [0064]    Developing along similar lines as that of a single crystal with series inductance as described above, the pulling range for the dual or twin crystal embodiment described above can be computed with the following equation:  
                       Δ                 f       f   c       =                f   l     -     f   h         f   c                   =                [       1   2          (     C01   C11     )       ]          [     1     1   +       CL   CO1            {     1   -       ω   2          Lx1   CL         }       -   1             ]       +                            [       1   2          (     C02   C12     )       ]          [     1     1   +       CL   CO2            {     1   -       ω   2          Lx2   CL         }       -   1             ]                     (   13   )                               
 
         [0065]    Where C 01  is the parallel capacitance of the first crystal, C 11  is the series capacitance of the first crystal, C L  is the load capacitance, C 02  is the parallel capacitance of the second crystal and C 12  is the series capacitance of the first crystal and ω is the frequency of resonance of the tank circuit, and L 2  and L 4  are the series inductance with each of the crystals. Simulations were done with the following capacitance and inductance values for the crystals:  
         [0066]    C 01 =2.5 pf;  
         [0067]    C 02 =2.5 pf;  
         [0068]    C 11 =0.03 pf;  
         [0069]    C 12 =0.03 pf;  
         [0070]    L 1 =0.08 H; and  
         [0071]    L 2 =0.08 H.  
         [0072]    The results of the simulation are plotted in FIG. 9. FIG. 9 depicts a graph, generally designated  140 , of tuning voltage (times 10) versus frequency change (in MHz). It can be seen that the frequency change can shift from approximately 10.63 to 10.76 MHz as a result of tuning voltages from 0.1 volts to 4 volts that vary the value of capacitor Cv in a manner not shown. The chart  140  shows a 128 Khz variation in the Oscillator frequency. This corresponds to a frequency pulling of minimum 1.2 percent.  
         [0073]    Referring now to FIG. 10, there is depicted another exemplary embodiment of the subject invention. Particularly, there is depicted a VCXO, generally designated  150 . In general, the VCXO  150  is a dual or twin crystal VCXO with the dual crystals disposed in parallel with a series inductance (inductor(s)) and voltage variable capacitance (capacitor(s)) in a feedback loop. In general, the VCXO  150  has two crystals connected in parallel, with fixed inductance L 1 , resistance Q 1 , and variable capacitance C 3  in series to ground. The variable capacitance C 3  is shunted by a voltage variable capacitor C 2  to provide electronic tunability for the circuit. As such, the VCXO  150  is operative to provide stable frequency output over wide pulling ranges.  
         [0074]    More particularly, the VCXO includes a crystal circuitry  142  and a transistor circuitry  144 . The crystal and/or crystal circuitry/logic  142  includes a main resonant structure  152  formed by a crystal resonant structure  154  and a tuning or tank circuit  160 . The crystal resonant structure  154  includes a first crystal Xtal 1  and a second crystal Xtal 2  disposed in parallel. The crystal resonant structure  154  is coupled at one end to the base of the transistor Q 2  and at another end to the tuning structure  160 . The tuning structure  160  includes inductance (as inductor L 1 ) and resistance (as resistor R 1 ). A tuning voltage injected from tuning voltage input  162  is input to the tuning circuit  160 . The overall value of the resonant frequency of the tuning circuit  160  should match the resonant frequency of the crystal resonant structure  154 . This composite network will resonate and allow a low impedance at the base of the transistor Q 2 . Pulling of the system is accomplished with R 1  and L 1 . R 1  and L 1  form a resonance circuit with C 3  and/or the internal parasitic capacitance of the crystals.  
         [0075]    Further, the transistor circuitry  144  of the VCXO  150  includes an NPN transistor Q 2  forming a Colpitts oscillator. A voltage feed back ratio is decided by capacitors C 4  and C 5  (feedback network) which are typically of the same value. The output of the transistor and/or transistor circuitry/logic  144  is provided to conditioning circuitry/logic  164 . The conditioning circuitry/logic  164  capacitively couples the transistor Q 2  output by capacitor C 6 . This output is buffered by FET F 2  and its associated amplifier circuitry/logic. The FET F 2  and its associated amplifier circuitry/logic provide an output  168 .  
         [0076]    Analysis is made on the tunability improvements made possible by adjustment of feedback capacitor values and series inductance. Temperature compensation is provided to a bi-polar transistor by biasing the transistor using a FET device that has an inverse temperature characteristic. Typical tunability of prior art VCXOs is on the order of 0.05% of F 0  while the subject VCXO  150  is on the order of 1.2% of F 0 , a 24 times improvement in tuning range.  
         [0077]    In one form, the VCXO  150  provides temperature compensated for the oscillator. Particularly, in accordance with one embodiment of the subject invention, operating stability of the VCXO over various temperature ranges (e.g. −20° C. to +55° C.) is accomplished by utilizing a FET current source  166  to bias a bi-polar transistor of the oscillator. Since FET and bi-polar transistors have opposite temperature characteristics, the overall system will achieve the objective of stable performance over the temperature range. The FET biasing circuit  166  is a constant current source. Additionally the FET biasing circuit  166  provides a change in voltage with temperature that is opposite to the change in voltage with temperature of the transistor Q 2 . The circuits are complementary, thus aiding in operation thereof.  
         [0078]    Stabilization of the performance of the subject VCXOs (output level and/or spectral characteristics), the VCXO output may be capacitively coupled using a capacitor C 6  (e.g. 2-3 pf) and then buffered by a FET amplifier circuit (F 2 ). This provides adequate isolation to the VCXO so that the output frequency and spectral properties remain relatively stable over varying load conditions.  
         [0079]    The subject VCXOs are capable of pulling a 10 MHZ crystal better than 100 KHz. Tests were done with various values of inductance and capacitance with respect to the crystal resonant structure. Tests indicated that with inductance at 10 μH and capacitance at 440 pf (series capacitance of 220 pf each), very stable results are achieved. Tunability can be increased with inductance increased to 12 μH. With respect to single crystal VCXO implementation, the subject dual crystal has very good tunability over such traditional signal crystal implementations. With two crystals and changing inductance from 6 μH to 12 μH, there is improved tunability for the oscillator from 50 kHz to 275 kHz. With a single crystal, typically only a 2-3 kHz pulling range can be achieved. When feedback capacitance C 2 , C 3  of FIG. 4 are selected at 220 pF, and the base to emitter feedback resistance R 2  chosen to be 81 Kohms, and the series inductance Lx at 10 μH, it was found that the frequency pulling range of the single crystal resonant structure was improved from 50 kHz to 140 kHz. An 18 Kohm resistor R 1  is preferably used as a shunt across L 1  to ensure smooth tunability over the operating range.  
         [0080]    While this invention has been described as having a preferred design, the present invention can be further modified within the spirit and scope of this disclosure. This application is therefore intended to cover any variations, uses, of adaptations of the invention using its general principles. Further, this application is intended to cover such departures from the present disclosure as come within known or customary practice in the art to which this invention pertains and which fall within the limits of the appended claims.