Abstract:
An inductive device includes an inductor having an inductance associated therewith, and a tuning ring disposed around the inductor. The tuning ring has an inductance associated therewith, wherein the tuning ring is coupled to the inductor to establish a mutual inductance between the tuning ring and the inductor. The inductance of the inductor, the inductance of the tuning ring, and the mutual inductance between the tuning ring and the inductor contribute to a total inductance of the inductive device. The tuning ring is configurable, and is selectively configured to achieve a certain value for the mutual inductance, and a certain value for the inductance of the tuning ring, without changing a footprint of the tuning ring.

Description:
TECHNICAL FIELD 
     Embodiments described herein relate to inductors, and in particular, to devices and methods for tuning inductors. 
     BACKGROUND 
     Tunable inductors are useful for fine-tuning/adjusting various circuit designs. One area where tunable inductors provide such benefits involves VCO (voltage controlled oscillator) circuit design, and in particular, advanced SerDes (serializer/deserializer) circuit designs. In such advanced SerDes circuit designs, inductance values are especially small and operating frequencies typically operate at frequencies of 10 GHz and above. Because of the nature of such circuit designs, accurate modeling of inductors becomes particularly challenging due to the unpredictable effects caused by the circuit environment (e.g., uncertainty in returning path formed from other circuit elements). 
     Whenever the operating frequency of the circuit falls outside of the desirable range, modifications must be made to the circuit in order to tune the circuit back within the desirable range. Such modifications typically involve modifying the design of particular circuit elements including inductors. Modifying the design of particular circuit elements results in changes to the circuit floorplan, which requires significant redesign of the entire circuit. Prior approaches have involved substituting circuit elements with alternative circuit elements in order to achieve such fine tuning. These approaches suffer from the requirement of significant circuit redesign and time-consuming layout changes. 
     SUMMARY 
     In accordance with some embodiments, an inductive device includes an inductor having an inductance associated therewith, and a tuning ring disposed around the inductor, the tuning ring having an inductance associated therewith. The tuning ring is coupled to the inductor to establish a mutual inductance between the tuning ring and the inductor. The inductance of the inductor, the inductance of the tuning ring, and the mutual inductance between the tuning ring and the inductor contribute to a total inductance of the inductive device. The tuning ring is configurable, and is selectively configured to achieve a certain value for the mutual inductance, and a certain value for the inductance of the tuning ring, without changing a footprint of the tuning ring. 
     In one or more embodiments, the tuning ring may include a plurality of metal stack layers and one or more vias, at least one of the metal stack layers being grounded, and the one or more vias may be selectively configured to connect to certain one or ones of the metal stack layers to thereby achieve the value for the mutual inductance. 
     In one or more embodiments, the value of the inductance of the tuning ring may increase, and the value of the mutual inductance may decrease, when a total number of the metal stack layers connected to the one or more vias is reduced, and the value of the inductance of the tuning ring may decrease, and the value of the mutual inductance may increase, when the total number of metal stack layers connected to the one or more vias is increased. 
     In one or more embodiments, the tuning ring may be selectively configurable during a manufacturing process of the tuning ring without changing the footprint of the tuning ring. 
     In one or more embodiments, the tuning ring may form a circular loop or a multi-sided loop around the inductor. 
     In one or more embodiments, the tuning ring may include a plurality of metal stack layers. 
     In one or more embodiments, the tuning ring may be selectively configurable during a manufacturing process of the tuning ring by changing a number of the metal stack layers without changing the footprint of the tuning ring. 
     In one or more embodiments, at least two of the metal stack layers may have different respective thicknesses. 
     In one or more embodiments, at least one of the metal stack layers may form a closed-loop. 
     In accordance with other embodiments, a configurable device for an inductor includes a plurality of metal stack layers disposed around the inductor. The metal stack layers are electrically connected by one or more vias, at least one of the metal stack layers being grounded. One or more of the metal stack layers are coupled to the inductor to establish a mutual inductance between the one or more of the metal stack layers and the inductor. The one or more vias are selectively configured to connect to certain one or ones of the metal stack layers to thereby achieve a certain value for the mutual inductance without changing a footprint of the metal stack layers. 
     In one or more embodiments, a value of the mutual inductance may decrease when a total number of the metal stack layers connected to the one or more vias is reduced, and the value of the mutual inductance may increase when the total number of metal stack layers connected to the one or more vias is increased. 
     In one or more embodiments, the one or more vias may be selectively configurable during a manufacturing process of a tuning ring that includes the metal stack layers without changing a footprint of the tuning ring. 
     In one or more embodiments, the plurality of metal stack layers may form a circular loop or a multi-sided loop around the inductor. 
     In one or more embodiments, the plurality of metal stack layers may include two metal stack layers. 
     In one or more embodiments, the one or more of the metal stack layers may include aluminum or copper. 
     In one or more embodiments, at least two of the metal stack layers may have different respective thicknesses. 
     In accordance with other embodiments, a method for configuring an inductive device includes determining a total inductance value to be achieved for the inductive device, the device having a tuning ring and an inductor, determining a configuration of the tuning ring using a processor for achieving the total inductance value for the inductive device without changing a footprint of the tuning ring, and storing information regarding the determined configuration in a non-transitory medium. 
     In one or more embodiments, the act of determining the configuration of the tuning ring may include determining a number of metal stack layers for the tuning ring. 
     In one or more embodiments, the act of determining the configuration of the tuning ring may include determining a configuration of one or more vias for connecting to one or more metal stack layers of the tuning ring. 
     In one or more embodiments, a self inductance of the tuning ring may increase and a value of a mutual inductance between the tuning ring and the inductor may decrease when a total number of the metal stack layers connected to the one or more vias is reduced, and the self inductance of the tuning ring may decrease and the value of the mutual inductance value may increase when the total number of the metal stack layers connected to the one or more vias is increased. 
     Other and further aspects and features will be evident from reading the following detailed description of the embodiments. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The drawings illustrate the design and utility of embodiments, in which similar elements are referred to by common reference numerals. These drawings are not necessarily drawn to scale. In order to better appreciate how the above-recited and other advantages and objects are obtained, a more particular description of the embodiments will be rendered, which are illustrated in the accompanying drawings. These drawings depict only typical embodiments and are not therefore to be considered limiting of its scope. 
         FIG. 1-1  illustrates a top-view schematic diagram of a tunable ring around an inductor in accordance with some embodiments. 
         FIG. 1-2  illustrates a cross-sectional view schematic diagram of a tunable ring around an inductor in accordance with some embodiments. 
         FIG. 2-1  illustrates a tunable ring configuration in accordance with some embodiments. 
         FIG. 2-2  illustrates another tunable ring configuration in accordance with other embodiments. 
         FIG. 3-1  illustrates a tunable ring around an inductor in accordance with other embodiments. 
         FIG. 3-2  illustrates a tunable ring around an inductor in accordance with other embodiments. 
         FIG. 4-1  illustrates a tunable range of inductive values for a tunable ring around an inductor in accordance with some embodiments. 
         FIG. 4-2  illustrates a tunable range of Q-values for a tunable ring around an inductor in accordance with some embodiments. 
         FIG. 5  illustrates a tuning ring having metal stack layers with different respective thickness, in accordance with some embodiments. 
         FIG. 6  is a flow diagram for a method of configuring an inductive device, in accordance with some embodiments. 
     
    
    
     DETAILED DESCRIPTION 
     Various embodiments are described hereinafter with reference to the figures. It should be noted that the figures are not drawn to scale and that the elements of similar structures or functions are represented by like reference numerals throughout the figures. It should be noted that the figures are only intended to facilitate the description of the embodiments. They are not intended as an exhaustive description of the invention or as a limitation on the scope of the invention. In addition, an illustrated embodiment need not have all the aspects or advantages shown. An aspect or an advantage described in conjunction with a particular embodiment is not necessarily limited to that embodiment and can be practiced in any other embodiments even if not so illustrated. Also, reference throughout this specification to “some embodiments” or “other embodiments” means that a particular feature, structure, material, or characteristic described in connection with the embodiments is included in at least one embodiment. Thus, the appearances of the phrase “in some embodiments” or “in other embodiments” in various places throughout this specification are not necessarily referring to the same embodiment or embodiments. 
       FIGS. 1-1  and  1 - 2  illustrate an inductive device  100  having an inductor  101  and a tuning ring  103  around the inductor  101  according to some embodiments.  FIG. 1-1  and  FIG. 1-2  are to be viewed together, where  FIG. 1A  illustrates a top-view schematic diagram of the tuning ring  103  around the inductor  101 , and where  FIG. 1-2  illustrates a cross-sectional view schematic diagram of the tuning ring  103  around the inductor  101 . The inductive device  100  is connected to a substrate  109 . In some embodiments, the substrate  109  may be a part of a circuit device. Also, in some embodiments, the circuit device may include a configurable integrated circuit, such as a field programmable gate array (“FPGA”), or another type of programmable logic device (“PLD”). In other embodiments, the substrate  109  may be a part of any circuit device, and may or may not include any programmable logic device. 
     In  FIG. 1-2 , the inductor  101  is depicted as a dashed rectangle in order to illustrate that the inductor  101  is surrounded by the tuning ring  103 . The tuning ring  103  is inductively coupled to the inductor  101  such that a mutual inductance is established between the tuning ring  103  and the inductor  101 . A total inductance value of the tunable inductive device  100  comprises the mutual inductance between the tuning ring  103  and the inductor  101 , as well as the inductance (self-inductance) of the inductor  101 , and the inductance (self-inductance) of the tuning ring  103 . In the illustrated embodiments, the inductor  101  is built from upper metal layers (M 6 -M 11 ). In other embodiments, the inductor  101  may be built from layers that are different from those shown. For example, in other embodiments, the inductor  101  may be built from layers M 5 -M 11 , or from layers M 5 -M 10 , etc. 
     As shown in  FIG. 1-2 , the tuning ring  103  may include a plurality of metal stack layers  105  which are selectively connectable to one or more vias  107 . In the illustrated embodiments, the tuning ring  103  has eleven metal stack layers  105  (layers M 1 -M 11 ). In other embodiments, the tuning ring  103  may have less than eleven metal stack layers  105  (e.g., one metal stack layer), or more than eleven metal stack layers  105 . In some embodiments, the metal stack layers  105  may be composed of different materials, such as aluminum or copper. For example, in the embodiments of  FIG. 1-2 , metal stack layers M 1 , M 2 , M 4 , M 5 , M 6 , M 8 , M 9 , and M 11  may be composed of aluminum, and metal stack layers M 3 , M 7 , and M 10  may be composed of copper. In other embodiments, the metal stack layers M 1 , M 2 , M 4 , M 5 , M 6 , M 8 , M 9 , and M 11  may be made from copper or another material, and/or the metal stack layers M 3 , M 7 , and M 10  may be made from aluminum or another material. Also, in other embodiments, the metal stack layers  105  may be made from more than two materials (e.g., three different materials, or more). In further embodiments, the metal stack layers  105  may be all made from a same material. 
     In the illustrated embodiments, the metal stack layers  105  all have the same thickness measured in a direction that is along a longitudinal axis of the tuning ring  103 . In other embodiments, the metal stack layers  105  may vary in thickness. For example, in other embodiments, at least two (e.g., all) of the metal stack layers  105  may have different respective thicknesses. In further embodiments, the tuning ring  103  may have metal stack layers  105  with different respective material compositions, and with different respective thicknesses. An example of a tuning ring  103  having metal stack layers  105  with different respective thickness is illustrated in  FIG. 5 , where metal stack layer M 8  and metal stack layer M 9  have different respective thicknesses than the other metal stack layers. 
     In some embodiments, each via  107  between two metal stack layers  105  may have a ring configuration. In such cases, the ring configuration may correspond with a cross sectional profile of the metal stack layers  105 . In other embodiments, the tuning ring  103  may include a plurality of vias  107  connected between each pair of metal stack layers  105 . Although a gap is shown between two adjacent metal stack layers  105 , in other embodiments, the tuning ring  103  may include an electrically insulative layer coupled between adjacent metal stack layers  105 . 
     In some embodiments, each of the metal stack layers  105  may form a closed-loop around the inductor  101 . In other embodiments, a plurality, but not all, of the metal stack layers  105  may each form a closed-loop around the inductor  101 . In further embodiments, only one of the metal stack layers  105  forms a closed loop around the inductor  101 . Thus, in some embodiments, one or more of the metal stack layers  105  may not form a closed-loop. Also, in some embodiments, at least one of the metal stack layers  105  is grounded (e.g., connected to the substrate  109 ) to form a returning path. 
     In the illustrated embodiments, the configuration of the tuning ring  103  is selectively modifiable to achieve a certain value for the self inductance of the tuning ring  103 , and/or a certain value for the mutual inductance between the tuning ring  103  and the inductor  101 , without changing a footprint of the tuning ring  103 . For example, in some embodiments, changing the configuration of the tuning ring  103  may result in a corresponding change in the self-inductance of the tuning ring  103 , as well as a corresponding change in the mutual inductance between the tuning ring  103  and the inductor  101 . Since the total inductance of the inductive device  101  is contributed at least in part by the mutual inductance provided by the tuning ring  103 , and at least in part by the self inductance of the tuning ring  103 , the total inductance of the inductive device  101  may be adjusted (“tuned”) by modifying the tuning ring  103  without changing its footprint or the floorplan layout of its corresponding circuit (not shown). As used herein, the term “footprint” refers to a component&#39;s layout with respect to its corresponding circuit. A tuning ring  103  may be considered to retain its “footprint”, when it is modified such that the other circuit elements of the corresponding circuit are able to remain unchanged (e.g., no need for layout redesign). Said otherwise, the tuning ring  103  may be modified to achieve a desired mutual inductance between the tuning ring  103  and the inductor  101  without requiring any other circuit elements to be modified, including the inductor  101  itself. 
     In some embodiments, the configuration of the tuning ring  103  may be modified by altering a configuration (e.g., location and/or number) of the via(s)  107  so that certain one or ones of the metal stack layers  105  are connected to the via(s)  107 . For example, one via  107  may be selectively removed to disconnect certain one(s) of the metal stack layers  105  from the rest, or may be selectively added to connect certain one(s) of the metal stack layers  105  to the rest. 
     For example, while the tuning ring  103  in the embodiments of  FIG. 1-2  has been configured so that the via(s)  107  connects to all of the eleven metal stack layers  105 , in other embodiments, the via(s)  107  may be configured differently so that it connects to a subset of the metal stack layers  105 .  FIG. 2-1  illustrates an example of another configuration of the tuning ring  103 . The tuning ring  103  is the same as that described with reference to  FIG. 1-2  (e.g., it has the same eleven metal stack layers M 1 -M 11 ), except that the via(s)  107  has been configured so that only certain ones of the metal stack layers  105  are connected. In the illustrated example, the metal stack layers  105  are not all electrically connected by via(s)  107 . In this embodiment, metal stack layers M 1 -M 6  are connected by via(s)  107 , and metal stack layers M 7 -M 11  are not connected by via(s)  107 . By selectively configuring certain one(s) of the metal stack layers  105  to be connected to the via(s)  107 , the tuning ring  103  is able to achieve a desired mutual inductance value with the inductor  101 . 
       FIG. 2-2  illustrates another configuration of the tuning ring  103  in which the via(s)  107  has been configured to connect certain ones of the eleven metal stack layers  105 . In the illustrated example, the metal stack layers  105  are again not all electrically connected by via(s)  107 . However in this embodiment, the subset of the metal stack layers  105  which are connected by via(s)  107  are not connected to the ground (e.g., substrate  109 ). As such, an additional electrical connection is formed between at least one of the metal stack layers  105  within the subset and the ground (e.g., substrate  109 ) in order to ensure proper operation of the tuning ring  103 . By selectively altering the number of the metal stack layers  105  that are connected to the via(s)  107 , the tuning ring  103  is able to achieve a certain desired mutual inductance value with the inductor  101 , and/or a certain desired self-inductance for the tuning ring  103 . 
     As illustrated in the above examples, since changing the configuration of the via(s)  107  does not affect the area occupied by the tuning ring  103  relative to the substrate  109 , such technique of changing the configuration of the tuning ring  103  to tune the inductive device  100  does not change the footprint of the tuning ring  103 . It also does not require any modification of the floorplan layout of any corresponding components on the substrate  109  in some embodiments. 
     In other embodiments, instead of changing the configuration of the via(s)  107 , the configuration of the metal stack layers  105  may be modified to configure the tuning ring  103 . For example, in some embodiments, the tuning ring  103  may be selectively configured by altering a number of the metal stack layer(s)  105  for the tuning ring  103 . In some embodiments, the tuning ring  103  may be selectively built to have only one stack layer  105 . In other embodiments, the tuning ring  103  may be selectively built to have other numbers of metal stack layers  105 . Since changing the number of metal stack layer(s)  105  affects the height of the tuning ring  103 , and not the area occupied by the tuning ring  103  relative to the substrate  109 , such technique of changing the configuration of the tuning ring  103  to tune the inductive device  100  does not change the footprint of the tuning ring  103 . It also does not require any modification of the floorplan layout of any corresponding components on the substrate  109  in some embodiments. 
     In other embodiments, the configuration of the metal stack layers  105  may be modified by changing a thickness of one or more metal stack layers  105 . In further embodiments, the configuration of the metal stack layers  105  may be modified by changing a material composition of one or more of the metal stack layers  105 . 
     In further embodiments, the configuration of the tuning ring  103  may be modified by both altering a configuration of the via(s)  107  and a configuration (e.g., number, dimension, composition, etc.) of the metal stack layer(s)  105  for the tuning ring  103 . Such technique of changing the configuration of the tuning ring  103  to tune the inductive device  100  does not change the footprint of the tuning ring  103 . It also does not require any modification of the floorplan layout of any corresponding components on the substrate  109  in some embodiments. 
     As discussed, the self inductance of the tuning ring  103  and the mutual inductance between the tuning ring  103  and the inductor  101  may be varied by changing the number of metal stack layers  105  within the tuning ring  103  and/or the configuration of the via(s)  107  within the tuning ring  103 . A tuning ring  103  with a smaller number of connected metal stack layers  105  (e.g., one metal stack layer  105 ) will result in higher self inductance of the tuning ring  103  and a lower mutual inductance between the tuning ring  103  and the inductor  101 . A tuning ring  103  with a greater number of connected metal stack layers  105  will result in lower self inductance of the tuning ring  103  and a higher mutual inductance between the tuning ring  103  and the inductor  101 . By selectively configuring the number of metal stack layer(s)  105  that the tuning ring  103  has, and/or by selectively configuring the via(s)  107  to connect certain one(s) of the metal stack layers  105 , the self inductance of the tuning ring  103  and the mutual inductance between the tuning ring  103  and the inductor  101  may be adjusted, thereby resulting in a desired total inductance (which is at least partially contributed by the mutual inductance between the tuning ring  103  and the inductor  101 , and by the self inductance of the tuning ring  103 ) for the inductive device  100 . Thus, providing multiple configurations for the metal stack layers  105 , and/or multiple configurations for the via(s)  107 , is advantageous in that the tuning ring  103  may be selectively configured to provide a wide range of mutual inductance values that are achievable between the tuning ring  103  and the inductor  101 , thereby allowing a desired total inductance for the inductive device  101  to be achieved. 
     In some embodiments, the configuration of the tuning ring  103  may be modified during a fabrication process (which may be considered a part of a manufacturing process) of the tuning ring  103 . In one implementation, the modification of the configuration of the tuning ring  103  may be achieved by modifying a set of masks applied to fabricate the tuning ring  103 . For example, adding or removing masks during the fabrication process may result in different tuning rings  103  with varying metal stack layers  105  and/or different configuration for the via(s)  107 . Thus, various configurations for the one or more metal stack layers  105  and/or one or more vias  107  are achievable during the fabrication process to provide different mutual inductance values between the tuning ring  103  and the inductor  101 , and/or different self-inductance values for the tuning ring  103 . In such cases, the act of configuring the tuning ring  103  may be considered performed during the fabrication process of the tuning ring  103 . 
     While the modification of the tuning ring  103  design may involve re-patterning the application of mask(s) used to fabricate the tuning ring  103 , the footprint of the tuning ring  103  remains unchanged. As such, the remaining circuit elements are negligibly affected or completely unaffected, and the inductance of the inductive device  100  may be “tuned” to achieve a desired value while retaining the original circuit layout and original circuit elements. Thus, embodiments of the inductive device  100  described herein, and embodiments of the technique to configure the inductive device  100 , are advantageous in that they saves cost and time that would otherwise be required to change the floorplan layout to redesign the circuit. 
     In other embodiments, the configuration of the tuning ring  103  may be modified during a design phase (which may be considered another part of a manufacturing process) of the tuning ring  103 . For example, during a design of the tuning ring  103 , the configuration of the tuning ring  103  may be modified using any of the techniques described herein (e.g., by changing the configuration of metal stack layers  105 , and/or the configuration of the via(s)  107 ). In such cases, the act of configuring the tuning ring  103  may be considered performed when the design of the tuning ring  103  is modified to change the configuration of the metal stack layers  105  and/or the via(s)  107 . Thus, the term “tuning ring” may refer to the actual tuning ring  103 , or a design version of the tuning ring  103 . Similarly, the terms “inductive device”, “inductor”, “stack metal layer”, “via” (or similar terms) may refer to the actual inductive device, the actual inductor, the actual stack metal layer, and the actual via, respectively, or may refer to design version of the inductive device, design version of the inductor, design version of the stack metal layer, and design version of the via, respectively. 
     In some embodiments, a method for configuring the inductive device  100  may include determining a total inductance value to be achieved for the inductive device  100  ( 602 ), determining a configuration of the tuning ring  103  for achieving the total inductance value for the inductive device without changing a footprint of the tuning ring  103  ( 604 ), and storing information regarding the determined configuration in a non-transitory medium ( 606 ). A flow diagram depicting this method  600  is shown in  FIG. 6 . The method may be performed during a design phase of the tuning ring  103  in some embodiments. In some embodiments, the stored information may be used to create one or more masks for constructing the tuning ring  103 . For example, the mask(s) may be used to configure the via(s)  107  to connect to certain one(s) of the metal stack layers  105  in some embodiments. 
     In some embodiments, the act of determining the total inductance value to be achieved may be performed by a processor. For example, in some embodiments, the processor may receive the total inductance value as input from a user or from another device. 
     In some embodiments, the act of determining the configuration of the tuning ring  103  for achieving the total inductance value may be performed by the processor (or another processor). For example, in some embodiments, the processor may receive information regarding the configuration of the tuning ring  103  for achieving the total inductance value for the inductive device  100  from a user or from another device. In other embodiments, the processor may perform calculation to determine the configuration of the tuning ring  103  based on the desired total inductance value to be achieved for the inductive device  100 , and based on certain design parameters (e.g., shape, dimension(s), material property, location, footprint, etc.) of the components (e.g., metal stack layer(s), via(s)) of the tuning ring  103 . For example, in some embodiments, the processor may obtain an inductance value of an inductor  101 , and may then compare the inductance value with a desired total inductance value that is to be achieved by the inductive device  100 . In one implementation, the processor may calculate a difference between the inductance value of an inductor  101  and the desired total inductance value, and determine a configuration for the tuning ring  103  so that the self inductance of the tuning ring  103  and the mutual inductance between the tuning ring  103  and the inductor  101  can make up for the calculated difference. In some embodiments, the processor may calculate the mutual inductance value between the tuning ring  103  and the inductor  101  based on the configuration of the inductor  101  and the configuration of the tuning ring  103 . The processor may also calculate the self-inductance value of the tuning ring  103  based on the configuration of the tuning ring  103 . 
     In some embodiments, the act of determining the configuration of the tuning ring  103  may include determining a number of metal stack layers  105  for the tuning ring  103 , and/or selecting certain one(s) of the metal stack layers  105  for connection by the via(s)  107 . In other embodiments, the act of determining the configuration of the tuning ring  103  may include determining a configuration of one or more vias  107  for connecting to one or more metal stack layers  105  of the tuning ring  103 . As discussed, in some embodiments, the mutual inductance value may decrease when a total number of the metal stack layers  105  connected to the one or more vias  107  is reduced, and the mutual inductance value may increase when the total number of the metal stack layers  105  connected to the one or more vias  107  is increased. 
     It should be noted that the cross sectional shape of the tuning ring  103  is not limited to the example illustrated previously, and that the tuning ring  103  may have different cross sectional shapes in other embodiments.  FIG. 3-1  is a top-view schematic diagram of an inductive device  100  comprising a tuning ring  103  surrounding an inductor  101  according to some further embodiment. In  FIG. 3-1 , the tuning ring  103  forms a rectangular loop around the inductor  101 .  FIG. 3-2  is a top-view schematic diagram of an inductive device  100  comprising a tuning ring  103  surrounding an inductor  101  according to other embodiments. In  FIG. 3-2 , the tuning ring  103  forms a circular loop around the inductor  101 . In further embodiments, the cross sectional shape of the tuning ring  103  may have other configurations. For example, in other embodiments, the cross section of the tuning ring  103  may have a triangular shape, an pentagon shape, or any of other multi-sided polygonal shapes. In still further embodiments, the cross sectional shape of the tuning ring  103  may have a customized shape (such as an irregular shape). 
     As discussed above, modifying the configuration of the tuning ring  103  (e.g., number of metal stack layers and/or number of vias) may allow for tuning the inductance of an inductive device  100 . Additionally, modifying the configuration of the tuning ring  103  may also allow for tuning of a Q-value peak associated with the inductive device  100 . Q-value is a dimensionless parameter that describes how underdamped an oscillator is. A higher Q-value peak indicates a lower rate of energy loss relative to the stored energy of the oscillator. In some embodiments, to improve circuit performance, it may be desirable to optimize inductor Q peak frequency to be the same as the circuit operating frequency.  FIGS. 4-1  and  4 - 2  illustrate exemplary tunable ranges of inductive values and Q-value peaks, respectively, for various tuning ring configurations. 
       FIG. 4-1  is a graph illustrating a tunable range of inductive values for a particular tuning ring  103  around an inductor  101  in accordance with some embodiments. The graph represents inductive values for various operating frequencies of an inductive device  100  for two different achievable configurations of the tuning ring  103 . In this example, the inductor  101  has an inductance value of 0.9 nH. The top line in  FIG. 4-1  illustrates inductive values generated by a first tuning ring configuration having a single metal stack layer  105  connected to the via(s)  107 . The bottom line in  FIG. 4-1  illustrates inductive values generated by a second tuning ring configuration having eleven metal stack layers all connected by via(s)  107 . The tunable range of inductive values is 42 pH in the illustrated embodiments. This provides a significant tuning range for small inductors, e.g., inductors below 0.4 nH. In other embodiments, the tunable range may have other values. Also, in some embodiments, for a 0.2 nH inductor, the above configuration offers a 21% tuning range. In other embodiments, the tuning range may have other percentages. 
     In addition to tuning inductance values for a circuit, the tuning ring  103  may also be configured to tune Q-values associated with a particular inductive device  101 .  FIG. 4-2  is a graph illustrating a tunable range of Q-value peaks for a particular tuning ring  103  around an inductor  101 . The graph represents Q-values for various operating frequencies of an inductive device  100  for two different configurations of the tuning ring  103 . Like the examples described with respect to  FIG. 4-1 , the inductor  101  has an inductance value of 0.9 nH. The top line in  FIG. 4-2  illustrates Q-values generated by a first tuning ring configuration having a single metal stack layer  105  connected to the via(s)  107 . The bottom line in  FIG. 4-2  illustrates Q-values generated by a second tuning ring configuration having eleven metal stack layers  105  all connected by the via(s)  107 . In this particular example, the Q-value peak has a range of 5.6 GHz for the tuning ring  103 . This provides a wide tuning widow for the inductor&#39;s operating frequency. 
       FIGS. 4-1  and  4 - 2  merely illustrate some examples of a tunable range of inductive values and Q-value peaks. Other tunable ranges may be attained by varying the inductive value of the inductor  101  and/or the configuration of the tuning ring  103 . In particular, while the above examples illustrate a tunable range of inductive values and a tunable range of Q-value peaks for a particular inductor  101  and particular tuning rings  103 , it is important to note that a variety of tunable ranges may be achieved for numerous different inductors  101  using different configurations of the tuning ring  103 . 
     Although particular embodiments have been shown and described, it will be understood that they are not intended to limit the claimed invention, and it will be made obvious to those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the claimed invention. The specification and drawings are, accordingly, to be regarded in an illustrative rather than restrictive sense. The claimed invention is intended to cover alternatives, modifications, and equivalents.