Patent Publication Number: US-2022221533-A1

Title: Circuit For Reducing An Offset Component Of A Plurality Of Vertical Hall Elements Arranged In One Or More Circles

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     Not Applicable. 
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH 
     Not Applicable. 
     FIELD OF THE INVENTION 
     This invention relates generally to magnetic field sensors, and, more particularly, to a magnetic field sensor having a plurality of vertical Hall elements that are combined in ways that reduce an offset component. 
     BACKGROUND 
     Magnetic field sensing elements can be used in a variety of applications. In one application, a magnetic field sensing element can be used to detect a direction of a magnetic field, i.e., an angle of the direction of the magnetic field. 
     Planar Hall elements and vertical Hall elements are known types of magnetic field sensing elements. A planar Hall element tends to be responsive to magnetic field perpendicular to a surface of a substrate on which the planar Hall element is formed. A vertical Hall element tends to be responsive to magnetic field parallel to a surface of a substrate on which the vertical Hall element is formed. 
     Other types of magnetic field sensing elements are known. For example, a so-called “circular vertical Hall” (CVH) sensing element, which includes a plurality of vertical Hall elements, is known and described in PCT Patent Application No. PCT/EP2008/056517, entitled “Magnetic Field Sensor for Measuring Direction of a Magnetic Field in a Plane,” filed May 28, 2008, and published in the English language as PCT Publication No. WO 2008/145662, which application and publication thereof are incorporated by reference herein in their entirety. The CVH sensing element is a circular arrangement of vertical Hall elements arranged over a common circular implant and diffusion region in a substrate. The common implant and diffusion region can be a common epi (epitaxial) region (e.g., layer) upon a substrate, bounded by semiconductor isolation structures. The CVH sensing element can be used to sense a direction (i.e., an angle) of a magnetic field in a plane of the substrate. 
     Various parameters characterize the performance of magnetic field sensing elements and magnetic field sensors that use magnetic field sensing elements. These parameters include sensitivity, which is a change in an output signal of a magnetic field sensing element in response to a change of magnetic field experienced by the magnetic sensing element, and linearity, which is a degree to which the output signal of the magnetic field sensing element varies in direct proportion to the magnetic field. These parameters also include an offset, which is characterized by an output signal from the magnetic field sensing element not representative of a zero magnetic field when the magnetic field sensing element experiences a zero magnetic field. 
     The above-described CVH sensing element is operable, with associated circuits, to provide an output signal representative of an angle of a direction of a magnetic field. Therefore, as described below, if a magnet is disposed upon or otherwise coupled to a so-called “target object,” for example, a camshaft in an engine, the CVH sensing element can be used to provide an output signal representative of an angle of rotation of the target object. 
     The CVH sensing element is but one element that can provide an output signal representative of an angle of a magnetic field, i.e., an angle sensor. For example, an angle sensor can be provided from a plurality of separate vertical Hall elements or a plurality of magnetoresistance elements arranged in a circle. Collectively, magnetic field sensing element(s) that generate an output signal related to an angle of a magnetic field are referred to herein “angle sensing elements.” 
     More parameters can characterize the performance of angle sensing element(s), e.g., a CVH sensing element. One such parameter is an angular accuracy of the output signal generated by the angle sensing element(s). Angular accuracy can have both an average angle error that is the same at all magnetic field pointing angles, and also an angle error that is different at different magnetic field angles (i.e. a non-linearity error). Another parameter is the speed with which the angle sensing element(s) can convey the angle of the magnetic field. It will be understood that the speed is particularly important for applications in which the angle of the magnetic field may be rapidly changing. 
     It is known that some parameters that can characterize an angle sensing element tend to change with temperature. 
     When an angle sensor uses a plurality of magnetic sensing elements, e.g., as used in a CVH sensing element or in separate magnetic field sensing elements, different offset voltages of the different magnetic field sensing elements can reduce an accuracy of an angle sensed by and angle sensor. 
     It would be desirable to provide circuits and techniques that can process output signals from a CVH sensing element or from separate magnetic field sensing elements and that can provide an improved measurement of angle at a relatively high speed. 
     SUMMARY 
     The present invention provides circuits and techniques that can process output signals from a CVH sensing element or from separate magnetic field sensing elements and that can provide an improved measurement of angle at a relatively high speed. 
     In accordance with an example useful for understanding an aspect of the present invention, a magnetic field sensor can include a semiconductor substrate and a plurality of electrical contacts arranged upon a circle over the semiconductor substrate. The magnetic field sensor can also include a sequence switches circuit electrically coupled to the plurality of electrical contacts and disposed over the semiconductor substrate and a current switches circuit electrically coupled to the plurality of electrical contacts and disposed over the semiconductor substrate. The sequence switches circuit and/or the current switches circuit can be operable to select a first group of electrical contacts and a second group of electrical contacts, the selected first and second groups of electrical contacts each having three and only three proximate electrical contacts, respectively, wherein the three proximate electrical contacts of the first and second groups of electrical contacts each have respective outer electrical contacts and a respective center electrical contact between the outer electrical contacts resulting in first and second center electrical contacts, wherein the first and second center electrical contacts are within a first quadrant of the circle, wherein the sequence switches circuit or the current switches circuit is operable to couple one of the outer electrical contact of the first group of electrical contacts to one and only one of the outer electrical contacts of the second group of electrical contacts, resulting in a first coupled pair of outer electrical contacts. 
     In accordance with another example useful for understanding another aspect of the present invention, a magnetic field sensor can include a semiconductor substrate and a plurality of electrical contacts arranged upon a circle over the semiconductor substrate. The magnetic field sensor can also include a sequence switches circuit electrically coupled to the plurality of electrical contacts and disposed over the semiconductor substrate and a current switches circuit electrically coupled to the plurality of electrical contacts and disposed over the semiconductor substrate. The sequence switches circuit and/or the current switches circuit are operable to select a first, second, third, fourth, fifth, and sixth groups of electrical contacts, the first, second, third, fourth, fifth, and sixth groups of electrical contacts each having three and only three proximate electrical contacts, respectively, wherein the three proximate electrical contacts of the first, second, third, fourth, fifth, and sixth groups of electrical contacts each have respective outer electrical contacts and a respective center electrical contact between the outer electrical contacts resulting in first, second, third, fourth, fifth, and sixth center electrical contacts, wherein one outer electrical contact of each of the first, second, and third groups of electrical contacts are coupled together, and wherein another one outer electrical contact of each of the first and second groups of electrical contacts are coupled together and also to an outer electrical contact of the sixth group of electrical contacts. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The foregoing features of the invention, as well as the invention itself may be more fully understood from the following detailed description of the drawings, in which: 
         FIG. 1  is a pictorial showing a circular vertical Hall (CVH) sensing element having a plurality of vertical Hall elements arranged in a circle over a common implant region upon a substrate, and a two pole magnet disposed close to the CVH sensing element; 
         FIG. 1A  is pictorial showing a plurality of magnetic field sensing elements; 
         FIG. 2  is a graph showing an output signal as may be generated by the CVH sensing element of  FIG. 1  or by the plurality of magnetic field sensing elements of  FIG. 1A ; 
         FIG. 3  is a block diagram of an exemplary magnetic field sensor having a CVH sensing element; 
         FIG. 4  is a graph showing ideal and non-ideal angle sensing operation of the magnetic field sensor of  FIG. 3 ; 
         FIG. 5  is a block diagram showing an exemplary prior art coupling of two vertical Hall elements arranged in a circle; 
         FIG. 6  is a block diagram showing two groups of three electrical contacts of a CVH sensing element as in  FIG. 1  or otherwise a plurality of separate elements as in  FIG. 1A ; 
         FIG. 7  is a block diagram showing equivalent resistances of the two groups three of electrical contacts of  FIG. 6 , either as separately isolated elements or within a common implant region of a CVH sensing element; 
         FIG. 8  is a schematic diagram showing an equivalent circuit modelling the two groups of three of electrical contacts of  FIG. 6 , either as separately isolated elements or within a common implant region of a CVH sensing element; 
         FIG. 9  is a block diagram showing four groups of three electrical (or two groups of six) contacts of a CVH sensing element as in  FIG. 1  or otherwise a plurality of separate elements as in  FIG. 1A ; 
         FIG. 10  is a schematic diagram showing an equivalent circuit modelling the four groups of three (or two groups of six) electrical contacts of  FIGS. 6 and 7 ; 
         FIGS. 11-11C  show four coupling arrangements (phases) of a CVH sensing element as in  FIG. 1  (or otherwise separate elements as in  FIG. 1A ) having four groups of three (or two groups of six) electrical contacts similar to the arrangement of  FIG. 9 ; 
         FIGS. 12-12C  show another four coupling arrangements (phases) of a CVH sensing element as in  FIG. 1  (or otherwise separate elements as in  FIG. 1A ) having four groups of three (or two groups of six) electrical contacts similar to the arrangement of  FIG. 9 ; 
         FIGS. 13-13C  show another four coupling arrangements (phases) of a CVH sensing element as in  FIG. 1  (or otherwise separate elements as in  FIG. 1A ) having four groups of three (or two groups of six) electrical contacts similar to the arrangement of  FIG. 9 ; 
         FIGS. 14-14C  show four coupling arrangements (phases) of a CVH sensing element as in  FIG. 1  (or otherwise separate elements as in  FIG. 1A ) having two groups of three (or one group of six) electrical contacts similar to the arrangement of  FIG. 6 ; 
         FIGS. 15-15C  show another four coupling arrangements (phases) of a CVH sensing element as in  FIG. 1  (or otherwise separate elements as in  FIG. 1A ) having two groups of three (or one group of six) electrical contacts similar to the arrangement of  FIG. 6 ; 
         FIGS. 16-16C  show four coupling arrangements (phases) of a CVH sensing element as in  FIG. 1  (or otherwise separate elements as in  FIG. 1A ) having six groups of three (or three groups of six, or two groups of six and two groups of three) electrical contacts similar to the arrangement of  FIG. 9 ; 
         FIG. 17  shows a coupling arrangement (phase) of a CVH sensing element as in  FIG. 1  (or otherwise separate elements as in  FIG. 1A ) having four groups of three (or two groups of six) electrical contacts similar to the arrangement of  FIG. 6 ; 
         FIG. 18  shows a coupling arrangement (phase) of a CVH sensing element as in  FIG. 1  (or otherwise separate elements as in  FIG. 1A ) having eight groups of three (or four groups of six) electrical contacts similar to the arrangement of  FIG. 9 ; 
         FIG. 19  shows a coupling arrangement (phase) of a CVH sensing element as in  FIG. 1  (or otherwise separate elements as in  FIG. 1A ) having eight groups of three (or four groups of six) electrical contacts similar to the arrangement of  FIG. 9 ; 
         FIG. 20  shows a coupling arrangement (phase) of a CVH sensing element as in  FIG. 1  (or otherwise separate elements as in  FIG. 1A ) having eight groups of three (or four groups of six) electrical contacts similar to the arrangement of  FIG. 9 ; 
         FIG. 21  shows a coupling arrangement (phase) of a CVH sensing element as in  FIG. 1  (or otherwise separate elements as in  FIG. 1A ) having four groups of three (or two groups of six) electrical contacts similar to the arrangement of  FIG. 6 ; 
         FIG. 22  shows a coupling arrangement (phase) of a CVH sensing element as in  FIG. 1  (or otherwise separate elements as in  FIG. 1A ) having eight groups of three (or four groups of six) electrical contacts similar to the arrangement of  FIG. 6 ; 
         FIG. 23  shows a coupling arrangement (phase) of a CVH sensing element as in  FIG. 1  (or otherwise separate elements as in  FIG. 1A ) having eight groups of three (or four groups of six) electrical contacts similar to the arrangement of  FIG. 6 ; 
         FIG. 24  shows a coupling arrangement (phase) of two CVH sensing elements as in  FIG. 1  (or otherwise separate elements as in  FIG. 1A ), each having eight groups of three (or four groups of six) electrical contacts similar to the arrangement of  FIG. 9 ; 
         FIG. 25  shows a coupling arrangement (phase) of two CVH sensing elements as in  FIG. 1  (or otherwise separate elements as in  FIG. 1A ), each having four groups of three (or two groups of six) electrical contacts similar to the arrangements of arrangement of  FIG. 9 ; and 
         FIG. 26  shows a coupling arrangement (phase) of two CVH sensing elements as in  FIG. 1  (or otherwise separate elements as in  FIG. 1A ), each having five groups of electrical contacts similar to the arrangement of  FIG. 9 . 
     
    
    
     DETAILED DESCRIPTION 
     Before describing the present invention, some introductory concepts and terminology are explained. 
     As used herein, the term “magnetic field sensing element” is used to describe a variety of electronic elements that can sense a magnetic field. The magnetic field sensing element can be, but is not limited to, a Hall effect element, a magnetoresistance element, or a magnetotransistor. As is known, there are different types of Hall effect elements, for example, a planar Hall element, a vertical Hall element, and a Circular Vertical Hall (CVH) element. As is also known, there are different types of magnetoresistance elements, for example, a semiconductor magnetoresistance element such as Indium Antimonide (InSb), a giant magnetoresistance (GMR) element, for example, a spin valve, an anisotropic magnetoresistance element (AMR), a tunneling magnetoresistance (TMR) element, and a magnetic tunnel junction (MTJ). The magnetic field sensing element may be a single element or, alternatively, may include two or more magnetic field sensing elements arranged in various configurations, e.g., a half bridge or full (Wheatstone) bridge. Depending on the device type and other application requirements, the magnetic field sensing element may be a device made of a type IV semiconductor material such as Silicon (Si) or Germanium (Ge), or a type III-V semiconductor material like Gallium-Arsenide (GaAs) or an Indium compound, e.g., Indium-Antimonide (InSb). 
     As is known, some of the above-described magnetic field sensing elements tend to have an axis of maximum sensitivity parallel to a substrate that supports the magnetic field sensing element, and others of the above-described magnetic field sensing elements tend to have an axis of maximum sensitivity perpendicular to a substrate that supports the magnetic field sensing element. In particular, planar Hall elements tend to have axes of sensitivity perpendicular to a substrate, while metal based or metallic magnetoresistance elements (e.g., GMR, TMR, AMR) and vertical Hall elements tend to have axes of sensitivity parallel to a substrate. 
     As used herein, the term “magnetic field sensor” is used to describe an assembly that uses one or more magnetic field sensing elements in combination with an electronic circuit, all disposed upon a common substrate, e.g., a semiconductor substrate. Magnetic field sensors are used in a variety of applications, including, but not limited to, an angle sensor that senses an angle of a direction of a magnetic field, a current sensor that senses a magnetic field generated by a current carried by a current-carrying conductor, a magnetic switch that senses the proximity of a ferromagnetic object, a rotation detector that senses passing ferromagnetic articles, for example, magnetic domains of a ring magnet or a ferromagnetic target (e.g., gear teeth) where the magnetic field sensor is used in combination with a back-biased or other magnet, and a magnetic field sensor that senses a magnetic field density of a magnetic field. 
     As used herein, the term “magnetic field signal” is used to describe any circuit signal that results from a magnetic field experienced by a magnetic field sensing element. 
     The terms “parallel” and“perpendicular” are used in various contexts herein. It should be understood that the terms parallel and perpendicular do not require exact perpendicularity or exact parallelism, but instead it is intended that normal manufacturing tolerances apply, which tolerances depend upon the context in which the terms are used. In some instances, the term “substantially” is used to modify the terms “parallel” or “perpendicular.” In general, use of the term “substantially” reflects angles that are beyond manufacturing tolerances, for example, within +/−ten degrees. 
     As used herein, the term “processor” is used to describe an electronic circuit that performs a function, an operation, or a sequence of operations. The function, operation, or sequence of operations can be hard coded into the electronic circuit or soft coded by way of instructions held in a memory device. A “processor” can perform the function, operation, or sequence of operations using digital values or using analog signals. 
     In some embodiments, the “processor” can be embodied in an application specific integrated circuit (ASIC), which can be an analog ASIC or a digital ASIC. In some embodiments, the “processor” can be embodied in a microprocessor with associated program memory. In some embodiments, the “processor” can be embodied in a discrete electronic circuit, which can be analog or digital. 
     As used herein, the term “module” can be used to describe a “processor.” However, the term “module” is used more generally to describe any circuit that can transform an input signal into an output signal that is different than the input signal. 
     A processor can contain internal processors or internal modules that perform portions of the function, operation, or sequence of operations of the processor. Similarly, a module can contain internal processors or internal modules that perform portions of the function, operation, or sequence of operations of the module. 
     While electronic circuits shown in figures herein may be shown in the form of analog blocks or digital blocks (e.g. processors or modules), it will be understood that the analog blocks can be replaced by digital blocks (e.g. processors or modules) that perform the same or similar functions and the digital blocks can be replaced by analog blocks that perform the same or similar functions. Analog-to-digital or digital-to-analog conversions may not be explicitly shown in the figures, but should be understood. 
     In particular, it should be understood that a so-called comparator can be comprised of an analog comparator having a two state output signal indicative of an input signal being above or below a threshold level (or indicative of one input signal being above or below another input signal). However, the comparator can also be comprised of a digital circuit having an output signal with at least two states indicative of an input signal being above or below a threshold level (or indicative of one input signal being above or below another input signal), respectively, or a digital value above or below a digital threshold value (or another digital value), respectively. 
     As used herein, the term “predetermined,” when referring to a value or signal, is used to refer to a value or signal that is set, or fixed, in the factory at the time of manufacture, or by external means, e.g., programming, thereafter. As used herein, the term “determined,” when referring to a value or signal, is used to refer to a value or signal that is identified by a circuit during operation, after manufacture. 
     As used herein, the term “amplifier” is used to describe a circuit element with a gain greater than one, less than one, or equal to one. 
     Referring to  FIG. 1 , a circular vertical Hall (CVH) element  12  includes a circular implant and diffusion region  18  in a substrate (not shown). The CVH sensing element  12  has a plurality of vertical Hall elements, of which a vertical Hall element  12   a  is but one example. In some embodiments, the common implant and diffusion region  18  can be characterized as a common epitaxial region upon a substrate, bounded by semiconductor isolation structures. 
     Each vertical Hall element has a plurality of Hall element contacts (e.g., four or five contacts), e.g.,  12   aa . Each vertical Hall element contact can be comprised of a metal contact over a contact diffusion region (a pickup) diffused into the common implant and diffusion region  18 . 
     A particular vertical Hall element (e.g.,  12   a ) within the CVH sensing element  12 , which, for example, can have five adjacent contacts, can share some, for example, four, of the five contacts with a next vertical Hall element (e.g.,  12   b ). Thus, a next vertical Hall element can be shifted by one contact from a prior vertical Hall element. For such shifts by one contact, it will be understood that the number of vertical Hall elements is equal to the number of vertical Hall element contacts, e.g.,  32  or  64 . However, it will also be understood that a next vertical Hall element can be shifted by more than one contact from the prior vertical Hall element, in which case, there are fewer vertical Hall elements than there are vertical Hall element contacts in the CVH sensing element. 
     As shown, a center of a vertical Hall element  0  can be positioned along an x-axis  20  and a center of vertical Hall element  8  can be positioned along a y-axis  22 . In the exemplary CVH sensing element  12 , there are thirty-two vertical Hall elements and thirty-two vertical Hall element contacts. However, a CVH can have more than or fewer than thirty-two vertical Hall elements and more than or fewer than thirty-two vertical Hall element contacts. 
     In some applications, a circular magnet  14  having a north side  14   b  and a south side  14   a  can be disposed over the CVH  12 . The circular magnet  14  tends to generate a magnetic field  16  having a direction from the north side  14   b  to the south side  14   a , here shown to be pointed to a direction of about forty-five degrees relative to x-axis  20 . 
     In some applications, the circular magnet  14  is mechanically coupled to a rotating target object, for example, an automobile steering shaft of an automobile camshaft, and is subject to rotation relative to the CVH sensing element  12 . With this arrangement, the CVH sensing element  12 , in combination with an electronic circuit described below, can generate a signal related to the angle of rotation of the magnet  14 , i.e., an angle of rotation of the target object to which the magnet is coupled. 
     Referring now to  FIG. 1A , a plurality of magnetic field sensing elements  30   a - 30   h , in a general case, can be any type of magnetic field sensing elements. The magnetic field sensing elements  30   a - 30   h  can be, for example, separate vertical Hall elements or separate magnetoresistance elements, each having an axis of maximum response parallel to a surface of a substrate  34 . These magnetic field sensing elements can be coupled to an electronic circuit the same as or similar to an electronic circuit described below in conjunction with  FIG. 3 . There can also be a magnet the same as or similar to the magnet  14  of  FIG. 1  disposed proximate to the magnetic field sensing elements  30   a - 30   h.    
     Referring now to  FIG. 2 , a graph  200  has a horizontal axis with a scale in units of CVH vertical Hall element position, n, around a CVH sensing element, for example, the CVH sensing element  12  of  FIG. 1 . The graph  200  also has a vertical axis with a scale in amplitude in units of millivolts. The vertical axis is representative of output signal levels from the plurality of vertical Hall elements of the CVH sensing element taken sequentially, one at a time, about the ring of contacts of the CVH sensing element. 
     The graph  200  includes a signal  202  representative of output signal levels from the plurality of vertical Hall elements of the CVH taken with the magnetic field of  FIG. 1  pointing in a direction of forty-five degrees. 
     Referring briefly to  FIG. 1 , as described above, vertical Hall element  0  is centered along the x-axis  20  and vertical Hall element  8  is centered along the y-axis  22 . In the exemplary CVH sensing element  12 , there are thirty-two vertical Hall element contacts and a corresponding thirty-two vertical Hall elements, each vertical Hall element having a plurality of vertical Hall element contacts, for example, five contacts. In other embodiments, there are sixty-four vertical Hall element contacts and a corresponding sixty-four vertical Hall elements. 
     In  FIG. 2 , for the magnetic field  16  pointing at positive forty-five degrees, a maximum positive signal is achieved from a vertical Hall element centered at position  4 , which is aligned with the magnetic field  16  of  FIG. 1 , such that a line drawn between the vertical Hall element contacts (e.g., five contacts) of the vertical Hall element at position  4  is perpendicular to the magnetic field. A maximum negative signal is achieved from a vertical Hall element centered at position  20 , which is also aligned with the magnetic field  16  of  FIG. 1 , such that a line drawn between the vertical Hall element contacts (e.g., five contacts) of the vertical Hall element at position  20  is also perpendicular to the magnetic field. 
     A sine wave  204  is provided to more clearly show ideal behavior of the signal  202 . The signal  202  has variations due to vertical Hall element offsets, which tend to cause corresponding variations of output signals causing them to be too high or too low relative to the sine wave  204 , in accordance with offset errors for each element. The offset signal errors are undesirable. 
     Full operation of the CVH sensing element  12  of  FIG. 1  and generation of the signal  202  of  FIG. 2  are described in more detail in the above-described PCT Patent Application No. PCT/EP2008/056517, entitled “Magnetic Field Sensor for Measuring Direction of a Magnetic Field in a Plane,” filed May 28, 2008, which is published in the English language as PCT Publication No. WO 2008/145662. 
     Groups of contacts of each vertical Hall element can be used in a chopped arrangement (also referred to herein as current spinning) to generate chopped output signals from each vertical Hall element. Thereafter, a new group of adjacent vertical Hall element contacts can be selected (i.e., a new vertical Hall element), which can be offset by one element from the prior group. The new group can be used in the chopped arrangement to generate another chopped output signal from the next group, and so on. 
     Each step of the signal  202  is representative of an unchopped output signal, i.e., from one respective group of vertical Hall element contacts, i.e., from one respective vertical Hall element. Thus, for a CVH sensing element having 32 vertical Hall elements taken sequentially, there are thirty-two steps in the signal  202  when current spinning is not used. However, for embodiments in which current spinning is used, each step of the signal  202  can be comprised of several sub-steps (not shown, e.g., four sub-steps), each sub-step indicative of a current spinning “phase.” 
     It will be understood that a phase of the signal  202  is related to an angle of the magnetic field  16  of  FIG. 1  relative to position zero of the CVH sensing element  12 . It will also be understood that a peak amplitude of the signal  202  is generally representative of a strength of the magnetic field  16 . Using electronic circuit techniques described above in PCT Patent Application No. PCT/EP2008/056517, or using other techniques described below, a phase of the signal  202  (e.g., a phase of the signal  204 ) can be found and can be used to identify the pointing direction of the magnetic field  16  of  FIG. 1  relative to the CVH sensing element  12 . 
     Referring now to  FIG. 3 , a magnetic field sensor  300  includes a CVH sensing element  302  having a plurality of vertical Hall elements, each vertical Hall element comprising a group of vertical Hall element contacts (e.g., five vertical Hall element contacts). In some embodiments, the CVH sensing element  302  can be the same as or similar to the CVH sensing element  12  described above in conjunction with  FIG. 1 , and can be disposed proximate to a two pole magnet  320  coupled to a target object  322 , which magnet  320  can be the same as or similar to the magnet  14  of  FIG. 1 . However, in some embodiments, the CVH sensing element  302  can be replaced by a group of magnetic field sensing elements the same as or similar to those described above in conjunction with  FIG. 1A . 
     The magnetic field sensor  300  can include a current switches circuit  306  to provide current signals  306   a - 306   d  to the CVH sensing element  302 . While four current signals  306   a - 306   d  are shown, in other embodiments, there can be more than or fewer than four current signals. Essentially, the current switches circuit  306  has access to and can provide current in any combination to any or all of the vertical Hall elements within the CVH sensing element  302 . 
     The magnetic field sensor  300  can also include sequence switches circuit  304 . The sequence switches circuit  304  is coupled to receive signals  302   a  from the CVH sensing element  302 . In some embodiments, the signals  302   a  are representative of signal coupling paths to all vertical Hall elements within the CVH sensing and  302 . 
     From discussion above in conjunction with  FIG. 1 , it will be appreciated that, in operation, the sequence switches circuit  304  and the current switches circuit  306  can be configured to switch sequentially around the CVH sensing element  302  providing the current signals  306   a - 306   d  to different sequential combinations of vertical Hall elements within the CVH sensing element  302 , and receiving different sequential combinations of the signals  302   a  from the CVH sensing element  302 . In some embodiments, the sequencing can include current spinning for each selected one or more of the vertical Hall elements within the CVH sensing element  302 . 
     From the sequence switches circuit  304  is provided one or more differential output signals, here shown as two differential signals  304   a ,  304   b . It should be understood to both the differential signals  304   a ,  304   b  can be sampled analog signals similar to the signal  202  of  FIG. 2 . 
     A phase adjustment module  305  can be coupled to either signal path, but is here shown to receive the differential signal  304   b  and to provide a phase adjusted differential signal  305   a . A differential amplifier  308  can be coupled to receive the differential signal  304   a  and the phase adjusted differential signal  305   a  and configured to generate an amplified signal  308   a.    
     A bandpass filter  310  coupled to receive the amplified signal  308   a  and configured to generate a filtered signal  300   a . It should be understood that the filtered signal  310   a  can be a sinusoid similar to the signal  204  of  FIG. 2 . 
     An analog-to-digital converter (ADC)  312  can be coupled to receive the filtered signal  310   a  and configured to generate a digital converted signal  312   a . An angle calculation module  314  is coupled to receive the converted digital signal  312   a  and configured to generate an x-y angle signal  314   a . As the magnet  320  rotates, values of the x-y angle signal  314   a  change according to an angle of the magnetic field generated by the magnet  320  in the plane of the CVH sensing element  302 . 
     The angle calculation module  314  is also coupled to receive clock signals  316   c ,  316   d  from an oscillator and logic module  316 . The clock signals  316   c ,  316   d  are used as references by the angle calculation module  314  in order to identify a phase of the converted digital signal  312   a , i.e., a phase of the filtered signal  310   a . For example, one of the clock signals  316   c ,  316   d  can be a clock signal having a frequency the same as the frequency of the filtered signal  310   a , i.e., a frequency of the signal  204  of  FIG. 2 . In operation, phases of the clock signal and of the converted signal  312   a  can be compared to generate the x-y angle signal  314   a , which is indicative of an angle of a magnetic field generated by the magnet  320 . 
     The oscillator and logic module  360  can also provide clock control signals  316   a ,  316   b  to the sequence switches circuit  304  and to the current switches circuit  306 , respectively. The clocks  316   a ,  316   b  result in the sequence switches circuit  304  and the current switches circuit  306  stepping around the CVH sensing element  302 , sequentially selected different ones of the vertical Hall elements within the CVH sensing element  302 , with or without chopping or current spinning. 
     Though not shown in  FIG. 3  certain ones of the vertical Hall elements within the CVH sensing element  302  can be combined by the sequence switches circuit  304  in ways described more fully below in conjunction with  FIGS. 11-26 . In some arrangements, the phase adjustment module  305  can be omitted. 
     While the magnetic field sensor  300  has a CVH sensing element  302 , it should be recognized that the same circuitry can be applied to any combination of separate vertical Hall elements (e.g., separately isolated N-well regions) arranged in a circle. See, e.g.,  FIG. 1A . 
     Referring now to  FIG. 4 , a graph  400  has a horizontal axis with a scale in units of angular degrees and a vertical axis with a scale in units of value of an x-y angle value magnitude, for example, a magnitude of the x-y angle value  314   a  of  FIG. 3 . 
     A line  402  is representative of an x-y angle value that has no angle error. When the x-y angle value has no angle error, the x-y angle value is perfectly straight-line linear with respect to actual angle, i.e., the x-y angle value is a perfect and true representation of the angle of the magnetic field generated by the magnet  320  of  FIG. 3 , and the line  402  passes through zero. 
     A line  404  is representative of an x-y angle value that has only an average or DC angle error, such that all angles represented by the x-y angle value are offset by a fixed number of degrees. The line  404  does not pass through zero. 
     A curve  406  is representative of an x-y angle value that has errors in representation of the true angle of the magnetic field generated by the magnet  320 , average or DC errors and also an error that has a sinusoidal appearance. 
     A curve  408  is representative of an x-y angle value that has other errors in representation of the true angle of the magnetic field generated by the magnet  320 . 
     A variety of circuit characteristics of the magnetic field sensor  300  contribute to the errors, i.e., to both the DC (or average) angle error represented by the curves  406 ,  408 , and to the sinusoidal shapes of the curves  406 ,  408 . One factor that contributes to the errors is switching noise generated by the sequence switches circuit  304  and/or by the current switches circuit  306  of  FIG. 3 . Another factor is different offset voltages among the vertical Hall elements within the CVH sensing element  302 , for example, different offset voltages described above in conjunction with the signal  202  of  FIG. 2 . Another factor is different sensitivities of the various vertical Hall elements. 
     First, regarding the sequence switches circuit  304 , it will be understood that charge injection or switching spikes (together referred to as noise) generated by the sequence switches circuit  304  are not necessarily exactly the same as each sequential vertical Hall element is selected in the CVH sensing element  302 . When the noise generated by the sequence switches circuit  304  is not the same as each vertical Hall element is selected, a DC (or average) angle error is generated and also a sinusoidal type error such as that represented by the curves  406 ,  408 . The sinusoidal error characteristic can be, in part, a result of the noise generated by the sequence switches being repetitive for each cycle around the CVH sensing element  302 , and thus, the noise will have an angle error frequency component at a frequency of the signal  202  of  FIG. 2 , and will add to the signal  402  ( 304   a  of  FIG. 3 ). The angle error frequency component is essentially fixed in phase relative the signals  304   a ,  304   b  and therefore, the addition of the angle error causes different phase shift errors in the summed signal depending on the phase of the signals  304   a ,  304   b . Higher harmonics can also result from the noise. 
     Next, regarding the current switches circuit  306 , it will be understood that charge injection or switching spikes (together referred to as noise) generated by the current switches circuit  306  are not necessarily exactly the same as each sequential vertical Hall element is selected in the CVH sensing element  302 . When the noise generated by the current switches circuit  306  is not the same as each vertical Hall element is selected, a DC (or average) angle error is generated and also a sinusoidal type error such as that represented by the curves  406 ,  408 . The sinusoidal error characteristic can, in part, result from the noise generated by the current switches circuit  306  being repetitive for each cycle around the CVH sensing element. 
     Other circuit characteristics can also contribute to the angle errors, i.e., to both the DC (or average) angle error represented by the error curves  406 ,  408 , and to the sinusoidal shapes of the error curves  406 ,  408 . Namely, a speed with which the dual differential amplifier  308  of  FIG. 3 , and also other circuit elements of  FIG. 3 , are unable to settle to final values as the sequence switches circuit  304  switches among the vertical Hall elements of the CVH sensing element  302 , and also as the current switches circuit  306  switch among the various current spinning phases, contribute to the errors. 
     The above-described circuit characteristics, including, but not limited to, different offset voltages of the various vertical Hall elements within the CVH sensing element  302  of  FIG. 3  (including or not including offset mismatches at different current spinning phases), differences of sensitivities of the various vertical Hall elements, and switching noise and lack of circuit elements settling to final values, tend to be influenced by (i.e., changed by) a variety factors including, but not limited to, temperature of the magnetic field sensor  300  of  FIG. 3 , a rate of sequencing around the CVH sensing element  302 , peak magnitude of the magnetic field experience by the CVH sensing element  302  as the magnet  320  rotates, and selected current spinning sequence(s) among the various vertical Hall elements. 
     Differences between the curves  406 ,  408  can be attributed to changes in the same factors, namely, changes in the temperature, changes in or differences in peak amplitude of the magnetic field experience by the CVH sensing element  302  as the magnet  320  rotates, changes in offset voltages of the vertical Hall elements within the CVH sensing element  302 , changes of sensitivities of the various vertical Hall elements, changes in or differences in rates of sequencing around the CVH sensing element  302 , and changes in or differences in selected current spinning sequence(s) among the various vertical Hall elements within the CVH sensing element  302 . Among these factors, it will be understood that the changes in the temperature can occur at any time. The changes in the peak amplitude of the magnetic field can be influenced by positional changes, i.e., air gap changes, between the magnet  320  and the CVH sensing element  302  of  FIG. 3 . The changes in the peak amplitude of the magnetic field can also be influenced by mechanical considerations, for example, wear of a bearing or a shaft upon which the magnet  320  rotates. However, the changes in sequencing rates and the changes in current spinning sequences can be fixed, and changed only for different applications of the magnetic field sensor  300 . The changes in offset voltages and changes in sensitivity of the vertical Hall elements tend to be influenced by changes in temperature. 
     In general, it has been determined that the dominant angle error frequency components occur at first and second harmonics of the frequency of the signal  202  (i.e.,  304   a ,  304   b ). The curves  406 ,  408  are representative of angle error functions dominated by first and second harmonics of the frequency of the signal  202  ( 304   a ,  304   b ). 
     The error curves  406 ,  408  can be mathematically described in the following way. 
     Mathematically, the angle error represented by the curves  406 ,  408  can be represented as: 
     
       
         
           
             
               
                 
                   
                     α 
                     err 
                   
                   = 
                   
                     OFF 
                     + 
                     
                       D 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         C 
                         ⁡ 
                         
                           ( 
                           T 
                           ) 
                         
                       
                     
                     + 
                     
                       
                         ∑ 
                         
                           n 
                           = 
                           1 
                         
                         ∞ 
                       
                       ⁢ 
                       
                         
                           
                             H 
                             
                               n 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               A 
                             
                           
                           ⁡ 
                           
                             ( 
                             T 
                             ) 
                           
                         
                         · 
                         
                           sin 
                           ⁡ 
                           
                             ( 
                             
                               
                                 n 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 α 
                               
                               + 
                               
                                 
                                   H 
                                   nP 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   T 
                                   ) 
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     where:
         α=measured angle with error;   n=a variable indicative of an nth harmonic;   T=temperature of magnetic field sensor  300 ;   OFF=a magnetic target positioning error, i.e., a mechanical misalignment of the CVH sensing element  302  in relation to the magnet  320  of  FIG. 3 , which is usually independent of the temperature, T;   DC (T)=an average of DC angle error, which is a function of the temperature, T;   H nA (T)=an amplitude of an nth-harmonic component of the error, which is a function of the temperature, T; and   H nP (T)=a phase of the nth-harmonic component, which is a function of the temperature, T.       

     Other factors described above, other than temperature, which affect the angle error, are not taken into account in equation 1. Namely, the rate of sequencing around the CVH sensing element  302  is not taken into account, the peak amplitude of the magnetic field experienced by the CVH sensing element  302  and generated by the magnet  320  is not taken into account, and the current spinning phase sequence generated by the current spinning sequence selection module  119  is not taken into account in the above expression. 
     An estimated and quantized angle error (rather than non-quantized error of equation (1)) can be mathematically expressed as: 
     
       
         
           
             
               
                 
                   
                     α 
                     err 
                     ′ 
                   
                   = 
                   
                     OFF 
                     + 
                     
                       D 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           C 
                           q 
                         
                         ⁡ 
                         
                           ( 
                           T 
                           ) 
                         
                       
                     
                     + 
                     
                       
                         ∑ 
                         
                           n 
                           = 
                           1 
                         
                         ∞ 
                       
                       ⁢ 
                       
                         
                           
                             H 
                             
                               n 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               A_q 
                             
                           
                           ⁡ 
                           
                             ( 
                             T 
                             ) 
                           
                         
                         · 
                         
                           sin 
                           ⁡ 
                           
                             ( 
                             
                               
                                 n 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 α 
                               
                               + 
                               
                                 
                                   H 
                                   nP_q 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   T 
                                   ) 
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     where:
         q stands for quantized values.       

     Yet another way to consider the undesirable offset voltage is given in an equation below: 
     
       
         
           
             
               
                 
                   
                     V 
                     1 
                   
                   = 
                   
                     
                       
                         
                           2 
                         
                         ⁢ 
                         π 
                       
                       
                         N 
                         
                           3 
                           / 
                           2 
                         
                       
                     
                     ⁢ 
                     
                       σ 
                       V 
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     where:
         σ v =standard deviation (i.e., variation) of offset voltages for sequentially selected vertical Hall elements, whether taken alone or in combinations by techniques described below;   N=number of vertical Hall elements, whether taken alone or in combinations, sampled in a sequence around a plurality of vertical Hall elements; and   V 1 =magnitude of first harmonic of offset error vector in the signals  308   a  or  310   a  of  FIG. 3 .       

     From equation (3) it should be apparent that making a variation of offset voltages smaller among a plurality of vertical Hall elements sampled in sequence by techniques described below, tends to make a magnitude of a resulting first harmonic offset error vector smaller. The first harmonic of the offset error vector still adds to the desired magnetic field direction measurement, but results in less error in the magnetic field direction measurement. 
     Referring now to  FIG. 5 , a prior art coupling arrangement  500  of two vertical Hall elements  502 ,  504  is shown, for which each of the vertical Hall elements  502 ,  504  has five electrical contacts. This prior art arrangement is described in U.S. Pat. No. 9,547,048, issued Jan. 17, 2017, which is assigned to the assignee of the present invention, and which is incorporated herein in its entirety. 
     As described in conjunction with the above issued patent, and which will be generally understood, a vertical Hall element with five electrical contacts can be coupled in at least four different ways to a power supply and to an amplifier that follows the vertical Hall element. These different coupling arrangements can be referred to as phases, i.e., phases zero, ninety, one hundred eighty, and two hundred seventy. 
     A first vertical Hall element  502  is arranged in a zero degree phase arrangement, and a second vertical Hall element  504  is arranged in a ninety degree phase arrangement. Output electrical contacts of the first and second vertical Hall elements are coupled together constructively. 
     The terms “constructively” and “destructively” are used herein to refer to addition or subtraction, respectively of magnetic field signals. 
     In some embodiments, the two vertical Hall elements  502 ,  504 , are vertical Hall elements within a CVH sensing element, for example, within the CVH sensing element  12  of  FIG. 1  or the CVH sensing element  302  of  FIG. 3 . In other embodiments, the two vertical Hall element  502 ,  504  are separately isolated vertical Hall elements, as may be represented by the arrangement of  FIG. 1A . 
     Signs (+, −) used herein are representative of polarities of magnetic field components of output signals, here from the two vertical Hall elements  502 ,  504  in response to a magnetic field pointed in a direction of an arrow  506 . It will be understood that the output signal from an individual vertical Hall element can be a differential signal, wherein one output contact is plus and the other output contact is minus according to the above convention. For a magnetic field in a direction opposite from the arrow  506 , the signs of each vertical Hall element reverse. 
     In response to an exemplary static, i.e., not moving, magnetic field, e.g.,  506 , output signals from the two vertical Hall elements  502 ,  504  are DC signals. In response to a moving or rotating magnetic field, output signals from the two vertical Hall elements  502 ,  504  are changing signals that having a changing AC component. In either case, output signals from the two vertical Hall element  502 ,  504  each include two components, a desirable external magnetic field component (e.g., Vext, either DC or AC) responsive to the external magnetic field (static or rotating) and an offset component (e.g., Voff), which is always a DC component. The offset voltage DC component changes sign depending upon the connection phase of the vertical Hall element. 
     In response to the exemplary static magnetic field  506 , a differential output signal (across + and − contacts) from the first vertical Hall element  502  is a combination of a first external magnetic field component and a first offset component, Vext 1 +Voff 1 . A differential output signal (across + and − contacts) from the second vertical Hall element  504  is a combination of a second external magnetic field component and a second offset component, Vext 2 −Voff 2 . Combining the two output signals from the two vertical Hall elements  502 ,  504  by coupling them together constructively as shown results in a combined differential signal: 
         Vm+,Vm −=[( V ext1 +V off1)+( V ext2 −V off2)]/2
 
       =( V ext1 +V ext2)/2+( V off1 −V off2)/2. 
     Assuming that Voff 1  approximately equals Voff 2 , and assuming that Vext 1  approximately equals Vext 2 , the resulting external magnetic field component of the combined differential signal Vm+, Vm− is approximately Vext, and the offset voltage in the combined signal is approximately canceled to zero. However, because Voff 1  does not exactly equal Voff 2 , a residual small offset, Voffresa, remains. 
     Factors of two in the above equations are the result of each one of the two vertical Hall elements behaving like a respective voltage source in series with a resistance. When coupled together, two vertical Hall elements tend to provide an output signal that is an average of the two output signals. 
     Thus, the two vertical Hall element  502 ,  504  can be coupled as shown, with the connection phases zero and ninety as shown, such that the external magnetic field components add constructively, and such that the offset components approximately cancel. 
     From  FIGS. 2 and 5 , it will be appreciated that a lower DC offset voltage for each sequentially selected vertical Hall element ultimately results in a more accurate x-y angle signal generated by a magnetic field sensor, e.g., a more accurate x-y angle signal  314   a  generated by the magnetic field sensor  300  of  FIG. 3 . 
     The couplings shown among the two vertical Hall elements can be accomplished, for example, by way of the sequence switches circuit  304  of  FIG. 3  and the current switched circuit  305  of  FIG. 3 . 
     In some embodiments, the two vertical Hall elements  502 ,  504  are current spun as described below. Then, the sequence can repeat for another two groups of five vertical Hall elements, e.g., groups that are shifted by one electrical contact from those shown. 
     In other embodiments, there is no current spinning and any one of the above four coupling phase combinations can remain static as different groups of five electrical contacts are selected. 
     While the vertical Hall element  502 ,  504  are shown to be statically coupled in a particular arrangement, for embodiments in which current spinning is employed, the two vertical Hall elements  502 ,  504  need only remain ninety degrees apart in the coupling phases as the current spinning progresses. The degree names given to the coupling arrangements are somewhat arbitrary for a vertical Hall element, and are derived from coupling arrangements of a planar Hall element. Thus, the coupling shown in  FIG. 5  can be representative of a first current spinning arrangement in four phase current spinning. For a second current spinning arrangement, the vertical Hall element  502  can be arranged in a ninety degree coupling arrangement, and the vertical Hall element  504  can be arranged in a one hundred eighty degree coupling arrangement. For a third current spinning arrangement, the vertical Hall element  502  can be arranged in a one hundred eighty degree coupling arrangement, and the vertical Hall element  504  can be arranged in a two hundred seventy degree coupling arrangement. For a fourth current spinning arrangement of vertical Hall element  502  can be arranged in a two hundred seventy degree coupling arrangement, and the vertical Hall element  504  can be arranged in a zero degree coupling arrangement. For all of the current spinning arrangements, signal output contacts of the vertical Hall elements  502 ,  504  are coupled together such that a magnetic field components of signals on the signal output contacts add constructively, and offset components of the signals on the signal output contacts cancel each other. 
     The above current spinning can be achieved, for example, by way of the sequence switches circuit  304  and the current switches circuit  305  of  FIG. 3 . 
     For embodiments in which there is no current spinning, once an output sample is achieved by the arrangement shown in  FIG. 5 , the sequence switches circuit  304  and the current switches circuit  305  can be stepped to a next vertical Hall element, which can be a rotation to the right or a rotation to the left in  FIG. 5 . For embodiments in which the two vertical Hall element  502 ,  504  are members of a set of vertical Hall elements within a CVH sensing element, the shift to the right or the left can be by one or more contacts of the CVH sensing element. 
     The first and second vertical Hall element  502 ,  504  each employ a respective five electrical contacts. Current flow and equivalent resistances of the five electrical contact vertical Hall elements  502 ,  504  are described in conjunction with U.S. Pat. No. 9,547,048, issued on Jan. 17, 2017, which is assigned to the assignee of the present invention, and which is incorporated herein by reference in its entirety. In accordance with  FIGS. 6-23  below, it will become apparent that vertical Hall elements with other numbers of electrical contacts can provide even lower offset voltages than those of the coupling arrangement  500 . 
       FIGS. 6-23  below describe various ways in which individual vertical Hall elements within a CVH sensing element, e.g., the CVH sensing element  302  of  FIG. 3  (or individual elements as in  FIG. 1A ), can be combined to result in lower offset voltage from any one of the combinations of vertical Hall elements and also a lower offset voltage variation as the CVH sensing element is sequenced to different vertical Hall elements, e.g., a lower variation of the signal  202  of  FIG. 2 . In other words, offset variation as the magnetic field sensor  300  sequences around the CVH sensing element  302  is reduced, resulting in a higher accuracy indication of a true direction of a magnetic field as reported in the x-y angle signal  314   a  of  FIG. 3 . 
     Current spinning is described in conjunction with  FIGS. 6-23 , but it will be understood that each one of the arrangements shown in figures below can be used without current spinning, maintaining but one of the indicated phases of current spinning for each step in the CVH element sampling sequence. 
     Referring now to  FIG. 6 , a coupling arrangement  600  can include a first group  602  of electrical contacts having a respective three and only three proximate electrical contacts  1 , 2 , 3  and a second group  604  of electrical contacts having a respective three and only three proximate electrical contacts  4 ,  5 ,  6 . The first and second groups of electrical contacts,  602 ,  604 , having separate N-well regions  602   a ,  604   a , can be arranged in a circle as in  FIG. 1A . Each one of the first and second groups of electrical contacts  602 ,  604  has a respective two outer electrical contacts  1 ,  3 ,  4 ,  6  and a respective center electrical contact  2 ,  5 , resulting in first and second center electrical contacts C 2 , C 4 . Together, the first and second groups of electrical contacts  602 ,  604  provide a plurality of electrical contacts.  1 ,  2 ,  3 ,  4 ,  5 ,  6 . 
     The first and second groups of electrical contacts  602 ,  604  can be coupled together so as to provide four electrical contacts C 1 , C 2 , C 3 , C 4  to other electronic elements, e.g., the magnetic field sensor  300  of  FIG. 3 . 
     The three electrical contacts  1 ,  2 ,  3  of the first group of electrical contacts  602  can be disposed over a first n-type epitaxial region  602   a  and the three electrical contacts  4 ,  5 ,  6  the second group of electrical contacts  604  can be disposed over a second n-type epitaxial region  604   a , all disposed over a semiconductor substrate  610 . 
     As indicated by  FIG. 1A , in some embodiments, the first and second epitaxial regions  602   a ,  604   a  can be separate (e.g., separately isolated). However, as indicated by  FIG. 1 , in some other embodiments, the first and second epitaxial regions  602   a ,  604   a  can be comprised of one contiguous and common n-type epitaxial implant and diffusion region formed as a circular region of a CVH sensing element (see, e.g.,  18  of  FIG. 1 ). 
     The sequence switches circuit  304  and/or the current switches circuit  306  can be operable to select the first group of electrical contacts  602  and the second group of electrical contacts  604 , the selected first and second groups of electrical contacts  602 ,  604  each having three and only three proximate electrical contacts, respectively. The sequence switches circuit and/or the current switches circuit can be operable to couple one of the outer electrical contact of the first group of electrical contacts  602  to one and only one of the outer electrical contacts of the second group of electrical contacts  604 , resulting in a first coupled pair  606  of outer electrical contacts  606 . 
     In some embodiments, the sequence switches circuit and/or the current switches circuit can be operable to couple another one of the outer electrical contact of the first group of electrical contacts  602  to another one and only one of the outer electrical contacts of the second group of electrical contacts  604 , resulting in a second coupled pair  608  of outer electrical contacts  608 . 
     Referring now to  FIG. 7 , in which like elements of  FIG. 6  are shown having like reference designations, for embodiments having the separate N-well regions  602   a ,  604   a  of  FIG. 6 , a cross section  700  shows the six electrical contacts  1 ,  2 ,  3 ,  4 ,  5 ,  6 , which can have vertical resistances Rv and horizontal resistances Rh within the epitaxial regions  602   a ,  604   a  and between adjacent electrical contacts. It will be appreciated that an electrical current can be imposed between two of the four electrical contacts, e.g., C 1 , C 3 , and the other two of the four electrical contacts, e.g., C 2 , C 4 , can generate a differential voltage signal related to an amplitude and an angle of an external magnetic field. 
     For embodiments having instead the one contiguous N-well region of a CVH sensing element as in  FIG. 1  instead of the separate N-well regions, e.g.,  602   a ,  604   a  indicative of the separate element arrangement of  FIG. 1A , another horizontal resistance Rh′ is shown. 
     Switches associated with the sequence switches circuit  304  and with the current switches circuit  306  are not shown in the cross section  700 , but are shown in conjunction with  FIG. 8  below. 
     Referring now to  FIG. 8 , in which like elements of  FIG. 7  are shown having like reference designations, an equivalent circuit  800  can be compared with the cross section  700 . Switches  802 ,  804 ,  806 ,  808  can be associated with the current switches circuit  306  of  FIG. 3 . Switches  810 ,  812  can be associated with the sequence switches circuit  304  of  FIG. 3 . 
     A current I can flow between two electrical contacts, e.g., C 1  and C 3 . A differential voltage signal between two electrical contacts, e.g., C 2  and C 4 , can be generated that is responsive to an external magnetic field. 
     As described above in conjunction with  FIG. 7 , for embodiments having instead the one contiguous N-well region of a CVH sensing element as in  FIG. 1 , the horizontal resistance Rh′ is shown. 
     Arrangements shown in figures below can apply equally well to separate magnetic field sensing elements, or to one or more CVH sensing elements, each having a contiguous N-well region through which current flows. However, arrangements and circuits shown below in  FIGS. 9 and 10  have separate N-well regions and do not show extra horizontal resistances such as the horizontal resistance Rh′ of  FIGS. 7 and 8 . Nevertheless, other arrangements comparable to  FIGS. 9 and 10  but having one contiguous N-well region as in a CVH sensing element will be understood. 
     For separate N-well regions as in  FIG. 6 , which do not have the horizontal resistance Rh′, the equivalent circuit  800  is entirely symmetrical, which can result in a particularly low offset voltage. For a contiguous N-well region, as in a CVH sensing element, which has the horizontal resistance Rh′, the equivalent circuit is nearly symmetrical and can also result in a low offset voltage. 
     Arrangements shown and described herein, like the arrangement of  FIGS. 6 and 7 , are based upon three element vertical Hall element building blocks, e.g., three element or six element vertical Hall element arrangements. In contrast, arrangements described in conjunction with earlier U.S. Pat. No. 9,547,048 are based upon five element vertical Hall element building blocks. It will be recognized that earlier U.S. Pat. No. 9,547,048, e.g., in earlier  FIG. 13 , did not show “head resistances” comparable the vertical resistances Rv shown herein. Taking head resistances into account, the five contact vertical Hall arrangements of earlier U.S. Pat. No. 9,547,048 can be shown to be less symmetrical than arrangements shown herein, and thus, generally result in a higher offset voltages than embodiments described herein. 
     Referring now to  FIG. 9 , a coupling arrangement  900  can include a first group  902  of electrical contacts having a respective three and only three proximate electrical contacts  1 ,  2 ,  3  and a second group  904  of electrical contacts having a respective three and only three proximate electrical contacts  4 ,  5 ,  6 . The first and second groups of electrical contacts  902 ,  904  are also identified as groups I and II. The first and second groups of electrical contacts,  602 ,  604  can be arranged in a circle as in  FIG. 1 or 1A . Each one of the first and second groups of electrical contacts  902 ,  904  has a respective two outer electrical contacts  1 ,  3 ,  4 ,  6  and a respective center electrical contact  2 ,  5 , resulting in first and second center electrical contacts C 1 , C 2 . Together, the first and second groups of electrical contacts provide a plurality of electrical contacts  1 ,  2 ,  3 ,  4 ,  5 ,  6 . 
     The coupling arrangement  900  can also include a third group  906  of electrical contacts having a respective three and only three proximate electrical contacts  7 ,  8 ,  9  and a fourth group  908  of electrical contacts having a respective three and only three proximate electrical contacts  10 ,  11 ,  12 . The third and fourth groups of electrical contacts  906 ,  908  are also identified as groups III and IV. The third and fourth groups of electrical contacts,  906 ,  908  can be arranged in the circle as in  FIG. 1 or 1A  along with the first and second groups of electrical contacts,  902 ,  904 . Each one of the third and fourth groups of electrical contacts  906 ,  908  has a respective two outer electrical contacts  7 ,  9 ,  10 ,  12  and a respective center electrical contact  8 ,  11 , resulting in third and fourth center electrical contacts C 3 , C 4 . Together, the first, second, third, and fourth groups of electrical contacts  902 ,  904 ,  906 ,  908  provide a plurality of electrical contacts  1 - 12 . 
     The first, second, third and fourth groups of electrical contacts  902 ,  904 ,  906 ,  908  can be coupled together so as to provide four electrical contacts C 1 , C 2 , C 3 , C 4  to other electronic elements, e.g., the magnetic field sensor  300  of  FIG. 3 . 
     The three electrical contacts  1 ,  2 ,  3  of the first group  902  of electrical contacts can be disposed over a first n-type epitaxial region  902   a , the three electrical contacts  4 ,  5 ,  6  of the second group  904  of electrical contacts can be disposed over a second n-type epitaxial region  904   a , the three electrical contacts  7 ,  8 ,  9  of the third group of electrical contacts  906  can be disposed over a third n-type epitaxial region  906   a , the three electrical contacts  10 ,  11 ,  12  of the fourth group of electrical contacts  908  can be disposed over a fourth n-type epitaxial region  908   a , all disposed over a semiconductor substrate  918 . 
     As indicated by  FIG. 1A , in some embodiments, the first, second, third, and fourth epitaxial regions  902   a ,  904   a ,  906   a ,  908   a  can be separate (e.g., separately isolated). However, as indicated by  FIG. 1 , in some embodiments, the first, second, third, and fourth epitaxial regions  902   a ,  904   a ,  906   a ,  908   a  can be comprised of one contiguous and common n-type epitaxial implant and diffusion region formed as a circular region of a CVH sensing element (see, e.g.,  18  of  FIG. 1 ). 
     Referring briefly to  FIG. 3 , the sequence switches circuit  304  can be electrically coupled to the plurality of electrical contacts (of the first, second, third, and fourth groups of electrical contacts  902 ,  904 ,  906 ,  908 ) and disposed over the semiconductor substrate  918 . The current switches circuit  306  can be electrically coupled to the plurality of electrical contacts (of the first, second, third, and fourth groups of electrical contacts  902 ,  904 ,  906 ,  908 ) and disposed over the semiconductor substrate  918 . 
     The sequence switches circuit  304  and/or the current switches circuit  306  can be operable to select the first, second, third, and fourth groups of electrical contacts  902 ,  904 ,  906 ,  908 , the selected first, second, third, and fourth groups of electrical contacts  902 ,  904 ,  906 ,  908  each having three and only three proximate electrical contacts, respectively. The sequence switches circuit  304  and/or the current switches circuit  306  can be operable to couple one of the outer electrical contact of the first group of electrical contacts  902  to one and only one of the outer electrical contacts of the second group of electrical contacts  904 , resulting in a first coupled pair (e.g.,  3 ,  4 ) of outer electrical contacts  910 . 
     The sequence switches circuit  304  and/or the current switches circuit  306  are further operable to select third and fourth groups of electrical contacts  906 ,  908 . The selected third and fourth groups of electrical contacts  906 ,  908  each have three and only three proximate electrical contacts  7 ,  8 ,  9 , and  10 ,  11 ,  12 , respectively. The three proximate electrical contacts of the third and fourth groups of electrical contacts  906 ,  908  can have respective outer electrical contacts  7 ,  9 ,  10 ,  12  and a respective center electrical contact  8 ,  11  between the outer electrical contacts, resulting in third and fourth center electrical contacts C 3 , C 4 . The sequence switches circuit  304  and/or the current switches circuit  306  is operable to couple one of the outer electrical contacts (e.g.,  9 ) of the third group of electrical contacts  906  to one and only one of the outer electrical contacts (e.g.,  10 ) of the fourth group of electrical contacts  908 , operable to couple another one of the electrical contacts (e.g.,  1 ) of the first group of electrical contacts  902  to another one of the one and only one of the outer contacts (e.g.,  12 ) of the fourth group of electrical contacts  908 , and operable to couple another one of the outer electrical contacts (e.g.,  6 ) of the second group of electrical contacts  904  to another one and only one of the outer electrical contacts (e.g.,  7 ) of the third group of electrical contacts  906 , resulting in second, third, and fourth coupled pairs (e.g.,  9 ,  10  and  1 ,  12  and  6 ,  7 ) of outer electrical contacts  914 ,  916 ,  912 . 
     Referring now to  FIG. 10 , in which like elements of  FIG. 9  are shown having like reference designations, an equivalent circuit  1000  can be compared with the equivalent circuit  600 . Switches  1002 ,  1004  can be associated with the current switches circuit  306  of  FIG. 3 . 
     Switches  1006 ,  1008  can be associated with the sequence switches circuit  304  of  FIG. 3 . 
     A current I can flow between two electrical contacts, e.g., C 1  and C 3 . A differential voltage signal between two electrical contacts, e.g., C 2  and C 4 , can be generated that is responsive to an external magnetic field. 
     The equivalent circuit  1000  is entirely symmetrical, which can result in a particularly low offset voltage. 
     Referring now to  FIGS. 11-11C , four groups of electrical contacts I, II, III, and IV are shown in four different coupling arrangements of a CVH sensing element labeled as 0, 90, 180, and 270. Each one of the four couplings 0, 90, 180, and 270 can be described in the same way as the description above in conjunction with  FIG. 9 , here arranged in a circle. Each coupling remains electrically symmetrical resulting in the substantially the same offset voltage, and element sensitivity of each coupling is substantially the same. 
     A differential signal, responsive to an external magnetic field, can be generated between electrical contacts labeled + and −. A driving current can be input to the CVH sensing element at an electrical contact labeled I and the current can flow out of the electrical contact terminating with a ground symbol. 
     Here, center contacts of the first and second groups I, II can be within a first quadrant of a circle and center contacts of the third and fourth groups III, IV can be within a second quadrant of the circle different than the first quadrant. 
     The first and second groups of electrical contacts I, II can be disposed proximate to each other. The third and fourth groups of electrical contacts III, IV can be disposed proximate to each other. The first and second groups of electrical contacts I, II can be disposed one hundred eighty degrees around the circle from the third and fourth groups of electrical contacts III, IV. 
     In some embodiments, the four selected groups I, II, III, and IV are selected by the sequence switches circuit  304  and by the current switches circuit  306 . During a current spinning operation, couplings to the four selected groups I, II, III, IV are changed sequentially to achieve the four current spinning phases (coupling arrangements), 0, 90, 180, and 270, in any phase sequence. Thereafter, a different four groups of electrical contacts can be selected and the four current spinning phases can be sequentially chosen for each selected four groups of electrical contacts. 
     In other embodiments, current spinning is not used and any one of the phases, 0, 90, 180, and 270, can remain static as different four groups of electrical contacts are selected. 
     Current spinning can provide lower average offset voltage than only one selected phase, even though each phase already has a high degree of electrical symmetry and an associated low offset voltage. 
     Referring now to  FIGS. 12-12C , four groups of electrical contacts I, II, III, and IV are shown in four different coupling arrangements of a CVH sensing element labeled as 0, 90, 180, and 270. Each one of the four groups of electrical contacts I, II, III, and IV can be described in the same way as the description above in conjunction with  FIG. 9 . 
     A differential signal, responsive to an external magnetic field, can be generated between electrical contacts labeled + and −. A driving current can be input to the CVH sensing element at an electrical contact labeled I and the current can flow out of the electrical contact terminating with a ground symbol. 
     Here, center contacts of the first and second groups I, II can be within a first quadrant of a circle and center contacts of the third and fourth groups III, IV can be within the first quadrant. 
     The first, second, third, and fourth groups of electrical contacts I, II, III, IV can be disposed proximate to each other. 
     In some embodiments, the four selected groups I, II, III, and IV are selected by the sequence switches circuit  304  and by the current switches circuit  306 . During a current spinning operation, couplings to the four selected groups I, II, III, IV are changed sequentially to achieve the four current spinning phases 0, 90, 180, and 270, in any phase sequence. Thereafter, a different four groups of electrical contacts can be selected and the four current spinning phases can be sequentially chosen for each selected four groups of electrical contacts. 
     In other embodiments, current spinning is not used and any one of the phases, 0, 90, 180, and 270, can remain static as different four groups of electrical contacts are selected. 
     Current spinning can provide lower average offset voltage than only one selected phase, even though each phase already has a high degree of electrical symmetry and an associated low offset voltage. 
     Referring now to  FIGS. 13-13C , four groups of electrical contacts I, II, III, IV are shown in four different coupling arrangements of a CVH sensing element labeled as 0, 90, 180, and 270. Each one of the four coupling arrangements 0, 90, 180, 270 can be described in the same way as the description above in conjunction with  FIG. 9 . 
     A differential signal, responsive to an external magnetic field, can be generated between electrical contacts labeled + and −. A driving current can be input to the CVH sensing element at an electrical contact labeled I and the current can flow out of the electrical contact terminating with a ground symbol. 
     Here, center contacts of the first and second groups I, II can be within first and second quadrants of a circle, respectively, and center contacts of the third and fourth groups III, IV can be within the third and fourth quadrants, respectively, each quadrant different than the other quadrants. 
     First, second, third, and fourth center electrical contacts of the first, second, third, and fourth groups of electrical contacts I, II, III, IV can be disposed in respective ninety degree relationships around the circle. 
     In some embodiments, the four selected groups I, II, III, and IV are selected by the sequence switches circuit  304  and by the current switches circuit  306 . During a current spinning operation, couplings to the four selected groups I, II, III, IV are changed sequentially to achieve the four current spinning phases, 0, 90, 180, 270, in any phase sequence. Thereafter, a different four groups of electrical contacts can be selected and the four current spinning phases can be sequentially chosen for each selected four groups of electrical contacts. 
     In other embodiments, current spinning is not used and any one of the phases, zero, ninety, one hundred eighty, and two hundred seventy, can remain static as different four groups of electrical contacts are selected. 
     Current spinning can provide lower average offset voltage than only one selected phase, even though each phase already has a high degree of electrical symmetry and an associated low offset voltage. 
     Referring now to  FIGS. 14-14C , two groups of electrical contacts I, II are shown in four different coupling arrangements of a CVH sensing element labeled as 0, 90, 180, and 270. Each one of the four coupling arrangements 0, 90, 180, 270 can be described in the same way as the description above in conjunction with  FIG. 6 . 
     A differential signal, responsive to an external magnetic field, can be generated between electrical contacts labeled + and −. A driving current can be input to the CVH sensing element at an electrical contact labeled I and the current can flow out of the electrical contact terminating with a ground symbol. 
     The first and second groups of electrical contacts I, II can be disposed proximate to each other around the circle. 
     In some embodiments, the first and second selected groups I, II are selected by the sequence switches circuit  304  and by the current switches circuit  306 . During a current spinning operation, couplings to the two selected groups I, II are changed sequentially to achieve the four current spinning phases, 0, 90, 180, 270, in any phase sequence. Thereafter, a different two groups of electrical contacts can be selected and the four current spinning phases can be sequentially chosen for each selected four groups of electrical contacts. 
     In other embodiments, current spinning is not used and any one of the phases, 0, 90, 180, and 270, can remain static as different four groups of electrical contacts are selected. 
     Current spinning can provide lower average offset voltage than only one selected phase, even though each phase already has a high degree of electrical symmetry and an associated low offset voltage. 
     Referring now to  FIGS. 15-15C , two groups of electrical contacts I, II are shown in four different coupling arrangements of a CVH sensing element labeled as 0, 90, 180, and 270. Each one of the four coupling arrangements 0, 90, 180, 270 can be described in the same way as the description above in conjunction with  FIG. 6 . 
     A differential signal, responsive to an external magnetic field, can be generated between electrical contacts labeled + and −. A driving current can be input to the CVH sensing element at an electrical contact labeled I and the current can flow out of the electrical contact terminating with a ground symbol. 
     The first and second groups of electrical contacts I, II can be disposed at one hundred eight relative degrees to each other around the circle. 
     In some embodiments, the first and second selected groups I, II are selected by the sequence switches circuit  304  and by the current switches circuit  306 . During a current spinning operation, couplings to the two selected groups I, II are changed sequentially to achieve the four current spinning phases, 0, 90, 180, 270, in any phase sequence. Thereafter, a different two groups of electrical contacts can be selected and the four current spinning phases can be sequentially chosen for each selected four groups of electrical contacts. 
     In other embodiments, current spinning is not used and any one of the phases, 0, 90, 180, and 270, can remain static as different four groups of electrical contacts are selected. 
     Current spinning can provide lower average offset voltage than only one selected phase, even though each phase already has a high degree of electrical symmetry and an associated low offset voltage. 
     Referring now to  FIGS. 16-16C , are shown in four different coupling arrangements of a CVH sensing element labeled as 0, 90, 180, and 270. Each one of the four coupling arrangements 0, 90, 180, 270 can be described in the same way as the description above in conjunction with  FIG. 9 . Here, multiple three contact vertical Hall elements are connected in parallel for reducing resistance. 
     A differential signal, responsive to an external magnetic field, can be generated between electrical contacts labeled + and −. A driving current can be input to the CVH sensing element at an electrical contact labeled I and the current can flow out of the electrical contact terminating with a ground symbol. 
     Four different coupling arrangements can be designated 0, 90, 180, 270. There can be six groups of electrical contacts, I, II, III, IV, V, VI, i.e., a plurality of electrical contacts. 
     The sequence switches circuit  304  and/or the current switches circuit  306  can be the operable to select a first, second, third, fourth, fifth, and sixth groups of electrical contacts I, II, III, IV, V, VI. The first, second, third, fourth, fifth, and sixth groups of electrical contacts I, II, III, IV, V, VI can each have three and only three proximate electrical contacts, respectively. The three proximate electrical contacts of the first, second, third, fourth, fifth, and sixth groups of electrical contacts I, II, III, IV, V, VI can each have respective outer electrical contacts and a respective center electrical contact between the outer electrical contacts resulting in first, second, third, fourth, fifth, and sixth center electrical contacts. One outer electrical contact of each of the first, second, and third groups of electrical contacts I, II, III can be coupled together. Another one outer electrical contact of each of the first and second groups of electrical contacts I, II can be coupled together and also to an outer electrical contact of the sixth group of electrical contacts IV. 
     In some embodiments, center contacts of the third and sixth groups of electrical contacts III, VI can be disposed at one hundred eighty degrees relative to each other around the circle. In some embodiments, the first and second groups of electrical contacts, I, II taken together can be disposed at one hundred eighty degrees relative to the fourth and fifth groups of electrical contacts IV, V taken together. In some embodiments, the first and second groups of electrical contacts I, II taken together, the third group of electrical contacts III, the fourth and fifth groups of electrical contacts IV, V taken together, and the sixth group of electrical contacts VI can be disposed ninety degrees relative to each other around the circle. 
     In some embodiments, the six selected groups of electrical contacts I, II, III, IV, V, VI are selected by the sequence switches circuit  304  and by the current switches circuit  306 . During a current spinning operation, couplings to the six selected groups I, II, III, IV, V, VI are changed sequentially to achieve the four current spinning phases, 0, 90, 180, 270, in any phase sequence. Thereafter, a different six groups of electrical contacts can be selected and the four current spinning phases can be sequentially chosen for each selected four groups of electrical contacts. 
     In other embodiments, current spinning is not used and any one of the phases, 0, 90, 180, 270, can remain static as different four groups of electrical contacts are selected. 
     Current spinning can provide lower average offset voltage than only one selected phase, even though each phase already has a high degree of electrical symmetry and an associated low offset voltage. 
       FIGS. 16-16C  are a representation of  FIG. 9  but using a pair of three contact vertical Hall elements for current driving contacts. However, this arrangement could be extended to N number of parallel three contact vertical Hall elements for the current driving contacts. 
       FIGS. 17-23  described below show various combinations of the phases of the coupling arrangements of selected ones of  FIGS. 11-16 , the combinations all within a single CVH sensing element as in  FIGS. 1 and 3  (or circle of separate vertical Hall elements as in  FIGS. 1A and 3 ). In contrast,  FIGS. 24-26  show various combinations of the phases of the coupling arrangements of selected ones of  FIGS. 11-16 , the combinations all within two (or more) CVH sensing elements, each as in  FIGS. 1 and 3  (or each a circle of separate vertical Hall elements as in  FIGS. 1A and 3 ). 
     Referring now to  FIG. 17 , a coupling arrangement of a CVH sensing element can include first, second, third, and fourth groups of electrical contacts I, II, III, IV, each having three electrical contacts comprising a respective two outer contacts and a respective two center contacts, resulting in first, second, third, and fourth center contacts. This arrangement is like two of the arrangements of  FIG. 6 , but with different current driving arrangements. This arrangement is also like two of the phases, here 0 and 90 degrees, of the arrangements of  FIGS. 14-14C . Various combinations of the phase pairs of  FIGS. 14-14C  are also possible, for example, phase pairs 0, 90, or 90, 180, or 180, 270, or 270, 0. 
     As with the arrangement of  FIGS. 14-14C , the first and second groups of electrical contacts I, II can be disposed proximate to each other around the circle. In some embodiments, the first, second, third, and fourth groups of electrical contacts I, II, III, IV can be disposed proximate to each other around the circle. 
     Two differential signals, responsive to an external magnetic field, can be generated between two pairs of electrical contacts labeled + and −. The two differential signals can be combined in series or in parallel, depending upon the application, resulting in one combined differential signal. 
     Regarding the third and fourth groups of electrical contacts III, IV, a driving current can be input to the CVH sensing element at an electrical contact labeled I and the current can flow out of a corresponding electrical contact terminating with a ground symbol. Regarding the first and second groups of electrical contacts I, II, another driving current can be input to the CVH sensing element at two electrical contacts labeled  112 , for a total current of I, and the current I can flow out of a coupled pair of corresponding electrical contacts terminating with a ground symbol. 
     Four phases like the arrangement shown can provide current spinning. Using the phases of  FIGS. 14-14C : 
     phase A: 0 and 90 phases of  FIGS. 14-14C  as shown 
     phase B: 90 and 180 phases 
     phase C: 180 and 270 phases 
     phase D: 270 and 0 phase 
     In some embodiments, the four selected groups of electrical contacts I, II, III, IV are selected by the sequence switches circuit  304  and by the current switches circuit  306 . During a current spinning operation, couplings to the four selected groups I, II, III, IV are changed sequentially to achieve the above four current spinning phases, A, B, C, D, in any phase sequence. Thereafter, a different four groups of electrical contacts can be selected and the four current spinning phases can be sequentially chosen for each selected four groups of electrical contacts. 
     In other embodiments, current spinning is not used and any one of the phases A, B, C, or D can remain static as different four groups of electrical contacts are selected. 
     Current spinning can provide lower average offset voltage than only one selected phase, even though each phase already has a high degree of electrical symmetry and an associated low offset voltage. 
     Referring now to  FIG. 18 , a coupling arrangement of a CVH sensing element can include eight groups of electrical contacts I, II, III, IV, V, VI, VII, and VIII, each having three electrical contacts comprising a respective two outer contacts and a respective two center contacts, resulting in first, second, third, fourth, fifth, sixth, seventh, and eighth center contacts. This arrangement is like two of the arrangements of  FIG. 9  above. This arrangement is also like two of the phases, here 0 and 90 degrees, of the arrangements of  FIGS. 11-11C . 
     As with the arrangement of  FIGS. 11-11C , the first and second groups of electrical contacts I, II can be disposed proximate to each other. The third and fourth groups of electrical contacts III, IV can be disposed proximate to each other. The first and second groups of electrical contacts I, II can be disposed one hundred eighty degrees around the circle from the third and fourth groups of electrical contacts III, IV. 
     Similarly, in some embodiments, the fifth and sixth groups of electrical contacts V, VI can be disposed proximate to each other. The seventh and eighth groups of electrical contacts VII, VIII can be disposed proximate to each other. The fifth and sixth groups of electrical contacts V, VI can be disposed one hundred eighty degrees around the circle from the seventh and eighth groups of electrical contacts VII, VIII. A ninety degree relationship between the pairs, i.e., first and second, the third and fourth, the fifth and sixth, and the seventh and eighth groups of electrical contracts can result. 
     Regarding the first, second, third, and fourth groups of electrical contacts I, II, III, IV, a first differential signal, responsive to an external magnetic field, can be generated between electrical contacts labeled + and −. Regarding the fifth, sixth, seventh, and eighth groups of electrical contacts V, VI, VII, VIII, a second differential signal, responsive to an external magnetic field, can be generated between electrical contacts labeled + and −. The two differential signals can be combined in series or in parallel, depending upon the application, resulting in one combined differential signal. 
     Regarding the first, second, third, and fourth groups of electrical contacts I, II, III, IV, a driving current I can be input to the CVH sensing element at an electrical contact labeled I and the current I can flow out of a corresponding electrical contact terminating with a ground symbol. Regarding the fifth, sixth, seventh, and eighth groups of electrical contacts V, VI, VII, VIII, another driving current I can be input to the CVH sensing element at an electrical contact labeled I and the current I can flow out of a corresponding electrical contacts terminating with a ground symbol. 
     Four phases like the arrangement shown can provide current spinning. Using the phases of  FIGS. 11-11C : 
     phase A: 0 and 90 phases of  FIGS. 11-11C  as shown 
     phase B: 90 and 180 phases 
     phase C: 180 and 270 phases 
     phase D: 270 and 0 phase 
     In some embodiments, the eight selected groups of electrical contacts I, II, III, IV, V, VI, VII, VIII are selected by the sequence switches circuit  304  and by the current switches circuit  306 . During a current spinning operation, couplings to the eight selected groups contacts I, II, III, IV, V, VI, VII, VIII are changed sequentially to achieve the above four current spinning phases, A, B, C, D, in any phase sequence. Thereafter, a different eight groups of electrical contacts can be selected and the four current spinning phases can be sequentially chosen for each selected four groups of electrical contacts. 
     In other embodiments, current spinning is not used and any one of the phases A, B, C, or D can remain static as different four groups of electrical contacts are selected. 
     Current spinning can provide lower average offset voltage than only one selected phase, even though each phase already has a high degree of electrical symmetry and an associated low offset voltage. 
     Referring now to  FIG. 19 , like the coupling arrangement of  FIG. 18 , a coupling arrangement of a CVH sensing element can include eight groups of electrical contacts I, II, III, IV, V, VI, VII, and VIII, each having three electrical contacts comprising a respective two outer contacts and a respective two center contacts, resulting in first, second, third, fourth, fifth, sixth, seventh, and eighth center contacts. This arrangement is like four of the arrangements of  FIG. 9  above. This arrangement is also like two of the phases, here 0 and 90 degrees, of the arrangements of  FIGS. 11-11C . 
     As with the arrangement of  FIGS. 11-11C , the first and second groups of electrical contacts I, II can be disposed proximate to each other. The third and fourth groups of electrical contacts III, IV can be disposed proximate to each other. The first and second groups of electrical contacts I, II can be disposed one hundred eighty degrees around the circle from the third and fourth groups of electrical contacts III, IV. 
     Similarly, in some embodiments, the fifth and sixth groups of electrical contacts V, VI can be disposed proximate to each other. The seventh and eighth groups of electrical contacts VII, VIII can be disposed proximate to each other. The fifth and sixth groups of electrical contacts V, VI can be disposed proximate to the seventh and eighth groups of electrical contacts VII, VIII. In some embodiments, the eight groups of electrical contacts I, II, III, IV, V, VI, VI, VII, VIII can each be disposed proximate to another one of the eight groups, respectively. 
     Other characteristics of the eight groups can be the same as or similar to the coupling arrangement of  FIG. 18 . 
     Referring now to  FIG. 20 , a coupling arrangement of a CVH sensing element can include eight groups of electrical contacts I, II, III, IV, V, VI, VII, and VIII, each having three electrical contacts comprising a respective two outer contacts and a respective two center contacts, resulting in first, second, third, fourth, fifth, sixth, seventh, and eighth center contacts. This arrangement is like four of the arrangements of  FIG. 9  above. This arrangement is also like two of the phases, here 0 and 90 degrees, of the arrangements of  FIGS. 12-12C . 
     The first, second, third, and fourth groups of electrical contacts I, II, III, IV can be disposed proximate to each other. The fifth, sixth, seventh, and eighth groups of electrical contacts V, VI, VII, VIII can be disposed next to each other. In some embodiments, the first, second, third, and fourth groups of electrical contacts I, II, III, IV can be disposed in a one hundred eighty degree relationship to the fifth, sixth, seventh, and eighth groups of electrical contacts V, VI, VII, VIII. 
     Regarding the first, second, third, and fourth groups of electrical contacts I, II, III, IV, a first differential signal, responsive to an external magnetic field, can be generated between electrical contacts labeled + and −. Regarding the fifth, sixth, seventh, and eighth groups of electrical contacts V, VI, VII, VIII, a second differential signal, responsive to an external magnetic field, can be generated between electrical contacts labeled + and −. The two differential signals can be combined in series or in parallel, depending upon the application, resulting in on combined differential signal. 
     Regarding the first, second, third, and fourth groups of electrical contacts I, II, III, IV, a driving current I can be input to the CVH sensing element at an electrical contact labeled I and the current I can flow out of a corresponding electrical contact terminating with a ground symbol. Regarding the fifth, sixth, seventh, and eighth groups of electrical contacts V, VI, VII, VIII, another driving current I can be input to the CVH sensing element at an electrical contact labeled I and the current I can flow out of a corresponding electrical contacts terminating with a ground symbol. 
     Four phases like the arrangement shown can provide current spinning. Using the phases of  FIGS. 12-12C : 
     phase A: 0 and 90 phases of  FIGS. 11-11C  as shown 
     phase B: 90 and 180 phases 
     phase C: 180 and 270 phases 
     phase D: 270 and 0 phase 
     In some embodiments, the eight selected groups of electrical contacts I, II, III, IV, V, VI, VII, VIII are selected by the sequence switches circuit  304  and by the current switches circuit  306 . During a current spinning operation, couplings to the eight selected groups contacts I, II, III, IV, V, VI, VII, VIII are changed sequentially to achieve the above four current spinning phases, A, B, C, D, in any phase sequence. Thereafter, a different eight groups of electrical contacts can be selected and the four current spinning phases can be sequentially chosen for each selected four groups of electrical contacts. 
     In other embodiments, current spinning is not used and any one of the phases A, B, C, or D can remain static as different four groups of electrical contacts are selected. 
     Current spinning can provide lower average offset voltage than only one selected phase, even though each phase already has a high degree of electrical symmetry and an associated low offset voltage. 
     Referring now to  FIG. 21 , a coupling arrangement of a CVH sensing element can include first, second, third, and fourth groups of electrical contacts I, II, III, IV, each having three electrical contacts comprising a respective two outer contacts and a respective two center contacts, resulting in first, second, third, and fourth center contacts. This arrangement is like two of the arrangements of  FIG. 6  above. This arrangement is also like two of the phases, here 0 and 90 degrees, of the arrangements of  FIGS. 14-14C , and also similar to the coupling arrangement of  FIG. 17 . 
     As with the arrangement of  FIGS. 14-14C , the first and second groups of electrical contacts I, II can be disposed proximate to each other around the circle. In some embodiments, the third, and fourth groups of electrical contacts III, IV can be disposed proximate to each other around the circle. In some embodiments, the first and second groups of electrical contacts I, II can be disposed in a one hundred eighty degree relationship to the third, and fourth groups of electrical contacts III, IV. 
     Two differential signals, responsive to an external magnetic field, can be generated between two pairs of electrical contacts labeled + and −. The two differential signals can be combined in series or in parallel, depending upon the application, resulting in one combined differential signal. 
     Regarding the third and fourth groups of electrical contacts III, IV, a driving current can be input to the CVH sensing element at an electrical contact labeled I and the current can flow out of a corresponding electrical contact terminating with a ground symbol. Regarding the first and second groups of electrical contacts I, II, another driving current can be input to the CVH sensing element at two electrical contacts labeled  112 , for a total current of I, and the current I can flow out of a coupled pair of corresponding electrical contacts terminating with a ground symbol. 
     Four phases like the arrangement shown can provide current spinning. Using the phases of  FIGS. 14-14C : 
     phase A: 0 and 90 phases of  FIGS. 14-14C  as shown 
     phase B: 90 and 180 phases 
     phase C: 180 and 270 phases 
     phase D: 270 and 0 phase 
     In some embodiments, the four selected groups of electrical contacts I, II, III, IV are selected by the sequence switches circuit  304  and by the current switches circuit  306 . During a current spinning operation, couplings to the four selected groups I, II, III, IV are changed sequentially to achieve the above four current spinning phases, A, B, C, D, in any phase sequence. Thereafter, a different four groups of electrical contacts can be selected and the four current spinning phases can be sequentially chosen for each selected four groups of electrical contacts. 
     In other embodiments, current spinning is not used and any one of the phases A, B, C, or D can remain static as different four groups of electrical contacts are selected. 
     Current spinning can provide lower average offset voltage than only one selected phase, even though each phase already has a high degree of electrical symmetry and an associated low offset voltage. 
     Referring now to  FIG. 22 , a coupling arrangement of a CVH sensing element can include eight groups of electrical contacts I, II, III, IV, V, VI, VII, and VIII, each having three electrical contacts comprising a respective two outer contacts and a respective two center contacts, resulting in first, second, third, fourth, fifth, sixth, seventh, and eighth center contacts. This arrangement is like four of the arrangements of  FIG. 6  above. This arrangement is also like all four of the phases, here 0, 90, 180, 270 degrees, of the arrangements of  FIGS. 14-14C . 
     As with the arrangements of  FIGS. 14-14C , the first and second groups of electrical contacts I, II can be disposed proximate to each other. The third and fourth groups of electrical contacts III, IV can be disposed proximate to each other. The first and second groups of electrical contacts I, II can be disposed one hundred eighty degrees around the circle from the third and fourth groups of electrical contacts III, IV. 
     Similarly, in some embodiments, the fifth and sixth groups of electrical contacts V, VI can be disposed proximate to each other. The seventh and eighth groups of electrical contacts VII, VIII can be disposed proximate to each other. The fifth and sixth groups of electrical contacts V, VI can be disposed one hundred eighty degrees around the circle from the seventh and eighth groups of electrical contacts VII, VIII. The first, second, fifth and sixth groups of electrical contacts, I, II, V, VI can be disposed proximate to each other. The third, fourth, seventh, and eighth groups of electrical contacts III, IV, VII, VIII can be disposed proximate to each other. 
     Regarding the first, second, third, and fourth groups of electrical contacts I, II, III, IV, a first differential signal, responsive to an external magnetic field, can be generated between electrical contacts labeled + and −. Regarding the fifth, sixth, seventh, and eighth groups of electrical contacts V, VI, VII, VIII, a second differential signal, responsive to an external magnetic field, can be generated between electrical contacts labeled + and −. The two differential signals can be combined in series or in parallel, depending upon the application, resulting in one combined differential signal. 
     Regarding the first, second, third, and fourth groups of electrical contacts I, II, III, IV, a driving current I can be input to the CVH sensing element at an electrical contact labeled I and the current I can flow out of a corresponding electrical contact terminating with a ground symbol. Regarding the fifth, sixth, seventh, and eighth groups of electrical contacts V, VI, VII, VIII, another driving current I can be input to the CVH sensing element at an electrical contact labeled I and the current I can flow out of a corresponding electrical contacts terminating with a ground symbol. 
     Four phases like the arrangement shown can provide current spinning. Using the phases of  FIGS. 14-14C : 
     phase A: 0 and 90 phases of  FIGS. 14-14C  as shown 
     phase B: 90 and 180 phases 
     phase C: 180 and 270 phases 
     phase D: 270 and 0 phase 
     In some embodiments, the eight selected groups of electrical contacts I, II, III, IV, V, VI, VII, VIII are selected by the sequence switches circuit  304  and by the current switches circuit  306 . During a current spinning operation, couplings to the eight selected groups contacts I, II, III, IV, V, VI, VII, VIII are changed sequentially to achieve the above four current spinning phases, A, B, C, D, in any phase sequence. Thereafter, a different eight groups of electrical contacts can be selected and the four current spinning phases can be sequentially chosen for each selected four groups of electrical contacts. 
     In other embodiments, current spinning is not used and any one of the phases A, B, C, or D can remain static as different four groups of electrical contacts are selected. 
     Current spinning can provide lower average offset voltage than only one selected phase, even though each phase already has a high degree of electrical symmetry and an associated low offset voltage. 
     Referring now to  FIG. 23 , a coupling arrangement is similar to the coupling arrangement of  FIG. 22 , again having all four of the coupling arrangements of  FIGS. 14-14C . However, unlike the coupling arrangement of  FIG. 22 , the first, second, third, and fourth groups of electrical contacts I, II, III, IV can be disposed in ninety degree relationships to each other around the circle. Other aspects of the coupling arrangement of  FIG. 22  apply to the coupling arrangement of  FIG. 23 . 
     Referring now to  FIG. 24 , a coupling arrangement of two CVH sensing elements can include a first and second CVH sensing elements having phases 0 and 90, respectively, of  FIGS. 11-11C . This coupling arrangement is similar to the coupling arrangement of  FIG. 18 , which has the combination of phases within only one CVH sensing element. 
     A coupling arrangement of a first CVH sensing element can include a first four groups of electrical contacts I, II, III, IV. A coupling arrangement of a second CVH sensing element can include another four groups of electrical contacts V, VI, VII, and VIII. Each group of electrical contacts can have three electrical contacts comprising a respective two outer contacts and a respective two center contacts, resulting in first, second, third, fourth, fifth, sixth, seventh, and eighth center contacts. This arrangement is like two of the arrangements of  FIG. 9  above, here disposed in two separate independent circles (e.g., separate CVH elements). This arrangement is also like two of the phases, here 0 and 90 degrees, of the arrangements of  FIGS. 11-11C . 
     As with the arrangement of  FIGS. 11-11C , on the first CVH sensing element, the first and second groups of electrical contacts I, II can be disposed proximate to each other. The third and fourth groups of electrical contacts III, IV can be disposed proximate to each other. The first and second groups of electrical contacts I, II can be disposed one hundred eighty degrees around the circle from the third and fourth groups of electrical contacts III, IV. 
     Similarly, in some embodiments, on the second CVH sensing element, the fifth and sixth groups of electrical contacts V, VI can be disposed proximate to each other. The seventh and eighth groups of electrical contacts VII, VIII can be disposed proximate to each other. The fifth and sixth groups of electrical contacts V, VI can be disposed one hundred eighty degrees around the circle from the seventh and eighth groups of electrical contacts VII, VIII. 
     Regarding the first, second, third, and fourth groups of electrical contacts I, II, III, IV, a first differential signal, responsive to an external magnetic field, can be generated between electrical contacts labeled + and −. Regarding the fifth, sixth, seventh, and eighth groups of electrical contacts V, VI, VII, VIII, a second differential signal, responsive to an external magnetic field, can be generated between electrical contacts labeled + and −. The two differential signals can be combined in series or in parallel, depending upon the application resulting in one combined differential signal. 
     Regarding the first, second, third, and fourth groups of electrical contacts I, II, III, IV, a driving current I can be input to the CVH sensing element at an electrical contact labeled I and the current I can flow out of a corresponding electrical contact terminating with a ground symbol. Regarding the fifth, sixth, seventh, and eighth groups of electrical contacts V, VI, VII, VIII, another driving current I can be input to the CVH sensing element at an electrical contact labeled I and the current I can flow out of a corresponding electrical contacts terminating with a ground symbol. 
     Four phases like the arrangement shown can provide current spinning. Using the phases of  FIGS. 11-11C : 
     phase A: 0 and 90 phases of  FIGS. 11-11C  as shown 
     phase B: 90 and 180 phases 
     phase C: 180 and 270 phases 
     phase D: 270 and 0 phase 
     In some embodiments, the eight selected groups of electrical contacts I, II, III, IV, V, VI, VII, VIII are selected by the sequence switches circuit  304  and by the current switches circuit  306 . During a current spinning operation, couplings to the eight selected groups contacts I, II, III, IV, V, VI, VII, VIII are changed sequentially to achieve the above four current spinning phases, A, B, C, D, in any phase sequence. Thereafter, a different eight groups of electrical contacts can be selected and the four current spinning phases can be sequentially chosen for each selected four groups of electrical contacts. 
     In other embodiments, current spinning is not used and any one of the phases A, B, C, or D can remain static as different four groups of electrical contacts are selected. 
     Current spinning can provide lower average offset voltage than only one selected phase, even though each phase already has a high degree of electrical symmetry and an associated low offset voltage. 
     Referring now to  FIG. 25 , a coupling arrangement of two CVH sensing elements can include a first and second CVH sensing elements having phases 0 and 90, respectively, of  FIGS. 13-13C . 
     A coupling arrangement of a first CVH sensing element can include a first four groups of electrical contacts I, II, III, IV. A coupling arrangement of a second CVH sensing element can include another four groups of electrical contacts V, VI, VII, and VIII. Each group of electrical contacts can have three electrical contacts comprising a respective two outer contacts and a respective two center contacts, resulting in first, second, third, fourth, fifth, sixth, seventh, and eighth center contacts. This arrangement is like two of the arrangements of  FIG. 9  above, here disposed in two separate independent circles (e.g., separate CVH elements). This arrangement is also like two of the phases, here 0 and 90 degrees, of the arrangements of  FIGS. 13-13C . 
     As with the arrangement of  FIGS. 13-13C , on the first CVH sensing element, the first and second groups of electrical contacts I, II can be disposed proximate to each other. The third and fourth groups of electrical contacts III, IV can be disposed proximate to each other. The first and second groups of electrical contacts I, II can be disposed one hundred eighty degrees around the circle from the third and fourth groups of electrical contacts III, IV. 
     Similarly, in some embodiments, on the second CVH sensing element, the fifth and sixth groups of electrical contacts V, VI can be disposed proximate to each other. The seventh and eighth groups of electrical contacts VII, VIII can be disposed proximate to each other. The fifth and sixth groups of electrical contacts V, VI can be disposed one hundred eighty degrees around the circle from the seventh and eighth groups of electrical contacts VII, VIII. 
     First, second, third, and fourth center electrical contacts of the first, second, third, and fourth groups of electrical contacts I, II, III, IV can be disposed in respective ninety degree relationships around the first CVH sensing element. Fifth, sixth, seventh, and eighth center electrical contacts of the fifth, sixth, seventh, and eighth groups of electrical V, VI, VII, and VIII can be disposed in respective ninety degree relationships around the second CVH sensing element. 
     Regarding the first, second, third, and fourth groups of electrical contacts I, II, III, IV, a first differential signal, responsive to an external magnetic field, can be generated between electrical contacts labeled + and −. Regarding the fifth, sixth, seventh, and eighth groups of electrical contacts V, VI, VII, VIII, a second differential signal, responsive to an external magnetic field, can be generated between electrical contacts labeled + and −. The two differential signals can be combined in series or in parallel, depending upon the application, resulting in one combined differential signal. 
     Regarding the first, second, third, and fourth groups of electrical contacts I, II, III, IV, a driving current I can be input to the CVH sensing element at an electrical contact labeled I and the current I can flow out of a corresponding electrical contact terminating with a ground symbol. Regarding the fifth, sixth, seventh, and eighth groups of electrical contacts V, VI, VII, VIII, another driving current I can be input to the CVH sensing element at an electrical contact labeled I and the current I can flow out of a corresponding electrical contacts terminating with a ground symbol. 
     Four phases like the arrangement shown can provide current spinning. Using the phases of  FIGS. 13-13C : 
     phase A: 0 and 90 phases of  FIGS. 13-13C  as shown 
     phase B: 90 and 180 phases 
     phase C: 180 and 270 phases 
     phase D: 270 and 0 phase 
     In some embodiments, the eight selected groups of electrical contacts I, II, III, IV, V, VI, VII, VIII are selected by the sequence switches circuit  304  and by the current switches circuit  306 . During a current spinning operation, couplings to the eight selected groups contacts I, II, III, IV, V, VI, VII, VIII are changed sequentially to achieve the above four current spinning phases, A, B, C, D, in any phase sequence. Thereafter, a different eight groups of electrical contacts can be selected and the four current spinning phases can be sequentially chosen for each selected four groups of electrical contacts. 
     In other embodiments, current spinning is not used and any one of the phases A, B, C, or D can remain static as different four groups of electrical contacts are selected. 
     Current spinning can provide lower average offset voltage than only one selected phase, even though each phase already has a high degree of electrical symmetry and an associated low offset voltage. 
     Referring now to  FIG. 26 , a coupling arrangement of two CVH sensing elements can include a first and second CVH sensing elements having phases 0 and 90, respectively, of  FIGS. 16-16C . 
     A coupling arrangement of a first CVH sensing element can include a first five groups of electrical contacts I, II, III, IV, V. A coupling arrangement of a second CVH sensing element can include another five groups of electrical contacts Ia, IIa, IIIa, IVa, Va. Each coupling of three electrical contacts comprising a respective two outer contacts and a respective two center contacts, resulting in first, second, third, fourth, fifth, sixth, seventh, and eighth center contacts. This arrangement is like two of the arrangements of  FIG. 9  above, but with a plurality of three contact vertical Hall elements in parallel, and here disposed in two separate independent circles (e.g., separate CVH elements). This arrangement is also like two of the phases, here 0 and 90 degrees, of the arrangements of  FIGS. 16-16C . 
     Four phases like the arrangement shown can provide current spinning. Using the phases of  FIGS. 16-16C : 
     phase A: 0 and 90 phases of  FIGS. 16-16C  as shown 
     phase B: 90 and 180 phases 
     phase C: 180 and 270 phases 
     phase D: 270 and 0 phase 
     In some embodiments, the ten selected groups of electrical contacts I, II, III, IV, V, Ia, IIa, IIIa, IVa, Va are selected by the sequence switches circuit  304  and by the current switches circuit  306 . During a current spinning operation, couplings to the ten selected groups of contacts I, II, III, IV, V, Ia, IIa, IIIa, IVa, Va are changed sequentially to achieve the above four current spinning phases, A, B, C, D, in any phase sequence. Thereafter, a different ten groups of electrical contacts can be selected and the four current spinning phases can be sequentially chosen for each selected four groups of electrical contacts. 
     In other embodiments, current spinning is not used and any one of the phases A, B, C, or D can remain static as different four groups of electrical contacts are selected. 
     Current spinning can provide lower average offset voltage than only one selected phase, even though each phase already has a high degree of electrical symmetry and an associated low offset voltage. 
     In  FIGS. 24-26 , groups of electrical contacts are equally spaced between first and second CVH sensing elements (or circular arrangements of separate vertical hall elements as in  FIG. 1A ). In other embodiments, the spit is not equal. In still other embodiments, more CVH sensing elements can provide the two phases indicated or more than the two phases indicated. 
     In some embodiments, four CVH sensing elements provide all four of the phases 0, 90, 180, 270. 
     CVH sensing elements are describe in conjunction with figures above. In embodiments, the CVH sensing elements can be replaced with separate vertical Hall elements as in  FIG. 1A . 
     All references cited herein are hereby incorporated herein by reference in their entirety. 
     Having described preferred embodiments, which serve to illustrate various concepts, structures and techniques, which are the subject of this patent, it will now become apparent that other embodiments incorporating these concepts, structures and techniques may be used. Accordingly, it is submitted that the scope of the patent should not be limited to the described embodiments but rather should be limited only by the spirit and scope of the following claims. Elements of embodiments described herein may be combined to form other embodiments not specifically set forth above. Various elements, which are described in the context of a single embodiment, may also be provided separately or in any suitable subcombination. Other embodiments not specifically described herein are also within the scope of the following claims.