the description below in conjunction with the accompanying drawings will further describe various embodiments of the present invention . fig2 shows a schematic diagram of a single - chip full - bridge magnetic field sensor of the present invention . the sensor comprises a substrate 1 , a wheatstone full - bridge deposited on the substrate 1 , eight shielding structures 42 and four pads 7 - 10 . the first bridge comprises reference arm r 1 and sense arm s 1 , while the second bridge arm comprises reference arm r 2 and sense arm s 2 ; the reference arms r 1 and r 2 include three reference element strings each respectively , three in the first reference arm , and three in the second reference arm ; the sense arms s 1 and s 2 include three sense element strings each respectively , three in the first sense arm , and three in the second sense arm . each reference element string and each sensor element string are composed of one or more identical magnetoresistive sense elements that are electrically interconnected . as shown in fig2 , reference arm r 1 and sense arm s 1 , reference arm r 2 and sense arm s 2 are composed of six identical magnetoresistive sensor elements . the first reference element string and the first sense element string have the same longitudinal spacing . the second reference element string and the second sense element string have the same longitudinal spacing . the first reference element string and the first sense element string have the same spacing between every two adjacent elements . the second reference element string and the second sense element string have the identical spacing between every two adjacent elements , and this spacing is defined as l . the first reference element string and the second reference element string are the nearest neighboring strings between the two bridge arms . the distance between the first reference element string and the second reference element string is 2 l . shield structure 42 has a specified gap 45 , and the size of the gap is the same for all adjacent shielding structures . each first reference element string and second reference element string sits under a corresponding shielding structure 42 , and each first sense element string and second sense element string is located in a gap 45 . there are four wire bond pads 7 - 10 , where the first wire bond pad 7 is for bias voltage , the second wire bond pad 9 and the third wire bond pad 10 are for output signals , and the fourth wire bond pad 8 is for grounding . reference arm r 1 , reference arm r 2 , sense arm s 1 , and sense arm s 2 each have a first end and a second end . the first bond pad 7 is connected to the second end of reference arm r 2 and the first end of sense arm s 1 . the second wire bond pad 9 is connected to the second end of reference arm r 1 and the second end of sense arm s 1 . the third wire bond pad 10 is connected to the first end of sense arm s 2 and the first end of reference arm r 2 . the fourth wire bond pad 8 is connected to the second end of sense arm s 2 and the first end of reference arm r 1 . the six sensing elements in each string are also electrically interconnected . there are several differences compared to fig1 : the present invention uses at least three shielding structures , as shown in fig2 there are 8 shielding structures 42 , whereas fig1 only shows two shielding structures 2 . the present invention has at least two gaps , and fig2 shows 7 gaps 45 , whereas fig1 only shows one gap 5 . each sensing arm includes at least two rows / columns of sense element strings 43 , each reference arm includes at least two rows / columns of reference element strings 44 . fig2 shows 6 sense element strings 43 and 6 reference element strings 44 , and fig1 shows only one of each type of string per arm . sense element strings 43 and reference element strings 44 are interleaved , where each sensing element string 43 and reference element string 44 are separated by a distance l . for an even number of shields 42 as shown in fig2 , in the middle between the adjacent reference element strings , the spacing is 2 l . for an odd number of shielding structures 42 as shown in fig3 , there can be two adjacent sense element strings , and these would be separated by distance 2 l . the length l is small , preferably from 20 um to 100 um . the sense element strings 43 and the reference element strings are composed of a multiplicity of amr , gmr , or tmr magnetoresistive elements that are electrically interconnected . each reference element string 44 has a corresponding shielding structure 42 , and each sense element string 43 sits in the gap 45 between adjacent shielding structures 42 . the shielding structures are composed a soft ferromagnetic alloy containing but not limited to ni , fe , co , si , b , ni , zr , or al . the sense arms , the reference arms , the wire bond pads 7 - 10 , and all 6 conductors are electrically connected . preferably the chip size is 0 . 5 mm × 0 . 5 mm , which is smaller than existing technology . according to requirements of different applications , the chip can be made smaller than 0 . 5 mm × 0 . 5 mm . the substrate 1 may contain cmos , where the cmos , sensing arm , reference arm , and the wire bond pads 7 - 10 , may be lithographically printed directly on the substrate . when the direction of the applied magnetic field 101 is parallel to the short dimension of the shield structure 42 , theoretically , the magnetization curves should appear as shown in fig4 . curve 11 is for a low aspect ratio shielding structure , and curve 12 is for a high aspect ratio shielding structure . as can be seen from fig4 , compared with the low aspect ratio shield structure , the use of a long strip shielding structure has a higher saturation point , and a better linearity . fig5 shows the magnetic field distribution around the reference element strings 44 and the sense element strings 43 shown in fig2 . form this figure , it can be observed the field present in the gaps 45 between shielding structures 42 acting on sense element strings 43 is increased , and the magnetic field under the shields 42 in the location of reference element strings 44 is decreased . fig6 shows the induced magnetic field at the position of the sense element strings 43 and the reference element strings 44 for the geometry in fig2 . b sns is defined as the field at the location of the sense element strings 43 , and b ref is defined as the field at the location of the reference element strings 44 , when the external magnetic field is b ext = 100 g . from this figure we can deduce : b sns = 160 g , b ref = 25 g . then according to equations ( 1 ) and ( 2 ) given below , we can determine the gain factor a sns and attenuation factor a ref . given b sns = 160 g , b ref = 25 g the above two equations indicate a sns = 1 . 6 , a ref = 0 . 25 . the bigger the ratio of a sns / a ref , the better the shielding design is , ideally a sns / a ref & gt ; 5 is acceptable for high sensitivity . in this case a sns / a ref = 1 . 6 / 0 . 25 = 6 . 4 & gt ; 5 , meaning that the invention has achieved high sensitivity and the shielding design is quite good . in the above design sense element string 43 is used for both the first and second sense element string , and reference element string 44 is used for both the first and second reference element strings . in this present example , the magnetoresistive sensors are aligned along the horizontal direction ( arranged as rows ), the first sense element strings and the first reference element strings are arranged in alternating rows , the second sense element strings and the second reference element strings are arranged in alternating rows , the shielding structures are aligned along the horizontal direction , and the gaps are aligned along the horizontal direction . obviously , when the magnetoresistive sensor elements are aligned along the longitudinal direction ( arranged as columns ) the first reference element string and first sensing element string are in alternating columns , and the second reference element string and second sense element string are arranged in columns . the shielding structures are aligned in the vertical direction , and the gaps are aligned in the vertical direction . the vertical arrangement is within the scope of the invention . fig3 shows another example implementation of the single - chip full - bridge magnetic field sensor . the difference with the fig2 example is there are 7 shielding structures 42 , the two end shielding structures have reference element strings beneath them , and the center shielding structure has no reference element string beneath it . the first bridge arm and the second bridge arm have the first and second sense element strings at their common border , where the gap between the first sense element string and the second sense element string is 2 l . fig1 shows another implementation of the present invention . the sensor consists of a substrate 1 , and onto the substrate a wheatstone half - bridge is deposited , it has 6 shielding structures 42 , and three wire bond pads 7 - 9 . the wheatstone half - bridge includes a reference arm r 1 and a sense arm s 1 , each individually including 3 horizontal reference element strings 44 and 3 horizontal sense element strings 43 , each reference element string 44 and each sense element string 43 includes a multitude of identical magnetoresistive sensing elements electrically interconnected , and there are 6 magnetoresistive elements per string shown in the figure . the sense element strings 43 and the reference element strings 44 are spaced vertically with respect to each other , and the spacing between the adjacent reference element strings 44 and sense element strings is l . the adjacent shielding structures 42 have a gap 45 between them , where the length and width of the gap 45 are different . each reference element string 44 is located beneath a corresponding shielding structure 42 , and each sense element string is located in the gap 45 . the sensing element strings 43 and the reference element strings may be composed of one of amr , gmr , or tmr electrically interconnected magnetoresistive sensing elements . the shielding structures 42 are composed of soft ferromagnetic alloys of one or more of the elements ni , fe , co , si , b , ni , zr , or al , but they need not be limited by these specific elements . the 6 elements in each sensor are electrically interconnected . in this example , the magnetoresistive sensor elements are aligned along the horizontal direction ( arranged in rows ), each sense element string and each reference element string alternate along the vertical direction , the shielding structures are aligned in the horizontal direction , and the gaps have a long dimension along the horizontal direction . alternatively , the magnetoresistive sensor elements may be aligned along the vertical direction ( arranged in columns ), each sense element string and each reference element string alternate along the horizontal direction , the shielding structures are aligned in the vertical direction , and the gaps have a long dimension along the vertical direction . alignment along the vertical direction is therefore not outside the scope of this invention . in the present embodiment , a single - chip magnetic sensor bridge includes three pads 7 - 9 , the three pads are a first pad 7 for supplying a bias voltage , a second pad 9 for outputting a signal , and a the third pad 8 for grounding . reference arm r 1 has a first end and a second end , and sense arm s 1 has a first end and a second end . the first wire bond pad 7 is electrically connected with the first end of reference arm r 1 , the third wire bond pad 8 is electrically connected with the first end of sense arm s 1 , and the second wire bond pad 9 is electrically connected with the second end of reference arm r 1 and the second end of sense arm s 1 . the difference between this example and the second example is the use of a quasi wheatstone bridge circuit . this single - chip magnetic field sensor bridge contains three wire bond pads , and of the three wire bond pads the first is used for grounding , while the second wire bond pad and the third wire bond pads are used for signal outputs . the wheatstone quasi - bridge includes two identical current sources i 1 and i 2 , a reference arm r 1 , and a sense arm s 1 . the current sources i 1 and i 2 , the reference arm r 1 and the sense arm s 1 each have a first end and a second end . the first wire bond pad is electrically connected with the first end of reference arm r 1 , the first end of sense arm s 1 , and the first end of the two current sources i 1 and i 2 . the second wire bond pad is electrically connected with the second end of reference are r 1 and the second end of current source i 2 . the third wire bond pad is electrically connected with the second end of sense arm s 1 and with the second end of current source i 1 . single - chip magnetic field sensor bridges may be designed to have linear or multilayer type response . for a single - chip magnetic field sensor bridge with linear response the sense element string 43 and the reference element string 44 are comprised of mtj elements , wherein the mtj elements have the following features : a pinning layer , a tunnel barrier , and a ferromagnetic free layer . the pinned layer includes at least one antiferromagnetic layer and at least one ferromagnetic layer , the antiferromagnetic layer can consist of irmn , ptmn , or other materials , the material for the ferromagnetic layers can be alloys of co . fe , ni , b , pd , tb , or hf , although it need not be limited to this set of materials . the pinned layer may also include a laminated layer , comprising two ferromagnetic layers magnetically coupled using a non - magnetic layer , the tow ferromagnetic layers can be nife , nifeo , cofe , co , but not limited to these materials , and the non - magnetic coupling layer is usually ru . the free layer material can be alloys of co , fe , ni , b , pd , tb , or hf , although it need not be limited to this set of materials . the magnetization of the pinned layer is presumed to be rigidly fixed in its direction , and it does not change orientation as with the external magnetic field , whereas , the magnetization of the free layer changes in response to the external magnetic field . in the absence of an external magnetic field , the free layer magnetization needs to be aligned perpendicular to the pinned layer magnetization , this can be achieved using additional layers above the free layer , by the use of permanent magnets , or using shape anisotropy . the tunnel barrier is an insulating material , usually in the form of an oxide , such as al 2 o 3 or mgo . preferably , the mtj has the following structure : silicon substrate / seed layer / pinned layer / tunnel barrier layer / free layer / bias layer / capping layer , wherein the pinned layer is ptmn / cofe / ru / cofeb , the tunnel barrier layer material is mgo , the free layer cofeb / nife , and the bias layer material is irmn . the transfer curve 20 of a single - chip magnetic field sensor element is shown in fig7 . when the applied magnetic field direction 101 and the pinning layer magnetization 19 are parallel , and the magnitude of the applied magnetic field is greater than − bs + bo ( 25 ), the magnetization direction of the magnetic free layer 18 aligns parallel with the applied magnetic field direction 101 , and thus parallel with the pinned layer magnetization direction 19 , such that the mtj element will be in the low resistance state r l ( 21 ). when the applied magnetic field direction 101 and the pinning layer magnetization 19 are anti - parallel , and the magnitude of the applied magnetic field is greater than bs + bo ( 26 ), the magnetization direction of the magnetic free layer 18 aligns parallel with the applied magnetic field direction 101 , and thus anti - parallel with the pinned layer magnetization direction 19 , such that the mtj element will be in the low resistance state r h ( 22 ). when the external applied magnetic field 101 has a magnitude of bo ( 23 ), the magnetization direction of the free layer 18 is perpendicular to the magnetization direction of the pinned layer 19 , then the mtj magnetoresistance will be at the midpoint between r l ( 21 ) and r h ( 22 ), that is ( r l + r h )/ 2 . − bs + bo ( 25 ) to bs + bo ( 26 ) represents the operating range of the single - chip magnetic field sensor bridge . from the figure we can see , curve 21 is linear from − bs + bo ( 25 ) to bs + bo ( 26 ), with slope ( r h − r l )/ 2 b s = δr / δb ( 4 ) from − bs + bo ( 25 ) to bs + bo ( 26 ) the magnetoresistance may be represented r ( b ext )= r l +( δ r / δb )* b ext ( 5 ) then according to equations ( 1 ) and ( 2 ), the magnetoresistance of the sense and reference arms is : r sns ( b ext )= r l + a sns *( δ r / δb )* b ext ( 6 ) r ref ( b ext )= r l + a ref *( δ r / δb )* b ext ( 7 ) the sense element string 43 and the reference element string 44 may also be composed of gmr spin - valve materials , with the same response curve as shown in fig6 . fig7 shows the sensor has good linearity . fig8 shows the schematic diagram for a linear single - chip full - bridge magnetic field sensor . in the figure , there are two sense arms s 1 ( 52 ) and s 2 ( 52 ′) and two reference arms r 1 ( 53 ) and r 2 ( 53 ′) electrically interconnected to form a full bridge . the sense arms s 1 ( 52 ) and s 2 ( 52 ′) and reference arms r 1 ( 53 ) and r 2 ( 53 ′) may be composed of amr , gmr , or tmr magnetoresistive elements , and if present , the direction of the pinning layer is the same in all bridge arms . in this structure , there are four wire bond pads , a wire bond pad for bias voltage v bias , two half - bridge voltage outputs ( v 1 , v 2 ) and a wire bond pad for grounding gnd . v bias is connected to an end of reference arm r 1 ( 53 ) and an end of sense arm s 1 ( 52 ), v 2 is connected to the an end of sense arm s 1 ( 52 ) and to an end of reference arm r 2 ( 53 ′), v 1 is connected to and end of reference arm r 1 ( 53 ) and an end of sense arm s 2 ( 52 ′), and gnd is connected with an end of sense arm s 2 ( 52 ′) and an end of reference arm r 2 ( 53 ′). the full - bridge sensor output may be written v = v ⁢ ⁢ 1 - v ⁢ ⁢ 2 = r sns r sns + r ref ⁢ v bias - r ref r sns + r ref ⁢ v bias = ( a sns - a ref ) ⁢ ( δ ⁢ ⁢ r δ ⁢ ⁢ b ) ⁢ b 2 ⁢ r l + ( a sns + a ref ) ⁢ ( δ ⁢ ⁢ r δ ⁢ ⁢ b ) ⁢ b ⁢ v bias ( 8 ) v v bias = ( a sns - a ref ) ⁢ ( δ ⁢ ⁢ r δ ⁢ ⁢ b ) ⁢ b 2 ⁢ r l + ( a sns + a ref ) ⁢ ( δ ⁢ ⁢ r δ ⁢ ⁢ b ) ⁢ b ( 9 ) for very small external magnetic field , that is when b is very small , the sensitivity ( 9 ) may be approximated fig9 shows a schematic diagram for a half - bridge single - chip linear magnetic field sensor . in this figure , there is a sense arm s 1 ( 52 ) and a reference arm r 1 ( 53 ), electrically interconnected as a half - bridge circuit . the sense arm s 1 ( 52 ) and the reference arms r 1 ( 53 ) may be composed of amr , gmr , or tmr magnetoresistive elements , and if present , the direction of the pinning layer is the same in all bridge arms . in this structure , there are three wire bond pads , a wire bond pad for bias voltage v bias , a half - bridge voltage output v 1 , and a wire bond pad for grounding gnd . vbias is connected to an end of reference arm r 1 ( 53 ), v 1 is connected to an end of sense arm s 1 ( 52 ) and to an end of reference arm r 1 ( 53 ), gnd is connected with an end of sense arm s 1 ( 52 ). the full - bridge sensor output may be written v v bias = r l + a sns ⁡ ( δ ⁢ ⁢ r δ ⁢ ⁢ b ) ⁢ b 2 ⁢ r l + ( a sns + a ref ) ⁢ ( δ ⁢ ⁢ r δ ⁢ ⁢ b ) ⁢ b ( 12 ) for very small external magnetic field , that is when b is very small , the sensitivity ( 12 ) may be approximated from ( 9 ) and ( 12 ) it can be seen , when the magnetic field is large , that is the magnetic field strength b is large , the above two half - bridge and full - bridge expressions for magnetic field strength b as a function of v / v bias are no longer linear , and this restricts the operating range of the sensors , for this reason , the circuit drawn in fig1 for a linear quasi - bridge magnetic field sensor is provided in order to give improved performance . this circuit comprises two current sources i 1 59 and 12 59 ′, a sense arm s 1 52 and a reference arm r 1 53 . these two current sources are equal in magnitude , both i bias . the sense arm s 1 52 and reference arm r 1 53 may be composed of amr , gmr , or mtj magnetoresistive sensor element , and if present the direction of magnetization pinned layer are the same in each arm . the structure has three pads , one of which is used as a ground terminal gnd , the other two as a half - bridge voltage output terminals ( v 1 , v 2 ), wherein gnd electrically connected to one end of the two current sources , one end of sense arm s 1 52 , and one end of reference arms r 1 53 . v 1 is connected to the other end of current source i 1 59 and sense arm s 1 59 . v 2 is connected to the other end of current source i 2 59 ′ and reference arm r 1 53 . the total output voltage of this circuit is v = v ⁢ ⁢ 1 - v ⁢ ⁢ 2 = ( a sns - a ref ) ⁢ ( δ ⁢ ⁢ r δ ⁢ ⁢ b ) ⁢ b * i bias ( 14 ) from ( 15 ) it can be seen that the sensitivity v / i bias has a linear relationship with the magnetic field strength b . if i bias = v bias / 2r l , then the quasi - bridge magnetic field sensor and the full - bridge magnetic field sensors have identical sensitivity , but the quasi - bridge magnetic field sensor has better linearity , making it more suitable for wide dynamic range sensing . in another implementation of this invention , a multilayer - response magnetoresistive element may be used , here the reference element string 44 and the sense element string 43 are utilize mtj elements , wherein the mtj elements have the following properties : a pinning layer , a tunnel barrier , and a ferromagnetic free layer . the pinning layer includes an antiferromagnetic layer and at least one ferromagnetic layer , the antiferromagnetic layer is usually irmn or ptmn , although other antiferromagnetic materials may be used , and the ferromagnetic layers may be alloys of co , fe , ni , b , pd , tb or hf , or other elements . the pinning layer magnetization is intended to be rigidly fixed in one orientation , so that it does not change in response to the applied magnetic field , but the magnetization direction of the ferromagnetic free layer is designed to change in response to the applied magnetic field . in the case of zero applied external magnetic field , the pinned and free layer magnetization directions are anti - parallel , and this can be achieved using stray flux coupling between the pinned and free layers , or by means of an additional pinned layer utilizing a synthetic antiferromagnet in the free layer , or by adding another antiferromagnet directly on top of the free layer . the tunnel barrier is composed of an insulating material , usually in the form of an oxide , such as al 2 o 3 or mgo . when the applied magnetic field is small , say b & lt ; 200 g , then the stray field from the pinned layer may force the free layer to align in the anti - parallel orientation state . the preferred mtj structure is given below : a silicon substrate / seed layer / pinned layer / tunnel barrier layer / free layer / capping layer . wherein the pinning layer is irmn / cofe / cofeb , the tunnel barrier layer material is mgo , the free layer of cofeb / nife . when the applied magnetic field is relatively large , such as the magnetic field intensity bs & gt ; 200 g , the use of a synthetic antiferromagnet in the pinned layer would be beneficial , and then an anti - ferromagnetic layer disposed above the free layer in the magnetization direction of the free layer in order to make it antiparallel with the pinned layer magnetization direction is necessary . in this case the structure of the mtj element is preferably as follows : silicon substrate / seed layer / pinned layer / tunnel barrier layer / free layer / antiferromagnetic layer / protective layer , wherein the pinned layer is irmn / cofe / ru / cofeb , the tunnel barrier layer is mgo , the free layer as cofeb / nife , capped with antiferromagnetic material irmn . the transfer curve of a multilayer magnetic field bridge sensor is given in fig1 . when the applied magnetic field 101 is aligned parallel to the pinning layer magnetization direction 19 , and if the magnetic field has a strength greater than − bs 31 or bs 32 , then the magnetic field 101 and the free layer magnetization direction 18 are parallel , and additionally they are parallel to the pinned layer magnetization direction 19 , such that the mtj sensor element is in the low resistance state , r l 28 . when the applied magnetic field is 0 , the magnetization of the free layer 18 and the magnetization of the pinned layer 19 are anti - parallel , such that the mtj sensor element is in the high resistance state , r h 27 . the measurement range of the multilayer single - chip magnetic fied sensor bridge is from − bs 31 to bs 32 . from the figure we can see , that between − bs 31 and bs 32 the curves 29 , 30 are linear with slope given by ( r l − r h )/ b s δ = r / δb ( 16 ) from − bs 31 to bs 32 the magnetoresistance may be written as r ( b ext )= r h −( δ r / δb )*| b ext | ( 17 ) from equations ( 1 ) and ( 2 ), the magnetoresistance of each bridge arm may be written : r sns ( b ext )= r h − a sns *( δ r / δb )*| b ext | ( 18 ) r ref ( b ext )= r h − a ref *( δ r / δb )*| b ext | ( 19 ) in addition , the sense element string 43 and the reference element string 44 may be a gmr multilayer film structure , that is , the multilayer structure cofe / cu / cofe configured the same as its response curve as that of fig1 . as can be seen from fig1 , the sensor has good linearity . similar to the linear single - chip bridge magnetic field sensors , the multilayer single - chip magnetic field bridge sensor can be prepared in three manners , a referenced full - bridge , a referenced half - bridge , and a quasi - bridge . the calculation of the response of these three different single - chip sensor bridges is similar to those previously derived for linear sensor bridges , and for the sake of brevity , only the solutions are summarized below : as can be seen from the above three formulas , the absolute value of the applied magnetic field b is used , suggesting the transfer curves are symmetric . in addition , the quasi - bridge and other two bridge structures have similar performance . the half - bridge , full - bridge , and quasi - bridge can utilize a silicon substrate containing cmos , such that a single chip sensor bridge including cmos may be implemented . the foregoing is only describes preferred embodiments of the present invention . it does not limit the present invention . those skilled in the art , can produce various modifications and changes of the present invention . any modification within the spirit and principles of the present invention , including any changes , equivalent replacements , or improvement are considered within the scope of the present invention .