Regulator circuit having a bandgap generator coupled to a voltage sensor, and method

A regulator (200) has a pass transistor (250) for transferring a voltage from an input (202) to an output (205). A voltage sensor (231) at the output (205) carries a PTAT current (I.sub.A) A generator with diode or transistor chains (271, 272) derives a voltage V.sub.RES from serially coupled base-emitter path of transistors (381-386) having different current densities. The generator (271, 272) and a transistor pair (273) form a bandgap reference circuit. Each chain (271, 272) has transistors alternatively of a first type (pnp) and second type (npn). The value ratio (R.sub.4 /R.sub.3) of resistances (240, 230) in the voltage sensor (231) can be chosen such, that the noise components of the voltage V.sub.OUT at the output (205) is low.

FIELD OF THE INVENTION
 The present invention generally relates to electronic circuits, and, more
 particularly, to a voltage regulator, and to a method therefor.
 BACKGROUND OF THE INVENTION
 In electronic circuits, voltage regulators provide substantially constant
 supply voltages for voltage sensitive portions of the circuit. Usually,
 regulators have a pass transistor to change a preferably low voltage drop
 between input and output, a voltage sensor at the output and a feedback
 unit which controls the pass transistor. The output voltage (e.g.,
 constant 5 volts) should be independent of temperature, so that a
 temperature compensation circuit is sometimes required.
 U.S. Pat. No. 5,686,821 to Brokaw [1] teaches a regulator with a
 two-resistor voltage sensor carrying a current proportional to the
 absolute temperature (PTAT). The resistors (R9 and R10 in FIG. 4 of [1])
 have a value ratio related to a voltage provided by a bandgap reference.
 Positive and negative temperature coefficients of the current and the
 bandgap voltage compensate each other. A further useful reference is:
 Horowitz, P., Hill, W.: "The art of electronics", Second Edition,
 Cambridge University Press, chapter 6.15: "Bandgap (V.sub.BE) reference",
 on pages 335-341 [2].
 The output voltage should also have low noise components. Also, the
 feedback unit should not cause the regulator to oscillate. Regulators can
 have so-called bypass capacitors which function as noise filters and pole
 suppression filters. But, the bypass capacitor increases the turn-on time
 of the regulator. Capacitors are also not wanted because of their physical
 size.
 The present invention seeks to provide regulators which mitigate or avoid
 these and other disadvantages and limitations of the prior art.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
 A regulator according to the present invention achieves features, such as,
 for example, substantial temperature independence, low noise, and
 stability in a low cost design. Sensor resistors in the regulator of the
 present invention can have value ratios which are substantially different
 than the value ratios in prior art bandgap references. The bandgap
 reference generator has multiple serially coupled base-emitter paths. This
 approach has the advantage that the noise density of the output voltage is
 low without the need for an external bypass capacitor.
 FIG. 1 illustrates a simplified schematic diagram of regulator circuit 100
 (hereinafter regulator 100) according to the present invention. Regulator
 100 receives an unregulated input voltage V.sub.IN (between terminals 102
 and 101) and provides a regulated output voltage V.sub.OUT (between
 terminals 105 and 101) to, for example, a voltage sensitive circuit
 portion (not shown). Regulator 100 comprises transistors 150 and 180,
 operational amplifier 160 ("controller"), resistor 110 having a value
 R.sub.1 ("magnitude"), resistor 120 having a value R.sub.2, resistor 130
 having a value R.sub.3, resistor 140 having a value R.sub.4, and multiple
 junction voltage generator 170 (hereinafter generator 170, dashed frame).
 As those of skill in the art understand, for resistors (or "impedances")
 110, 120, 130, and 140 any electrical components can be used that exhibits
 a resistance to the flow of current. Such impedances can be passive or
 active devices.
 Transistor 150 is the pass transistor in the function of a variable
 resistance. An emitter (letter "E") of transistor 150 is coupled to input
 terminal 102 and a collector (letter "C") is coupled to output terminal
 105. A base (letter "B") of transistor 150 is coupled to output 163 of
 operational amplifier 160. The collector of transistor 150 is also coupled
 to reference terminal 101 via resistor 110, node 115 and resistor 120.
 Transistor 180 has a collector coupled to input terminal 102 and an
 emitter coupled to reference terminal 101 via node 135, resistor 130, node
 145, and resistor 140. Resistors 130 and 140 form voltage sensor 131, and
 resistors 110 and 120 form voltage sensor 111 (dashed frames). The base of
 transistor 180 is coupled to node 115.
 Preferably, generator 170 has voltage sources 171, 173 and 172 serially
 coupled across resistor 130 (nodes 135 and 145). Voltage source 173 is in
 parallel coupled to inputs 162 and 161 of operational amplifier 160. The
 arrangement of voltage sources 171-173 in generator 170 is illustrated as
 an example to indicate that a fraction V.sub.AMP of a voltage V.sub.RES
 across resistor 130 goes into operational amplifier 160. Voltage sources
 171 and 172 are, preferably, implemented by pn-junction chains (e.g., see
 FIG. 2). Preferably, inputs 162 and 161 of operational amplifier 160 are
 inverting ("-") and non-inverting ("+") inputs, respectively. This is
 convenient, but not essential for the present invention.
 The term `transistor` is intended to include any device having current
 electrodes (e.g., C and E) and control electrodes (e.g., B), such as for
 example, bipolar devices. Other types of transistors can also be used.
 Instead of transistor 180, any other pn-junction can also be used. The
 term "pn-junction" is intended to include junctions from a p-doped
 semiconductor to an n-doped semiconductor (e.g., base to emitter of an npn
 transistor) or vice versa from n-doped to p-doped semiconductors (e.g.,
 base to emitter of a pnp transistor).
 Regulator 100 is intended to be a non-limiting example for illustration. A
 person of skill in the art is able based on the following description to
 make changes without departing from the scope of the present invention.
 In FIG. 1, voltages and currents are illustrated by arrows. The direction
 of the arrows is chosen only for convenience of explanation. Unless
 otherwise noted, voltages are referred to reference terminal 101 (labeled
 "GND" for "ground"). For example, the voltage V.sub.OUT refers to the
 voltage difference between output terminal 105 and reference terminal 101.
 A person of skill in the art is able to otherwise define currents and
 voltages. To have the following description applicable for different types
 of semiconductor devices (e.g., diodes, pnp-, npn-transistors), voltages
 are conveniently given in .vertline. .vertline. symbols for absolute
 values.
 Regulator 100 receives input voltage V.sub.IN at input terminal 102 and
 provides output voltage V.sub.OUT at output terminal 105 depending on the
 emitter-collector voltage V.sub.EC ("dropout voltage") of transistor 150,
 that is:
EQU .vertline.V.sub.OUT.vertline.=.vertline.V.sub.IN.vertline.-.vertline.V.sub.
 EC.vertline. (1)
 Persons of skill in the art know how to select transistors to keep
 .vertline.V.sub.EC.vertline. as small as possible. The pn-junction voltage
 across the base and emitter of transistor 180 is referred to as
 V.sub.BEQA.
 Voltage sensor 111 derives a measurement voltage V.sub.M (across resistor
 120) from output voltage V.sub.OUT. Part of V.sub.M is fed back to
 operational amplifier 160 which controls transistor 150. Using well known
 voltage divider relations and considering voltage V.sub.RES across
 resistor 130, output voltage V.sub.OUT can be estimated by the following
 equation:
 ##EQU1##
 Current I.sub.A =V.sub.RES /R.sub.3 flowing from the emitter of transistor
 180 to reference terminal 101 is preferably, proportional to the absolute
 temperature (PTAT). Therefore, the voltage (V.sub.RES +V.sub.R4) across
 resistors 130 and 140 (carrying I.sub.A) has, preferably, a positive
 temperature coefficient which compensates a negative temperature
 coefficient of V.sub.BEQA.
 To appreciate the advantages of the present invention, equation (2) is
 analyzed regarding parasitic noise voltages at
 .vertline.V.sub.OUT.vertline.. At node 115, the noise components of
 .vertline.V.sub.RES.vertline. appear multiplied by the ratio R.sub.4
 /R.sub.3. On the way to output terminal 105, the noise components of
 .vertline.V.sub.RES.vertline. are further multiplied by R.sub.1 /R.sub.2.
 A low ratio R.sub.4 /R.sub.3 would provide low noise, or, vice versa, a
 high ratio R.sub.4 /R.sub.3 would cause high noise. To have a low R.sub.4
 /R.sub.3 ratio, the voltage .vertline.V.sub.RES.vertline. should be high.
 According to the present invention, this is achieved with multiple
 serially coupled pn-junctions in generator 170.
 FIG. 2 illustrates a simplified schematic diagram of circuit 200 which is a
 preferred embodiment of regulator 100. In FIGS. 1-2, reference numbers
 101/201, 102/202, 105/205, 110/210, 115/215, 120/220, 130/230, 131/231,
 135/235, 140/240, 145/245, 150/250, 160/260, 161/261, 162/262, 163/263,
 171/271, 172/272, 173/273, 180/280 and symbols V.sub.IN, V.sub.RES,
 V.sub.EC, V.sub.BEQA, and I.sub.A stand for analogous components or
 signals. However, their function can differ as explained below. Among
 them, operational amplifier 260, voltage sensor 231, and chains 271, 272,
 273 (cf. voltage sources in FIG. 1) are illustrated by dashed frames.
 Circuit 200 further comprises transistors 361, 362, 363, 364, 365 and 366
 forming operational amplifier 260, transistors 371 and 372 forming pair
 273 (or "chain 273"), transistors 381, 383 and 385 forming chain 271,
 transistors 382, 384 and 386 forming chain 272, current sources 315, 369,
 391, 392, 393, 394, 395 and 396, and resistors 310, 320. In chains 271 and
 272, transistors 385/383/381 and 386/384/382, respectively, are serially
 coupled via their base-emitter paths. Preferably, these chain transistors
 are alternatively of opposite types, as, for example, first type (385),
 second type (383) and again first type (381) in chain 371. The terms
 "first type" (e.g., for npn- or pnp-transistors) and "second type" (e.g.,
 for pnp- or npn-transistors) are intended to distinguish complementary
 transistors of opposite conductivity. "First type" and "second type" can
 refer to either npn or pnp transistors, as the case may be.
 In the preferred embodiment of circuit 200, transistors 385, 381, 386 and
 382 are pnp-transistors ("first type"); and transistors 383 and 384 are
 npn-transistors ("second type"). The types of transistors which do not
 form a chain, are not important for the present invention. For example,
 transistors 250, 361, 362 and 366 are preferably pnp-transistors; and
 transistors 280, 363, 364, 371, 372, 365 are preferably npn-transistors.
 Current sources 315, 369, and 391 to 396 provide currents I.sub.P1,
 I.sub.P2, and I.sub.1 to I.sub.6, respectively. For convenience of
 explanation, these currents and current I.sub.A are directed to reference
 terminal 201. Persons of skill in the art can implement the current
 sources, for example, by transistors. Transistor 371 is conveniently
 referred to by index ".alpha."; and transistor 372 is referred to by index
 ".beta.". The voltage between the bases of transistors 371 and 372 is
 referred to as chain voltage V.sub.BB. Resistors 210, 220, 230, 240 have
 values R.sub.1, R.sub.2, R.sub.3, and R.sub.4, respectively (as in FIG.
 1); resistor 310 has value R.sub..alpha., and resistor 320 has value
 R.sub..beta..
 In the following explanation, the transistor electrodes are conveniently
 cited by the letters "C" for "collector", "E" for "emitters" or "B" for
 "base" in connection with the transistors number. FIG. 2 illustrates the
 letters at transistor 250. For example, "E-250" stands for "emitter of
 transistor 250". Plural terms are given as "Cs", "Es", and "Bs". The
 transistors are illustrated as discrete components. This convention is
 convenient for explanation and intended to include that (a) a single
 transistor can have multiple electrodes with similar function (i.e.,
 multiple E, multiple C, and multiple B) and that (b) two or more
 transistors can share electrodes (e.g., common E of two transistors).
 Input terminal 202 is coupled to E-250. C-250 is coupled to output terminal
 205. B-250 is coupled to C-366 and B-366 which form output node 263 of
 operational amplifier 260. Output terminal 205 is coupled to reference
 terminal 201 via resistors 210, node 215 and resistor 220. Node 215 is
 coupled to B-280. C-280 is coupled to input terminal 202. E-280 is coupled
 to reference terminal 201 via node 235, resistor 230, node 245 and
 resistor 240. In operational amplifier 260, B-361 is coupled to C-372 of
 chain 273 and forms input 261; and B-362 is coupled to C-371 of chain 273
 and forms input 262. Current source 369 is coupled between input terminal
 202 and a node of E-361 and E-362. Transistors 361 and 362 form a
 differential pair. The pair is further coupled to reference terminal 201
 via a current mirror. The mirror is formed by transistors 363 and 364
 coupled as follows: C-361 to C-363 and to B-363/B-364;
 C-362 to C-364, and E-363, E-364 to terminal 201. B-365 is coupled to
 C-362. E-365 is coupled to terminal 201. C-365 is coupled to C-366, B-366
 and B-250 (output 263). E-366 is coupled to terminal 202. Transistors 366
 and 250 also form a current mirror. Resistor 310 is coupled between input
 terminal 202 and C-371; and resistor 320 is coupled to C-372. E-371 and
 E-372 are coupled together to terminal 201 via current source 315. The
 opposite coupled base-emitter path of transistors 371 and 372 form chain
 273 having the chain voltage V.sub.BB. Chain 273 is coupled to chains 271
 and 273 through B-371 coupled to E-381 and B-372 coupled to E-382,
 respectively. Chain 371 is coupled to resistor 230 by B-385 at node 235;
 and chain 372 is coupled to resistor 230 by B-386 at node 245. Further, in
 chain 371, E-385 is coupled to B-383; and E-383 is coupled to B-381. In
 chain 372, E-386 is coupled to B-384; and E-384 is coupled to B-382.
 There are multiple current paths k=1 to K between terminals 202 and 201. In
 the example of FIG. 2, K=6. In FIG. 2, the paths (reference numbers
 301-306, or "30k") are surrounded by dashed frame 300. In each path, a
 current source and an emitter-collector path of a transistor are coupled
 between input terminal 202 and reference terminal 201.
 In path 1, current source 391 is coupled between terminal 202 and E-381;
 and C-381 is coupled to terminal 201. In path 2, current source 392 is
 coupled between terminal 202 and E-382; and C-382 is coupled to terminal
 201. In path 3, C-383 is coupled to terminal 202; and E-383 is coupled to
 terminal 201 via current source 393. In path 4, C-384 is coupled to
 terminal 202; and E-384 is coupled to terminal 201 via current source 394.
 In path 5, current source 395 is coupled between terminal 202 and E-385;
 and C-385 is coupled to terminal 201. In path 6, current source 396 is
 coupled between terminal 202 and E-386; and C-386 is coupled to terminal
 201.
 As explained above, the N.sub.1 =3 transistors 381, 383 and 385 (chain 371)
 of odd numbered paths 1, 3 and 5 are serially coupled with pn-junctions
 (base and emitter). The N.sub.2 =3 transistors 382, 384, 386 (chain 372)
 of even numbered paths 2, 4 and 6 are also serially coupled with
 pn-junctions. The numbers N.sub.1 and N.sub.2, are, preferably equal
 (N.sub.1 =N.sub.2 =N) so that the total number of chain transistors
 K=N.sub.1 +N.sub.2 is even. The example of circuit 200 in FIG. 2 is
 illustrated the present invention with N =3 transistors in each of chains
 371 and 372. This is convenient, but not essential for the present
 invention.
 Transistors 381 to 386 have emitter areas A.sub.1 to A.sub.6, respectively
 (A.sub.k for transistor 38k). Currents I.sub.1 to I.sub.6 flow through
 transistors 381 to 386, respectively (I.sub.k for 38k). Conveniently,
 currents I.sub.k and areas A.sub.k are chosen such, that current densities
 I.sub.k /A.sub.k of neighboring paths k and (k+1) differ. Current density
 ratios Y.sub.qp between any pairs of transistors "q" and "p" among
 transistors 381-386 and 371/372 can be defined as:
 ##EQU2##
 For example, Y.sub.12 is the density ratio between transistors 391 and 392;
 and Y.sub..alpha..beta. the ratio between transistors 371 and 372.
 Therefore, base-emitter voltages V.sub.BE1 to V.sub.BE6 of transistors 381
 to 386, respectively, are also different. The voltage V.sub.RES across
 resistor 230 calculated using the mesh law for chains 371, 373 and 372 as
 follows:
EQU V.sub.RES +V.sub.BE5 +V.sub.BE3 +V.sub.BE1 -V.sub.BB -V.sub.BE2 -V.sub.BE4
 -V.sub.BE6 (4)

##EQU3##
 The base-emitter voltages V.sub.BE of transistors of first and second types
 have different signs. For example, V.sub.BEk of pnp-transistors 381, 382,
 385, 386 are negative (V.sub.BEk &lt;0); and V.sub.BEk of npn-transistors 383
 and 384 are positive (V.sub.BEk &gt;0). V.sub.BE.alpha. of npn-transistor 371
 and V.sub.BE.beta. of npn-transistor 372 are also positive. Therefore,
 V.sub.BE -voltages within chains 371 and 372 partly compensate each other.
 This is an important aspect of the present invention. Writing
EQU V.sub.BB =V.sub.BE.alpha. -V.sub.BE.beta. (6)
EQU equation (5) can be expressed as: (7)
EQU V.sub.RES =-V.sub.BE.alpha. +V.sub.BE.beta. +V.sub.BE1 -V.sub.BE2
 +V.sub.BE3 -V.sub.BE4 +V.sub.BE5 -V.sub.BE6 V.sub.RES
 =-V.sub.BE.alpha..vertline.+.vertline.V.sub.
 BE.beta..vertline.-.vertline.V.sub.BE1.vertline.+.vertline.V.sub.BE2
 +.vertline.V.sub.BE3.vertline.-.vertline.V.sub.BE4.vertline.-"V.sub.
 BE5.vertline.+.vertline.V.sub.BE6.vertline. (8)
 V.sub.RES depends also on the current density ratios Y.sub.qp and on the
 temperature voltage V.sub.T as follows:
 ##EQU4##
 wherein "In" stands for logarithm naturalis operation and symbols "*" and
 ".PI." stand for multiplication. For convenience, superscript index (m)
 also identifies transistor pairs. M is the number of transistor pairs
 which have density ratios Y.sub.qp. Preferably, M is an even number. M is
 conveniently half the number of transistors in chains 371 and 372 (e.g.,
 K=6) plus 2 for transistors 371/372, that is
EQU M=K/2+2 (10)
EQU M=6/2+2=4 (11)
 as shown for example in circuit 200. Temperature voltage V.sub.T is known
 in the art and described e.g., in [2] as
EQU V.sub.T =k*T/e.sub.0, (12)
 with k=1.38*10.sup.-23 Joule/Kelvin, e.sub.0 =1.60*10.sup.-19 Coulomb, and
 T the absolute temperature in Kelvin. For T=300 K, VT is around 26 mV
 (millivolts).
 As mentioned above, the current densities are conveniently chosen such that
 (V.sub.RES +V.sub.R4) has a positive temperature coefficient to compensate
 the negative temperature coefficient of V.sub.BEQA.
 Current density ratios Y.sub.qp can have any positive values of integers
 (e.g., 1, 2, 3 . . . ) or real numbers (e.g., 0.25, 4.25). A convenient
 value range for current density ratios Y.sub.qp is 1.ltoreq.Y.sub.qp &lt;100.
 Preferred values of Y.sub.qp are in the range 6.ltoreq.Y.sub.qp &lt;20. For
 example, and not intended to be limiting, current density ratios
 Y.sub.qp.sup.(m) are Y.sub..alpha..beta..sup.(1) =16 (transistors 371 and
 372), Y.sub.12.sup.(2) =9 (transistors 391 and 392), Y.sub.34.sup.(3) =16
 (transistors 393 and 394), Y.sub.56.sup.(4) =12 (transistors 395 and 396).
 According to equation (9), V.sub.RES is estimated as, approximately,
EQU V.sub.RES =26 mV*ln(16*9*16*12).apprxeq.270 mV (13)
 Preferably, the voltage (V.sub.RES +V.sub.R4) across resistors 230 and 240
 has similar absolute values as a transistor base-emitter voltage (e.g.,
 270 mV+330 mV=600 mV, R.sub.4 /R.sub.3.apprxeq.1.2 less than in prior
 art).
 Having described a preferred embodiment, the present invention is
 considered as regulator circuit 100 which comprises: (a) transistor 150
 which receives input voltage V.sub.IN (at E-150) and providing output
 voltage V.sub.OUT (at C-150); (b) voltage sensor 111 with resistor 110 and
 resistor 120 serially coupled for deriving a measurement voltage V.sub.M
 (e.g., voltage across resistor 120) from output voltage V.sub.OUT ; (c) a
 controller (e.g., operational amplifier 160) which receives measurement
 voltage V.sub.M (e.g., via transistor 180) and which controls transistor
 150; and (d) a multiple V.sub.BE voltage generator (e.g., by generator
 170, sensor 130, and transistor 180) which is coupled to resistor 110. In
 the multiple V.sub.BE bandgap reference, voltage V.sub.RES having a first
 temperature coefficient (e.g., positive coefficient) is provided by
 pn-junction chains (e.g., chains 271, 272) in which the pn-junctions
 (e.g., transistors 381-386) have different current densities.
 Further, the present invention can be described as a circuit with the
 following properties: Transistor 150 receives unregulated input voltage
 V.sub.IN at a first main terminal (e.g., at the emitter) and provides
 regulated output voltage V.sub.OUT to a second main terminal (e.g.,
 collector). Controller 160 controls transistor 150 via a transistor
 control terminal (e.g., a base). Resistor 110 and resistor 120 are
 serially coupled between the second main terminal of transistor 150 and
 reference terminal 101 via node 115. A pn-junction (e.g., between base and
 emitter of transistor 180) provides a voltage (e.g., V.sub.BEQA) with a
 first temperature coefficient (e.g., negative). A first junction terminal
 (e.g., a base) is coupled to node 115. Resistor 130 and resistor 140 are
 serially coupled between a second junction terminal (e.g., emitter) of the
 pn-junction and reference terminal 101. Resistors 130 and 140 are coupled
 to controller 160. A multiple junction voltage generator (chains 171-173)
 is coupled across resistor 130 and provides a second, compensating
 temperature coefficient (e.g., positive).
 Still further, the present invention can be described, e.g., in connection
 with circuit 100, which regulates output voltage V.sub.OUT by controlling
 a variable resistance (e.g., transistor 150) through a measurement signal
 (e.g., V.sub.M). The measurement signal is derived from output voltage
 V.sub.OUT by voltage sensor 130. Circuit 100 is characterized by: (a) A
 plurality of K current paths (e.g., 30k) each having a current source
 (e.g., 39k) and a pn-junction (e.g., transistors 38k). The pn-junctions
 have areas A.sub.k and different current densities J.sub.k =I.sub.k
 /A.sub.k so that some or all voltages V.sub.BEk across the pn-junctions
 are different. The pn-junctions k are serially coupled in pairs (e.g.,
 transistors 381/382, 383/384, 385/386). (b) A first number of pn-junctions
 is arranged in a first direction (e.g., base-emitter of pnp-transistors)
 and a second number of pn-junctions is arranged in a second, opposite
 direction (e.g., base-emitter of npn-transistors) so that only the
 differences of V.sub.BEk, but not their absolute values
 .vertline.V.sub.BEk.vertline. are combined (e.g., added) to voltage
 V.sub.RES present in voltage sensor 130 (e.g., across resistor 130).
 Having explained the function of regulator circuit 100 in detail above, a
 method of the present invention is described as a method for regulating
 output voltage V.sub.OUT. The method has the following steps: (a)
 receiving input voltage V.sub.IN by pass transistor 150 and providing
 output voltage V.sub.OUT as difference (e.g.,
 .vertline.V.sub.EC.vertline., see equation (1)) to input voltage V.sub.IN
 ; (b) providing a PTAT current to a voltage divider (e.g., sensor 131 with
 resistors 130 and 140); (c) providing voltage V.sub.RES from a plurality
 of serially coupled pn-junctions (e.g., transistors 381-386) to one part
 (e.g., resistor 130) of the voltage divider; and (d) measuring output
 voltage V.sub.OUT by the voltage divider and changing the difference
 accordingly.
 Preferably, in providing step (c), voltage V.sub.RES is derived from
 pn-junctions of transistors with alternatively opposite type (e.g.,
 pnp-transistors and npn-transistors), wherein in pairs of pn-junctions
 (e.g., of transistors 381-386), the current densities are different.
 It is an important advantage of the present invention, that a regulator
 without an external bypass capacitor can be implemented together with the
 voltage sensitive circuit portion on a single semiconductor substrate.
 It will be appreciated that although only one particular embodiment of the
 invention has been described in detail, various modifications and
 improvements can be made by a person skilled in the art based on the
 teachings herein without departing from the scope of the present
 invention. Accordingly, it is the intention to include such modifications
 as will occur to those of skill in the art in the claims that follow.