Abstract:
A method of detecting a relatively weak signal includes providing an oscillatory loop that can sustain oscillations, wherein the oscillatory loop has no more than one or an even-number of stages. The loop includes a first weakly bistable differential amplifier and a second weakly bistable differential amplifier. At least one of the first and second weakly bistable differential amplifiers is connected to a behavior perturbing coupling which is operative to introduce into the connected-to amplifier a behavior tipping signal where, even if the behavior tipping signal is much weaker than an oscillation of the one or multistage oscillatory loop, the relatively weak behavior tipping signal can nonetheless alter the oscillatory behavior of the multistage oscillatory loop in a distinguishable way. The system may be used for detecting outside a patient&#39;s body weak manifestations of internal nerve firings.

Description:
FIELD OF DISCLOSURE 
       [0001]    The present disclosure of invention relates generally to detection of analog signal events. The disclosure relates more specifically to detection of weak-magnitude analog signal events such as extracranial manifestations of intracranial neuron firings. 
       RELATED APPLICATIONS 
       [0002]    U.S. patent application Ser. No. 13/912,900 [Attorney Docket No. JING00001 US] filed on Jun. 7, 2013 by Mee H. CHOI et al. and which is originally entitled “Ultrasensitive and Compact Device for Noninvasive acquisition of Low Strength Bio Signals and Method of Using Same” is incorporated by reference herein. 
       RELATED TECHNOLOGY 
       [0003]    Typically, when it is desirable to detect and measure analog signals, an analog amplifier is used where the amplifier has a relatively smooth (e.g., linear) and continuous transfer characteristic (e.g., output voltage over input voltage) over the input signal range of interest. The sensitivity of such smooth-continuum analog amplifiers may be limited, for example due to circuit components used to provide the relatively smooth (e.g., linear) and continuous transfer characteristic. Yet more specifically, when amplification components such as transistors are operated in the linear or saturated regions of their IV (current versus voltage) characteristic curves, they tend to have less sensitivity to minute input perturbations than when operated near their threshold nonlinear region of operation. 
         [0004]    The inventive concept, at least in part, stems from the discovery that a relatively smooth (e.g., linear) and continuous transfer characteristic is not always necessary for signal detection and measurement. For example, signal detection and measurement may be performed in cases of sporadic analog events such as the extracranial manifestations of intracranial neuron firings, or other such non-continuous input events with weak signals. 
         [0005]    In some instances it is desirable to simultaneously detect and/or measure a large number of noncontinuous and weak signal input events. This may be achieved by distributing extracranial signal collectors at many locations around a patient&#39;s skull (e.g., 10 or more such collectors). In some instances, it is desirable for the signal collecting devices to be low cost and/or disposable. Some signal collecting device designs that have active electronic circuits incorporated in them call for a large number of circuit stages. This requirement for a large number of circuit stages leads to the disadvantage of individual signal collection devices being relatively large, more prone to failure (due to internal complexity) and high in cost. 
         [0006]    It is to be understood that this background of the technology section is intended to provide useful background for understanding the here disclosed technology and as such, the technology background section may include ideas, concepts or recognitions that were not part of what was known or appreciated by those skilled in the pertinent art prior to corresponding invention dates of subject matter disclosed herein. 
       SUMMARY 
       [0007]    In one aspect, the inventive concept pertains to a signal sensing device that includes a first weakly bistable differential amplifier, a second weakly bistable differential amplifier, and a behavior perturbing coupling connected to at least one of the first and second weakly bistable differential amplifiers. The first weakly bistable differential amplifier is provided as a stage within an oscillatory loop configured to sustain oscillations, the oscillatory loop having no more than one stage of an even-number of stages. The second weakly bistable differential amplifier is provided also as a stage within the oscillatory loop. The behavior perturbing coupling may operate to introduce into the amplifier to which it is connected a behavior tipping signal where the behavior tipping signal alters the oscillatory behavior of the oscillatory loop in a distinguishable way. This may be true even if the behavior tipping signal is weaker than an oscillation of the oscillatory loop. 
         [0008]    In another aspect, the inventive concept pertains to a method of detecting a weak signal by providing a multistage oscillatory loop configured to sustain oscillations. The loop includes, as at least one or two of its stages, first weakly bistable differential amplifier and a second weakly bistable differential amplifier where at least one of the first and second weakly bistable differential amplifiers is further connected to a behavior perturbing coupling that is operative to introduce into the amplifier to which it is connected a behavior tipping signal. Even if the behavior tipping signal is weaker than an oscillation of the oscillatory loop, the behavior tipping signal alters the oscillatory behavior of the oscillatory loop in a distinguishable way. The method also entails providing either the weak signal or a signal derived therefrom as the weak behavior tipping signal to the at least one of the first and second weakly bistable differential amplifiers. 
         [0009]    Other aspects of the disclosure will become apparent from the below detailed description. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0010]    The below detailed description section makes reference to the accompanying drawings, in which: 
           [0011]      FIG. 1A  is a diagram of a two-element intercoupled oscillatory system that may be operated in accordance with the present disclosure; 
           [0012]      FIG. 1B  is a diagram of a four-element intercoupled oscillatory system that may be operated in accordance with an embodiment of the disclosure; 
           [0013]      FIG. 1C  is a diagram of a six-element intercoupled oscillatory system that may be operated in accordance with an embodiment of the disclosure; 
           [0014]      FIG. 2  is a schematic diagram showing a combined differential amplifier and weak bistable switch each implemented as a bipolar NPN differential-pair for controlling imbalanced current flow through generalized, current-splitting impedances; 
           [0015]      FIG. 3  is a block diagram representation of a weakly bistable element block with control and tail currents; 
           [0016]      FIG. 4  is a block diagram representation showing two weakly bistable elements with control and tail currents; 
           [0017]      FIG. 5  shows a connection methodology for two weakly bistable elements; 
           [0018]      FIG. 6  shows a generalized connection methodology for an even number of 2N weakly bistable elements; 
           [0019]      FIG. 7  is a circuit-block realization of the two element system showing tail-current and sense current blocks; 
           [0020]      FIG. 8  shows a bipolar NPN differential-pair realization of a weakly bistable element block with a passive RC differential load; 
           [0021]      FIG. 9  shows an active-current source circuit for creating matched tail currents; 
           [0022]      FIG. 10  shows an operational amplifier realization of a sense-current multiplier for generating matched control currents; 
           [0023]      FIG. 11  shows an embodiment of the two-element system showing a discrete resistor approach for creating matched tail currents; 
           [0024]      FIG. 12  shows an embodiment of the two-element system showing the transistor-level and operational amplifier-level schematics; 
           [0025]      FIG. 13  is a plot produced from an HSPICE simulation result showing the differential output voltages for the two weakly bistable element system; and 
           [0026]      FIG. 14  is a plot produced from an HSPICE simulation result showing the differential output voltages when a behavior-tipping and weak sense current is applied as an increasing ramp over time. 
           [0027]      FIG. 15  shows an alternative embodiment of the sense current block interfaced with the two element system. 
           [0028]      FIG. 16A  shows an embodiment of the one element system, and  FIG. 16B  shows a plot produced from an HSPICE simulation result showing the differential output voltages when a behavior-tipping and weak sense current is applied as an increasing ramp over time. 
       
    
    
     DETAILED DESCRIPTION 
       [0029]    Structures and methods may be provided in accordance with the present disclosure of invention for minimizing the cost, size and/or complexity of each weak signal collecting device. 
         [0030]    One can aim that the signal collection units can be made smaller, more power efficient, and more reliable by reducing the number of circuit components at each signal collection location. In accordance with one aspect of the present disclosure, a two-stage system (a system with just two weakly bistable Voltage Controlled Oscillatory stages, a.k.a. wb-VCO stages, per collection location) is made possible. The two-stage system can be even further expanded into any even number stage system or can be further simplified to one-stage system. 
         [0031]      FIG. 1A  is a diagram of an oscillatory loop  100 . The oscillatory loop  100  may detect and measure an input voltage or other weak-magnitude input signal (e.g., a low magnitude current). The particular embodiment that is depicted has two weakly-bistable Input Controlled Oscillatory stages  102 ,  104  (wb-ICO stages  102 ,  104  are respectively labeled as A and B). A cross-influencing, positive feedback coupling component  106  couples the two wb-ICOs  102 ,  104  to each other. 
         [0032]    When no input signal (not shown) is applied to each of the wb-ICO&#39;s stages A and B, the combination of the two stages ( 102  and  104 ) and their cross-influencing coupling component  106  is such that one of two zero-input conditions is true: (1) the two wb-ICO stages, A and B, influence one another to be in an easily perturbed, first oscillating state; or (2) the two wb-ICO stages, A and B, influence one another to be not oscillating but additionally to be just outside of an easily perturbed-into (easily entered-into) second oscillating state. Then, when a weak magnitude input signal (e.g., voltage or current) is thereafter applied to each of the two wb-ICO stages ( 102  and  104 ), the two wb-ICO stages A and B influence one another to nonlinearly switch into an alternate state that is easily distinguishable from the original state. “Distinguishable” means the frequency of the oscillation changes (i.e. the frequency of an oscillation can change from 100 Hz to 0 Hz, or vice versa, making the oscillation appear or disappear.) More specifically, if the first zero-input condition (1) was true, then the application of the non-zero input signal would tip the two wb-ICO stages A and B out of the easily perturbed, first oscillating state and into either a nonoscillating state or a third oscillating state that is easily distinguishable from the first oscillating state. On the other hand, if the second zero-input condition (2) was true, then the application of the non-zero input signal would tip the two wb-ICO stages A and B out of their not-oscillating state and into their easily entered-into second oscillating state. 
         [0033]    While the above and relatively generalized introduction may appear somewhat abstract, a brief look at the plots of  FIGS. 13 and 14  will clarify what a first oscillating state ( FIG. 13 ) might look like and what easily distinguishable other oscillating states and/or a non-oscillating state ( FIG. 14 ) might look like. 
         [0034]      FIG. 2  depicts one implementation of the wb-ICO stages shown in  FIG. 1A ,  FIG. 1B , and  FIG. 1C . The below circuit descriptions assume a level of skill of a trained electrical engineer who designs mixed signal, analog and digital integrated circuits (monolithically integrated circuits) where the concepts of circuit blocks or cells are well understood, by such a skilled person as are the concepts of circuit elements, circuit branches, voltage nodes, and simple network theory. Additionally, the fundamental characteristics of capacitors, resistors, NPN bipolar transistors, PNP bipolar transistors, NMOS, and PMOS circuit should be familiar to such an artisan. In addition, terms such as positive, negative, non-inverting, inverting, S-plane or Laplace transform and the like, should be familiar to such a person. 
         [0035]    Accordingly,  FIG. 2  will be understood to be an example of an NPN bipolar differential-pair realization of one (e.g., A) of the two wb-ICO stages, A and B of  FIG. 1A . Although not explicitly shown, the other stage (e.g., B) of the two wb-ICO stages has the same design and where the input signal is of a weak magnitude, behavior-tipping input signal can be a differential voltage signal or a differential current signal applied at nodes  112  and  116 . A behavior-tipping input signal of a weak magnitude has a current of a magnitude less than 100 nA. In some embodiments, the weak behavior-tipping signal has a magnitude less than 25 nA. In designing a weakly-bistable oscillatory system such as that of  FIG. 1A , the one stage portion shown in  FIG. 2  may be used as a single stage of a multi-stage weakly-bistable VCO or ICO. In  FIG. 2 , a first NPN transistor  110  and a second NPN transistor  114  (where  110  and  114  may be monolithically integrated replicas of one another) are connected to form a differential, current splitting pair. As used in reference to  FIG. 2 - FIG. 16 , “connected” means electrically connected, either directly or with intervening elements. The emitter of NPN  110  connects to the emitter of NPN  114  to define a common-emitter node VEC  118 . The collector of NPN  110  connects to one end of impedance Z 1   130  and impedance Z 2   134  to define a respective first (minus) output node VOM  126 . The impedances  130 ,  132 , and  134  are part of “a differential load portion,” and they are connected to a “first current-splitting node”  136 . The collector of NPN  114  connects to one end of another and identical impedance Z 1 ′  132  and to the other end of impedance Z 2   134  to form the second (positive) output-node VOP  128 . The other ends of impedance Z 1   130  and of impedance Z 1   132  connect together at a power rail voltage node VP  136 . In this diagram third NPN transistor  120  and fourth NPN transistor  122  also form a differential current splitting pair except that they are not driven by the differential input voltage signal applied at nodes  112  and  116 . Nodes  112  and  116  are herein referred to as “a differential amplifier portion.” Instead, the base of NPN  120  connects to the collector of NPN  122  and similarly, the base of NPN  122  connects to the collector of NPN  120 . NPN  120  and NPN  122  are herein referred to as “a latch portion.” Additionally, the emitter of NPN  120  connects to the emitter of NPN  122  to form the common-emitter node VES  124 . The collector of NPN  120  also connects to output-node VOM  126  while the collector of NPN  122  also connects to output-node VOP  128 . The base of NPN  110  is the positive (non-inverting) input node VIP  112  while the base of NPN  114  is the minus (inverting) input node VIM  116 . It is to be understood that the illustrated circuit is preferably all fabricated on a single monolithically integrated circuit chip such that the differential current splitting components are essentially identical. While in each differential pair of NPN transistors, the respective current splitting transistors (e.g.,  112  and  116 ) should be of the same size as each other (e.g., same PN junction widths and/or lengths), it is within the contemplation of the present disclosure that the other pair (e.g.,  120  and  122 ) may be constituted by same but smaller or larger such NPN transistors. In one embodiment, transistors  120  and  122  are smaller than corresponding NPN transistors  112  and  116 . 
         [0036]    Those skilled in the art will appreciate from  FIG. 2  that within each such wb-VCO or wb-ICO stage there are two current splitting functions present, a first due to how the differential input signal VIP-VIM tips the first and second transistors ( 110  and  114 ) out of balance and a second due to how the third and fourth transistors ( 122  and  120 ) tip the differential output signal VOP-VOM out of balance. 
         [0037]    As briefly mentioned above, it is possible to operate at least the pair of differential amplifier transistors  110  and  114  in the nonlinear and near threshold region of operation such that even small perturbations in the differential input currents that enter the base terminals of NPN transistors  110  and  114  will create a greatly amplified difference at the corresponding output nodes ( 126  and  128 ) because one of the so-perturbed transistors is urged closer to, or over its threshold point while the other is urged below or further below its respective threshold point. In other words, by operating in the low current, nonlinear regions of the IV curves of at least the differential amplifier transistors pair,  110  and  114 , a relatively high degree of sensitivity to even small perturbations in input current (base currents of  110  and  114 ) may be obtained. Operation in the low current, nonlinear regions may be established by appropriately controlling the sink current (common tail current) drawn out of the VEC node  118 . The VEC node  118  is herein also referred to as “an amplifier biasing portion.” 
         [0038]    When considered alone, the differential amplifier formed by NPN transistors  110  and  114  can be thought of as a highly sensitive playground swing that can easily be tipped from a perfectly balanced state to an imbalanced state by application of a weak magnitude tipping force. On the other hand, when the weak bistable latch circuit of NPN transistors  120  and  122  is added, a degree of bi-stability is imparted onto the wb-ICO stage. The amount of added bi-stability can be controlled by appropriately adjusting the sink current (common tail current) drawn out of the VES node  124 . The VES node  124  is herein referred to as “a latch biasing portion.” When the current through the VES node  124  is zero, the bistable latch NPN transistors  120  and  122  do not bleed any currents out of the impedance branches ( 130 ,  132 ) of the differential amplifier and thus do not impart a degree of bi-stability to it. When the current flowing out through the VES node  124  is relatively small, the bistable latch NPN transistors  120  and  122  can be caused to operate in their near-threshold states whereby even small perturbations of output voltage between nodes  128  (VOP) and  126  (VOM) can switch the weakly bistable latch circuit ( 120  and  122 ) from one bistable state to an opposed bistable state. 
         [0039]      FIG. 3  schematically represents the circuitry of  FIG. 2  as a weakly bistable (wb) differential circuit block  150  having input nodes VIP ( 112 ) and VIM ( 116 ); output nodes VoP ( 128 ) and VoM ( 126 ); power voltage node VP ( 136 ) and current conducting branches IC ( 138 ), IS ( 140 ), IXP ( 142 ) and IXM ( 144 ). Current conducting branches IC ( 138 ) and IS ( 140 ) respectively emanate from common emitter nodes VEC ( 118 ) and VES ( 124 ). Current conducting branches IXP ( 142 ) and IXM ( 144 ) respectively emanate from output nodes VOP ( 128 ) and VOM ( 126 ). In one embodiment, the branched-off currents, IXP ( 142 ) and IXM ( 144 ) that are bled off from their respective current conducting branches, operate as oscillatory-state altering currents. 
         [0040]    For sake of completeness, the labeling in  FIG. 3  names the voltage difference between input nodes VIP  112  and VIM  116  as the differential input signal Vi 1   146 . Similarly, it names the voltage difference between output nodes VOP  128  and VOM  126  as differential output signal Vo 1   148 . By convention, the differential signal Vi 1   146  represents VIP  112  minus VIM  116 , and the differential signal Vo 1   148  represents VOP  128  minus VOM  126 . 
         [0041]    In one embodiment, the magnitudes of each of the IC ( 138 ) and IS ( 140 ) branch currents are respectively controlled by respective current sourcing circuits (e.g., constant current sourcing circuits). In one embodiment, the magnitudes of each of the IXP ( 142 ) and IXM ( 144 ) branch currents are respectively controlled by respective, but at the same time variable current sourcing circuits (in other words, not constant current sourcing circuits). In one embodiment, the so-called, external tail currents that are drawn out of current conducting branches IXP ( 142 ) and IXM ( 144 ) are determined by an attached (not shown) sensing interface circuit. (See briefly  FIG. 7  which is detailed later below.) 
         [0042]    In one embodiment, the head current entering into top node  136  is provided by a constant voltage source, VP. 
         [0043]    In one embodiment, the weakly bistable differential amplifier stage ( 150 ) depicted in  FIG. 3  is replicated so as to define an even number (two or more) of such stages on a monolithically integrated circuit chip. The illustrated connections can give the following set of analysis equations  152  which relate nonlinear Ebers Moll terms (on the right sides of the equations) with the Laplace transform L(−1) or the complex impedance terms “s” (on the left side). 
         [0000]        L   −1 ( V   o   /Z   n )= I   c ×tan  h ( V   i1 )− I   s ×tan  h ( V   o1 )− I   x  
 
         [0000]    
       
      
       V 
       o1 
       =VOP−VOM  
      
     
         [0000]    
       
      
       V 
       i1 
       =VIP−VIM  
      
     
         [0000]    
       
      
       I 
       x 
       =IXP−IXM  
      
     
         [0000]      1/ Z   n =1/ Z   1 +2/ Z   2  is a complex impedance expressed in “ s” 
 
         [0000]    A more detailed Ebers Moll derivation is also provided in U.S. Pat. No. 8,212,569 B1. 
         [0044]      FIG. 4  shows a monolithically integrated circuit having two identical weakly bistable element stages formed thereon: stage  150  and stage  250 . Both stages are configured to be biased with identical VEC and VES tail current biases as well as same head end VP ( 136 ,  236 ) power voltages. Moreover, the minus side output bleeder currents IXM  144  and  244  are identical and the positive side output bleeder currents IXP  142  and  242  are identical. Therefore, as indicated by the following set of equations  252 , it is possible to derive a set of circuit block equations relating the nonlinear Ebers Moll terms (on the right) with the Laplace transform L(−1) of the complex impedance term in “s” (on the left). 
         [0000]        L   −1 ( V   o   /Z   n )= I   c ×tan  h ( V   i )− I   s ×tan  h ( V   out )− I   x  
 
         [0000]    
       
      
       V 
       out 
       =VOP−VOM  
      
     
         [0000]    
       
      
       V 
       i 
       =VIP−VIM  
      
     
         [0000]    
       
      
       I 
       x 
       =IXP−IXM  
      
     
         [0000]      1/ Z   n =1/ Z   1 +2/ Z   2  is a complex impedance expressed in “ s” 
 
         [0000]    In the case of the second stage  250  in  FIG. 4 , the differential input voltage is denoted as Vi 2  ( 246 ) and the differential output voltage is denoted as Vo 2  ( 248 ). 
         [0045]    The wb-differential circuit block  150  is herein also referred to as “a first weakly bistable differential amplifier.” Where there are two stages, as in  FIG. 4 , the second stage  250  may herein be referred to as “a second weakly bistable differential amplifier.” The positive coupling component  106  may herein be referred to as “a behavior perturbing coupling.” 
         [0046]      FIG. 5  shows a substantially same monolithically integrated circuit as  FIG. 4  but an interstage coupling component  106  is provided such that Vi 2 =Vo 1  and Vi 1 =−Vo 2 . The positive feedback coupling component  106  shown in  FIG. 1  corresponds to a combination of elements  126 ,  128 ,  212 , and  216 . An inversion function (times negative one) is included in the feedback coupling from the second stage  250  to the first stage  150 . This interstage coupling is summarized in the equation set  254  shown below: 
         [0000]        Vi 1=− Vo 2
 
         [0000]        Vi 2=+ Vo 1 
         [0047]    More specifically, node VIP  112  of stage element  150  is connected to node VOM  226  of stage element  250 ; while node VIM  116  of stage element  150  is connected to node VOP  228  of stage element  250 . This causes the condition Vi 1   146  to be equal to the negative of Vo 2   248 . Also, node VOP  128  of stage element  150  is connected directly to node VIP  212  of stage element  250 ; while node VOM  126  of stage element  150  is connected directly to node VIM  216  of stage element  250 . This causes the condition Vi 2   246  to be equal to Vo 1   148 . 
         [0048]    It should be noted that the variable bleeder current IXM  144  can be seen as perturbing the input current that feeds the base of the NPN transistor inside of stage  250  and coupled to minus node VIM  216 . Similarly, the variable bleeder current IXM  244  can be seen as perturbing the input current that feeds the base of the NPN transistor inside of stage  150  and coupled to positive node VIP  112 . Additionally, the variable bleeder current IXP  142  can be seen as perturbing the input current that feed the base of the NPN transistor inside of stage  250  and coupled to positive node VIP  212 . Similarly, the variable bleeder current IXP  242  can be seen as perturbing the input current that feed the base of the NPN transistor inside of stage  150  and coupled to minus node VIN  116 . Because the respective NPN transistors inside stage  150  and  250  are being biased to be within or close to their respective nonlinear operation regions (e.g., subthreshold), they are very sensitive to even the smallest of changes in their respective bleeder currents: IXM&#39;s  144  and  244  and IXP&#39;s  142  and  242 . Thus these bleeder currents may be used as inputs for controlling the behavior of the negative feedback wise coupled pair of weakly bistable differential amplifier stages  150  and  250 . 
         [0049]    In one embodiment of the monolithically integrated circuit shown in  FIG. 5 , if the output voltages Vo 1  and Vo 2  are initially preset to zero and all the bleeder currents (IXM&#39;s  144  and  244  and IXP&#39;s  142  and  242 ) are initially preset to zero and the Is bistability-adding currents ( 140  and  240 ) are sufficiently high, then the feedback-wise coupled system will remain essentially balanced. Then even a very minute perturbation (e.g., in the nanoAmpere range) of the bleeder currents (IXM&#39;s  144  and  244  and IXP&#39;s  142  and  242 ) will tip the feedback-wise coupled system into an easily detected oscillatory mode. Accordingly, the illustrated circuit ( FIG. 5 ) may be used to detect the occurrence of a very small signal change where that signal change is introduced within one or more of the bleeder currents (IXM&#39;s  144  and  244  and IXP&#39;s  142  and  242 ). For example the very small signal change may be that induced outside of a health patient&#39;s body (supra-cutaneously) by one or more nerve cells (e.g., intra-cranial nerve cells) firing inside the patient&#39;s body. After the weak signal firing is detected by observing the transition of the two-stage system ( 150 - 250 ) from an oscillatory mode to a non-oscillatory mode in which detuning of the frequency of the oscillation occurs. This detuning of the oscillation can be automatically recorded and the degree in which the detuning occurs depends on the strength of the input signal. In other words, the circuit is tuned to an oscillatory mode where the residence time distribution (duty cycle) changes, and a signal that is outside the operating range of the tuned circuit (e.g., too strong) will induce a non-oscillatory mode. When the input signal disappears, the two-stage system can be automatically be reset to await the next detection of the weak signal event. In one embodiment, the illustrated two-stage system ( 150 - 250 ) is incorporated into a weak signal collection device that is attached adhesively or otherwise to the patient&#39;s skin at a desired location on the body. 
         [0050]      FIG. 6  shows a generalized multi-stage feedback system that may be operated in accordance with the present teachings. An even number of cascaded circuit stages 2N is provided, where N represents an arbitrary whole number (1, 2, 3, . . . ). In the drawing, only the first two stages, stage  150  and stage  250 , and the final two stages, stage  350  and stage  450  are shown for the case of N equal to or greater than 2. The stages are designed to be equivalent with equivalent currents and equivalent biases. Each stage has elements, voltages, and currents which are equivalent in concept and design to those of  FIG. 3 . The concepts of  FIG. 4  and  FIG. 5  are generalized with the understanding that the notations of  FIG. 3  apply and with the idea that all stages are replicas. Therefore, stage  350  also represents a “Diff Block” composed of the elements of  FIG. 2  with respective and independent labels to distinguish it from other stages. Again using the two-port electrical engineering convention, the element stage is drawn with its input nodes VIP and VIM on the left and the output nodes VOP and VOM on the right. This two port representation shows differential input signal Vi(2N−1)  346  and differential output signal Vo(2N−1)  348 . Again by convention the differential signal Vi(2N−1)  346  represents VIP minus VIM, and the differential signal Vo(2N−1)  348  represents VOP minus VOM. In this schematic, the additional current source Ic  338  provides another tail current of value Ic. The additional current source Is  340  provides another tail current of value Is. The additional bleeder currents (which can be controlled by corresponding current sources) IXP  342  and IXM  344  are control currents that in one embodiment (see  FIG. 7 ), are derived from a sensing interface circuit. Moreover, stage  450  also represents a “Diff Block” composed of the elements of  FIG. 2  with independent labels to distinguish it from other stages. Using two-port electrical engineering convention, the element stage is drawn with its input nodes VIP and VIM on the left and the output nodes VOP and VOM on the right. This two port representation shows differential input signal Vi(2N)  446  and differential output signal Vo(2N)  448 . Again by convention the differential signal Vi(2N)  446  represents VIP minus VIM, and the differential signal Vo(2N)  448  represents VOP minus VOM. In this schematic the additional current source Ic  438  provides another tail current of value Ic. The additional current source Is  440  provides another tail current of value Is. The additional current sources IXP  442  and IXM  444  are control currents which can be derived from a sensing interface circuit. These 2N stages are also connected in a negative-feedback configuration suitable for creating oscillations. The connection concept is summarized in equations below: 
         [0000]        Vi 1=− VoN  
 
         [0000]        Vi ( k+ 1)=+ Vok  for  k= 1,2,3, . . .  N− 1 
         [0000]    The differential input Vi 1   146  is connected so as to equal to the negative of the differential output Vo(2N)  448 , while the remainder of the differential inputs Vi(k+1) are connected so as to be equal to the respectively preceding differential outputs Vo(k) for k=1, 2, . . . (N−1). 
         [0051]      FIG. 7  illustrates one possible way in which the two-stage weakly bistable system can be coupled and driven for sensing an external voltage signal (input signal)  502 . In this diagram the control currents are provided from the sense interface circuit block  500 , and the tail currents are controlled by a tail currents generator block  504 . The purpose of the sense interface circuit block  500 , referred to as the “Interface Circuit”, is to convert the to-be-sensed voltage signal  502  into appropriate control currents IXP and/or IXM. Here the connections are as follows: the sense signal, either a voltage or a current signal, is detected at signal input port  502 ; control current IXP  142  of the interface circuit block  500  connects to node VOP  128  of stage  150 ″; control current IXP  242  of the interface circuit block  500  connects to node VOP  228  of stage  250 ; control current IXM  144  of the interface circuit block  500  connects to node VOM  126  of stage  150 ; control current IXM  244  of interface circuit block  500  connects to node VOP  226  of stage  250 . 
         [0052]    The purpose of circuit block  504 , referred to as a “Tail Current Generator”, is to provide respective tail currents of value Ic and of value Is to each of the stages. Here the connections are as follows: circuit block  504  tail current Ic  138  connects to node VEC  118  of stage  150 ″; circuit block  504  tail current Is  140  connects to node VES  124  of stage  150 ; circuit block  504  tail current Ic  238  connects to node VEC  218  stage  250 ; circuit block  504  tail current Is  240  connects to node VES  224  of stage  250 . 
         [0053]      FIG. 8  shows an embodiment of the circuit stage of  FIG. 2 . In this embodiment the element Z 1   130  is a resistor R 1   530 , and the element Z 1   132  is an identical and monolithically integrated resistor R 1   532 . Also, the element Z 2   134  is a capacitor C  534  that may be monolithically integrated on the same circuit chip. The capacitor C  534  provides AC coupling between the VOP and VOM nodes ( 128  and  126 ). The capacitance of capacitor C  534  may be varied as appropriate for the desired oscillatory behaviors of the system. 
         [0054]      FIG. 9  shows a circuit technique for creating the tail current generator block  504  of  FIG. 7 . In this circuit embodiment the tail currents Ic  138  and Ic  238  are created from the active current source comprised of operational amplifier OA  542 , NPN  544 , NPN  546 , resistor Rc  548 , and voltage reference signal VREFC  540 . The voltage signal VREFC  540  connects to the noninverting (plus) terminal of OA  542 . The base of NPN  544  and of NPN  546  connect to the output of OA  542 . One end of resistor Rc  548  connects to the emitter of NPN  544 , the emitter of NPN  546 , and the inverting input (minus) terminal of OA  542 . The other end of resistor Rc  548  connects to ground. This embodiment shows the technique for creating two equal tail currents Ic  138  and Ic  238 , and this technique may be generalized to create any number of equal tail currents by adding additional transistors in parallel. The illustrated circuit components may be monolithically integrated on the same chip as that of the multi-stage weakly-bistable oscillatory system (e.g.,  150 ,  250 , . . . ). 
         [0055]    In a similar manner, in  FIG. 9 , the tail currents Is  140  and Is  240  are created from the active current source comprised of operational amplifier OA  552 , NPN  554 , NPN  556 , resistor Rs  558 , and voltage reference signal VREFS  550 . The voltage signal VREFS  550  connects to the non-inverting (plus) terminal of OA  552 . The base of NPN  554  and of NPN  556  connect to the output of OA  552 . One end of resistor Rs  558  connects to the emitter of NPN  554 , the emitter of NPN  556 , and the inverting input (minus) terminal of OA  552 . The other end of resistor Rs  558  connects to ground. This embodiment shows the technique for creating two equal tail currents Is  140  and Is  240 , and this technique may also be generalized to create any number of equal tail currents by adding additional transistors in parallel. 
         [0056]      FIG. 10  shows a circuit technique for creating the interface circuit block  500  of  FIG. 7 . In this circuit embodiment only the control currents IXP  142  and IXP  242  are created as a single ended embodiment of circuit block  500 . In addition, the sense signal input  502  is a current signal. In this embodiment control current IXP  142  is the collector current of NPN  566 , and control current IXP  242  is the collector current of NPN  568 . Also there are three operational amplifiers OA  560 , OA  562 , and OA  564 . There is a fixed voltage reference VREFA  574 , and there are two resistors Rf  570  and Ra  572 . Operational amplifier OA  560  is connected with shunt feedback resistor Rf  570  so that the signal input  502  connects to the inverting (minus) input of OA  560  and to one end of Rf  570 . The other end of Rf  570  connects to the output of OA  560  and to the non-inverting (plus) input of OA  562 . The voltage reference VREFA  574  connects to the non-inverting (plus) inputs of OA  560  and OA  564 . The inverting (minus) input of OA  564  connects to the output of OA  564  and to one end of resistor Ra  572 . The other end of Ra  572  connects to the emitter of NPN  566 , the emitter of NPN  568 , and to the inverting input of OA  562 . The output of OA  562  connects to the base of NPN  566  and NPN  568 . This embodiment shows the technique for creating two equal control currents IXP  142  and IXP  242  and may also be generalized to create any number of equal tail currents by adding additional transistors in parallel. 
         [0057]      FIG. 11  illustrates an embodiment of  FIG. 7  where the tail currents are created with use of resistors. In this simplified embodiment the four tail currents Ic  138 , Is  140 , Ic  238 , and Is  240  are created by using resistors Rc  600 , Rs  602 , Rc  604 , and Rs  606 . More specifically, one end of resistor Rc  600  is connected to circuit stage  150  “Diff Block” node VEC  118 . The other end of resistor Rc  600  is connected to ground  616 . Similarly, one end of resistor Rs  602  is connected to node VES  124  of circuit stage  150 . The other end of resistor Rs  602  is connected to ground  616 . This connection scheme is repeated for the second stage  250  “Diff Block” where one end of resistor Rc  604  is connected to circuit stage  250  “Diff Block” node VEC  218 . The other end of resistor Rc  604  is connected to ground  616 . Finally, one end of resistor Rs  606  is connected to circuit stage  250  “Diff Block” node VES  224 , and the other end of resistor Rs  606  is connected to ground  616 . Also, this connection methodology may be extended to more than two circuit stages using additional resistors Rc and Rs for each node VEC and VES. Finally, a power supply or battery connection VBAT  618  is provided to node VP  136  of stage  150  and to node VP  236  of stage  250 . 
         [0058]      FIG. 12  shows an equivalent transistor-level schematic of the combined embodiments of  FIG. 8 ,  FIG. 10 , and  FIG. 11 . This simplified embodiment uses the element transistor-level configuration of  FIG. 8  where the supply rails VP become connected to common supply VBAT  618  with resistors Rc  138  through Rs  240  connected as in  FIG. 11 . The sense interface circuit of  FIG. 10  is drawn at the bottom and connects IXP  142  to stage node VOP 1   128  and connects IXP  242  to stage node VOP 2   228 . In this diagram, connections are shown with wires and with node labels. When a node label is repeated it indicates a wire connection. This applies specifically to nodes VOP 2   228  and nodes VOM 2   226  in which the wire connections are not shown. Instead, the connections for forming a feedback loop are implicit through the equivalent label, and a design engineer familiar with EDA design tools and schematic diagrams would recognize this methodology of connecting like nodes. The operational amplifiers OA  560 , OA  562 , and OA  564  are symbolic and the design engineer would follow standard practice for connecting supply and ground rails for operational amplifiers. 
         [0059]    While the above disclosure describes possible ways of interconnecting an even number of blocks or stages with an input signal, this next section discusses possible ways of designing and operating such blocks in order to produce oscillatory behavior. In one embodiment, the goal may be to generate an oscillatory output signal whose fundamental frequency (f0) varies inversely with the magnitude of the variable and to be detected and/or measured input signal. The input signal, in turn, may be either a voltage signal or a current signal, and an important nonlinear transfer function becomes the frequency output relative to the signal input. Therefore, the first aspect of the design is to assure oscillation. Oscillations are guaranteed when the unperturbed, zero-signal-input, system is designed as an oscillator. While the connection algorithms automatically assure negative feedback, there are other variables, such as tail current and loading conditions, which are now addressed to assure the system has sufficient gain to behave as a differential ring oscillator. The design steps are discussed below with respect to the figures, and a design example, with specific component values, is provided to teach the engineer how to build a sense circuit capable of providing a frequency sensitive to low-level signal inputs. 
         [0060]    In designing an oscillator, the engineer should understand the concepts of feedback theory and also understand how to use simulation tools such as HSPICE. A combination of theory and simulation are invaluable in predicting sense circuit performance and in studying how variables will affect the overall circuit performance. The concept discussed here regarding output and input signals finds application in the field of nonlinear dynamical systems. An input may be any type of signal input applied for example to both element A  102  and element B  104  of  FIG. 1 . The output may be observed at either element A  102  or element B  104 . 
         [0061]    Consider, in this regard, the circuit of  FIG. 2 , namely, the weakly bistable element with two differential pairs, where this is part of a larger system that functions as a ring oscillator. For proper operation and design, it is valuable to understand the variables of design. Here, the variables are the loads, comprised of Z 1   130 , Z 1   132 , and Z 2   134 , the tail currents which connect at terminals VEC  118  and VES  124 , and the supply voltage VP  136 . The designer should provide a supply voltage VP which allows enough voltage for adequate common-mode range, a standard electrical engineering concept. Also, this stage is intended to be part of a differential ring oscillator operated such that VIP  112  and VIM  116  are the non-inverting and inverting inputs, respectively, while VOP  128  and VOM  126  are the non-inverting and inverting stage outputs, respectively. In building the ring oscillator from several stages, each stage is designed to be matched, or identical. Mismatch tolerances should be studied with tools such as HSPICE and with experimentation. 
         [0062]    Referring back to  FIG. 3 , the block diagram extension of  FIG. 2 , shows the additional currents Ic  138 , Is  140 , IXP  142 , and IXM  144 . Here Ic  138  and Is  140  are the tail currents which connect to VEC  118  and VES  124 , respectively. These currents are design variables, and in one embodiment, Is  140  is larger in magnitude than Ic  138 . The control currents IXP  142  and IXM  144  are currents which occur as a result of sensing a signal. These typically are scaled replicas of the sensed input, which may be a current or voltage. Each block or element of the complete system should be equivalent. So if one block receives just an IXP  142  input, then all blocks should receive just an IXP input of equivalent value. Thus, the system must be designed with “matched” currents. Matching errors should be studied and characterized as part of the design procedure, and circuit simulation allows the designer to study the effect of matching errors. Also, in normal operation, the circuit may be modeled with the simplified Ebers-Moll equations  152 . In equations  152  the left-hand side of the equation, representing the linear term in Vo, has been written in terms of an inverse Laplace transform. In this way the impedances Z 1  and Z 2  may be expressed in the s-plane for convenience. The right-hand side of the equation, representing the nonlinear terms in Vo and Vi, is expressed in the time domain. 
         [0063]      FIG. 4  and  FIG. 5  represent the two-stage oscillator system operating as an oscillator with frequency dependent upon the control currents IXP  142  and IXM  144 . In order to guarantee that the system will oscillate, one may use the Ebers Moll derivation giving a system of nonlinear equations similar to that of equation  252 . An alternative electrical engineering approach would be to analyze the system as a feedback system and to use a control theory approach such as the Barkhausen stability criterion, which is a mathematical condition to determine when a linear electronic circuit will oscillate. This requires analyzing the small-signal gain of the differential stages and writing a transfer function for the control loop of interest. Either approach—the Ebers Moll nonlinear system analysis or the Barkhausen criterion—can be a starting point in the design. An HSPICE or similar computer-aided simulation analysis which uses more detailed models for transistors and for components would usually provide a better estimation of frequency and oscillator behavior. 
         [0064]    Consider next and in this regard, the circuit of  FIG. 6  which is a 2N generalization of  FIG. 5  and it also is operated as an oscillator with matched currents. While there may be advantages to using more than two stages as shown in the embodiment of  FIG. 6 , the two-stage system offers the advantage of simplicity, including fewer stages and fewer components, and is explored here further as a preferred embodiment. Because this system is predicated upon matched elements and matched currents, the risk of mismatch errors from one element to the next is reduced when the design uses a minimum number of stages. 
         [0065]      FIG. 7  shows the system-level block-diagram design of the two-stage sense-circuit. This operates as a system which senses the input signal  502  and then generates output signals Vo 1   148  and Vo 2   248  with frequency dependent upon the sense signal  502 . The maximum frequency occurs when the input signal is zero such that the control currents IXP  142 , IXP  242 , IXM  144 , and IXM  244  are zero. The frequency decreases monotonically with the control currents IXP  142 , IXP  242 , IXM  144 , and IXM  244  until a DC condition is reached. For reliable circuit performance, the interface circuit  500  should therefore provide a scaled, predictable relationship between the sensed signal  502  and the control currents. In this way the output frequency will have a unique and predictable value as a function of the input sense signal  502 . The tail currents of tail current generator  504  are design variables. Here tail currents Ic  138  and Ic  238  should be matched currents of equal value, to within design tolerance determined by simulation. Similarly, the tail currents Is  140  and Is  240  should be matched currents of equal value, to within design tolerance determined by simulation. Moreover, in one embodiment, the magnitude of Is is greater than the magnitude of Ic. 
         [0066]      FIG. 8  shows a simplified embodiment of  FIG. 2  where Z 1   130 , Z 1   132 , and Z 2   134 , have been replaced with passive components R 1   530 , R 1   532 , and C  534 , respectively. Here the value of R 1   530  and R 1   532  is selected to be equal and such that the large-signal DC voltage drop across the resistor is small. This assures that the differential pairs will remain within common-mode range during normal operation. The capacitor C  534  is selected as a time-constant variable such that its value combined with R 1  will represent a passive-load time constant. This time constant, in part, will affect the frequency of oscillation. The overall frequency is determined by the tail currents and the passive-load time constant, and HSPICE simulations are useful in predicting the frequency of the ring oscillator. 
         [0067]      FIG. 9  shows one method for creating matched tail currents Ic  138  and Ic  238 , and matched tail currents Is  140  and Is  240 . In this active current source approach, the values Ic  138  and Ic  238  will be equal to half of VREFC  540  divided by Rc  548 . Similarly, the values Is  140  and Is  240  will be equal to half of VREFS  550  divided by Rs  558 . The values of VREFC  540  and VREFS  550  are constrained to voltage levels which allow the transistors to operate as current sources. The designer should verify correct operation through simulation. By way of example, suppose the desired value of Is  140  and Is  240  is 300 uA while the desired value of Ic  138  and Ic  238  is 200 uA. One approach is to use resistors Rc  548  and Rs  558  both equal to 1K and to select VREFC  540  and VREFS  550  equal to 0.4 V and 0.6 V, respectively. 
         [0068]      FIG. 10  shows an interface-circuit method for creating matched control currents IXP  142  and IXP  242  from a current signal input  502 . This interface circuit is operated as an interface circuit to scale an input current  502  by a scale factor equal to Rf  570  divided by Ra  572 . The designer may determine by computer simulation the desired control values of I×P  142  and IXP  242  in order to realize a transfer function of frequency output versus control current level IXP. Then the sense level may be set by selecting an appropriate scale factor. For instance, suppose it is determined that based upon the tail currents an appropriate value of IXP  142  and IXP  242  is on the order of 10 uA; then a scale factor of 100 would be appropriate for sensing a current signal on the order of 100 nA. Say Ra  572  is selected as 10K (ohms), then Rf  570  would be 1 Meg (ohms). In this embodiment, the reference voltage VREFA  574  is selected as 0.5V and the sense input  502  is a current sink forcing the voltage across resistor Ra  572  to be positive. Therefore, this interface circuit is operated with the complete system as a monitor of a “sinked” current. Its function is to scale the sinked current by a predictable constant. 
         [0069]      FIG. 11  again shows the system-level block-diagram design of the two-stage sense-circuit. However, in this embodiment the tail currents Ic  138 , Ic  238 , Is  140 , and Is  240  are created by using matched or precision resistors Rc  600 , Rc  604 , Rs  602 , and Rs  606 , respectively. In this embodiment, suitable for a discrete-component PC board, the designer calculates Ic  138 , Ic  238 , Is  140 , and Is  240  by knowing the large-signal voltages VEC 1   608 , VEC 2   612 , VES 1   610 , and VES 2   614 . If by design these voltages levels are approximately constant, then this procedure allows an alternative to using the current source of  FIG. 9 , and the tail currents are easily calculated using Ohm&#39;s law. For instance, Ic  138  is given by VEC 1   608  divided by Rc  600 . 
         [0070]      FIG. 12  shows the two-stage transistor-level design of one embodiment with control currents IXP  142  and IXP  242  of  FIG. 10 . This also uses the passive tail-current approach of  FIG. 11 . There are no control currents IXM  144  and IXM  244  in this embodiment for sensing a sink current  502 . This design uses the following component values: each Rc equal to 28K ohms, each Rs equal to 10K ohms, each capacitor C equal to 560 pF, each R 1  equal to 500 ohms, a scale factor Rf/Ra equal to 150. The value Rf is selected to be 1.5 Meg ohm and Ra is thus equal to 10K ohms. A sink-directed current signal is sensed at sense input  502  while the output signal is measured across either capacitor C as VOP 1  minus VOM 1  or as VOP 2  minus VOM 2 . A battery supply of 3.2 V is applied at VBAT, and VREFA is set to 0.5 V. Matched NPN bipolar transistors from a CA3086 monolithically integrated chip are used to create the NPN differential pairs and matched currents. 
         [0071]    Using the transistor HSPICE models from the CA3086 datasheet and the parameters discussed above in  FIG. 12 , an HSPICE simulation gives a maximum frequency of 35.9 kHz when the control currents IXP are zero. The simulation also calculates the tail currents: tail-current value Ic equals 92 uA, and tail-current value Is equals 255 uA. 
         [0072]    Working Example: A complete circuit as shown in  FIG. 12  has been tested on a proto-board for evaluation; and additionally a corresponding HSPICE simulation were found to correctly predict the maximum (zero control current) frequency to within 10 percent. Error between simulation and breadboard results are attributed to mismatch errors of matched components including mismatch among the differential pairs. Other sources of error may be parasitic board capacitance, probe capacitance, and voltage errors relating to using an unregulated power source. To attain consistent and predictable circuit performance the designer could use a regulated power supply or use a voltage regulator to regulate the supply voltage labeled as VBAT. Also, the system design is not limited to using a protoboard; and the designer may wish to use a PC-board or a monolithic integrated solution to fabricate the sense circuit. 
         [0073]      FIG. 13  shows the simulated differential output voltages VO 1  and VO 2  of the circuit in  FIG. 12 . Here VO 1  is defined as VOP 1   128  minus VOM 1   126  while VO 2  is defined as VOP 2   228  minus VOM 2   226 . These HSPICE generated waveforms substantially agree with the experimental waveforms of the working example. 
         [0074]      FIG. 14  shows the simulated output response to a current sink signal at sense input  502 . In this simulated example, the sensed current is ramped from zero to 75 nA over the indicated time interval and it may be seen by measuring pulse width that the fundamental frequency varies inversely with sense current. The interface circuit scale factor, determined by Rf  570  and Ra  572 , has been adjusted in this example to force the frequency to be zero (no oscillation) for values of sense current greater than 75 nA and to have maximum transfer gain when the sense current reaches 10 nA. Here, transfer gain refers to the magnitude of the transfer function of output frequency with respect to sense current input. By forcing this characteristic, the sense circuit is highly sensitive and has maximum transfer gain, when the sink current signal is between 10 nA and 75 nA. It is within the contemplation of the present disclosure to otherwise vary the control parameters to obtain desired sensitivity and oscillation cut-off at other values. 
         [0075]      FIG. 13  and  FIG. 14  as described above therefore provide insight into how a person may elect to operate the sense circuit in view of the present teachings. In the simulated examples of  FIG. 13  and  FIG. 14 , a to-be-sensed current signal of just several nano-amps (nA) may cause the output signals VO 1  and VO 2  of  FIG. 12  to change (e.g., decrease) substantially and thus distinguishably. The above and merely exemplary and not limiting design provides an observable change of fundamental output frequency based upon the input signal at sense input  502 . The shape of the waveform also changes as seen in  FIG. 14 . It is within the contemplation of the disclosure to change design variables, such as tail current (values Is and Ic) and passive load (values Z 1  and Z 2 ), in order to realize different frequency transfer characteristics. For instance, it is possible, in theory, to vary Is and Ic to change the zero-input frequency to a range of 100 kHz and to change the sensed current level to less than 1 nA. Another variable is the interface circuit gain, and this too could be adjusted to shift the sensed-current level. 
         [0076]    The present disclosure is to be taken as illustrative rather than as limiting the scope, nature, or spirit of the subject matter claimed below. Numerous modifications and variations will become apparent to those skilled in the art after studying the disclosure, including use of equivalent functional and/or structural substitutes for elements described herein, use of equivalent functional couplings for couplings described herein, and/or use of equivalent functional steps for steps described herein. Such insubstantial variations are to be considered within the scope of what is contemplated here. Moreover, if plural examples are given for specific means, or steps, and extrapolation between and/or beyond such given examples is obvious in view of the present disclosure, then the disclosure is to be deemed as effectively disclosing and thus covering at least such extrapolations. As an example,  FIG. 15  shows an alternative way to connecting the interface circuit to the diff-pair unit. In this case, instead of connecting the interface circuit to the diff-pair collectors, one can connect them directly to the diff-pair emitters and modulate the frequency. 
         [0077]    More specifically, the present disclosure provides an oscillatory ring or loop that includes at least two weakly bistable (wb) differential amplifiers such as the one shown in  FIG. 2  where the wb-differential amplifiers are biased such that at the ring (loop) will be in a first oscillatory mode (or not oscillating) when no weak tipping signal is applied to one or more of the at least two wb-differential amplifiers and such that a weak tipping signal (e.g., one in a range of about 2 nA to 75 nA as shown in  FIG. 14 ), when applied to at least one of the two or more wb-differential amplifiers will discernibly shift the loop into a different oscillatory mode (or into a not oscillating mode) so that the discernible shift indicates the detection of the weak tipping signal. Although the exemplary wb-differential amplifier of  FIG. 2  uses NPN bipolar transistors operating in their nonlinear and near threshold regions, it is within the contemplation of the present disclosure to instead use PNP transistors, JFET transistors (of P or N channel type), OnFETs (of P or N channel type), other forms of IGFETs (Insulated Gated Field effect transistors), Darlington pairs and/or combinations of IGFETs and bipolar transistors for obtaining similar functionalities from such other active devices. While one embodiment uses just two stages each having only 4 transistors, the concepts provided here may be generalized to using any even number of such stages where the overall feedback coupling allows for oscillations and a weak tipping signal can tip the loop or ring from one oscillatory mode to a distinguishable second oscillatory mode (or to a non-oscillatory mode as shown for example at the right end of  FIG. 14 ). 
         [0078]      FIG. 16A  depicts a stage of a one-element oscillatory system that may be operated in accordance with the present disclosure. As shown in  FIGS. 16A and 16B , one stage with oscillation can be perturbed toward a non-oscillatory mode. 
         [0079]    Therefore, one, two or any even number of stages can be used to sense weak signals. Previously, it went unnoticed that the oscillation regime transitions into a non-oscillatory regime, therefore exhibiting a bifurcation process due to a non-linear process, even with an even-number of stage loops (e.g., a two-stage loop shown in  FIG. 1A ). U.S. Pat. No. 8,212,569 to In et al. and entitled “Coupled bi-stable circuit for ultra-sensitive electric field sensing utilizing differential transistor pairs” and U.S. Pat. No. 7,420,366 to In et al. and entitled “Coupled nonlinear sensor system,” for example, describe systems with odd-number of oscillators based on general transistor(s) but do not contemplate even-numbered or single-numbered oscillators. The inventive concept disclosed herein is based on the discovery that the transition between the oscillation and non-oscillatory regimes can be achieved with even-number of stage loops, and in fact, can even be achieved with a one-stage loop as shown in  FIG. 16A  and  FIG. 16B . 
         [0080]    Furthermore, the input sense circuit can be further modified to inject voltage input rather than current input into one or multistage system such that one can sense the voltage with which many electrically excitable biophysical measurements can be applied. 
         [0081]    If any disclosures are incorporated herein by reference and such incorporated disclosures conflict in part or whole with the present disclosure, then to the extent of conflict, and/or broader disclosure, and/or broader definition of terms, the present disclosure controls. If such incorporated disclosures conflict in part or whole with one another, then to the extent of conflict, the later-dated disclosure controls. 
         [0082]    Unless expressly stated otherwise herein, ordinary terms have their corresponding ordinary meanings within the respective contexts of their presentations, and ordinary terms of art have their corresponding regular meanings within the relevant technical arts and within the respective contexts of their presentations herein. Descriptions above regarding related technologies are not admissions that the technologies or possible relations between them were appreciated by artisans of ordinary skill in the areas of endeavor to which the present disclosure most closely pertains. 
         [0083]    Given the above disclosure of general concepts and specific embodiments, the scope of protection sought is to be defined by the claims appended hereto and their equivalents. The inventive concept(s) disclosed herein as taken alone or in various combinations (including but not limited to embodiments of  FIGS. 1A-16B ) are intended to be claimed. The issued claims are not to be taken as limiting Applicant&#39;s right to claim disclosed, but not yet literally claimed, subject matter. A general claim to all here disclosed and inventive matter is hereby made.