# Patent

## Title
Integrated electronic circuit including non-linear inductor devices

## Abstract

An integrated electronic circuit includes a plurality of active circuits connected together in cascade. A feedback loop is between an output of a last active circuit and an input of a first active circuit so that the plurality of active devices function as a non-linear device, such as an inductor. The integrated electronic circuit may be integrated or used in association with a circuit network including other non-linear devices.

## Background
FIELD OF THE INVENTION
The present invention relates generally to non-linear electronic devices, such as non-linear inductors. More specifically, but not exclusively, the present invention relates to an electronic device integrated on a semiconductor substrate, with the electronic device being integrated or used in association with a circuit network including non-linear devices.
BACKGROUND OF THE INVENTION
Data detection for transmission channels is based on the use of a network of non-linear devices, as readily understood by those skilled in the art. Data detection with non-linear devices is becoming more popular because of the simplicity of the circuit network, and because of a corresponding lower production cost.
A circuit network including non-liner devices requires that the non-linearity of such devices be well controlled and follow a well-defined rule. Once these conditions are met, then the resulting network provides some advantages in data detection when compared with other more complex approaches.
The devices used in this kind of network are usually capacitors and inductors that have a non-linear relation between capacitance and voltage for the capacitors, and a non-linear relation between inductance and current for the inductors. One of the main difficulties for manufacturing an integrated circuit network including non-linear devices is that the non-linear components are to be provided as discrete elements. An integrated non-linear capacitor or inductor is hard to form based upon current technology.
For instance, U.S. Pat. No. 6,166,604 relates to a semiconductor amplifier including a distortion compensation circuit. The disclosed amplifier comprises a non-linear amplifying element connected to an integrated capacitor that prevents a direct current from flowing through a passive circuit. The integrated capacitor is formed in a known manner.
Up to now, there have not been any straightforward approaches for easily integrating an electronic circuit that includes non-linear passive components. Consequently, there is a need for implementing non-linear passive devices into a semiconductor electronic circuit, thus allowing the construction of a network of non-linear devices for data detection in transmission channels.
SUMMARY OF THE INVENTION
The scope of the present invention is to provide a method for integrating a non-linear passive device, such as a non-linear inductor, and to provide a corresponding circuit.
More specifically, the present invention may provide a non-linear inductor with the following relationship: 



  L
  =
  
    
      L
      0
    
    ·
    
      1
      
        1
        -
        
          k
          ·
          
            I
            L
            2
          
        
      
    
  




wherein, IL is a non-linear inductance current, L0 and k are constant values for generating the equation based on IL.

The present invention is based on the fact that non-linear passive devices are formed by using active components connected in a feedback loop for emulating the same behavior of the non-linear passive device. In other words, the present invention utilizes active devices operating in a feedback loop to implement the function of a non-linear inductor.
Other objects, features, and advantages of the present invention will become apparent from the following detailed description. It should be understood, however, that the detailed description and specific examples, while indicating preferred embodiments of the present invention, are given by way of illustration only and various modifications may naturally be performed without deviating from the present invention.



BRIEF DESCRIPTION OF THE DRAWINGS
A more complete understanding of the present invention may be had by reference to the following detailed description when taken in conjunction with the accompanying drawings, wherein:
FIG. 1 is a block diagram of a first embodiment of an electronic circuit in accordance with the present invention;
FIG. 2 is a detailed schematic diagram of the electronic circuit in accordance with the present invention;
FIG. 3 is a graph showing an inductance value versus current for the electronic circuit illustrated in FIG. 2; and
FIG. 4 is a graph showing a flow value versus current for the electronic circuit illustrated in FIG. 2.



DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
Referring now to FIG. 1, a block diagram of an embodiment of an integrated electronic circuit 1 in accordance with the present invention is shown. The integrated electronic circuit 1 implements a non-linear inductor Leq, and more specifically, a non-linear inductor having the following relationship: 



  L
  =
  
    
      L
      0
    
    ·
    
      1
      
        1
        -
        
          k
          ·
          
            I
            L
            2
          
        
      
    
  




wherein, IL is a non-linear inductance current, L0 and k are constant values for generating the equation based on IL.

The electronic circuit 1 includes a first logarithmic amplifier block 2 receiving an input current Iin at an input terminal 3. The input current Iin passes through a shunt block 8 or node receiving as input just the input current. The logarithmic amplifier block 2 has an output 4 connected to an input of a derivative block 5 performing a d/dt function on the input current signal Iin. A gain block 6 is connected in cascade downstream of the derivative block 5. The various blocks of the electronic circuit 1 are on a semiconductor substrate 12.
The input is also connected to the output of the gain block 6, and the current that is flowing from the input node is read by a shunt device and feed to the logarithmic amplifier block 2. The feedback connection 7 includes the gain block 6 for providing a feedback loop between the output of the derivative block 5 and the shunt block 8.
The present invention is implemented by interconnecting several blocks into a feedback loop as shown in FIG. 1, thus forming a non-linear inductor. The implemented function will be explained by starting with the relationship between voltage and current at the input terminals of the electronic circuit 1: 



  
    V
    
      i
      ⁢
      
         
      
      ⁢
      n
    
  
  =
  
    
      A
      ·
      
        d
        
          d
          t
        
      
    
    ⁢
    
      (
      
        log
        ⁡
        
          (
          
            
              1
              +
              
                I
                
                  i
                  ⁢
                  
                     
                  
                  ⁢
                  n
                
              
            
            
              1
              -
              
                I
                
                  i
                  ⁢
                  
                     
                  
                  ⁢
                  n
                
              
            
          
          )
        
      
      )
    
  




As may be appreciated, the gain term A represents the function of the gain block 6, the d/dt portion in parentheses is the operative result presented by the output of the derivative block 5 while the logarithmic block 2 works on the input current signal Iin.
Solving the derivative term: 



  
    
      d
      
        d
        t
      
    
    ⁢
    
      (
      
        log
        ⁡
        
          (
          
            
              1
              +
              
                I
                
                  i
                  ⁢
                  
                     
                  
                  ⁢
                  n
                
              
            
            
              1
              -
              
                I
                
                  i
                  ⁢
                  
                     
                  
                  ⁢
                  n
                
              
            
          
          )
        
      
      )
    
  
  =
  
    
      1
      
        (
        
          
            1
            +
            
              I
              
                i
                ⁢
                
                   
                
                ⁢
                n
              
            
          
          
            1
            -
            
              I
              
                i
                ⁢
                
                   
                
                ⁢
                n
              
            
          
        
        )
      
    
    ·
    
      
        
          
            
              d
              
                I
                
                  i
                  ⁢
                  
                     
                  
                  ⁢
                  n
                
              
            
            
              d
              t
            
          
          ·
          
            (
            
              1
              -
              
                I
                
                  i
                  ⁢
                  
                     
                  
                  ⁢
                  n
                
              
            
            )
          
        
        +
        
          
            
              d
              
                I
                
                  i
                  ⁢
                  
                     
                  
                  ⁢
                  n
                
              
            
            
              d
              t
            
          
          ·
          
            (
            
              1
              +
              
                I
                
                  i
                  ⁢
                  
                     
                  
                  ⁢
                  n
                
              
            
            )
          
        
      
      
        
          (
          
            1
            -
            
              I
              
                i
                ⁢
                
                   
                
                ⁢
                n
              
            
          
          )
        
        2
      
    
  




and simplifying: 



  
    
      
        
          d
          
            I
            
              i
              ⁢
              
                 
              
              ⁢
              n
            
          
        
        
          d
          t
        
      
      ·
      
        (
        
          1
          -
          
            I
            
              i
              ⁢
              
                 
              
              ⁢
              n
            
          
          +
          1
          +
          
            I
            
              i
              ⁢
              
                 
              
              ⁢
              n
            
          
        
        )
      
    
    
      
        (
        
          1
          +
          
            I
            
              i
              ⁢
              
                 
              
              ⁢
              n
            
          
        
        )
      
      ·
      
        (
        
          1
          -
          
            I
            
              i
              ⁢
              
                 
              
              ⁢
              n
            
          
        
        )
      
    
  
  =
  
    
      2
      ·
      
        
          d
          
            I
            
              i
              ⁢
              
                 
              
              ⁢
              n
            
          
        
        
          d
          t
        
      
    
    
      (
      
        1
        -
        
          I
          
            i
            ⁢
            
               
            
            ⁢
            n
          
          2
        
      
      )
    
  




a final result according to the following relationship (Eq. 1) is obtained: 



  
    
      
        
          V
          
            i
            ⁢
            
               
            
            ⁢
            n
          
        
        =
        
          
            
              A
              ·
              
                d
                
                  d
                  t
                
              
            
            ⁢
            
              (
              
                log
                ⁡
                
                  (
                  
                    
                      1
                      +
                      
                        I
                        
                          i
                          ⁢
                          
                             
                          
                          ⁢
                          n
                        
                      
                    
                    
                      1
                      -
                      
                        I
                        
                          i
                          ⁢
                          
                             
                          
                          ⁢
                          n
                        
                      
                    
                  
                  )
                
              
              )
            
          
          =
          
            A
            ·
            
              2
              
                (
                
                  1
                  -
                  
                    I
                    
                      i
                      ⁢
                      
                         
                      
                      ⁢
                      n
                    
                    2
                  
                
                )
              
            
            ·
            
              
                d
                
                  I
                  
                    i
                    ⁢
                    
                       
                    
                    ⁢
                    n
                  
                
              
              
                d
                t
              
            
          
        
      
    
    
      
        Eq
        .
        
           
        
        ⁢
        1
      
    
  




The relationship between voltage and current for a non-linear inductor is the following (Eq. 2): 



  
    
      
        
          V
          L
        
        =
        
          
            L
            ⁡
            
              (
              
                I
                L
              
              )
            
          
          ·
          
            
              d
              
                I
                L
              
            
            
              d
              t
            
          
        
      
    
    
      
        Eq
        .
        
           
        
        ⁢
        2
      
    
  




By comparing equations 1 and 2, a new relationship may be obtained (Eq. 3): 



  
    
      
        
          L
          ⁡
          
            (
            
              I
              L
            
            )
          
        
        =
        
          A
          ·
          
            2
            
              (
              
                1
                -
                
                  I
                  
                    i
                    ⁢
                    
                       
                    
                    ⁢
                    n
                  
                  2
                
              
              )
            
          
        
      
    
    
      
        Eq
        .
        
           
        
        ⁢
        3
      
    
  




This equation (Eq. 3) gives a relationship between current and voltage that follows the required behavior, except for a k factor that could be easily added by inserting a gain stage before the logarithmic amplifier 2.

One possible embodiment of the circuit 1 is shown in the schematic diagram of FIG. 2. The logarithmic amplifier block 2 is implemented by a transconductance differential cell 9 having differential current inputs 3′, 3′′ and corresponding current outputs 4′, 4′′. The cell 9 has two symmetric transistor branches 9′, 9′′ each coupled to a first voltage supply reference Vd through a current generator Ix, and to a second voltage reference GND through a resistor R9, or as an alternative, a current generator.
The transistors of each branch 9′, 9′′ could be bipolar transistors, or a bipolar transistor and a MOS transistor. More specifically, two input bipolar transistors and two out bipolar transistors are used in this embodiment. The current inputs 3′, 3′′ are set between the current generator Ix and the first input transistor of each branch 9′, 9′′ according to FIG. 2. This is while the current outputs 4′, 4′′ are set between the input and the output transistors of each branch.
Each current output 4′, 4′′ (Ix+Is; Ix−Is) is connected to the driving terminal of a bipolar transistor 5′, 5′′ having the first conduction terminal respectively coupled to the first voltage reference Vd and to the second voltage reference GND. The second conduction terminal of each transistor 5′, 5′′ is coupled to the second voltage reference GND through a current generator.
The second conduction terminal of each transistor 5′, 5′′ is also coupled through a capacitor C to a corresponding input terminal 10′, 10′′ of a double ended gain stage 10 having a resistor R feedback connected between each corresponding output 11′, 11′′ and input 10′, 10′′ terminals. A voltage potential Vo is detectable between the output terminals 11′, 11′′. Both the output terminals 11′, 11′′ of the gain stage 10 are feedback connected to the input terminals 3′, 3′′ thus closing the feedback loop 7.
The activity of the electronic circuit 1 shown in FIG. 2 may be summarized by the following relationship: 



  
    V
    ⁢
    
       
    
    ⁢
    o
  
  =
  
    
      V
      ⁢
      
         
      
      ⁢
      s
    
    =
    
      
        d
        
          d
          t
        
      
      ⁢
      
        
          {
          
            
              V
              T
            
            ⁢
            
              ln
              ⁡
              
                (
                
                  
                    1
                    +
                    
                      
                        I
                        ⁢
                        
                           
                        
                        ⁢
                        s
                      
                      
                        I
                        ⁢
                        
                           
                        
                        ⁢
                        x
                      
                    
                  
                  
                    1
                    -
                    
                      
                        I
                        ⁢
                        
                           
                        
                        ⁢
                        s
                      
                      
                        I
                        ⁢
                        
                           
                        
                        ⁢
                        x
                      
                    
                  
                
                )
              
            
          
          }
        
        ·
        C
        ·
        R
      
    
  






  
    V
    ⁢
    
       
    
    ⁢
    s
  
  =
  
    
      
        
          C
          ·
          R
          ·
          
            V
            T
          
        
        
          I
          ⁢
          
             
          
          ⁢
          x
        
      
      ·
      2
      ·
      
        1
        
          1
          -
          
            
              (
              
                
                  I
                  ⁢
                  
                     
                  
                  ⁢
                  s
                
                
                  I
                  ⁢
                  
                     
                  
                  ⁢
                  x
                
              
              )
            
            2
          
        
      
      ·
      
        
          
            d
            I
          
          ⁢
          
             
          
          ⁢
          s
        
        
          d
          t
        
      
    
    =
    
      L
      ⁢
      
         
      
      ⁢
      e
      ⁢
      
         
      
      ⁢
      
        q
        ·
        
          
            
              d
              I
            
            ⁢
            
               
            
            ⁢
            s
          
          
            d
            t
          
        
      
    
  




where Vs is the input voltage, Is is the input current, Ix is the biasing current and Leq is the equivalent inductance value of the whole circuit 1 according to the following formula: 



  
    L
    ⁢
    
       
    
    ⁢
    e
    ⁢
    
       
    
    ⁢
    q
  
  =
  
    
      
        C
        ·
        R
        ·
        
          V
          T
        
        ·
        2
      
      
        I
        ⁢
        
           
        
        ⁢
        x
      
    
    ·
    
      1
      
        1
        -
        
          
            (
            
              
                I
                ⁢
                
                   
                
                ⁢
                s
              
              
                I
                ⁢
                
                   
                
                ⁢
                x
              
            
            )
          
          2
        
      
    
  




The corresponding flow value is given by: 



  
    ∫
    
      V
      ⁢
      
         
      
      ⁢
      
        s
        ·
        
          d
          t
        
      
    
  
  =
  
    
      
        C
        ·
        R
        ·
        
          V
          T
        
        ·
        1
      
      ⁢
      
        n
        ⁢
        
          (
          
            
              1
              +
              
                
                  I
                  ⁢
                  
                     
                  
                  ⁢
                  s
                
                
                  I
                  ⁢
                  
                     
                  
                  ⁢
                  x
                
              
            
            
              1
              -
              
                
                  I
                  ⁢
                  
                     
                  
                  ⁢
                  s
                
                
                  I
                  ⁢
                  
                     
                  
                  ⁢
                  x
                
              
            
          
          )
        
      
    
    =
    
      ∅
      ⁢
      
        (
        Is
        )
      
    
  




The graphs in FIGS. 4 and 5 show the evolution of the inductance value Lep and the flow value φ versus the current input Is for the circuit as described above.

Having described and illustrated the principles of the invention in a preferred embodiment thereof, it should be apparent that the invention can be modified in arrangement and detail without departing from such principles. We claim all modifications and variations within the scope of the following claims.

## Claims

1. An integrated electronic circuit comprising:
a plurality of active circuits connected together in cascade, said plurality of active circuits comprising a logarithmic amplifier circuit; and 
a feedback loop between an output of a last active circuit and an input of a first active circuit so that said plurality of active devices function as a non-linear inductor.

2. An integrated electronic circuit according to claim 1, wherein said plurality of active circuits further comprise a derivative circuit connected to said logarithmic amplifier circuit, and a gain circuit connected to said derivative circuit; and wherein said feedback loop is between an output of said gain circuit and an input of said logarithmic amplifier circuit.

3. An integrated electronic circuit according to claim 2, wherein said logarithmic amplifier circuit comprises a transconductor differential cell.

4. An integrated electronic circuit according to claim 1, wherein the inductor has the following relationship: 



  L
  =
  
    
      L
      0
    
    ·
    
      1
      
        1
        -
        
          k
          ·
          
            I
            L
            2
          
        
      
    
  




wherein, IL is a non-linear inductance current, L0 and k are constant values for generating the equation based on IL.

5. An integrated electronic circuit comprising:
a logarithmic amplifier circuit; 
a derivative circuit connected to an output of said logarithmic amplifier circuit; 
a gain circuit connected to an output of said derivative circuit; and 
a feedback loop between an output of said gain circuit and an input of said logarithmic amplifier circuit so that said logarithmic amplifier circuit, said derivative circuit, and said gain circuit function as a non-linear inductor.

6. An integrated electronic circuit according to claim 5, wherein said logarithmic amplifier circuit comprises a transconductor differential cell.

7. An integrated electronic circuit according to claim 5, wherein the inductor has the following relationship: 



  L
  =
  
    
      L
      0
    
    ·
    
      1
      
        1
        -
        
          k
          ·
          
            I
            L
            2
          
        
      
    
  




wherein, IL is a non-linear inductance current, L0 and k are constant values for generating the equation based on IL.

8. An electronic circuit comprising:
a semiconductor substrate; 
a logarithmic amplifier circuit on said semiconductor substrate; 
a derivative circuit on said semiconductor substrate and connected to an output of said logarithmic amplifier circuit; 
a gain circuit on said semiconductor substrate and connected to an output of said derivative circuit; an 
a feedback loop between an output of said gain circuit and an input of said logarithmic amplifier circuit so that said logarithmic amplifier circuit, said derivative circuit, and said gain circuit function as a non-linear inductor.

9. An electronic circuit according to claim 8, wherein said logarithmic amplifier circuit comprises a transconductor differential cell.

10. An electronic circuit according to claim 9, wherein the inductor has the following relationship: 



  L
  =
  
    
      L
      0
    
    ·
    
      1
      
        1
        -
        
          k
          ·
          
            I
            L
            2
          
        
      
    
  




wherein, IL is a non-linear inductance current, L0 and k are constant values for generating the equation based on IL.

11. A method for providing a non-linear inductor comprising:
connecting a plurality of active circuits together in cascade, the plurality of active circuits comprising a logarithmic amplifier circuit; and 
providing a feedback loop between an output of a last active circuit and an input of a first active circuit so that the plurality of active circuits function as the non-linear inductor.

12. A method according to claim 11, wherein the plurality of active circuits further comprise a derivative circuit, and a gain circuit connected together; and wherein the feedback loop is between an output of the gain circuit and an input of the logarithmic amplifier circuit.

13. A method according to claim 11, wherein the logarithmic amplifier circuit comprises a transconductor differential cell.

14. A method according to claim 11, wherein the inductor has the following relationship: 



  L
  =
  
    
      L
      0
    
    ·
    
      1
      
        1
        -
        
          k
          ·
          
            I
            L
            2
          
        
      
    
  




wherein, IL is a non-linear inductance current, L0 and k are constant values for generating the equation based on IL.