# Patent

## Title
Filter with combined resonator and integrator

## Abstract

A filter comprises an integrator, a signal feeding path, a first operational amplifier and a second capacitor. The integrator comprises a first input terminal and a first output terminal. The signal feeding path comprises: a first resistor, having a first terminal coupled to the first output terminal; a first capacitor, having a first terminal coupled to the second terminal of the first resistor; and a second resistor, having a first terminal coupled to the integrator and having a second terminal coupled to the second terminal of the first capacitor. The first operational amplifier comprises a second input terminal coupled to the second terminal of the first resistor and the first terminal of the first capacitor, and comprises a second output terminal. The second capacitor comprises a first terminal coupled to the second terminal of the first capacitor, and comprises a second terminal coupled to the second output terminal.

## Background
BACKGROUND
A continuous-time delta-sigma ADC (Analog to Digital Converter) always includes a resonator having a single op-amp (operational amplifier). The resonator determines notch points that can suppress noise. However, the notch points are determined by gain values for the op-amp included in the resonator, and it is difficult to achieve high gain via single op-amp. The performance loss due to finite op-amp gain may no longer be neglected for high dynamic range device.
FIG. 1 is a circuit diagram illustrating a related art resonator having a single operational amplifier. As shown in FIG. 1, the input signal V1n has been processed by the integrator 101 before enters the resonator 103. The resonator 103 includes an op-amp OP and a plurality of resistors RC2-RC5 and CC2-CC5. As above-mentioned description, high gain can not be provided by only one op-amp, thus the resonator 103 has above-mentioned disadvantage. Some related arts provide resonators having more than one op-amps, such resonator also occupies a large circuit region, however.
SUMMARY
Therefore, one objective of the present application is to provide a filter (e.g., a delta-sigma modulator) that can provide high gain via utilizing less operational amplifiers. By structurally combining a resonator and an integrator, the proposed filter can have n-th order while less than n op-amps are required. For example, a 3rd order loop filter with only two op-amps can be achieved. The power dissipation and performance are thus improved.
One embodiment of the present application discloses a filter, which comprises an integrator, a signal feeding path, a first operational amplifier and a second capacitor. The integrator comprises a first input terminal and a first output terminal. The signal feeding path comprises: a first resistor, having a first terminal coupled to the first output terminal, and having a second terminal; a first capacitor, having a first terminal coupled to the second terminal of the first resistor, and having a second terminal; and a second resistor, having a first terminal coupled to the integrator and having a second terminal coupled to the second terminal of the first capacitor. The first operational amplifier comprises a second input terminal coupled to the second terminal of the first resistor and the first terminal of the first capacitor, and comprising a second output terminal. The second capacitor comprises a first terminal coupled to the second terminal of the first capacitor, and comprising a second terminal coupled to the second output terminal. Such embodiment can be varied to process differential input.
Another embodiment of the present application discloses a filter comprising a first operational amplifier, a first resistor a first capacitor, a signal feeding path and an integrator. The first operational amplifier comprises a first op-amp input terminal and a first op-amp output terminal. The first resistor comprise a first terminal coupled to a first input terminal, and comprises a second terminal coupled to the first op-amp input terminal. The first capacitor comprises a first terminal coupled to the second terminal of the first resistor, and comprises a second terminal. The signal feeding path comprises a second capacitor having a first terminal coupled to the second terminal of the first capacitor and having a second terminal coupled to the first op-amp output terminal; and a second resistor, having a first terminal coupled to the second terminal of the first capacitor, and having a second terminal coupled to the integrator. The integrator comprises a second input terminal coupled to the first op-amp output terminal and comprises a first output terminal. Such embodiment can be varied to process differential input.
In view of above-mentioned embodiments, a resonator can be formed based on a single op-amp and a part of circuit of an integrator, thus high gain can be acquired and the problem of large circuit region can be avoided.
These and other objectives of the present invention will no doubt become obvious to those of ordinary skill in the art after reading the following detailed description of the preferred embodiment that is illustrated in the various figures and drawings.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a circuit diagram illustrating a related art resonator having a single operational amplifier.
FIG. 2 is a circuit diagram illustrating a filter having a single ended input and output, according to one embodiment of the present application.
FIG. 3 is an example of a detail circuit structure for the embodiment illustrated in FIG. 2.
FIG. 4 is a circuit diagram illustrating a filter having a differential input and output, according to one embodiment of the present application.
FIG. 5 is an example of a detail circuit structure for the embodiment illustrated in FIG. 4.
FIG. 6 is a circuit diagram illustrating a filter having a single ended input and output, according to another embodiment of the present application.
FIG. 7 is an example of a detail circuit structure for the embodiment illustrated in FIG. 6.
FIG. 8 is a circuit diagram illustrating a filter having a differential input and output, according to another embodiment of the present application.
FIG. 9 is an example of a detail circuit structure for the embodiment illustrated in FIG. 8.



DETAILED DESCRIPTION
The filter disclosed by the present application is detailedly explained in the following description, but please note that the filter disclosed by the present application can be utilized to provide other functions besides the continuous-time sigma-delta modulator. FIG. 2 is a circuit diagram illustrating a filter 200 having a single-ended input and output, according to one embodiment of the present application. As shown in FIG. 2, the filter 200 comprises an integrator 201, a RC path comprising a resistor R1, a capacitor C1 and a resistor R2, an operational amplifier OP1, and a capacitor C2.
For more detail, the integrator 201 comprises an input terminal IN1 and an output terminal Out1. The resistor R1 has a first terminal coupled to the output terminal Out1, and has a second terminal. The capacitor C1 has a first terminal coupled to the second terminal of the resistor R1, and has a second terminal. The resistor R2 has a first terminal coupled to the integrator 201 and has a second terminal coupled to the second terminal of the capacitor C1. The operational amplifier OP1 comprises an input terminal IN2 coupled to the second terminal of the resistor R1 and the first terminal of the capacitor C1, and comprises another output terminal Out2. The capacitor C2 comprises a first terminal coupled to the second terminal of the capacitor C1, and comprises a second terminal coupled to the output terminal Out2. Please note some terminals in FIG. 2 and the following figures are not marked by symbols for simplicity of drawings, for example, the first, second terminals of the resistor R1, R2, C1. Persons skilled in the art can easily understand the meaning via the figures and the description thereof.
If a signal is transmitted to the input terminal IN1, the signal is processed by the integrator 201 and then processed by another integrator stage formed by the operational amplifier OP1, the resistor R1, and the capacitors C1, C2. Moreover, the output signal from the output terminal Out1 is also transmitted back to the integrator 201 via the RC signal feeding path comprising the resistor R1, the capacitor C1 and the resistor R2. The integrator 201, the RC signal feeding path and the operational amplifier OP1 together provide functionalities of a resonator. Therefore, the signal at the output terminal Out2 is generated not only based on the signal transmitted to the input terminal IN1 but also the signal feed backed via the signal feeding path. Under this circuit structure, a high gain may be acquired while power dissipation is also suppressed.
FIG. 3 is an example of a detail circuit structure for the embodiment illustrated in FIG. 2. As shown in FIG. 3, the integrator 201 comprises: an operational amplifier OP2, a capacitor C3, and a resistor R3. The operational amplifier OP2 comprises an op-amp output terminal OOP1 served as the output terminal Out1, and an op-amp input terminal INOP1. The capacitor C3 comprises a first terminal coupled to the op-amp input terminal INOP1 and comprises a second terminal coupled to the output terminal Out1. The resistor R3 comprises a first terminal coupled to the input terminal IN1, and comprises a second terminal coupled to the op-amp input terminal INOP1.
In this embodiment, the op-amp input terminal INOP1 has a polarity opposite to which of the output terminal Out1. The input terminal IN2 receives a signal having a polarity the same as which of the signal output by the output terminal Out1. Therefore, in this embodiment, the filter 200 further comprises an inverter INV. The inverter INV is provided between the resistor R2 and the op-amp input terminal INOP1, to invert output from the first terminal of the resistor R2 to the op-amp input terminal INOP1. However, the inverter INV may be omitted if the integrator 201 has different structures (an example will be given later).
The frequency response of the integrator 201 in FIG. 3 is




  
    K
    0
  
  S




and the frequency response for the operational amplifier OP1, resistors R1, R2 and capacitors C1, C2 is





  
    K
    1
  
  ⁢
  
    
      
        
          
            K
            2
          
          ⁢
          S
        
        +
        
          K
          3
        
      
      
        S
        2
      
    
    .
  




Also, the frequency response for the whole circuit in FIG. 3 is





  
    
      
        K
        4
      
      +
      
        
          K
          5
        
        ⁢
        S
      
    
    
      S
      ⁡
      
        (
        
          
            S
            2
          
          +
          
            W
            0
            2
          
        
        )
      
    
  
  .




In the above-mentioned frequency response equations,





  
    
      K
      0
    
    =
    
      1
      
        
          R
          3
        
        ⁢
        
          C
          3
        
      
    
  
  ,
  
    
      K
      1
    
    =
    1
  
  ,








  
    
      K
      2
    
    =
    
      
        (
        
          
            C
            1
          
          +
          
            C
            2
          
        
        )
      
      
        
          R
          1
        
        ×
        
          C
          1
        
        ×
        
          C
          2
        
      
    
  
  ,








  
    
      K
      3
    
    =
    
      1
      
        
          R
          1
        
        ×
        
          R
          2
        
        ×
        
          C
          1
        
        ×
        
          C
          2
        
      
    
  
  ,








  
    
      K
      4
    
    =
    
      1
      
        
          R
          1
        
        ×
        
          R
          2
        
        ×
        
          R
          3
        
        ×
        
          C
          1
        
        ×
        
          C
          2
        
        ×
        
          C
          3
        
      
    
  
  ,








  
    
      K
      5
    
    =
    
      
        
          C
          1
        
        +
        
          C
          2
        
      
      
        
          R
          1
        
        ×
        
          R
          3
        
        ×
        
          C
          1
        
        ×
        
          C
          2
        
        ×
        
          C
          3
        
      
    
  
  ,








  
    W
    0
  
  =
  
    
      
        (
        
          1
          
            
              R
              1
            
            ×
            
              R
              2
            
            ×
            
              C
              1
            
            ×
            
              C
              3
            
          
        
        )
      
      0.5
    
    .
  




The notch point of the filter 300 is determined by the resistors R1, R2 and capacitors C1, C3. The notch shape is sharp enough because it implements the resonator with two op-amps OP1, OP2. As can be seen, by structurally combining resonator and integrator, the filter 300 has 3-rd order while only two op-amps are utilized. The power dissipation and resonator performance are thus improved.

FIG. 4 is a circuit diagram illustrating a filter having a differential input and output, according to one embodiment of the present application. In FIG. 4, the integrator 401, the resistor R11, the capacitor C11, the resistor R21, the operational amplifier OP1, and the capacitor C21 have similar arrangements of the integrator 201, the resistor R1, the capacitor C1, the resistor R2, the operational amplifier OP1, and the capacitor C2 in FIG. 2. The resistor R12, the capacitor C12, the resistor R22, and the capacitor C22 have an arrangement symmetric with the resistor R11, the capacitor C11, the resistor R21 and the capacitor C21.
FIG. 5 is an example of a detail circuit structure for the embodiment illustrated in FIG. 4. As shown in FIG. 5, the integrator 401 comprises: an amplifier OP2, resistors R3, R4, and capacitors C3, C4. The operational amplifier OP2 comprises op-amp input terminals INOP1, INOP2, and op-amp output terminals OOP1, OOP2. In this embodiment, the op-amp output terminal OOP1 serves as the output terminal Out11 and the op-amp output terminal OOP2 serves as the output terminal Out12. The capacitor C3 comprises a first terminal coupled to the op-amp input terminals INOP1 and the first terminal of the resistor R22, and comprises a second terminal coupled to the output terminal Out11. The resistor R3 comprises a first terminal coupled to the input terminal IN11, and comprises a second terminal coupled to the op-amp input terminal INOP1. The capacitor C4 comprises a first terminal coupled to the op-amp input terminals INOP2 and the first terminal of the resistor R21, and comprises a second terminal coupled to the output terminal Out12. The resistor R4 comprises a first terminal coupled to the input terminal IN12, and comprises a second terminal coupled to the op-amp input terminal INOP2. Since the op-amps have differential structure, the inverter INV shown in FIG. 3 can be omitted. To be more detailed, a negative signal feedback path is formed from the positive op-amp output terminal OOP1 to the negative op-amp output terminal OOP2, through the resistor R11, the capacitor C11, the resistor R21, and the capacitor C4, and another negative signal feedback path is formed from the negative op-amp output terminal OOP2 to the positive op-amp output terminal OOP1, through the resistor R12, the capacitor C12, the resistor R22, and the capacitor C3. The op-amp input terminals INOP1 has a polarity opposite to which of the output terminal Out11, the op-amp input terminals INOP2 has a polarity opposite to which of the output terminal Out12, the input terminal IN21 receives a signal having a polarity to the same as which of a signal output by the output terminal Out11, and the input terminal IN22 receives a signal having a polarity the same as which of the signal output by the output terminal Out12. The notch point of the filter is determined by the impedance values of the resistor R11, the capacitor C11, the resistor R21, the capacitor C4, the resistor R12, the capacitor C12, the resistor R22, and the capacitor C3.
In one embodiment, the resistors R11, R12 have substantially the same resistance value, the capacitor C11, C12 have substantially the same capacitance value, the resistors R21, R22 have substantially the same resistance value. The capacitors C3 and C4 have substantially the same capacitance value. Therefore, the frequency response thereof will be similar to which in FIG. 3. That is, the notch shape is sharp enough since the resonator is implemented by two op-amps OP1, OP2, and by structurally combining resonator and integrator, the differential filter shown in FIG. 4 or FIG. 5 has 3-rd order while only two op-amps are utilized. The power dissipation and resonator performance are thus improved.
The arrangements for the embodiments shown in FIG. 2-FIG. 5 can be swapped. FIG. 6 is a circuit diagram illustrating a filter having a single ended input and output, according to another embodiment of the present application. As shown in FIG. 6, the filter 600 comprises: an operational amplifier OP1, resistors R1, R2 capacitors C1, C2 and an integrator 601. The operational amplifier OP1 comprises an op-amp input terminal INOP1 and an op-amp output terminal OOP1. The resistor R1 has a first terminal coupled to an input terminal IN1, and has a second terminal coupled to the op-amp input terminal INOP1. The capacitor C1 has a first terminal coupled to the second terminal of the resistor R1, and has a second terminal. The resistor R2 has a first terminal coupled to the second terminal of the capacitor C1, and has a second terminal coupled to the integrator 601. The capacitor C2 has a first terminal coupled to the second terminal of the capacitor C1 and has a second terminal coupled to the op-amp output terminal OOP1. The integrator 601 comprises an input terminal IN2 coupled to the op-amp output terminal OOP1 and comprises an output terminal Out1.
In the embodiment of FIG. 6, the signal inputted to the input terminal IN1 is processed by an integrator formed by the operational amplifier OP1, the resistor R1, capacitors C1, C2 and then transmitted to the input terminal IN2. Also, there is a signal feeding path comprising resistor R2 and the capacitor C2. The integrator 601, the signal feeding path (e.g., R2, C2) and the operational amplifier OP1 together provide functionalities of a resonator. Therefore, similar performance can be obtained as compared with the above embodiments.
FIG. 7 is an example of a detail circuit structure for the embodiment illustrated in FIG. 6. As shown in FIG. 7, the integrator 601 comprises an operational amplifier OP2, a capacitor C3, and a resistor R3. The second operational amplifier OP2 comprises an op-amp output terminal OOP2 served as the output terminal Out1, and an op-amp input terminal INOP2. The capacitor C3 comprises a first terminal coupled to the op-amp input terminal INOP2 and comprises a second terminal coupled to the first output terminal Out1. The third resistor R3 comprises a first terminal coupled to the input terminal IN2, and comprises a second terminal coupled to the op-amp input terminal INOP2. In this embodiment, the filter 700 further comprises an inverter INV. The inverter INV is provided between the resistor R2 and the op-amp input terminal INOP2, to invert output from the second terminal of the resistor R2 to the op-amp input terminal INOP2. The frequency response for the circuit in FIG. 7 is the same as which of the embodiment in FIG. 3, thus it is omitted for brevity here.
FIG. 8 is a circuit diagram illustrating a filter having a differential input and output, according to one embodiment of the present application. The operational amplifier OP1, the resistor R11, the capacitor C11, the resistor R21, the integrator 801, and the capacitor C21 in FIG. 8 have similar arrangement as which of the operational amplifier OP1, the resistor R1, the capacitor C1, the resistor R2, the integrator 601, and the capacitor C2 in FIG. 6. The resistor R12, the capacitor C12, the resistor R22, and the capacitor C22 have an arrangement symmetric with the resistor R11, the capacitor C11, the resistor R21, and the capacitor C21, thus the detail description thereof is omitted for brevity here.
FIG. 9 is an example of a detail circuit structure for the embodiment illustrated in FIG. 8. As shown in FIG. 9, the integrator 801 comprises an operational amplifier OP2, resistors R31, R32, capacitors C31, C32. The operational amplifier OP2 comprises op-amp input terminals INOP3, INOP4 and op-amp output terminal OOP3, OOP4. The op-amp output terminal OOP3 serves as the output terminal Out21, and the op-amp output terminal OOP4 serves as the output terminal Out22. The capacitor C31 comprises a first terminal coupled to the op-amp input terminal INOP3 and comprises a second terminal coupled to the op-amp output terminal OOP3. The resistor R31 comprises a first terminal coupled to the input terminal IN21, and comprises a second terminal coupled to the op-amp input terminal INOP3 coupled to a terminal of the resistor R22. The capacitor C32 comprises a first terminal coupled to the op-amp input terminal INOP4 and comprises a second terminal coupled to the op-amp output terminal OOP4. The resistor R32 comprises a first terminal coupled to the input terminal IN22, and comprises a second terminal coupled to the op-amp input terminal INOP4 coupled to a terminal of the resistor R21.
Since the op-amps have differential structure, the inverter INV shown in FIG. 7 can be omitted. To be more detailed, a negative signal feedback path is formed from the positive op-amp output terminal (e.g, the output terminal Out11), through the resistor R31, the capacitor C31, the resistor R22, the capacitor C22, to the negative op-amp output terminal (e.g, the output terminal Out12), and another negative signal feedback path is formed from the negative op-amp output terminal, through the resistor R32, the capacitor C32, the resistor R21, the capacitor C21, to the positive op-amp output terminal. The notch point of the filter is determined by the impedance values of the resistor R31, the capacitor C31, the resistor R22, the capacitor C22, the resistor R32, the capacitor C32, the resistor R21, and the capacitor C21.
In one embodiment, the resistors R11, R12 have substantially the same resistance value, the capacitor C11, C12 have substantially the same capacitance value, the resistors R21, R22 have substantially the same resistance value. The capacitors C21 and C22 have substantially the same capacitance value. In such case, the frequency response is similar as which of the embodiment in FIG. 7.
To conclude, the proposed filter may be regarded as comprising a first integrator, a second integrator and an impedance element. The first integrator (such as the integrator 201/401/601/801) comprises a first op-amp (such as OP2), and a first across-network (such as the capacitor C3/C4/C31/C32) coupling across the first op-amp. The second integrator comprises a second op-amp (such as OP1), and a second across-network (such as the capacitors C1 and C2/C12 and C22/C11 and C21) coupling across the second op-amp. The impedance element, such as the resistor R2/R21/R22, has a first terminal coupled to a terminal of the first across-network and has a second terminal coupled to an intermediate point of the second across-network. As shown in the embodiments in figures, the second across-network comprises a first impedance network (ex. C1) and a second impedance network (ex. C2), the first impedance network is coupled between an input of the second op-amp and the intermediate point, and the second impedance network is coupled between the intermediate point and an output of the second op-amp.
Also, to put it in another way, the proposed filter can be regarded as comprising a resonator and an integrator. The resonator comprises a first op-amp (ex. OP2), a second op-amp (ex. OP1) and a negative feedback path comprising a plurality of impedance elements so arranged such that at least a notch point is provided. The negative feedback path comprises a first resistor and a first capacitor (ex. R1 and C1 in FIG. 3, or R12 and C12, or R11 and C11 in FIG. 5). The integrator comprises the second op-amp (ex. the OP1), the first resistor, the first capacitor and a second capacitor (ex. C2 in FIG. 3, or C22, or C21 in FIG. 5). The first resistor, the first capacitor and the second capacitor forms at least a portion of a RC network for the integrator.
In view of above-mentioned embodiments, a filter that can provide high gain (e.g., good notch shaping performance) via utilizing less operational amplifiers is achieved. By structurally combining a resonator and an integrator, the proposed filter can have n-th order while less than n op-amps are required. The power dissipation and performance are thus improved, and the problem of large circuit region can be avoided.
Those skilled in the art will readily observe that numerous modifications and alterations of the device and method may be made while retaining the teachings of the invention. Accordingly, the above disclosure should be construed as limited only by the metes and bounds of the appended claims.

## Claims

1. A filter, comprising:
an integrator, comprising a first input terminal and a first output terminal;
a first signal feeding path, comprising:
a first resistor, having a first terminal coupled to the first output terminal, and having a second terminal;
a first capacitor, having a first terminal coupled to the second terminal of the first resistor, and having a second terminal; and
a second resistor, having a first terminal coupled to the integrator and having a second terminal coupled to the second terminal of the first capacitor;

a first operational amplifier, comprising a second input terminal coupled to the second terminal of the first resistor and the first terminal of the first capacitor, and comprising a second output terminal; and
a second capacitor, comprising a first terminal coupled to the second terminal of the first capacitor, and comprising a second terminal coupled to the second output terminal.

2. The filter of claim 1, further comprising an inverter, wherein the integrator comprises:
a second operational amplifier, comprising a op-amp output terminal served as the first output terminal, and a op-amp input terminal;
a third capacitor, comprising a first terminal coupled to the op-amp input terminal and comprising a second terminal coupled to the first output terminal; and
a third resistor, comprising a first terminal coupled to the first input terminal, and comprising a second terminal coupled to the op-amp input terminal;
where the inverter is provided between the second resistor and the op-amp input terminal, to invert output from the first terminal of the second resistor to the op-amp input terminal.

3. The filter of claim 1, wherein the integrator comprises a second operational amplifier having an op-amp input terminal having a polarity opposite to which of the first output terminal, where the second input terminal receives a signal having a polarity the same as which of the signal output by the first output terminal.

4. The filter of claim 1, wherein impedance values of the first resistor, the first capacitor, the second resistor and a capacitor of the integrator determine at least one notch point of the filter.

5. The filter of claim 1, wherein:
the integrator further comprises a third input terminal and a third output terminal;
wherein the first operational amplifier further comprises a fourth input terminal and a fourth output terminal;
wherein the filter further comprises:
a second signal feeding path, comprising:
a third resistor, having a first terminal coupled to the third output terminal, and having a second terminal coupled to the fourth input terminal;
a third capacitor, having a first terminal coupled to the second terminal of the third resistor, and having a second terminal; and
a fourth resistor, having a first terminal coupled to the integrator and having a second terminal coupled to the second terminal of the third capacitor; and

a fourth capacitor, comprising a first terminal coupled to the second terminal of the third capacitor, and comprising a second terminal coupled to the fourth output terminal.

6. The filter of claim 5, wherein the integrator further comprises:
a second operational amplifier, comprising a first op-amp input terminal, a second op-amp input terminal, a first op-amp output terminal, and a second op-amp output terminal, wherein the first op-amp output terminal serves as the first output terminal and the second op-amp output terminal serves as the second output terminal;
a fifth capacitor, comprising a first terminal coupled to the first op-amp input terminal and the first terminal of the fourth resistor, and comprising a second terminal coupled to the first output terminal;
a fifth resistor, comprising a first terminal coupled to the first input terminal, and comprising a second terminal coupled to the first op-amp input terminal;
a sixth capacitor, comprising a first terminal coupled to the second op-amp input terminal and the first terminal of the second resistor, and comprising a second terminal coupled to the second output terminal; and
a sixth resistor, comprising a first terminal coupled to the second input terminal, and comprising a second terminal coupled to the second op-amp input terminal.

7. The filter of claim 6, wherein the first op-amp input terminal has a polarity opposite to which of the first output terminal, where the second op-amp input terminal has a polarity opposite to which of the third output terminal, where the second input terminal receives a signal having a polarity the same as which of a signal output by the first output terminal, where the fourth input terminal receives a signal having a polarity the same as which of the signal output by the third output terminal.

8. The filter of claim 5, wherein impedance values of the first resistor, the second resistor, the third resistor, the fourth resistor, the first capacitor, the third capacitor and capacitors of the integrator determine at least one notch point of the filter.

9. The filter of claim 5, wherein the first resistor and the third resistor have substantially the same resistance value, the first capacitor and the third capacitor have substantially the same capacitance value, the second resistor and the fourth resistor have substantially the same resistance value, and the second capacitor and the fourth capacitor have substantially the same capacitance value.

10. A filter, comprising:
a first operational amplifier, comprising a first op-amp input terminal and a first op-amp output terminal;
a first resistor, having a first terminal coupled to a first input terminal, and having a second terminal coupled to the first op-amp input terminal;
a first capacitor, having a first terminal coupled to the second terminal of the first resistor, and having a second terminal;
a first signal feeding path, comprising:
a second capacitor, having a first terminal coupled to the second terminal of the first capacitor and having a second terminal coupled to the first op-amp output terminal;
and
a second resistor, having a first terminal coupled to the second terminal of the first capacitor, and having a second terminal coupled to an integrator; and

the integrator, comprising a second input terminal coupled to the first op-amp output terminal and comprising a first output terminal.

11. The filter of claim 10, further comprising an inverter, wherein the integrator comprises:
a second operational amplifier, comprising a second op-amp output terminal served as the first output terminal, and a second op-amp input terminal;
a third capacitor, comprising a first terminal coupled to the second op-amp input terminal and comprising a second terminal coupled to the first output terminal; and
a third resistor, comprising a first terminal coupled to the second input terminal, and comprising a second terminal coupled to the second op-amp input terminal;
where the inverter is provided between the second resistor and the second op-amp input terminal, to invert output from the second terminal of the second resistor to the second op-amp input terminal.

12. The filter of claim 10, wherein impedance values of the second resistor, the second capacitor, and the integrator determine at least one notch point of the filter.

13. The filter of claim 10, wherein the first operational amplifier further comprises a second op-amp input terminal, and a second op-amp output terminal;
wherein the filter further comprises:
a third resistor, having a first terminal coupled to a third input terminal, and having a second terminal coupled to the second op-amp input terminal;
a third capacitor, having a first terminal coupled to the second terminal of the third resistor, and having a second terminal; and
a second signal feeding path, comprising:
a fourth capacitor, having a first terminal coupled to the second terminal of the third capacitor and having a second terminal coupled to the second op-amp output terminal; and
a fourth resistor, having a first terminal coupled to the second terminal of the third capacitor, and having a second terminal coupled to the integrator;

wherein the integrator further comprises a fourth input terminal coupled to the second op-amp output terminal.

14. The filter of claim 13, wherein the integrator comprises:
a second operational amplifier, comprising a third op-amp input terminal, a fourth op-amp input terminal, a third op-amp output terminal and a fourth op-amp output terminal, wherein the third op-amp output terminal serves as the first output terminal, and the fourth op-amp output terminal serves as the second output terminal;
a fifth capacitor comprising a first terminal coupled to the third op-amp input terminal and comprising a second terminal coupled to the third op-amp output terminal; and
a fifth resistor, comprising a first terminal coupled to the second input terminal, and comprising a second terminal coupled to the third op-amp input terminal that is coupled to the second terminal of the fourth resistor;
a sixth capacitor, comprising a first terminal coupled to the fourth op-amp input terminal and comprising a second terminal coupled to the fourth op-amp output terminal; and
a sixth resistor, comprising a first terminal coupled to the fourth input terminal, and comprising a second terminal coupled to the fourth op-amp input terminal that is coupled to the second terminal of the second resistor.

15. The filter of claim 13, wherein impedance values of the second resistor, the fourth resistor, the second capacitor, the fourth capacitor and the integrator determine at least one notch point of the filter.

16. The filter of claim 13, wherein the first resistor and the third resistor have substantially the same resistance value, the first capacitor and the third capacitor have substantially the same capacitance value, the second resistor and the fourth resistor have substantially the same resistance value, the second capacitor and the fourth capacitor have substantially the same capacitance value.

17. A filter, comprising:
a first integrator, comprising a first op-amp and a first across-network coupling across the first op-amp;
a second integrator, comprising a second op-amp and a second across-network coupling across the second op-amp; and
a impedance element having a first terminal coupled to a terminal of the first across-network and having a second terminal coupled to an intermediate point of the second across-network.

18. The filter of claim 17, wherein the second across-network comprises a first impedance network and a second impedance network, the first impedance network is coupled between an input of the second op-amp and the intermediate point, and the second impedance network is coupled between the intermediate point and an output of the second op-amp.

19. A filter, comprising:
a resonator comprising a first op-amp, a second op-amp and a negative feedback path comprising a plurality of impedance elements so arranged such that at least a notch point is provided, wherein the negative feedback path comprises a first resistor and a first capacitor; and
an integrator comprising the second op-amp, the first resistor, the first capacitor and a second capacitor, wherein the first resistor, the first capacitor and the second capacitor forms at least a portion of a RC network for the integrator.