CN106803749A - A kind of wave filter and its quality factor compensation method - Google Patents

Abstract

The invention discloses a filter and a quality factor compensation method thereof, comprising a first filter circuit, a second filter circuit, a third filter circuit, an input circuit and an output circuit; the first filter circuit and the second filter circuit are connected in series , the third filter circuit is connected in parallel with the first filter circuit and the second filter circuit; the input circuit is connected with the first filter circuit and the third filter circuit respectively, and the output circuit is connected with the second filter circuit respectively The circuit is connected to the third filter circuit. The advantages and beneficial effects of the present invention are: by compensating the Q value of the quality factor of the filter, relatively ideal filter characteristics can be maintained when the performance of the operational amplifier of the filter is not good, so the technical scheme not only improves the Q value of the filter Compensation is carried out, and at the same time, there is no need to increase the gain-bandwidth product of the operational amplifier, the area of the resistor is saved, the consumption of power consumption is reduced, the structure is simple, and the controllability is strong.

Description

A filter and its quality factor compensation method

technical field

The invention relates to the field of electronic information, in particular to a filter and a quality factor compensation method thereof.

Background technique

Filters are important in RF receiver chips. Its main function is to filter out out-of-band interference and suppress image signals. In low-IF receivers, IF complex filters are often used to simultaneously achieve filtering and image suppression. However, the existing IF complex filters have a relatively high center frequency and a relatively large bandwidth. At this time, the limited gain-bandwidth product of the operational amplifier will cause the filter characteristics to deviate from their ideal state, making the quality factor Q value larger. The increase of the Q value of the quality factor will lead to the decrease of the cutoff frequency and the bandwidth, and a relatively high gain overshoot will appear near the cutoff frequency, which will destroy the flatness of the passband, as shown in Figure 3. If the gain-bandwidth product of the operational amplifier is increased, a large amount of power consumption will be consumed, and the cost is relatively high.

Contents of the invention

In order to solve the above problems, the present invention provides a filter and a quality factor compensation method thereof. The present invention compensates the Q value of the quality factor of the filter, so that when the performance of the operational amplifier of the filter is not good, it can maintain relatively ideal filtering characteristics, and avoids the relatively high gain of the frequency characteristic curve of the filter near the cut-off frequency. impact, destroying the flatness of the passband; therefore, this technical solution not only compensates the Q value of the filter, but also does not need to increase the gain-bandwidth product of the operational amplifier, saves the area of the resistor, and reduces the consumption of power consumption. Simple and highly controllable.

A filter in the present invention includes a first filter circuit, a second filter circuit, a third filter circuit, an input circuit and an output circuit; the first filter circuit and the second filter circuit are connected in series, and the third filter circuit The circuit is connected in parallel with the first filter circuit and the second filter circuit; the input circuit is connected with the first filter circuit and the third filter circuit respectively, and the output circuit is connected with the second filter circuit and the third filter circuit respectively connect.

In the above solution, the first filter circuit includes an operational amplifier OP1, a resistor R2, a resistor R3, a resistor R4, and a capacitor C1;

The operational amplifier OP1, capacitor C1, resistor R2 and resistor R3 are connected in parallel; one end of the capacitor C1, resistor R2 and resistor R3 is connected to the input circuit, and the other end of the capacitor C1 and resistor R2 is connected to the input circuit. The resistor R4 is connected;

The resistor R4 is connected to the output terminal of the operational amplifier OP1, the inverting input terminal of the operational amplifier OP1 is connected to the input circuit, and the positive input terminal of the operational amplifier OP1 is connected to a common-mode voltage.

In the solution above, the first filter circuit further includes an inverting amplifier D1, the input terminal of the inverting amplifier D1 is connected to the resistor R3, and the output terminal of the inverting amplifier D1 is connected to the resistor R4.

In the above solution, the second filtering circuit includes an operational amplifier OP2, a resistor R5, a capacitor C2 and a buffer amplifier H1; the operational amplifier OP2, the resistor R5 and the capacitor C2 are connected in parallel;

One end of the resistor R5 and the capacitor C2 is connected to the resistor R4, and the other end of the capacitor C2 is connected to the input end of the buffer amplifier H1;

The positive input terminal of the operational amplifier OP2 is connected to the common mode voltage, the negative input terminal of the operational amplifier OP2 is connected to the resistor R4, the output terminal of the operational amplifier OP2 is connected to the input terminal of the buffer amplifier H1 connect.

In the above solution, the second filter circuit also includes an inverting amplifier D2, the input of the inverting amplifier D2 is connected to the resistor R5, and the output of the inverting amplifier D2 is connected to the input of the buffer amplifier H1 .

In the above solution, the third filter circuit includes a capacitor C3 and a resistor R6 connected in parallel, one end of the capacitor C3 and the resistor R6 is connected to the input circuit, the resistor R3, the resistor R2, the capacitor C1 and the op amp OP1. connected to the input terminal, and the other terminal of the capacitor C3 and the resistor R6 is connected to the output circuit and the output terminal H1 of the buffer amplifier.

In the above solution, the input terminal includes an input terminal Z1 and a resistor R1, the input terminal is connected to one end of the resistor R1, and the other end of the resistor R1 is connected to the inverting input terminal of the operational amplifier OP1 and the capacitor C1 , Resistor R2 and resistor R3 are connected.

In the above solution, the output terminal includes an output terminal Z2, and the output terminal Z1 is respectively connected to the output terminal of the buffer amplifier H1, the capacitor C3, and the resistor R6.

A quality factor compensation method of a filter, comprising the following steps:

S1. Set resistor R6, resistor R2, resistor R4, capacitor C2 and buffer amplifier H1 as the first loop, input terminal Z1 receives the electrical signal Vin and after one cycle of the first loop, a hysteresis voltage will be generated at point A The first signal of the 90° phase of the signal Vin causes the capacitor C2 in the first loop to discharge and attenuate the resistor R6, the resistor R2 or the resistor R4;

S2. Resistor R6, capacitor C1, resistor R4, capacitor C2 and buffer amplifier H1 are set as the second loop, and after the electrical signal Vin passes through the second loop for one cycle, a lagging electrical signal Vin 180 will be generated at point A ° phase of the second signal;

S3. Capacitor C3, resistor R2, resistor R4, capacitor C2 and buffer amplifier H1 are set as the third loop; after the electrical signal Vin passes through the third loop for one cycle, a hysteresis electrical signal Vin will be generated at point A A third signal of 180° phase;

S4. Capacitor C3, capacitor C1, resistor R4, capacitor C2 and buffer amplifier H1 are set as the fourth loop, and after the electrical signal Vin passes through the fourth loop for one cycle, a hysteresis electrical signal will be generated at point A The fourth signal of Vin 270° phase causes the capacitor C1, capacitor C2 and capacitor C3 in the fourth loop to discharge the resistor R4 and attenuate it;

S5. The phases of the second signal and the third signal lag behind the electrical signal Vin by 180°, therefore, the second signal and the third signal can generate oscillations in the second loop and the third loop respectively;

S6. described resistance R6, electric capacity C1 and operational amplifier OP1 are set as integrator, described electric capacity C3, resistance R2 and operational amplifier OP1 are set as differentiator, electric signal Vin will be in through integrator and differentiator respectively Point B produces a cancellation that reduces the maximum energy stored in the filter to reduce the filter's quality factor.

In the above solution, in the step S6, the following steps are also included:

S61. After the electrical signal Vin passes through the capacitor C1, the resistor R4, the capacitor C2 and the buffer amplifier H1 of the second loop, an electrical signal E1 will be formed at point C, and after the electrical signal E1 passes through the integrator again, it will be at B point to generate an oscillating signal V1;

S62. After the electrical signal Vin passes through the resistor R2, the resistor R4, the capacitor C2 and the buffer amplifier H1 of the third loop, an electrical signal E2 will be formed at point C, and after the electrical signal E2 passes through the differentiator again, it will be at B point to generate an oscillating signal V2;

S63. The oscillation signal V1 satisfies the formula: V1=((-1/(R6*C1))∫E1dt;

The oscillation signal V2 satisfies the formula: V2=-i*R2=-(R2*C3)dE1/dt;

Make the direction of the oscillation signal V1 and the oscillation signal V2 opposite;

S64. The quality factor Q of the filter satisfies the formula:

Among them, Q is the quality factor,

Eosc is the maximum energy stored in the circuit,

The total energy consumed by the Econs circuit in one cycle;

The oscillating signal V1 and the oscillating signal V2 cancel at point B, reducing the maximum energy stored in the filter, so as to reduce the quality factor of the filter.

The advantages and beneficial effects of the present invention are: the present invention provides a filter and its quality factor compensation method. The present invention compensates the quality factor Q value of the filter, so that when the performance of the operational amplifier of the filter is not good, it can maintain relatively ideal filtering characteristics. Therefore, the technical solution not only compensates the Q value of the filter, but also does not need The gain-bandwidth product of the operational amplifier is improved, the area of the resistor is saved, the consumption of power consumption is reduced, the structure is simple, and the controllability is strong.

Description of drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only These are some embodiments of the present invention. For those skilled in the art, other drawings can also be obtained according to these drawings on the premise of not paying creative efforts.

Fig. 1 is the structural representation of a kind of filter of the present invention;

Fig. 2 is a kind of filter of the present invention after the quality factor compensation method of filter reduces quality factor, the frequency characteristic curve of filter;

Fig. 3 is a frequency characteristic curve of the filter described in the background art.

detailed description

The specific implementation manners of the present invention will be further described below in conjunction with the drawings and examples. The following examples are only used to illustrate the technical solution of the present invention more clearly, but not to limit the protection scope of the present invention.

As shown in Figures 1-2, the present invention is a filter, including a first filter circuit, a second filter circuit, a third filter circuit, an input circuit and an output circuit; the first filter circuit and the second filter circuit The third filter circuit is connected in parallel with the first filter circuit and the second filter circuit; the input circuit is connected with the first filter circuit and the third filter circuit respectively, and the output circuit is connected with the first filter circuit respectively. The second filter circuit is connected to the third filter circuit.

The working principle of the above technical solution is: the input circuit receives the electrical signal Vin, and makes the electrical signal Vin pass through the first filter circuit, the second filter circuit and the third filter circuit in order to reduce the maximum energy stored in the filter and reduce the quality The quality factor of the factor is then transmitted to the output circuit, so that the output circuit outputs the electrical signal Vout.

Specifically, the first filter circuit includes an operational amplifier OP1, a resistor R2, a resistor R3, a resistor R4, and a capacitor C1;

The operational amplifier OP1, capacitor C1, resistor R2 and resistor R3 are connected in parallel; one end of the capacitor C1, resistor R2 and resistor R3 is connected to the input circuit, and the other end of the capacitor C1 and resistor R2 is connected to the input circuit. The resistor R4 is connected;

The resistor R4 is connected to the output terminal of the operational amplifier OP1, the inverting input terminal of the operational amplifier OP1 is connected to the input circuit, and the positive input terminal of the operational amplifier OP1 is connected to a common-mode voltage; wherein, The common-mode voltage is about half of the voltage of the electrical signal Vin.

Further, the first filter circuit further includes an inverting amplifier D1, an input terminal of the inverting amplifier D1 is connected to the resistor R3, and an output terminal of the inverting amplifier D1 is connected to the resistor R4.

Wherein, the inverting amplifier D1 is used as an equivalent circuit, which is formed by the equivalent resistance of the IQ two circuits, and is used to generate a complex quantity.

Specifically, the second filter circuit includes an operational amplifier OP2, a resistor R5, a capacitor C2, and a buffer amplifier H1; the operational amplifier OP2, resistor R5, and capacitor C2 are connected in parallel;

One end of the resistor R5 and the capacitor C2 is connected to the resistor R4, and the other end of the capacitor C2 is connected to the input end of the buffer amplifier H1;

The positive input terminal of the operational amplifier OP2 is connected to the common mode voltage, the negative input terminal of the operational amplifier OP2 is connected to the resistor R4, the output terminal of the operational amplifier OP2 is connected to the input terminal of the buffer amplifier H1 connection; wherein, the common-mode voltage is about half of the voltage of the electrical signal Vin.

Further, the second filter circuit further includes an inverting amplifier D2, the input terminal of the inverting amplifier D2 is connected to the resistor R5, and the output terminal of the inverting amplifier D2 is connected to the input terminal of the buffer amplifier H1.

Wherein, the inverting amplifier D2 is used as an equivalent circuit, which is formed by the equivalent resistance of the IQ two circuits, and is used to generate a complex quantity.

Specifically, the third filter circuit includes a capacitor C3 and a resistor R6 connected in parallel, one end of the capacitor C3 and the resistor R6 is connected to the reverse side of the input circuit, the resistor R3, the resistor R2, the capacitor C1 and the operational amplifier OP1 The input terminals are connected, and the other terminals of the capacitor C3 and the resistor R6 are connected with the output circuit and the output terminal H1 of the buffer amplifier.

Specifically, the input terminal includes an input terminal Z1 and a resistor R1, the input terminal is connected to one end of the resistor R1, and the other end of the resistor R1 is connected to the inverting input terminal of the operational amplifier OP1, the capacitor C1, Resistor R2 and resistor R3 are connected.

Specifically, the output terminal includes an output terminal Z2, and the output terminal Z1 is respectively connected to the output terminal of the buffer amplifier H1, the capacitor C3, and the resistor R6.

A quality factor compensation method of a filter, comprising the following steps:

S1. Set resistor R6, resistor R2, resistor R4, capacitor C2 and buffer amplifier H1 as the first loop, input terminal Z1 receives the electrical signal Vin and after one cycle of the first loop, a hysteresis voltage will be generated at point A The first signal of the 90° phase of the signal Vin causes the capacitor C2 in the first loop to discharge and attenuate the resistor R6, the resistor R2 or the resistor R4;

S2. Resistor R6, capacitor C1, resistor R4, capacitor C2 and buffer amplifier H1 are set as the second loop, and after the electrical signal Vin passes through the second loop for one cycle, a lagging electrical signal Vin 180 will be generated at point A ° phase of the second signal;

S3. Capacitor C3, resistor R2, resistor R4, capacitor C2 and buffer amplifier H1 are set as the third loop; after the electrical signal Vin passes through the third loop for one cycle, a hysteresis electrical signal Vin will be generated at point A A third signal of 180° phase;

S4. Capacitor C3, capacitor C1, resistor R4, capacitor C2 and buffer amplifier H1 are set as the fourth loop, and after the electrical signal Vin passes through the fourth loop for one cycle, a hysteresis electrical signal will be generated at point A The fourth signal of Vin 270° phase causes the capacitor C1, capacitor C2 and capacitor C3 in the fourth loop to discharge the resistor R4 and attenuate it;

S5. The phases of the second signal and the third signal lag behind the electrical signal Vin by 180°, therefore, the second signal and the third signal can generate oscillations in the second loop and the third loop respectively;

S6. described resistance R6, electric capacity C1 and operational amplifier OP1 are set as integrator, described electric capacity C3, resistance R2 and operational amplifier OP1 are set as differentiator, electric signal Vin will be in through integrator and differentiator respectively Point B produces a cancellation that reduces the maximum energy stored in the filter to reduce the filter's quality factor.

Further, in the step S6, the following steps are also included:

S61. After the electrical signal Vin passes through the capacitor C1, the resistor R4, the capacitor C2 and the buffer amplifier H1 of the second loop, an electrical signal E1 will be formed at point C, and after the electrical signal E1 passes through the integrator again, it will be at B point to generate an oscillating signal V1;

S62. After the electrical signal Vin passes through the resistor R2, the resistor R4, the capacitor C2 and the buffer amplifier H1 of the third loop, an electrical signal E2 will be formed at point C, and after the electrical signal E2 passes through the differentiator again, it will be at B point to generate an oscillating signal V2;

S63. The oscillation signal V1 satisfies the formula: V1=((-1/(R6*C1))∫E1dt;

The oscillation signal V2 satisfies the formula: V2=-i*R2=-(R2*C3)dE1/dt;

Make the direction of the oscillation signal V1 and the oscillation signal V2 opposite;

S64. The quality factor Q of the filter satisfies the formula:

Among them, Q is the quality factor,

Eosc is the maximum energy stored in the circuit,

The total energy consumed by the Econs circuit in one cycle;

The oscillating signal V1 and the oscillating signal V2 are offset at point B, reducing the maximum energy stored in the filter to reduce the quality factor of the filter; wherein the oscillating signal V1 and the oscillating signal V2 are offset at point B, reducing the filter The maximum energy stored in the filter reduces the quality factor and avoids the relatively high gain overshoot in the frequency characteristic curve of the filter near the cutoff frequency, which destroys the flatness of the passband.

Further, verify the above filter and its quality factor compensation method:

The filter receives the electrical signal Vin from the input terminal Z1, and outputs the electrical signal -Vout from the output terminal Z2,

Therefore, the phase of the electrical signal -Vout satisfies the following formula:

Among them, wp is the dominant pole of the operational amplifier, and WGBW is the gain-bandwidth product of the operational amplifier OP1, so it can be judged that the quality factor Q is inversely proportional to the phase, and the electrical signal -Vout has an additional lag phase -2wp/WGBW;

Use the quality factor compensation method of the filter to compensate the quality factor of the filter, and the electrical signal -Vout output from the output terminal Z2 of the filter has obtained a compensation phase in satisfy the following formula,

Therefore, it is avoided that the frequency characteristic curve of the filter has a relatively high gain overshoot near the cutoff frequency, which destroys the flatness of the passband.

The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included in the scope of the present invention. within the scope of protection.

Claims (10)

1. A filter, characterized in that it comprises a first filter circuit, a second filter circuit, a third filter circuit, an input circuit and an output circuit; the first filter circuit and the second filter circuit are connected in series, and the first filter circuit The three filter circuits are connected in parallel with the first filter circuit and the second filter circuit; the input circuits are respectively connected with the first filter circuit and the third filter circuit, and the output circuits are respectively connected with the second filter circuit and the third filter circuit. filter circuit connection. 2. A kind of filter according to claim 1, is characterized in that, described first filtering circuit comprises operational amplifier OP1, resistance R2, resistance R3, resistance R4 and electric capacity C1; The operational amplifier OP1, capacitor C1, resistor R2 and resistor R3 are connected in parallel; one end of the capacitor C1, resistor R2 and resistor R3 is connected to the input circuit, and the other end of the capacitor C1 and resistor R2 is connected to the input circuit. The resistor R4 is connected; The resistor R4 is connected to the output terminal of the operational amplifier OP1, the inverting input terminal of the operational amplifier OP1 is connected to the input circuit, and the positive input terminal of the operational amplifier OP1 is connected to a common-mode voltage. 3. A kind of filter according to claim 2, it is characterized in that, described first filtering circuit also comprises inverting amplifier D1, the input terminal of described inverting amplifier D1 is connected with described resistor R3, and described inverting amplifier D1 The output terminal of the phase amplifier D1 is connected to the resistor R4. 4. A kind of filter according to claim 2, is characterized in that, described second filter circuit comprises operational amplifier OP2, resistance R5, electric capacity C2 and buffer amplifier H1; Described operational amplifier OP2, resistance R5 and electric capacity C2 connected in parallel with each other; One end of the resistor R5 and the capacitor C2 is connected to the resistor R4, and the other end of the capacitor C2 is connected to the input end of the buffer amplifier H1; The positive input terminal of the operational amplifier OP2 is connected to the common mode voltage, the negative input terminal of the operational amplifier OP2 is connected to the resistor R4, the output terminal of the operational amplifier OP2 is connected to the input terminal of the buffer amplifier H1 connect. 5. A kind of filter according to claim 4, it is characterized in that, described second filtering circuit also comprises inverting amplifier D2, and the input end of inverting amplifier D2 is connected with described resistance R5, and described inverting amplifier The output terminal of D2 is connected with the input terminal of the buffer amplifier H1. 6. A kind of filter according to claim 4, characterized in that, the third filtering circuit comprises a capacitor C3 and a resistor R6 connected in parallel, one end of the capacitor C3 and resistor R6 is connected to the input circuit, The resistor R3, the resistor R2, the capacitor C1 are connected to the inverting input terminal of the operational amplifier OP1, and the other terminals of the capacitor C3 and the resistor R6 are connected to the output circuit and the output terminal H1 of the buffer amplifier. 7. A filter according to claim 6, wherein the input terminal comprises an input terminal Z1 and a resistor R1, the input terminal is connected to one end of the resistor R1, and the other end of the resistor R1 It is connected with the inverting input terminal of the operational amplifier OP1, the capacitor C1, the resistor R2 and the resistor R3. 8 . The filter according to claim 6 , wherein the output terminal comprises an output terminal Z2 , and the output terminal Z1 is respectively connected to the output terminal of the buffer amplifier H1 , the capacitor C3 and the resistor R6 . 9. A quality factor compensation method of a filter, characterized in that, comprising the following steps: S1. Set resistor R6, resistor R2, resistor R4, capacitor C2 and buffer amplifier H1 as the first loop, input terminal Z1 receives the electrical signal Vin and after one cycle of the first loop, a hysteresis voltage will be generated at point A The first signal of the 90° phase of the signal Vin causes the capacitor C2 in the first loop to discharge and attenuate the resistor R6, the resistor R2 or the resistor R4; S2. Resistor R6, capacitor C1, resistor R4, capacitor C2 and buffer amplifier H1 are set as the second loop, and after the electrical signal Vin passes through the second loop for one cycle, a lagging electrical signal Vin 180 will be generated at point A ° phase of the second signal; S3. Capacitor C3, resistor R2, resistor R4, capacitor C2 and buffer amplifier H1 are set as the third loop; after the electrical signal Vin passes through the third loop for one cycle, a hysteresis electrical signal Vin will be generated at point A A third signal of 180° phase; S4. Capacitor C3, capacitor C1, resistor R4, capacitor C2 and buffer amplifier H1 are set as the fourth loop, and after the electrical signal Vin passes through the fourth loop for one cycle, a hysteresis electrical signal will be generated at point A The fourth signal of Vin 270° phase causes the capacitor C1, capacitor C2 and capacitor C3 in the fourth loop to discharge the resistor R4 and attenuate it; S5. The phases of the second signal and the third signal lag behind the electrical signal Vin by 180°, therefore, the second signal and the third signal can generate oscillations in the second loop and the third loop respectively; S6. described resistance R6, electric capacity C1 and operational amplifier OP1 are set as integrator, described electric capacity C3, resistance R2 and operational amplifier OP1 are set as differentiator, electric signal Vin will be in through integrator and differentiator respectively Point B produces a cancellation that reduces the maximum energy stored in the filter to reduce the filter's quality factor. 10. the quality factor compensation method of a kind of filter according to claim 9, is characterized in that, in described step S6, also comprises the following steps: S61. After the electrical signal Vin passes through the capacitor C1, the resistor R4, the capacitor C2 and the buffer amplifier H1 of the second loop, an electrical signal E1 will be formed at point C, and after the electrical signal E1 passes through the integrator again, it will be at B point to generate an oscillating signal V1; S62. After the electrical signal Vin passes through the resistor R2, the resistor R4, the capacitor C2 and the buffer amplifier H1 of the third loop, an electrical signal E2 will be formed at point C, and after the electrical signal E2 passes through the differentiator again, it will be at B point to generate an oscillating signal V2; S63. The oscillation signal V1 satisfies the formula: V1=((-1/(R6*C1))∫E1dt; The oscillation signal V2 satisfies the formula: V2=-i*R2=-(R2*C3)dE1/dt; Make the direction of the oscillation signal V1 and the oscillation signal V2 opposite; S64. The quality factor Q of the filter satisfies the formula: $\mathrm{<span\; class="notranslate">\; Q</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; to</span>}}}{{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; con</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; os</span>}\mathrm{<span\; class="notranslate">\; c</span>}}}{{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; con</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}}}$ Among them, Q is the quality factor, E _osc is the maximum energy stored in the circuit, E _cons The total energy consumed by the circuit in one cycle; The oscillating signal V1 and the oscillating signal V2 cancel at point B, reducing the maximum energy stored in the filter, so as to reduce the quality factor of the filter.