CN103973254B - A kind of across resistance type integrated band pass filter method for designing - Google Patents

Abstract

A kind of across resistance type integrated band pass filter method for designing, comprise the following steps: (1) derives across resistance type passive LC band pass filter with signal flow graph, obtains the signal flow diagram of LC wave filter；(2) realize signal flow diagram with inverting integrator, obtain full limit based on inverting integrator across stopband bandpass filter；(3) substitute inverting integrator with fully differential integrator further, obtain across resistance type fully differential Active RC bandwidth-limited circuit.Use the method design across resistance wave filter, can directly be connected with the device such as the sensor being output as electric current or D/A converter, it is to avoid the conversion of current/voltage.

Description

A kind of across resistance type integrated band pass filter method for designing

Technical field

The invention belongs to Electronics and Information Engineering field, relate to a kind of across resistance type integrated band pass filter method for designing.

Background technology

Wave filter is in addition to most popular analog circuit element beyond amplifier, is the core parts constituting filter circuit. Communication technology and developing rapidly of multimedia technology propose the highest requirement to signal processing.And wave filter is as signal The key element processed, the quality of its performance directly influences the performance of over all Integration circuit.Traditional wave filter is all to use The form of voltage input-voltage output, when it is connected with the element of current forms, needs access current-voltage conversion in centre Device, adds number of elements and the power consumption of circuit.Across resistance wave filter as a kind of Novel Filter, its input is current signal, It is output as voltage signal, can directly be connected with the sensor being output as electric current or D/A converter etc., it is to avoid current-voltage Conversion, reduce the overall complexity of hardware.Little because of its input impedance across resistance wave filter, low noise, and can linearly improve The voltage swing of frequency mixer, has obtained the concern of Many researchers.

Traditional integrated Design of Active Filter is often with transmission function as starting point, real with biquadratic joint and single order link respectively Existing, the most again it is carried out cascade and obtain.It is known that Cascade Design has design simply, debug the advantages such as convenient, But its shortcoming is in response to component variation sensitivity high.Feedback Design has the modular feature of cascade structure, is provided that again ratio The sensitivity characteristic that cascade structure is superior, but this circuit structure is more complicated, regulation difficulty so that it is application is by a fixed limit System.The Passive LC ladder network that both-end is carried has the advantages that response is low to component variation sensitivity, and circuit structure is simple, Debugging is convenient, it is adaptable to design the active filter carving component accuracy and stability requirement lotus.

Summary of the invention

The present invention seeks to solve of the prior art high to component variation sensitivity across the design of resistance type integrated band pass filter, set The problems such as meter process is complicated, it is provided that a kind of across resistance type integrated band pass filter method for designing.The wave filter that the method obtains is one Plant new filter implementations, and there is the advantages such as sensitivity is low, dynamic range is big.

The technical solution used in the present invention is as follows:

A kind of across resistance type integrated band pass filter method for designing, the method comprises the following steps:

1st, derive across resistance type passive LC band pass filter with signal flow graph, obtain this passive LC band pass filter Signal flow diagram；

1.1st, first full limit is obtained across LC band filter prototype according to the technical specification of band filter, and to electricity The each component parameters in road and branch voltage and branch current are labeled.

1.2nd it follows that according to KCL, KVL and VCR, write out the pass between each branch voltage and branch current variable It is formula, to inductance row write current equation, electric capacity row is write voltage equation, obtains relational expression as follows:

$\begin{array}{cc}& I_0=\frac{V_1}{R_S}\\ V_1=I_1\×\frac{1}{{\mathrm{SC}}_1};& I_1=I_{in}-I_0-I_2-V_1\×\frac{1}{{\mathrm{SL}}_1}\\ V_2=V_1-V_3-I_2\×\frac{1}{{\mathrm{SC}}_2};& I_2=V_2\×\frac{1}{{\mathrm{SL}}_2}\\ V_3=I_3\×\frac{1}{{\mathrm{SC}}_3};& I_3=I_2-I_4-V_3\×\frac{1}{{\mathrm{SL}}_3}\\ & I_4=\frac{V_3}{R_L}\end{array}---\left(1\right)$

Wherein, I₁、I₂、I₃、I₄Represent each branch current, V respectively₁、V₂、V₃Represent each branch node voltage, L₁、L₂、 L₃It is respectively shunt inductance, C₁、C₂、C₃It is respectively branch road electric capacity, I_inFor input current, I_oFor output electric current, R_LIt is negative Carry resistance.

1.3rd, formula (1) being represented with signal flow diagram, in signal flow diagram, upper node is all current forms, and lower node is all Voltage form, for the ease of using inverting integrator to realize this signal flow diagram, makes input/output signal be voltage, by this letter In number flow graph, all current variable are multiplied by proportion resistor R and become voltage form.

2nd, realize signal flow diagram with inverting integrator, obtain full limit based on inverting integrator across stopband bandpass filter；

2.1st, according to the signal flow diagram in above-mentioned 1.3rd step, after drawing conversion, the relation of branch voltage and branch current is

$\begin{array}{cc}& V_0=V_1\×\frac{R}{R_S}\\ V_1={V_1}^{\′}\×\frac{1}{{\mathrm{SC}}_{1}R};& {V_1}^{\′}=I_{in}R-V_0-{V_2}^{\′}-V_1\×\frac{R}{{\mathrm{SL}}_1}\\ V_2=V_1-V_3-{V_2}^{\′}\×\frac{1}{{\mathrm{SC}}_{2}R};& {V_2}^{\′}=V_2\×\frac{R}{{\mathrm{SL}}_2}\\ V_3={V_3}^{\′}\×\frac{1}{{\mathrm{SC}}_{3}R};& {V_3}^{\′}={V_2}^{\′}-{V_4}^{\′}-V_3\×\frac{R}{{\mathrm{SL}}_3}\\ & {V_4}^{\′}=V_3\×\frac{R}{R_L}\end{array}---\left(2\right)$

Wherein, V₁', V₂', V₃', V₄', V_oIt is respectively the magnitude of voltage after the conversion of original signal flow graph electric current element, is positioned at signal On flow graph at node.

2.2nd, abbreviation

Make R=R_S=R_L=1 Ω, thus V₀=V₁, V₄'=V₃, then above formula can be further simplified as

$V_1=\[-I_{in}R+V_1+{V_2}^{\′}-V_1\×(-\frac{R}{SL})\]\×(-\frac{1}{{\mathrm{SC}}_{1}R})---\left(3\right)$

${V_2}^{\′}=\[-V_1+V_3-{V_2}^{\′}\×(-\frac{1}{{\mathrm{SC}}_{2}R})\]\×(-\frac{R}{{\mathrm{SL}}_2})---\left(4\right)$

$V_3=\[-{V_2}^{\′}+V_3-V_3\×(-\frac{R}{{\mathrm{SL}}_3})\]\×(-\frac{1}{{\mathrm{SC}}_{3}R})---\left(5\right)$

Formula (3), (4), (5) realize with inverting integrator and represent with accompanying drawing；

2.3rd, 3 accompanying drawings in above-mentioned 2.2nd step are carried out comprehensively, obtain full limit based on inverting integrator across resistance Band filter；

3rd, substitute inverting integrator with fully differential integrator further, obtain across resistance type fully differential Active RC bandpass filtering Circuit.

Advantages of the present invention and good effect:

1, present invention LC based on Two-Port Load filtered circuit, the integrated filter obtained has response to element sensitivity Low feature.

2, the invention provides a kind of new wave filter implementation method, i.e. across resistance integrated band pass filter, use electric current input The form of-voltage output, provides stable electric current for filter circuit, is adapted for carrying out low-voltage, low-power consumption and the most dynamic State range filters.

Accompanying drawing explanation

The full limit of Fig. 1 is across hindering six rank LC band filter prototypes.

Fig. 2 full limit band leads to LC filter prototype signal flow diagram.

Signal flow diagram after Fig. 3 conversion.

Fig. 4 formula (3) realizes with inverting integrator.

Fig. 5 formula (4) realizes with inverting integrator.

Fig. 6 formula (5) realizes with inverting integrator.

Fig. 7 full limit based on inverting integrator is across stopband bandpass filter circuit.

Fig. 8 fully differential is active across stopband bandpass filter.

Fig. 9 is across resistance low pass LC filter circuit.

The conversion that Figure 10 low pass is led to band.

Figure 11 leads to LC filter prototype circuit across stopband.

Figure 12 six rank lead to active RC filter across stopband.

Figure 13 six rank are across stopband bandpass filter amplitude-frequency characteristic.

The present invention will be further described in detail with detailed description of the invention below in conjunction with the accompanying drawings.

Detailed description of the invention

The present invention provide across resistance type integrated band pass filter method for designing, comprise the following steps:

(1) derive across resistance type passive LC band pass filter with signal flow graph, obtain the signal flow diagram of LC wave filter；

(2) realize signal flow diagram with inverting integrator, obtain full limit based on inverting integrator across stopband bandpass filter；

(3) substitute inverting integrator with fully differential integrator further, obtain across resistance type fully differential Active RC bandpass filtering Circuit.Specific as follows:

In described step (1), first obtain full limit according to the technical specification of band filter former across LC band filter Type, and component parameters each to circuit and branch voltage and branch current be labeled.As shown in Figure 1.

It follows that according to KCL, KVL and VCR, write out the relational expression between each branch voltage and branch current variable, right Electric capacity row are write voltage equation, are obtained relational expression as follows by inductance row write current equation:

$\begin{array}{cc}& I_0=\frac{V_1}{R_S}\\ V_1=I_1\×\frac{1}{{\mathrm{SC}}_1};& I_1=I_{in}-I_0-I_2-V_1\×\frac{1}{{\mathrm{SL}}_1}\\ V_2=V_1-V_3-I_2\×\frac{1}{{\mathrm{SC}}_2};& I_2=V_2\×\frac{1}{{\mathrm{SL}}_2}\\ V_3=I_3\×\frac{1}{{\mathrm{SC}}_3};& I_3=I_2-I_4-V_3\×\frac{1}{{\mathrm{SL}}_3}\\ & I_4=\frac{V_3}{R_L}\end{array}---\left(1\right)$

Wherein, I₁、I₂、I₃、I₄Represent each branch current, V respectively₁、V₂、V₃Represent each branch node voltage, L₁、L₂、 L₃It is respectively shunt inductance, C₁、C₂、C₃It is respectively branch road electric capacity, I_inFor input current, I_oFor output electric current, R_LIt is negative Carry resistance.

Formula (1) is represented with signal flow diagram, as shown in Figure 2.

In signal flow diagram, upper node is all current forms, it means that the input and output of integrator always one be electric current, one Individual is voltage.Voltage form can be become, conversion by current variable all in signal flow diagram are multiplied by proportion resistor R After signal flow diagram be shown in Fig. 3.

In described step (2), realize signal flow diagram with inverting integrator, obtain full limit based on inverting integrator across resistance Band filter, it specifically comprises the following steps that

According to above-mentioned signal flow diagram, after drawing conversion, the relation of branch voltage and branch current is

$\begin{array}{cc}& V_0=V_1\×\frac{R}{R_S}\\ V_1={V_1}^{\′}\×\frac{1}{{\mathrm{SC}}_{1}R};& {V_1}^{\′}=I_{in}R-V_0-{V_2}^{\′}-V_1\×\frac{R}{{\mathrm{SL}}_1}\\ V_2=V_1-V_3-{V_2}^{\′}\×\frac{1}{{\mathrm{SC}}_{2}R};& {V_2}^{\′}=V_2\×\frac{R}{{\mathrm{SL}}_2}\\ V_3={V_3}^{\′}\×\frac{1}{{\mathrm{SC}}_{3}R};& {V_3}^{\′}={V_2}^{\′}-{V_4}^{\′}-V_3\×\frac{R}{{\mathrm{SL}}_3}\\ & {V_4}^{\′}=V_3\×\frac{R}{R_L}\end{array}---\left(2\right)$

Wherein, V₁', V₂', V₃', V₄', V_oIt is respectively the magnitude of voltage after the conversion of original signal flow graph electric current element, is positioned at signal On flow graph at node.

Make R=R_S=R_L=1 Ω, thus V₀=V₁, V₄'=V₃, then above formula can be further simplified as

$V_1=\[-I_{in}R+V_1+{V_2}^{\′}-V_1\×(-\frac{R}{{\mathrm{SL}}_1})\]\×(-\frac{1}{{\mathrm{SC}}_{1}R})---\left(3\right)$

${V_2}^{\′}=\[-V_1+V_3-{V_2}^{\′}\×(-\frac{1}{{\mathrm{SC}}_{2}R})\]\×(-\frac{R}{{\mathrm{SL}}_2})---\left(4\right)$

$V_3=\[-{V_2}^{\′}+V_3-V_3\×(-\frac{R}{{\mathrm{SL}}_3})\]\×(-\frac{1}{{\mathrm{SC}}_{3}R})---\left(5\right)$

Formula (3) inverting integrator realizes, and represents as shown in Figure 4.

Formula (4) inverting integrator realizes, and represents as shown in Figure 5.

Formula (5) inverting integrator realizes, and represents as shown in Figure 6.

Above-mentioned 3 figures are carried out comprehensively, obtains full limit based on inverting integrator across stopband bandpass filter, as shown in Figure 7.

In described step (3), substitute inverting integrator with fully differential integrator, obtain across resistance type fully differential Active RC band Bandpass filter circuit, as shown in Figure 8.

Embodiment 1

One specific embodiment of the present invention be use signal flow graph design one across resistance type band filter, its technology refers to It is designated as:

Lower cut-off frequecy of passband: f₁=0.67MHz, upper cut-off frequecy of passband: f_u=1.5MHz；

Stopband lower-cut-off frequency: f_s1=0.4MHz, stopband upper cut-off frequency: f_su=2.5MHz；

The maximum attenuation that passband allows: A_max=1dB, the minimal attenuation that stopband allows: A_min=20dB；

R_S=R_L=10K Ω.

It is frequency converted, the amplitude-frequency characteristic of available low pass filter.

Utilize formula ω_LP=1,The normalization technical specification that can calculate low pass filter is:

Cut-off frequecy of passband f_p=1Hz, the maximum attenuation that passband allows: A_max=1dB,

Stopband cut-off frequency: f_s=2.53Hz, the minimal attenuation that stopband allows: A_min=20dB；

Both-end carries R_S=R_L=1 Ω.

Select Chebyshev to approach, calculate low pass filter exponent number N,

$n=\frac{{\cosh }^{-1}\[\sqrt{({10}^{0.1A_{\min }}-1)/({10}^{0.1A_{\max }}-1)}\]}{{\cosh }^{-1}({\mathrm{\ω}}_s/{\mathrm{\ω}}_p)}---\left(6\right)$

N=2.32 can be calculated, upwards take N=3.Certain difference can be produced during rounding, be N-n here, Also it is the reason causing Chebyshev wave filter low frequency pass band part to fluctuate.In order to reduce passband fluctuation, use hereReplace For A_max, the exponent number N that will obtain substitutes in formula (6), is used for solving

$A_{\max }^{New}=10{\log }_{10}(\frac{{10}^{0.1A_{\min }}-1}{{\{\cosh \[N{\cosh }^{-1}\left(\frac{{\mathrm{\ω}}_s}{{\mathrm{\ω}}_p}\right)\]\}}^2}+1)---\left(7\right)$

Calculated by formula (7)Take

Fig. 9 be gained across resistance low pass LC filter circuit.

Carrying out the low-passing LC chain parameter transformation to the logical lc circuit of band, its transformation relation such as Figure 10, wherein B represents passband Bandwidth, ω₀Represent the mid frequency of passband.

By above-mentioned conversion, the lc circuit prototype across stopband bandpass filter can be obtained, as shown in figure 11.

Utilize previously described method that Figure 11 circuit carries out full limit to derive, finally across the signal flow diagram of stopband bandpass filter Obtain six rank and lead to Active RC filter circuit figure across stopband, as shown in figure 12.

In figure, all resistances are all 1 Ω, capacitance C₁=C₂=235.385nF, C₃=C₄=107.612nF, C₅=C₆=114.615nF, C₇=C₈=221.004nF, C₉=C₁₀=235.385nF, C₁₁=C₁₂=107.612nF.

Parameter in Fig. 8 is carried out renormalization, makes k_m=10000, then

$\begin{array}{c}{R}_{new}=k_m{R}_{lod}\\ C_{new}=\frac{C_{old}}{k_m}\end{array}---\left(8\right)$

According to formula (8), obtain the circuit parameter R after renormalization_s=R_L=10k Ω, C₁=C₂=23.54pF, C₃=C₄=10.76pF, C₅=C₆=11.46pF, C₇=C₈=22.1pF, C₉=C₁₀=23.54pF, C₁₁=C₁₂=10.76pF.

Here fully differential integrator uses LMH6551 model.Figure 12 is set up netlist, and utilizes Hspice to imitate Very, simulation result is obtained as shown in figure 13.

From simulation result it can be seen that meet technical requirement with the active filter of the method design, filtering performance is good, Both remained general active filter have the advantage that, also there is the feature that passive filter is low to component parameters sensitivity.

Summary simulation result and analysis show, use the present invention design integrated active across resistance type band filter have with The advantage of lower several respects: 1. design is based on the Passive LC ladder circuit that both-end is carried, trapezoidal interior to characterizing LC The math equation of portion's behavior is simulated, and has the muting sensitivity characteristic of Passive LC ladder-type filter；2. achieve across resistance filter This new filter form of ripple device, uses the form of electric current input-voltage output, provides stable electricity for filter circuit Stream；3. create collection and help the limit netlist across stopband bandpass filter, and it is imitative to utilize circuit simulating software Hspice to achieve Very.The effectiveness of simulation results show design and feasibility.

Claims (1)

1. one kind across resistance type integrated band pass filter method for designing, it is characterised in that the method comprises the following steps:

1st, derive across resistance type passive LC band pass filter with signal flow graph, obtain this passive LC band pass filter Signal flow diagram；

1.1st, first full limit is obtained across LC band filter prototype according to the technical specification of band filter, and to electricity The each component parameters in road and branch voltage and branch current are labeled；

1.2nd it follows that according to KCL, KVL and VCR, write out the pass between each branch voltage and branch current variable It is formula, to inductance row write current equation, electric capacity row is write voltage equation, obtains relational expression as follows:

$\begin{array}{cc}& I_0=\frac{V_1}{R_S}\\ V_1=I_1\×\frac{1}{{\mathrm{SC}}_1};& I_1=I_{in}-I_0-I_2-V_1\×\frac{1}{{\mathrm{SL}}_1}\\ V_2=V_1-V_3-I_2\×\frac{1}{{\mathrm{SC}}_2};& I_2=V_2\×\frac{1}{{\mathrm{SL}}_2}\\ V_3=I_3\×\frac{1}{{\mathrm{SC}}_3};& I_3=I_2-I_4-V_3\×\frac{1}{{\mathrm{SL}}_3}\\ & I_4=\frac{V_3}{R_L}\end{array}---\left(1\right)$

Wherein, I₁、I₂、I₃、I₄Represent each branch current, V respectively₁、V₂、V₃Represent each branch node voltage, L₁、L₂、 L₃It is respectively shunt inductance, C₁、C₂、C₃It is respectively branch road electric capacity, I_inFor input current, I_oFor output electric current, R_LIt is negative Carrying resistance, Rs is current source parallel resistance, and variable S is plural number, can be obtained through Laplace transform by time-domain signal, again Claim " complex frequency domain "；

1.3rd, formula (1) being represented with signal flow diagram, in signal flow diagram, upper node is all current forms, and lower node is all Voltage form, for the ease of using inverting integrator to realize this signal flow diagram, makes input/output signal be voltage, by this letter In number flow graph, all current variable are multiplied by proportion resistor R and become voltage form；

2nd, realize signal flow diagram with inverting integrator, obtain full limit based on inverting integrator across stopband bandpass filter；

2.1st, according to the signal flow diagram in above-mentioned 1.3rd step, after drawing conversion, the relation of branch voltage and branch current is

$\begin{array}{cc}& V_0=V_1\×\frac{R}{R_S}\\ V_1={V_1}^{\′}\×\frac{1}{{\mathrm{SC}}_{1}R};& {V_1}^{\′}=I_{in}R-V_0-{V_2}^{\′}-V_1\×\frac{R}{{\mathrm{SL}}_1}\\ V_2=V_1-V_3-{V_2}^{\′}\×\frac{1}{{\mathrm{SC}}_{2}R};& {V_2}^{\′}=V_2\×\frac{R}{{\mathrm{SL}}_2}\\ V_3={V_3}^{\′}\×\frac{1}{{\mathrm{SC}}_{3}R};& {V_3}^{\′}={V_2}^{\′}-{V_4}^{\′}-V_3\×\frac{R}{{\mathrm{SL}}_3}\\ & {V_4}^{\′}=V_3\×\frac{R}{R_L}\end{array}---\left(2\right)$

Wherein, V₁', V₂', V₃', V₄', V_oIt is respectively the magnitude of voltage after the conversion of original signal flow graph electric current element, is positioned at signal On flow graph at node；

2.2nd, abbreviation

Make R=R_S=R_L=1 Ω, thus V₀=V₁, V₄'=V₃, then formula (2) can be further simplified as

$V_1=\[-I_{in}R+V_1+{V_2}^{\′}-V_1\×(-\frac{R}{{\mathrm{SL}}_1})\]\×(-\frac{1}{{\mathrm{SC}}_{1}R})---\left(3\right)$

${V_2}^{\′}=\[-V_1+V_3-{V_2}^{\′}\×(-\frac{1}{{\mathrm{SC}}_{2}R})\]\×(-\frac{R}{{\mathrm{SL}}_2})---\left(4\right)$

$V_3=\[-{V_2}^{\′}+V_3-V_3\×(-\frac{R}{{\mathrm{SL}}_3})\]\×(-\frac{1}{{\mathrm{SC}}_{3}R})---\left(5\right)$

Formula (3), (4), (5) realize with inverting integrator；

2.3rd, 3 formula in above-mentioned 2.2nd step are carried out comprehensively, obtain full limit based on inverting integrator across resistance Band filter；

3rd, substitute inverting integrator with fully differential integrator further, obtain across resistance type fully differential Active RC bandpass filtering Circuit.