CN105244572B - A kind of filter design method based on Chebyshev's impedance transformer network technology - Google Patents
A kind of filter design method based on Chebyshev's impedance transformer network technology Download PDFInfo
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Abstract
The present invention relates to a kind of filter design methods based on Chebyshev's impedance transformer network technology, it the steps include: the passband and stopband insertion attenuation value of the given filter of being designed, and obtain the component number N and normalization component values of low-pass filter according to corresponding technology formula, chart, parameter.According to the cutoff frequency and singal source resistance of filter, the structure type (input filter inductances or input filter tances) of ladder network is selected, the true value of each element is calculated.It calculates, the characteristic impedance value of the high and low impedance of selected transmission line section, and calculates the lateral dimension of each section of transmission line.The length of each high and low impedance line segment is calculated according to the actual components numerical value of filter.The present invention has many advantages, such as that structure size is small, production easy to process, is easy to and element matching.With good linear, and Parameter adjustable, finally give computer artificial result.Not only required element is minimum for the microwave filter of comprehensive design of the present invention.
Description
Technical field
The present invention relates to a kind of filter design methods based on Chebyshev's impedance transformer network technology, belong to microwave electricity
Sub- line area.
Background technique
With the arrival of information age, signal processing and filter are designed in information science technology field one can not
Or scarce content.However since half a century, the basic theories of filter design never changes, and existing technology is only
Only support a kind of filter implementation method, such as the filter of passive LRC filter, active RC filter, digital filter, switching capacity
Wave device, the first step from index request to actual design are all based on the base of many forefathers such as O.J.Zoble, R.M.Foster
Plinth work.The design theory generated therefrom results in the stylized of filter initial designs: given index is converted into the domain S
Or the transmission function in the domain z, or it is converted into LC filter construction.The filter for designing high performance index has the performance of microwave circuit
There is important meaning.Narrowband, small in size, Out-of-band rejection degree height are the current developing direction for developing filter.
Summary of the invention
Technical problem to be solved: in view of the above problems, the present invention provides one kind can be arbitrarily introduced into transmission zero,
With the big filter design side based on Chebyshev's impedance transformer network technology of squareness factor height, narrow bandwidth, power capacity
Method.
Technical solution: the passive filter based on Chebyshev's impedance transformer network technology requires emphasis to consider passband boundary
When frequency and pass band damping, stopband edge frequency are with phase shift in stopband attenuation, the standing wave ratio of input voltage of passband, passband and group
Prolong.First two are description attenuation characteristics, are the key technical indexes of filter, determine that the performance of filter and type are (high
Logical, low pass, band logical, band resistance etc.)；Standing wave ratio of input voltage describes the size of the reflection loss of filter；Group delay refers to net
The change rate of the phase shift versus frequency of network, is defined as dU/df, and when group delay is constant, signal will not just generate phase by network
Position distortion.
Microwave filter is a kind of device for separating different frequency microwave signal.It is converted based on Chebyshev's impedance
The passive filter of network technology allows low frequency signal to pass to output port from input port with the attenuation of very little, when signal frequency
After rate exceeds cutoff frequency, the attenuation of signal will be increased dramatically, so that the signal amplitude of output port be made to decline.From collection Headquarters of the General Staff
Number prototype is set out, and replaces inductance and capacitor (as shown in Figure 1) in prototype circuit with microwave component appropriate.When solution low-pass filtering
When L and C of device, a kind of method is given Zoh、Zol、Yol=1/ZolThen change l, another method is given Zoh、ZolValue
Come L and C value required for simulating, but usually all using the method for changing l.In addition Z is givenoh、ZolAfterwards, the value of l must satisfy
Certain relationship:OrBecause the ratio between high impedance and Low ESR is bigger, the performance of filter is closer to reason
By characteristic；Conversely, difference is bigger.And the ratio between the high impedance and Low ESR of strip line can not be big, microstrip line has medium
Loss influences, therefore uses coaxial line.
Shown in following Fig. 1 (a) to Fig. 1 (b), generally when stub is very short or does not require very accurate, it is considered as
It is an individual reactance component.Such as the stub in Fig. 1 (a), when the low-impedance line of its two terminations high impedance line, then Fig. 1 (b)
The series reactance X meeting very little on middle both sides, and the reactance of the high impedance line of series connection with it is very big, so series reactance X can also be neglected
Slightly disregard, so only one shunt capacitance B in T-type equivalent circuit.
When TEM stub two terminates the high impedance line of low-impedance line, then shunt admittance B in Fig. 1 (c) can very little, and with
The susceptance of its low-impedance line in parallel is very big, so shunt susceptance can be ignored, so there was only one in IT type equivalent circuit
A series inductance X.In fact, this realizes series inductance with high impedance line namely in TEM (transverse electro-magnetic wave) microwave filter,
The reason of shunt capacitance is realized by low-impedance line.
In Fig. 1 (b),
In Fig. 1 (c)
The step of using simulation L and C design Chebyshev's lowpass prototype filter are as follows:
(1) give the filter of being designed passband and stopband insertion attenuation value, and according to corresponding technology formula,
Chart, parameter obtain the component number N and normalization component values of low-pass filter；
(2) according to the cutoff frequency of filter and singal source resistance, the structure type (input filter inductances of ladder network are selected
Or input filter tances), calculate the true value of each element；
(3) it calculates, the characteristic impedance value of the high and low impedance of selected transmission line section, and calculates the lateral ruler of each section of transmission line
It is very little；
(4) length of each high and low impedance line segment is calculated according to the actual components numerical value of filter；
Chebyshev filter have the precipitous excessive characteristic of passband-stopband, but the steep of its pass-band performance with
It is related with interior ripple；Low-pass filter is specifically designed according to above-mentioned design procedure:
(1) filter element number and normalization component values are calculated
Given chebyshev low-pass filter technical parameter is as follows:
Characteristic impedance: Z0(W)；
The cutoff frequency of 3dB: fc(Hz)；
Stop-band frequency: fx(Hz)；
Passband ripple peak value: LAr(dB)；
Stopband attenuation amount: LA(dB)
The calculation formula of element number is
In formulaN is filter element number, takes immediate larger odd-integral number；Because n is bigger, stopband declines
It is steeper to subtract curve, that is to say, that the selectivity of filter is better；And it is because Chebyshev's low-pass prototype exists that n, which mostly uses odd-integral number,
When even level, input is differed with output impedance.
Then lumped parameter normalized value is in ptototype filter
In formula, g0,g1,L gk L gn,gn+1Numerical value in indication circuit after lumped parameter normalization,
(2) ladder network structure type is selected, and calculates each element true value
Ladder network structure is divided into string L simultaneously c-type or simultaneously C string L-type, therefore the ladder of Chebyshev's ptototype filter determining first
L network structure type, then calculate actual inductance capacitance value.Fig. 2 and Fig. 3 is the circuit prototype of two kinds of structures respectively
By characteristic impedance value Z0With normalization component value gn, obtain each element true value in ladder circuit are as follows:
(a) string L and c-type
(b) and C go here and there L-type
G in formula0,g1,L gkL g2n,g2n+1The numerical value of each element, L in indication circuitkIndicate inductance member in ladder circuit
The true value of part, CkIndicate the true value of capacity cell in ladder circuit.And in practical applications, low-pass filter prototype
Component values are to g0Normalized is done, frequency is to ω '1Normalized, i.e. g0=1, ω '1=1；And such normalization class
Type is easily transformed into the filter of other impedance levels and frequency standard, and transformation for mula is as follows:
Resistance or conductance:
Inductance:
Capacitor:
It is the attenuation characteristic of chebyshev low-pass filter, mathematic(al) representation as shown in Figure 4 are as follows:
L in formulaArIt is passband ripple peak value, LAIt is stopband attenuation amount, for indicating the amplitude response of filter；ω1' it is logical
L is decayed in belt edgeArWhen frequency, i.e. passband edge cutoff frequency, that is to say, that 0~ω1' it is passband, ω1' the above are
Stopband；N is the reactance component number of circuit, and when n is even number, responds interior LAr=0 frequency hasIt is a；When n is odd number,
LA=0, frequency hasIt is a；R0Indicate resistance per unit length, R0' indicate that the resistance per unit length after normalization, G indicate conductance,
G' indicates the conductance after normalization, G0Indicate unit length conductance, G0' indicating the unit length conductance after normalization, L' expression is returned
Inductance after one change, C' indicate that the capacitor after normalization, ω indicate input frequency, ω ' expression output frequency.
(3) diameter of each high and low impedance line is calculated
Microwave circuit uses electromagnetic transmission signal, therefore is affected by element with distributed parameters.Chebyshev's microwave is low
The microwave of Design of Bandpass Filter is realized, i.e., realizes that series inductor, one section of low-impedance line realize shunt capacitance with one section of high impedance line.
The junction of the different coaxial line of adjacent two sections of internal diameters is stairstepping (as shown in Figure 4), and magnetic distribution will become at this
Change.For same impedance, outer conductor ladder is smaller than the edge capacitance of inner conductor ladder, therefore uses inner conductor step edges electricity
Hold to indicate its influence to relevant parameter.Fig. 5 is coaxial line longitudal section figure, and Fig. 6 is its equivalent circuit, but equivalent circuit is to work as
Frequency is just set up when being lower than the cutoff frequency of first height mould.
There is edge capacitance
Cd=Cd'×4b (11)
Simultaneously
In formulaa1For high impedance section coaxial inner conductor diameter, a2For Low ESR section coaxial inner conductor
Diameter, b are coaxial outer conductor diameter；Permittivity of vacuum ε=8.85 × 10-12F/m；
As shown in fig. 7, setting the outer diameter of the inner conductor of coaxial line as d, the internal diameter of outer conductor is D, fills and is situated between two conductors
The relative dielectric constant of matter is εr, relative permeability μr(usual μr=1), ignore coaxial line loss, then its characteristic impedance are as follows:
Therefore given characteristic impedance Z0Inner conductor outer diameter d and outer conductor internal diameter D can be solved by formula (11), formula (13)
The diameter of each section of high and low impedance line；
(4) length of each high and low impedance line is calculated
Inductance L' and capacitor C' difference in coaxial line unit length:
ν in formulapFor the phase velocity of wave transmission；
To obtain: the coaxial line segments length of corresponding inductance L:
The coaxial line length of corresponding capacitor C:
Z in formulaohFor high characteristic impedance, ZolFor low characteristic impedance；
Then examine whether the length of each high low-impedance line meets relational expression:Or
The utility model has the advantages that the present invention, according to network synthesis, a kind of novel tunable High Linear of research and development is based on Chebyshev
The passive filter of impedance transformer network technology has many advantages, such as that structure size is small, production easy to process, is easy to and element matching.
With good linear, and Parameter adjustable, finally give computer artificial result.The microwave filtering of comprehensive design of the present invention
Not only required element is minimum for device, but also can obtain optimal design result, while simplifying design process, and then significantly
It must improve work efficiency.
Detailed description of the invention
Fig. 1 (a) is TEM cutting back line chart.
Fig. 1 (b) is the T-type equivalent circuit of TEM stub.
Fig. 1 (c) is the IT type equivalent circuit of TEM stub.
Fig. 2 is string L and c-type low-pass filter circuit prototype.
Fig. 3 is simultaneously C string L-type low-pass filter circuit prototype.
Fig. 4 is the response wave shape of Chebyshev.
Fig. 5 is coaxial line longitudal section figure.
Fig. 6 is high Low ESR section coaxial line equivalent circuit diagram.
Fig. 7 is coaxial line cross section.
Fig. 8 (a) is the output curve diagram for inputting Chebyshev filter when frequency is 100Hz.
Fig. 8 (b) is the output curve diagram for inputting Chebyshev filter when frequency is 1kHz.
Fig. 8 (c) is the output curve diagram for inputting Chebyshev filter when frequency is 5kHz.
Fig. 8 (d) is the output curve diagram for inputting Chebyshev filter when frequency is 10kHz.
Fig. 8 (e) is the output curve diagram for inputting Chebyshev filter when frequency is 15kHz.
Fig. 8 (f) is the output curve diagram for inputting Chebyshev filter when frequency is 27kHz.
Fig. 9 is 2220~2290MHz lumped parameter Filter Principle figure.
Figure 10 is the insertion loss of Chebyshev filter.
Figure 11 is the passband ripple of Chebyshev filter.
Figure 12 is the input/output port standing-wave ratio of Chebyshev filter.
Specific embodiment
With reference to the accompanying drawing, invention is further described in detail.
The design uses electromagnetic simulation software ADS, is based on Chebyshev's impedance transformer network technology, passes through network synthesis
Model is emulated, a 2220~2290MHz lumped parameter filter is designed.
1. design objective requires
Table 1 2220~2290MHz lumped parameter filter design requirement
| Title | Passband/MHz | Stopband/MHz | Ap/dB | As/dB | VSWR |
| Index value | 2220~2290 | 2180/2330 | < 0.3 | > 40 | < 1.2 |
2. specification and simulating schematic diagram
The design is that band connection frequency is 2220~2290MHz, and stopband cutoff frequency is respectively 2180MHz and 2330MHz
Lumped parameter bandpass filter emulates function by the tuning of ADS using the design structure based on Chebyshev's type filter
It can obtain optimal component values.Its specific principle of simulation is as shown in Figure 9.R1, R2 are Chebyshev filter inputs in figure
The impedance matching resistor of output end, L1, L2, L3, L4, L5, L6, L7, L8, L9 are inductance in Chebyshev filter, C1, C2,
C3, C4, C5, C6, C7, C8, C9 are capacitors in Chebyshev filter.Signal source connects the tie point in R1 and L1 when emulation, shows
Wave device connects the tie point in R2 and C9.
Simulation result and analysis
Simulation result mainly includes insertion loss, passband ripple and the standing-wave ratio of each port of filter etc..It is imitative in detail
True result is as shown in Figure 10,11,12.M1 is passband start frequency in Figure 10, and m2 is cut-off frequecy of passband, and m3 is stopband cutoff frequency
Rate, m4 are stopband start frequency.M1 is passband ripple maximum value present position in Figure 11.Chebyshev filter standing wave in Figure 12
Than maximum value present position.
Interpretation of result:
(1) it can be seen that in all preferable resonance to frequency band of insertion loss, passband ripple, standing-wave ratio from simulation result；
(2) passband ripple is all in 0.03dB hereinafter, flatness is fine, the index request preferably met；
(3) standing-wave ratio also all meets design objective requirement in entire passband, illustrates the preferable of Circuit Matching, did not had
More back waves exists.
3. comprehensive simulating design result
Table 2 2220~2290MHz lumped parameter filter simulation result
| Title | Passband/MHz | Stopband/MHz | Ap/dB | As/dB | VSWR |
| Index value | 2220~2290 | 2180/2330 | < 0.3 | > 40 | < 1.2 |
| Simulation value | 2220~2229 | 2180/2330 | < 0.03 | > 41 | < 1.18 |
4. conclusion
The design uses under set index and is based on Chebyshev's impedance transformer network technology, be to band connection frequency
2220~2290MHz, stopband cutoff frequency are respectively that the lumped parameter bandpass filter of 2180MHz and 2330MHz is set
Meter, and emulation is completed by ADS.Simulation result shows that ripple coefficient in entire passband, VSWR and stopband attenuation are all fine
Meet design requirement.
The foregoing is only a preferred embodiment of the present invention, is not restricted to the present invention, for the technology of this field
For personnel, the invention may be variously modified and varied.All within the spirits and principles of the present invention, made any to repair
Change, equivalent replacement, improvement etc., should be included within scope of the presently claimed invention.
Claims (1)
1. a kind of filter design method based on Chebyshev's impedance transformer network technology, it is characterised in that: including following step
It is rapid:
(1) passband and stopband for giving the filter of being designed are inserted into attenuation value, and according to corresponding technology formula, figure
Table, parameter obtain the component number N and normalization component values of low-pass filter；
(2) according to the cutoff frequency of filter and singal source resistance, the ladder network of input filter inductances or input filter tances is selected
Structure type, calculate the true value of each element；
(3) it calculates, the characteristic impedance value of the high and low impedance of selected transmission line section, and calculates the lateral dimension of each section of transmission line；
(4) length of each high and low impedance line segment is calculated according to the actual components numerical value of filter；
Chebyshev filter have the precipitous excessive characteristic of passband-stopband, but the steep of its pass-band performance with interior
Ripple is related；Low-pass filter is specifically designed according to above-mentioned design procedure:
(1) filter element number and normalization component values are calculated
Given chebyshev low-pass filter technical parameter is as follows:
Characteristic impedance: Z0(Ω)；
The cutoff frequency of 3dB: fc(Hz)；
Stop-band frequency: fx(Hz)；
Passband ripple peak value: LAr(dB)；
Stopband attenuation amount: LA(dB)
The calculation formula of element number is
In formulaN is filter element number, takes immediate larger odd-integral number；Because n is bigger, stopband attenuation is bent
Line is steeper, that is to say, that the selectivity of filter is better；And it is because Chebyshev's low-pass prototype is in even number that n, which mostly uses odd-integral number,
When grade, input is differed with output impedance；
Then lumped parameter normalized value is in ptototype filter
In formula, g0, g1... gk…gn, gn+1Numerical value in indication circuit after lumped parameter normalization,
(2) ladder network structure type is selected, and calculates each element true value
Ladder network structure is divided into string L simultaneously c-type or simultaneously C string L-type, therefore the ladder net of Chebyshev's ptototype filter determining first
Network structure type, then calculate actual inductance capacitance value；
By characteristic impedance value Z0With normalization component value gn, obtain each element true value in ladder circuit are as follows:
(a) string L and c-type
(b) and C go here and there L-type
G in formula0, g1... gk…g2n, g2n+1The numerical value of each element, L in indication circuitkIndicate inductance element in ladder circuit
True value, CkIndicate the true value of capacity cell in ladder circuit；And in practical applications, the element of low-pass filter prototype
Numerical value is to g0Normalized is done, frequency is to ω '1Normalized, i.e. g0=1, ω '1=1；And such normalization type is easy
It is transformed into the filter of other impedance levels and frequency standard, transformation for mula is as follows:
Resistance or conductance:
Inductance:
Capacitor:
The mathematic(al) representation of the attenuation characteristic of chebyshev low-pass filter are as follows:
L in formulaArIt is passband ripple peak value, LAIt is stopband attenuation amount, for indicating the amplitude response of filter；ω'1It is passband side
L is decayed on edgeArWhen frequency, i.e. passband edge cutoff frequency, that is to say, that 0~ω '1For passband, ω '1The above are stopbands；
N is the reactance component number of circuit, and when n is even number, responds interior LAr=0 frequency hasIt is a；When n is odd number, LA=
0, frequency hasIt is a；R0Indicate resistance per unit length, R0' indicate that the resistance per unit length after normalization, G indicate conductance, G' table
Conductance after showing normalization, G0Indicate unit length conductance, G0' indicating the unit length conductance after normalization, L' indicates normalization
Inductance afterwards, C' indicate that the capacitor after normalization, ω indicate input frequency, and ω ' indicates output frequency；
(3) diameter of each high and low impedance line is calculated
Microwave circuit uses electromagnetic transmission signal, therefore is affected by element with distributed parameters；Chebyshev's microwave low pass filtered
The microwave of wave device design is realized, i.e., realizes that series inductor, one section of low-impedance line realize shunt capacitance with one section of high impedance line；It is adjacent
The junction of the different coaxial line of two sections of internal diameters is stairstepping, and magnetic distribution will change at this；With regard to same impedance
Speech, outer conductor ladder is smaller than the edge capacitance of inner conductor ladder, therefore indicates it to phase using inner conductor step edges capacitor
Close the influence of parameter；But equivalent circuit is just set up when frequency is lower than the cutoff frequency of first height mould；
There is edge capacitance
Cd=Cd'×4b (11)
Simultaneously
In formulaa1For high impedance section coaxial inner conductor diameter, a2For Low ESR section coaxial inner conductor diameter,
B is coaxial outer conductor diameter；Permittivity of vacuum ε=8.85 × 10-12F/m；
If the outer diameter of the inner conductor of coaxial line is d, the internal diameter of outer conductor is D, and the opposite dielectric of filled media is normal between two conductors
Number is εr, relative permeability μr, μr=1, ignore coaxial line loss, then its characteristic impedance are as follows:
Therefore given characteristic impedance Z0Inner conductor outer diameter d and outer conductor internal diameter D can solve each section by formula (11), formula (13)
The diameter of high and low impedance line；
(4) length of each high and low impedance line is calculated
Inductance L' and capacitor C' difference in coaxial line unit length:
ν in formulapFor the phase velocity of wave transmission；
To obtain: the coaxial line segments length of corresponding inductance L:
The coaxial line length of corresponding capacitor C:
Z in formulaohFor high characteristic impedance, ZolFor low characteristic impedance；
Then examine whether the length of each high low-impedance line meets relational expression:Or
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| DE19821353A1 (en) * | 1998-05-13 | 1999-11-18 | Bosch Gmbh Robert | Filter arrangement for transferring high frequency electromagnetic waves, esp. radio waves, e.g. for satellite communications systems, is very compact compared to conventional arrangements whilst realising two damping poles |
| WO2013056729A1 (en) * | 2011-10-18 | 2013-04-25 | Telefonaktiebolaget L M Ericsson (Publ) | A microstrip to closed waveguide transition |
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