CN102569956B - A Varactor Electrically Tunable Filter - Google Patents

Abstract

The invention discloses a varactor electric adjustable filter. The varactor electrically tunable filter includes: an input microstrip line, a first microstrip resonator, a second microstrip resonator and an output microstrip line; wherein, the first microstrip resonator and the second microstrip resonator The openings are arranged side by side as mirror images, and the adjacent parts of the two form direct coupling; the input microstrip line and the output microstrip line are respectively located under the first microstrip resonator and the second microstrip resonator, and are arranged side by side as mirror images, and the two The ends of both are deflected by 90 degrees in the direction away from the first microstrip resonator and the second microstrip resonator, and the two deflected parts are parallel to each other to form a cross-coupling, which is opposite in sign to the direct coupling. The transfer function of the varactor electric tunable filter produces a transmission zero point, which has the characteristics of an elliptic function, so that the filter has a good square coefficient and improves the filtering performance.

Description

A Varactor Electrically Tunable Filter

technical field

The invention relates to the technical field of signal processing in the electronics industry, and in particular to a variable capacitance tube electrically adjustable filter.

Background technique

Electrically tunable filters are used in occasions where frequency changes, especially in the field of radar detection, to filter signals, so as to obtain a relatively pure spectrum and improve the anti-interference ability of the system. Electrically tunable filters are generally divided into two types: Yttrium Iron Garnet (YIG for short) electrically tunable filters and varactor electrically tunable filters. YIG electric tunable filter has a high quality factor, but due to the influence of hysteresis effect, its tuning speed is slow, so it cannot be applied to frequency agility occasions. The tuning speed of the varactor electronically tuned filter is fast, which can meet the needs of agile frequency conversion, and a high quality factor can be obtained by selecting a high quality factor varactor.

Due to the difficulties in coupling and design, varactor electric tuning filters are usually comb filter structures, which cannot achieve elliptic function-like filtering characteristics and cannot suppress the adjacent passband lower. The elliptic function filter can generate transmission zeros near the passband, so its filtering performance is greatly improved, but it has specific requirements for the coupling form of the filter.

In the process of realizing the present invention, the applicant realizes that the following technical defects exist in the prior art: the existing varactor electric tuning filter usually adopts Butterworth synthesis or Chebyshev synthesis, and the rectangular coefficient of the design scheme of these filters is not good, specifically Generally speaking, there is no steep edge, so the filtering effect on the sideband is not good, so it cannot meet the demand in occasions with high requirements for sideband suppression.

Contents of the invention

(1) Technical problems to be solved

In order to solve the above-mentioned problems, the present invention provides a kind of varactor electric tunable filter, utilizes the microstrip resonator loaded by two varactors to design a similar elliptic function filter, and the sidebands form a pair of transmission zeros, reaching Good sideband suppression effect; at the same time, by adjusting the bias voltage applied to the varactor, the center frequency of the varactor electronically adjustable filter changes with the applied voltage to meet the needs of agile frequency conversion.

(2) Technical solution

According to one aspect of the present invention, a varactor electrically tunable filter is provided. The varactor electrically tunable filter includes: an input microstrip line, a first microstrip resonator, a second microstrip resonator and an output microstrip line; wherein, the first microstrip resonator and the second microstrip resonator The openings are arranged side by side as mirror images, and the adjacent parts of the two form direct coupling; the input microstrip line and the output microstrip line are respectively located under the first microstrip resonator and the second microstrip resonator, and are arranged side by side as mirror images, and the two The ends of each are deflected by 90 degrees in a direction away from the first microstrip resonator and the second microstrip resonator, forming a cross-coupling which is opposite in sign to the direct coupling.

(3) Beneficial effects

It can be seen from the above technical solutions that the varactor electric tunable filter of the present invention has the following beneficial effects:

(1) The first microstrip resonator and the second microstrip resonator are adjacent to each other to form a direct coupling; the ends of the input microstrip line and the output microstrip line form a cross-coupling, and the direct coupling and the cross-coupling sign are opposite , so that the transfer function of the filter produces a transmission zero point, which has the characteristics of an elliptic function, so that the filter has a good rectangular coefficient and improves the filtering performance;

(2) Due to the adoption of the varactor electric adjustment structure, the center frequency of the filter is changed by changing the tuning voltage on the varactor, while keeping the shape of the filter curve unchanged, the center frequency of the filter has a very fast tuning speed, Meet the needs of agile frequency conversion;

(3) Owing to having adopted input microstrip line and output microstrip line, utilize this input microstrip line and output microstrip line as the cross-coupling of filter, make varactor electric tunable filter of the present invention than traditional type Elliptic function filters require fewer resonators, while traditional elliptic function filters require at least one pair of resonators to construct cross-coupling.

Description of drawings

FIG. 1 is a schematic structural view of a varactor electric tunable filter according to an embodiment of the present invention;

FIG. 2 is a schematic structural view of a resonator in a varactor electrically tunable filter according to an embodiment of the present invention;

FIG. 3 is a simulation and measured response curve of a varactor electrically tunable filter according to an embodiment of the present invention.

Detailed ways

In order to make the object, technical solution and advantages of the present invention clearer, the present invention will be described in further detail below in conjunction with specific embodiments and with reference to the accompanying drawings. While illustrations of parameters containing particular values may be provided herein, it should be understood that the parameters need not be exactly equal to the corresponding values, but rather may approximate the corresponding values within acceptable error margins or design constraints.

In the theory of electromagnetic field, electromagnetic waves are transmitted in the form of sine waves on the transmission line, and there will be voltage peak points and wave nodes at specific positions. At the voltage peak point, the voltage reaches the maximum value, and the current is 0 at this time, which is expressed in the form of an electric field. ; At the voltage wave node, the voltage reaches the minimum value, and the current reaches the maximum value, which is manifested in the form of a magnetic field. The coupling of electromagnetic energy by electric field is called electric coupling, the coupling by magnetic field is called magnetic coupling, and the coupling by electric field and magnetic field is called hybrid coupling.

For any transmission line structure, since the current at the open end cannot pass through, the current is 0 at this time, and the electromagnetic wave always presents a voltage peak point, which is expressed as an electric field, and the coupling of electromagnetic energy here is electrical coupling. At the grounding point of the transmission line, the voltage reaches the minimum value, and it can be considered that there is no voltage difference between it and the ground. At this time, the current of the electromagnetic wave reaches the maximum value, which is expressed in the form of a magnetic field. The coupling here is magnetic coupling. For a half-wave open-loop resonator, its two ends are open, the electromagnetic wave reaches the maximum voltage at both ends of the resonator, which is manifested as an electric field, and can only be electrically coupled; in the middle of the open-loop resonator, due to the periodic law of electromagnetic waves, only Can be a voltage wave node, manifested as a magnetic field, where only magnetic coupling can be performed; in other positions, it is hybrid coupling.

FIG. 1 is a schematic structural diagram of a varactor electrically tunable filter of the present invention. In FIG. 1 , for the sake of clarity, the bias circuit of the varactor is not shown, and the bias circuit will be described in detail in FIG. 2 . As shown in Figure 1, the filter includes an input microstrip line, a first microstrip resonator, a second microstrip resonator and an output microstrip line. Among them, the opening of the first microstrip resonator and the second microstrip resonator are arranged side by side in a mirror image, and the parts adjacent to each other form a direct coupling, that is, the coupling between adjacent serial number transmission units; the input microstrip line and the output The microstrip lines are respectively located below the first microstrip resonator and the second microstrip resonator, mirrored side by side, and both ends are deflected by 90 in a direction away from the first microstrip resonator and the second microstrip resonator The degree of cross coupling is formed, that is, the coupling between non-adjacent serial number transmission units. The sign of the direct coupling and the cross coupling is opposite, that is, the magnetic coupling is positive, and the electrical coupling is negative. The model and specification of the first microstrip resonator and the second microstrip resonator are the same.

According to the Levy approximate synthesis model, if the transfer function of the cross-coupling filter is to obtain a transmission zero point, the direct coupling and cross-coupling between the transmission units constituting the cross-coupling must have opposite signs. For this embodiment, a cross-coupled transmission unit is formed by the input microstrip line, the first microstrip resonator, the second microstrip resonator and the output microstrip line. The coupling between the first microstrip resonator and the second microstrip resonator constitutes a direct coupling.

The magnetic coupling mode is adopted between the first microstrip resonator and the second microstrip resonator shown in FIG. 1 , so the input microstrip line and the output microstrip line must adopt the electrical coupling mode. In addition, if the first microstrip resonator and the second microstrip resonator adopt the electrical coupling mode, then the input microstrip line and the output microstrip line should adopt the magnetic coupling mode.

In this embodiment, the input microstrip line is coupled to the first microstrip resonator in parallel, and a mixed coupling mode exists between the two, that is, electric coupling and magnetic coupling act together. A magnetic coupling mode exists between the first microstrip resonator and the second microstrip resonator. The output microstrip line is coupled in parallel to the second microstrip resonator with hybrid coupling mode between the two. A magnetic coupling mode exists between the first microstrip resonator and the second microstrip resonator. Therefore, the transfer function of the entire varactor tunable filter generates a pair of transmission zeros at the edge of the passband, which improves the ability to suppress signals of adjacent channels.

Each component of the varactor electrically tunable filter will be described in detail below.

1. Resonator. The resonator is the basic unit of the filter, and the filter of the present invention adopts a half-wave resonator structure, which is composed of a microstrip resonant line and a varactor. The positive pole of the varactor is connected to one end of the open circuit of the microstrip resonant line, and the negative pole is connected to the other end of the open circuit of the microstrip resonant line in series with a DC blocking capacitor. The tuning voltage Vt is added to the negative pole of the varactor through the bias resistor R1 to adjust The center frequency of the filter, the microstrip resonant line is grounded through the bias resistor R2, that is, it is grounded in the middle of the resonator, where the signal voltage node is, and the parasitic parameters introduced are the smallest, forming the bias path of the varactor, namely The resonator structure shown in Figure 2.

a. Microstrip resonant line

The microstrip resonance line adopts a 50 ohm characteristic impedance transmission line, and the length d of the microstrip resonance line is calculated according to formula 1.

When the varactor is loaded with a half-wave resonator, the calculation formula for the length of the microstrip resonant line is:

$\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}\mathrm{<span\; class="notranslate">\; arctg</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

Where f ₀ is the center frequency of the filter, Z ₀ is the characteristic impedance of the transmission line, C is the intermediate capacitance value of the varactor, and β is the propagation constant of the guided wave, which is determined by the dielectric constant and thickness of the transmission medium.

b. Varactor

In order to reduce the insertion loss, try to use a high-Q varactor. The capacitance should be as small as possible under the condition of meeting the frequency adjustment range, that is, the Q value of the varactor is inversely proportional to the capacitance. It is preferable to use a varactor with a model of SMV1233 Tube. In the case of a given microstrip line length, assuming that the center frequency adjustment range of the filter is required to be f ₁ ~ f ₂ , the capacitance value of the varactor is required to vary in the range C ₁ ~ C ₂ . The capacitance adjustment range requirement of the varactor is calculated by formula 2:

$\left.\begin{array}{c}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="C"\; filenames="HDA0000139069840000011.png"\; state="\{\{state\}\}">C</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\mathrm{<span\; class="notranslate">\; tg</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&beta;d</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}\\ {\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="C"\; filenames="HDA0000139069840000011.png"\; state="\{\{state\}\}">C</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\mathrm{<span\; class="notranslate">\; tg</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&beta;d</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}\end{array}\right\}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

Among them, β is the propagation constant of the guided wave, d is the length of the microstrip resonance line, f ₁ and f ₂ are the upper and lower ranges of the center frequency adjustment of the filter, and Z ₀ is the characteristic impedance of the transmission line.

2. Input microstrip line and output microstrip line

The input and output microstrip lines adopt 50 ohm characteristic impedance microstrip transmission lines to provide a pair of cross-coupling for the filter to form a pair of transmission zeros. In Figure 1, a pair of parallel electrical couplings are constructed at the open ends of the input and output microstrip lines to form cross-coupling-electrical coupling. The length and shape of the input and output microstrip lines vary with the coupling coefficient.

The size of the coupling coefficient M _io between the input and output microstrip lines can be calculated according to formula 3. The size of its coupling determines how far the position of the transmission zero is from the passband. If the coupling is too large, the transmission zero point is very close to the passband, and the out-of-band suppression performance will decrease; if the coupling is too small, the transmission zero point is too far away from the accommodation band, and the square coefficient of the filter will deteriorate.

${\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; io</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; *</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="f"\; filenames="HDA0000139069840000011.png"\; state="\{\{state\}\}">f</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; *</span>\frac{{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}}{{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

where M ₁₂ is the magnitude of the coupling coefficient between the first resonator and the second resonator, Q _e is the external load quality factor (which represents the connection relationship between the input and output lines and the resonator), and f ₀ is the center frequency , f ₁ and f ₂ are the frequencies of the two transmission zero points to be set respectively, k is the coupling factor, and the k value has been synthesized to be 1.597, which is determined by the length and spacing of the input and output microstrip lines, and other values can also be used. Changing the value of k will shift the position of the transmission zero.

The design formula of a distributed parameter filter is usually called a comprehensive formula. There is no rigorous mathematical expression, and there are various comprehensive models. According to the comprehensive model, a filter design with a specific structure can be carried out, and various models are not universal. For filters with complex structures, there is no ready-made comprehensive model to use, but the method of extracting coupling coefficients and external quality factors can be used for design, which is universal, that is: first optimize a filter based on experience; The optimized filter extracts its coupling coefficient and external quality factor; subsequent designers can design based on it. For the varactor electrically tunable filter of this embodiment, the design process is roughly as follows:

1. Design parameters: The center frequency adjustment range is 1.4GHz to 1.85GHz, and the relative bandwidth FBW is 0.04. The relevant parameters of the copper-clad microstrip board used are: dielectric constant: 3.2, dielectric thickness: 1mm;

2. From the above design parameters and peripheral parameters, set the loading capacitance of the resonator as 1.2pF to obtain the length d of the microstrip resonant line as 32mm, and the capacitance variation range calculated by formula 3 is at least 1pF to 1.5pF. Considering the obtained capacitance In this embodiment, the value of the varactor is connected in series with a 3pF DC blocking capacitor, and the corresponding range of capacitance of the varactor should be at least 1.5pF to 3pF. According to the results of the above calculation, the model SMV1233 can be selected. Varactor (its corresponding capacitance value is 1.1pF6V, 3pF1V);

3. Adjust the spacing between the first resonator and the second resonator, the bending length of the input microstrip line and the output microstrip line to obtain the best filtering curve, and then extract the coupling of the adjusted filter Coefficient and external quality factor, the same type of filter can be designed according to the optimized coupling coefficient and external quality factor normalized to the required center frequency. The coupling coefficient and external quality factor of the filter are:

$\left.\begin{array}{c}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0.078</span>}\\ {\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; io</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.0044</span>}\\ {\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 14.89</span>}\end{array}\right\}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

The specific structural parameters of the filter are (the dielectric constant of the medium is 3.3, and the thickness of the medium is 1mm): the coupling length of the input and output microstrip lines is 3mm, and the spacing is 1mm; between the first resonator and the second resonator The coupling length is 5mm, the spacing is 0.7mm, the spacing between the input and output microstrip lines and the first resonator and the second resonator is 12mm, and the spacing is 0.2mm, and the total length of the microstrip section in the resonator is 32mm.

Figure 3 is the S parameter S21 response curve of the filter, in which the solid line is the actual measurement curve, and the dotted line is the simulation curve, and the simulation curve and the actual measurement curve are in good agreement. When the applied voltage of the varactor is adjusted from 1V to 5V, the center frequency of the filter is moved from 1.4GHz to 1.85GHZ, while S21 always maintains a pair of transmission zeros.

Affected by the Q value of the varactor, the insertion loss of the varactor electric tuning filter is relatively large at the frequency end. The reason is that when the bias voltage is low, the Q value of the varactor is relatively small, and the insertion loss is small at the high end of the frequency , in practical applications, amplification and compensation can be performed after filtering, or only the adjustable frequency at the high end of the frequency can be selected. In this embodiment, the center frequency is between 1.6GHz and 1.85GHz, and the insertion loss is small. In this embodiment, the resonator microstrip The length of the line and the varactor used can be changed accordingly according to the formula, as long as the frequency adjustment range of the filter can be satisfied. Especially after using varactors with higher Q value, such as MA4ST250, the insertion loss at the low frequency end can be improved to a certain extent.

The specific embodiments described above have further described the purpose, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above descriptions are only specific 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 within the protection scope of the present invention.

Claims (9)

1. A varactor electrically tunable filter comprising: the microstrip line comprises an input microstrip line, a first microstrip resonator, a second microstrip resonator and an output microstrip line; wherein,

the first microstrip resonator and the second microstrip resonator are provided with outward openings and are arranged in a side-by-side mirror image mode, and the adjacent parts of the first microstrip resonator and the second microstrip resonator form direct coupling which is magnetic coupling;

the input microstrip line and the output microstrip line are respectively positioned below the first microstrip resonator and the second microstrip resonator and are arranged in a side-by-side mirror image mode, the tail ends of the input microstrip line and the output microstrip line are deflected by 90 degrees along the direction far away from the first microstrip resonator and the second microstrip resonator, the two deflected parts are parallel to each other to form cross coupling, the sign of the cross coupling is opposite to that of the direct coupling, and the cross coupling is electric coupling.

2. The varactor electrically tunable filter of claim 1, wherein the input microstrip line forms a hybrid coupling with a first microstrip resonator; the output microstrip line and the second microstrip resonator form hybrid coupling.

3. The varactor electrically tunable filter of claim 1, wherein said first and second microstrip resonators are each a half-wave resonator comprising:

the microstrip resonant line is grounded through a second bias resistor; and

the positive pole of the varactor is connected to one end of the microstrip resonant line open circuit, the negative pole of the varactor is connected to the other end of the microstrip resonant line open circuit after being connected with the DC blocking capacitor in series, and the tuning voltage is added to the negative pole of the varactor through the first bias resistor.

4. The varactor electrically tunable filter of claim 3, wherein the microstrip resonant line is a 50 ohm characteristic impedance transmission line having a length d, where d satisfies:

<math> <mrow> <mi>d</mi> <mo>=</mo> <mfrac> <mn>2</mn> <mi>&beta;</mi> </mfrac> <mi>arctg</mi> <mrow> <mo>(</mo> <mfrac> <mn>1</mn> <mrow> <mi>&pi;</mi> <msub> <mi>f</mi> <mn>0</mn> </msub> <msub> <mi>Z</mi> <mn>0</mn> </msub> <mi>C</mi> </mrow> </mfrac> <mo>)</mo> </mrow> </mrow> </math>

wherein f is₀Is the center frequency, Z, of the filter₀Characteristic of transmission lineImpedance, C is the intermediate capacitance of the varactor, and β is the propagation constant of the guided wave.

5. The varactor electrically tunable filter of claim 4, wherein the varactor has a capacitance value ranging of at least C₁～C₂In which C is₁、C₂Satisfies the following conditions:

<math> <mrow> <mfenced open='' close='}'> <mtable> <mtr> <mtd> <msub> <mi>C</mi> <mn>1</mn> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mi>&pi;</mi> <msub> <mi>f</mi> <mn>1</mn> </msub> <msub> <mi>Z</mi> <mn>0</mn> </msub> <mi>tg</mi> <mrow> <mo>(</mo> <mi>&beta;d</mi> <mo>/</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> </mfrac> </mtd> </mtr> <mtr> <mtd> <msub> <mi>C</mi> <mn>2</mn> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mi>&pi;</mi> <msub> <mi>f</mi> <mn>2</mn> </msub> <msub> <mi>Z</mi> <mn>0</mn> </msub> <mi>tg</mi> <mrow> <mo>(</mo> <mi>&beta;d</mi> <mo>/</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> </mfrac> </mtd> </mtr> </mtable> </mfenced> <mo>.</mo> </mrow> </math>

6. the varactor electrically tunable filter of claim 5, wherein a coupling coefficient between the input and output microstrip lines is M_ioThe coupling coefficient between the first resonator and the second resonator is M₁₂Then M is_ioAnd M₁₂Satisfies the following conditions:

$M_{\mathrm{io}}=-k*\frac{f_0}{f_2-f_1}*\frac{M_{12}}{Q_e}$

wherein Q is_eTo express the external load quality factor of the connection between the input-output line and the resonator, f₀Is the center frequency, f₁And f₂K =1.597 is the coupling factor, respectively the frequency of the two transmission zeros to be set.

7. The varactor electrically tunable filter of claim 6, having a center frequency tuning range of 1.4GHz to 1.85GHz and a relative bandwidth of 0.04;

coefficient of coupling M_ioCoefficient of coupling M₁₂And the external quality factor satisfies:

$\left.\begin{array}{c}{M}_{12}=0.078\\ M_{\mathrm{io}}=-0.0044\\ Q_e=14.89\end{array}\right\}.$

8. the varactor electrically tunable filter of claim 6, having a center frequency tuning range of 1.4GHz to 1.85GHz and a relative bandwidth of 0.04;

the dielectric constant of the used microstrip plate medium is 3.2, and the thickness is 1 mm;

the capacitance variation range of the middle capacitance value C of the varactor is C1-C2: C₁=1.1pF、C₂=3pF；

The coupling length of the input and output microstrip lines is 3mm, and the distance is 1 mm;

the coupling length between the first resonator and the second resonator is 5mm, and the distance between the first resonator and the second resonator is 0.7 mm;

the distance between the input and output microstrip line and the first resonator and the distance between the input and output microstrip line and the second resonator are 12mm and 0.2mm, and the total length of the microstrip resonance line in the first resonator and the second resonator is 32 mm.

9. The varactor electrically tunable filter of any one of claims 1 to 8, which is an elliptic function-like filter.

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