CN102064461A - Frequency temperature compensation method of hydrogen maser sapphire resonant cavity - Google Patents

Abstract

The invention discloses a frequency temperature compensation method of a hydrogen maser sapphire resonant cavity. The hydrogen maser sapphire resonant cavity comprises a resonant cavity bottom cover (1), a resonant cavity tube (2), a sapphire (3), a piston (4), a resonant cavity top cover (5), a spring (6) and strontium titanate crystal wafers (7). The resonant cavity is assembled by determining the strontium titanate crystal wafers (7) and designing the diameter, the thickness and the number of the strontium titanate crystal wafers (7). The strontium titanate crystal wafers (7) are evenly distributed on the upper and the lower surfaces of the sapphire (3); temperature coefficient of a resonant cavity of the sapphire (3) is measured; and the frequency temperature coefficient of the resonant cavity is finally compensated. The frequency temperature compensation method has the advantages of replacing a mechanical temperature compensation method and largely descending temperature coefficient of the resonant cavity of the sapphire and realizing miniaturization of the hydrogen frequency standard.

Description

A kind of frequency-temperature compensation method of hydrogen maer sapphire resonant cavity

Technical field

The present invention relates to a kind of frequency-temperature compensation method, particularly a kind of frequency-temperature compensation method of hydrogen maer sapphire resonant cavity.

Background technology

Along with the continuous popularization that hydrogen maer is used, its miniaturization is extremely urgent.Resonant cavity is the important component part of hydrogen frequency marking, and its size has directly determined whole clock size.For minification, adopted the dielectric loading chamber---be the cylindrical cavity of filled media with the sapphire, thereby improved the Q value, constant in resonance frequency, do not lose under the situation of accuracy and stability, dwindled cavity size.But along with the metal resonant cavity size diminishes, expect same frequency, the sapphire filled media in the wire chamber increases, and such result will cause the temperature coefficient of microwave cavity to become big, strengthen the difficulty of temperature control after temperature coefficient increases.The temperature control level is difficult to reach so high requirement at present, thereby causes whole clock index to be difficult to improve.

Reduce temperature coefficient and need adopt technique for temperature compensation, but the general in the past mechanical compensation that adopts promptly adopts big alloy, for example magnadure is made to encircle and is supported.When the hydrogen maer resonant cavity size increased with the temperature rising, the ring height is elongation simultaneously also, thereby actual resonant cavity size is diminished on the contrary, reaches the effect of temperature-compensating.But the method is more coarse, and the height of alloy hoop is difficult to design, and along with variation of temperature is difficult to accurate control frequency, the frequency of resonant cavity is affected by environment bigger.

Summary of the invention

The object of the invention is to provide a kind of frequency-temperature compensation method of hydrogen maer sapphire resonant cavity, solves the problem that the mechanical temperature compensation method is difficult to effectively reduce hydrogen maer resonant cavity temperature coefficient.

A kind of concrete steps of frequency-temperature compensation method of hydrogen maer sapphire resonant cavity are:

The first step is determined the strontium titanate crystals sheet

Sapphire is the uniaxial anisotropy crystal, is respectively 9.4 and 11.6 perpendicular to optical axis and the relative dielectric constant that is parallel to optical axis, and its loss tangent perpendicular to optical axis direction is 1 * 10 in the time of 47 ℃ ^-5The strontium titanate crystals sheet is an aeolotropic crystal, and relative dielectric constant is 300, and its loss tangent is 8 * 10 in the time of 47 ℃ ^-4The relative dielectric constant of strontium titanate crystals sheet is to be 30 times of sapphire relative dielectric constant, and the strontium titanate crystals sheet is the negative temperature coefficient crystal, and its dielectric constant reduces along with the rising of temperature, and is opposite with the variation of sapphire dielectric constant.When variations in temperature, the strontium titanate crystals sheet just can compensate the variation of sapphire dielectric constant and the variation of the resonant cavity frequency that causes, therefore selects the strontium titanate crystals sheet as frequency-temperature compensation.

Diameter, thickness, the sheet number of second step design strontium titanate crystals sheet

The strontium titanate crystals sheet is a column type, because the crystal growth ability is limit, diameter is 17mm to the maximum, and selecting strontium titanate crystals sheet diameter is 10mm～17mm.Select different thickness and number to calculate the frequency-temperature coefficient of resonant cavity then, select the optimal size of strontium titanate crystals sheet according to result of calculation.

At first dielectric constant, sapphire thickness, sapphire height, resonant cavity height and the radius of finding the solution when sapphire and strontium titanate crystals sheet according to formula has small quantity changes delta ε _T1, Δ ε _T2, Δ d, Δ h ₂, Δ h ₁During with Δ a, bring the quantitative change Δ f of resonance frequency accordingly, obtain coefficient A thus.

$A_{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HSA00000361960400011.png"\; state="\{\{state\}\}">r</figure-callout>}1}=\frac{{\mathrm{\&epsiv;}}_{t1}}{f}\frac{\mathrm{\&Delta;f}}{{\mathrm{\&Delta;\&epsiv;}}_{t1}}---\left(1\right)$

Formula (1) is found the solution when sapphire dielectric constant has minor variations, the corresponding quantitative change coefficient A that brings resonance frequency _R1, ε wherein _T1Be sapphire dielectric constant.

$A_{r2}=\frac{{\mathrm{\&epsiv;}}_{t2}}{f}\frac{\mathrm{\&Delta;f}}{{\mathrm{\&Delta;\&epsiv;}}_{t2}}---\left(2\right)$

Formula (2) is found the solution when the dielectric constant of strontium titanate crystals sheet has minor variations, the corresponding quantitative change coefficient A that brings resonance frequency _R2, ε wherein _T2Dielectric constant for the strontium titanate crystals sheet.

$A_d=\frac{d}{f}\frac{\mathrm{\&Delta;f}}{\mathrm{\&Delta;d}}---\left(3\right)$

Formula (3) is found the solution when sapphire thickness generation minor variations, the corresponding quantitative change coefficient A that brings resonance frequency _d, wherein d is sapphire thickness.

$A_a=\frac{a}{f}\frac{\mathrm{\&Delta;f}}{\mathrm{\&Delta;a}}---\left(4\right)$

Formula (4) is found the solution when the radius generation minor variations of resonant cavity, the quantitative change coefficient A of the resonance frequency of bringing accordingly _a, wherein a is the radius of resonant cavity.

$A_{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HSA00000361960400011.png"\; state="\{\{state\}\}">h</figure-callout>}1}=\frac{h_1}{f}\frac{\mathrm{\&Delta;f}}{\mathrm{\&Delta;}{h}_1}---\left(5\right)$

Formula (5) is found the solution when the height generation minor variations of resonant cavity, the quantitative change coefficient A of the resonance frequency of bringing accordingly _H1, h wherein ₁Height for resonant cavity.

$A_{h2}=\frac{h_2}{f}\frac{\mathrm{\&Delta;f}}{\mathrm{\&Delta;}{h}_2}---\left(6\right)$

Formula (6) is found the solution when sapphire height generation minor variations, the quantitative change coefficient A of the resonance frequency of bringing accordingly _H1, h wherein ₂Be sapphire height.

Because the height and the thickness of strontium titanate crystals sheet are very little with respect to resonant cavity, it is owing to the thermal expansion that variations in temperature causes can be ignored.

Find the solution the temperature coefficient of sapphire relative dielectric constant, strontium titanate crystals sheet relative dielectric constant, sapphire radial and axial and resonant cavity.

Then according to the computing formula of resonant cavity frequency-temperature coefficient:

$\frac{\&PartialD;f}{\&PartialD;T}=[\frac{\&PartialD;f}{{\&PartialD;\mathrm{\&epsiv;}}_t}\frac{{\&PartialD;\mathrm{\&epsiv;}}_t}{\&PartialD;T}+\frac{\&PartialD;f}{\&PartialD;d}\frac{\&PartialD;d}{\&PartialD;T}+\frac{\&PartialD;f}{\&PartialD;{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HSA00000361960400011.png"\; state="\{\{state\}\}">h</figure-callout>}}_1}\frac{{\&PartialD;\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HSA00000361960400011.png"\; state="\{\{state\}\}">h</figure-callout>}}_1}{\&PartialD;T}+\frac{\&PartialD;f}{\&PartialD;a}\frac{\&PartialD;a}{\&PartialD;T}+\frac{\&PartialD;f}{{\&PartialD;h}_2}\frac{{\&PartialD;h}_2}{\&PartialD;T}]---\left(7\right)$

When Practical Calculation,

The approximate Δ f/ Δ ε that replaces to _t, other partial derivative is also replaced after the same method, can release formula (8) thus:

τ _f＝(A _r1τ _r1+A _r2τ _r2+A _dτ _α1+A _h1τ _α2+A _aτ _c+A _h2τ _c)(8)

Wherein: τ _fThe temperature coefficient of resonance frequency f, τ _R1, τ _R2, τ _{α 1}, τ _{α 2}, τ _cBe constant all, be respectively the thermal coefficient of expansion of sapphire relative dielectric constant temperature coefficient, strontium titanate crystals sheet relative dielectric constant temperature coefficient, sapphire radial and axial thermal coefficient of expansion, resonant cavity.

The thickness of strontium titanate crystals sheet and height substitution above-mentioned formula are calculated the frequency-temperature coefficient of resonant cavity, select, determine that strontium titanate crystals sheet thickness is 5mm～7mm according to result of calculation.The strontium titanate crystals sheet is 8～32, and is the even number sheet.

The 3rd step assembling resonant cavity

The strontium titanate crystals sheet evenly is bonded in sapphire upper and lower surface, and upper and lower surface patch number is identical, and the strontium titanate crystals sheet on upper and lower surface is respectively formed regular polygon.The sapphire screw thread is fixed on the resonant cavity bottom, and resonant cavity tube and resonant cavity bottom screw are fixed.Piston places the sapphire top, and spring places the groove on the piston, and six springs are formed regular hexagon, and the resonant cavity top cover places on the spring, resonant cavity top cover and resonant cavity tube screw.

The frequency-temperature coefficient of the 4th step compensation resonant cavity

When working temperature raise, the resonant cavity volume increased, and it is big that sapphire dielectric constant becomes, according to formula (4), (5) and (1), A _a, A _H1And A _R1Become big, and result of calculation is positive number.According to formula (8), the frequency-temperature coefficient of resonant cavity increases.Because the strontium titanate crystals sheet is the negative temperature coefficient crystal, so the result of formula (2) is a negative.According to formula (8), strontium titanate crystals sheet dielectric constant is 30 times of sapphire dielectric constant, offsets resonant cavity because the frequency change that the sapphire change in dielectric constant causes.When working temperature reduced, the resonant cavity volume reduced, and sapphire dielectric constant diminishes, and it is big that the dielectric constant of strontium titanate crystals sheet becomes, and reduced the frequency-temperature coefficient of resonant cavity.

Sapphire resonant cavity temperature coefficient is decided in the 5th pacing

Carry out the measurement of sapphire resonant cavity temperature coefficient, whole resonant cavity is put into high-low temperature chamber, design temperature T ₁, whole resonant cavity reaches hygral equilibrium after 6 hours, and recording current frequency is f ₁Set second temperature T ₂, recording frequency after the resonant cavity hygral equilibrium is f ₂Measure repeatedly with this, utilize the difference computing formula, obtain the temperature coefficient of resonant cavity frequency:

$f{\mathrm{\&tau;}}_f=\frac{\underset{i=2}{\overset{n}{\mathrm{\&Sigma;}}}[(f_i-f_{i-1})/(T_i-T_{i-1})]}{n-1}---\left(9\right)$

The substitution test data, the temperature coefficient that calculates resonant cavity is lower than present-60kHz/ ℃ for-9.7kHz/ ℃.

Advantage of the present invention is by design strontium titanate crystals sheet, and the strontium titanate crystals sheet is evenly distributed on the sapphire upper and lower surface.Thereby replace the mechanical temperature compensation method, reduce the temperature coefficient of sapphire resonant cavity significantly, realize the miniaturization of hydrogen frequency marking.

Description of drawings

The device schematic diagram of the frequency-temperature compensation method of a kind of hydrogen maer sapphire of Fig. 1 resonant cavity.

1. resonant cavity bottom 2. resonant cavity tubes 3. sapphires 4. pistons 5. resonant cavity top covers 6. springs 7. strontium titanate crystals sheets

Embodiment

A kind of concrete steps of frequency-temperature compensation method of hydrogen maer sapphire resonant cavity are:

The first step is determined strontium titanate crystals sheet 7

Sapphire 3 is uniaxial anisotropy crystal, is respectively 9.4 and 11.6 perpendicular to optical axis and the relative dielectric constant that is parallel to optical axis, and its loss tangent perpendicular to optical axis direction is 1 * 10 in the time of 47 ℃ ^-5Strontium titanate crystals sheet 7 is aeolotropic crystals, and relative dielectric constant is 300, and its loss tangent is 8 * 10 in the time of 47 ℃ ^-4The relative dielectric constant of strontium titanate crystals sheet 7 is to be 30 times of sapphire 3 relative dielectric constants, and strontium titanate crystals sheet 7 is the negative temperature coefficient crystal, and its dielectric constant reduces along with the rising of temperature, and is opposite with the variation of sapphire 3 dielectric constants.When variations in temperature, strontium titanate crystals sheet 7 just can compensate the variation of sapphire 3 dielectric constants and the variation of the resonant cavity frequency that causes, therefore selects strontium titanate crystals sheet 7 as frequency-temperature compensation.

Diameter, thickness, the sheet number of second step design strontium titanate crystals sheet 7

Strontium titanate crystals sheet 7 is a column type, because the crystal growth ability is limit, selecting strontium titanate crystals sheet 7 diameters is 10mm.Select different thickness and number to calculate the frequency-temperature coefficient of resonant cavity then, select the optimal size of strontium titanate crystals sheet 7 according to result of calculation.

At first dielectric constant, sapphire 3 thickness, sapphire 3 height, resonant cavity height and the radius of finding the solution when sapphire 3 and strontium titanate crystals sheet 7 according to formula has small quantity changes delta ε _T1, Δ ε _T2, Δ d, Δ h ₂, Δ h ₁During with Δ a, bring the quantitative change Δ f of resonance frequency accordingly, obtain coefficient A thus.

$A_{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HSA00000361960400011.png"\; state="\{\{state\}\}">r</figure-callout>}1}=\frac{{\mathrm{\&epsiv;}}_{t1}}{f}\frac{\mathrm{\&Delta;f}}{{\mathrm{\&Delta;\&epsiv;}}_{t1}}---\left(1\right)$

Formula (1) is found the solution when the dielectric constant of sapphire 3 has minor variations, the corresponding quantitative change coefficient A that brings resonance frequency _R1,

ε wherein _T1Dielectric constant for sapphire 3.

$A_{r2}=\frac{{\mathrm{\&epsiv;}}_{t2}}{f}\frac{\mathrm{\&Delta;f}}{{\mathrm{\&Delta;\&epsiv;}}_{t2}}---\left(2\right)$

Formula (2) is found the solution when the dielectric constant of strontium titanate crystals sheet 7 has minor variations, the corresponding quantitative change coefficient A that brings resonance frequency _R2, ε wherein _T2Dielectric constant for strontium titanate crystals sheet 7.

$A_d=\frac{d}{f}\frac{\mathrm{\&Delta;f}}{\mathrm{\&Delta;d}}---\left(3\right)$

Formula (3) is found the solution when the thickness generation minor variations of sapphire 3, the corresponding quantitative change coefficient A that brings resonance frequency _d, wherein d is the thickness of sapphire 3.

$A_a=\frac{a}{f}\frac{\mathrm{\&Delta;f}}{\mathrm{\&Delta;a}}---\left(4\right)$

Formula (4) is found the solution when the radius generation minor variations of resonant cavity, the quantitative change coefficient A of the resonance frequency of bringing accordingly _a, wherein a is the radius of resonant cavity.

$A_{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HSA00000361960400011.png"\; state="\{\{state\}\}">h</figure-callout>}1}=\frac{h_1}{f}\frac{\mathrm{\&Delta;f}}{\mathrm{\&Delta;}{h}_1}---\left(5\right)$

Formula (5) is found the solution when the height generation minor variations of resonant cavity, the quantitative change coefficient A of the resonance frequency of bringing accordingly _H1, h wherein ₁Height for resonant cavity.

$A_{h2}=\frac{h_2}{f}\frac{\mathrm{\&Delta;f}}{\mathrm{\&Delta;}{h}_2}---\left(6\right)$

Formula (6) is found the solution when the height generation minor variations of sapphire 3, the quantitative change coefficient A of the resonance frequency of bringing accordingly _H1, h wherein ₂Height for sapphire 3.

Because the height and the thickness of strontium titanate crystals sheet 7 are very little with respect to resonant cavity, it is owing to the thermal expansion that variations in temperature causes can be ignored.

Find the solution the temperature coefficient of the radial and axial and resonant cavity of sapphire 3 relative dielectric constants, strontium titanate crystals sheet 7 relative dielectric constants, sapphire 3.

Then according to the computing formula of resonant cavity frequency-temperature coefficient:

$\frac{\&PartialD;f}{\&PartialD;T}=[\frac{\&PartialD;f}{{\&PartialD;\mathrm{\&epsiv;}}_t}\frac{{\&PartialD;\mathrm{\&epsiv;}}_t}{\&PartialD;T}+\frac{\&PartialD;f}{\&PartialD;d}\frac{\&PartialD;d}{\&PartialD;T}+\frac{\&PartialD;f}{\&PartialD;{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HSA00000361960400011.png"\; state="\{\{state\}\}">h</figure-callout>}}_1}\frac{{\&PartialD;\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="HSA00000361960400011.png"\; state="\{\{state\}\}">h</figure-callout>}}_1}{\&PartialD;T}+\frac{\&PartialD;f}{\&PartialD;a}\frac{\&PartialD;a}{\&PartialD;T}+\frac{\&PartialD;f}{{\&PartialD;h}_2}\frac{{\&PartialD;h}_2}{\&PartialD;T}]---\left(7\right)$

When Practical Calculation,

The approximate Δ f/ Δ ε that replaces to _t, other partial derivative is also replaced after the same method, can release formula (8) thus:

τ _f＝(A _r1τ _r1+A _r2τ _r2+A _dτ _α1+A _h1τ _α2+A _aα _c+A _h2α _c)(8)

Wherein: τ _fThe temperature coefficient of resonance frequency f, τ _R1, τ _R2, τ _{α 1}, τ _{α 2}, τ _cBe constant all, be respectively sapphire 3 relative dielectric constant temperatures coefficient, strontium titanate crystals sheet 7 relative dielectric constant temperatures coefficient, the radial and axial thermal coefficient of expansion of sapphire 3, the thermal coefficient of expansion of resonant cavity.

The thickness of strontium titanate crystals sheet 7 and height substitution above-mentioned formula are calculated the frequency-temperature coefficient of resonant cavity, select, determine that strontium titanate crystals sheet 7 thickness are 5mm according to result of calculation.Strontium titanate crystals sheet 7 is 8.

The 3rd step assembling resonant cavity

8 strontium titanate crystals sheets 7 evenly are bonded in the upper and lower surface of sapphire 3, and each 4 on upper and lower surface, each forms square the strontium titanate crystals sheet on upper and lower surface 7.Sapphire 3 screw threads are fixed on resonant cavity bottom 1, and resonant cavity tube 2 is fixed with resonant cavity bottom 1 screw.Piston 4 places sapphire 3 tops, and spring 6 places the groove on the piston 4, and six springs 6 are formed regular hexagon, and resonant cavity top cover 5 places on the spring 6, resonant cavity top cover 5 and resonant cavity tube 2 screw.

The frequency-temperature coefficient of the 4th step compensation resonant cavity

When working temperature raise, the resonant cavity volume increased, and it is big that the dielectric constant of sapphire 3 becomes, according to formula (4), (5) and (1), A _a, A _H1And A _R1Become big, and result of calculation is positive number.According to formula (8), the frequency-temperature coefficient of resonant cavity increases.Because strontium titanate crystals sheet 7 is the negative temperature coefficient crystal, so the result of formula (2) is a negative.According to formula (8), strontium titanate crystals sheet 7 dielectric constants are 30 times of sapphire 3 dielectric constants, offset resonant cavity because the frequency change that sapphire 3 change in dielectric constant cause.When working temperature reduced, the resonant cavity volume reduced, and the dielectric constant of sapphire 3 diminishes, and it is big that the dielectric constant of strontium titanate crystals sheet 7 becomes, and reduced the frequency-temperature coefficient of resonant cavity.

Sapphire 3 resonant cavity temperatures coefficient are decided in the 5th pacing

Carry out the measurement of sapphire 3 resonant cavity temperatures coefficient, whole resonant cavity is put into high-low temperature chamber, design temperature T ₁, whole resonant cavity reaches hygral equilibrium after 6 hours, and recording current frequency is f ₁Set second temperature T ₂, recording frequency after the resonant cavity hygral equilibrium is f ₂Measure repeatedly with this, utilize the difference computing formula, obtain the temperature coefficient of resonant cavity frequency:

$f{\mathrm{\&tau;}}_f=\frac{\underset{i=2}{\overset{n}{\mathrm{\&Sigma;}}}[(f_i-f_{i-1})/(T_i-T_{i-1})]}{n-1}---\left(9\right)$

The substitution test data, the temperature coefficient that calculates resonant cavity is lower than present-60kHz/ ℃ for-9.7kHz/ ℃.

Claims (1)

1. the frequency-temperature compensation method of a hydrogen maer sapphire resonant cavity is characterized in that the concrete steps of this method are:

The first step is determined strontium titanate crystals sheet (7)

Sapphire (3) is the uniaxial anisotropy crystal, is respectively 9.4 and 11.6 perpendicular to optical axis and the relative dielectric constant that is parallel to optical axis, and its loss tangent perpendicular to optical axis direction is 1 * 10 in the time of 47 ℃ ^-5Strontium titanate crystals sheet (7) is an aeolotropic crystal, and relative dielectric constant is 300, and its loss tangent is 8 * 10 in the time of 47 ℃ ^-4The relative dielectric constant of strontium titanate crystals sheet (7) is for being 30 times of sapphire (3) relative dielectric constant, and strontium titanate crystals sheet (7) is the negative temperature coefficient crystal, its dielectric constant reduces along with the rising of temperature, and is opposite with the variation of sapphire (3) dielectric constant; When variations in temperature, strontium titanate crystals sheet (7) just can compensate the variation of sapphire (3) dielectric constant and the variation of the resonant cavity frequency that causes, therefore selects strontium titanate crystals sheet (7) as frequency-temperature compensation;

Diameter, thickness, the sheet number of the second step design strontium titanate crystals sheet (7)

Strontium titanate crystals sheet (7) is a column type, because the crystal growth ability is limit, diameter is 17mm to the maximum, and selecting strontium titanate crystals sheet (7) diameter is 10mm～17mm; Select different thickness and number to calculate the frequency-temperature coefficient of resonant cavity then, select the optimal size of strontium titanate crystals sheet (7) according to result of calculation;

At first according to formula find the solution dielectric constant when sapphire (3) and strontium titanate crystals sheet (7), sapphire (3) thickness, sapphire (3) highly, resonant cavity height and radius have small quantity changes delta ε _T1, Δ ε _T2, Δ d, Δ h ₂, Δ h ₁During with Δ a, bring the quantitative change Δ f of resonance frequency accordingly, obtain coefficient A thus;

$A_{r1}=\frac{{\mathrm{\&epsiv;}}_{t1}}{f}\frac{\mathrm{\&Delta;f}}{{\mathrm{\&Delta;\&epsiv;}}_{t1}}---\left(1\right)$

Formula (1) is found the solution when the dielectric constant of sapphire (3) has minor variations, the corresponding quantitative change coefficient A that brings resonance frequency _R1, ε wherein _T1Dielectric constant for sapphire (3);

$A_{r2}=\frac{{\mathrm{\&epsiv;}}_{t2}}{f}\frac{\mathrm{\&Delta;f}}{{\mathrm{\&Delta;\&epsiv;}}_{t2}}---\left(2\right)$

Formula (2) is found the solution when the dielectric constant of strontium titanate crystals sheet (7) has minor variations, the corresponding quantitative change coefficient A that brings resonance frequency _R2, ε wherein _T2Dielectric constant for strontium titanate crystals sheet (7);

$A_d=\frac{d}{f}\frac{\mathrm{\&Delta;f}}{\mathrm{\&Delta;d}}---\left(3\right)$

Formula (3) is found the solution when the thickness generation minor variations of sapphire (3), the corresponding quantitative change coefficient A that brings resonance frequency _d, wherein d is the thickness of sapphire (3);

$A_a=\frac{a}{f}\frac{\mathrm{\&Delta;f}}{\mathrm{\&Delta;a}}---\left(4\right)$

Formula (4) is found the solution when the radius generation minor variations of resonant cavity, the quantitative change coefficient A of the resonance frequency of bringing accordingly _a, wherein a is the radius of resonant cavity;

$A_{h1}=\frac{h_1}{f}\frac{\mathrm{\&Delta;f}}{\mathrm{\&Delta;}{h}_1}---\left(5\right)$

Formula (5) is found the solution when the height generation minor variations of resonant cavity, the quantitative change coefficient A of the resonance frequency of bringing accordingly _H1, h wherein ₁Height for resonant cavity;

$A_{h2}=\frac{h_2}{f}\frac{\mathrm{\&Delta;f}}{\mathrm{\&Delta;}{h}_2}---\left(6\right)$

Formula (6) is found the solution when the height generation minor variations of sapphire (3), the quantitative change coefficient A of the resonance frequency of bringing accordingly _H1, h wherein ₂Height for sapphire (3);

Because the height and the thickness of strontium titanate crystals sheet (7) are very little with respect to resonant cavity, it is owing to the thermal expansion that variations in temperature causes can be ignored;

Find the solution the temperature coefficient of the radial and axial and resonant cavity of sapphire (3) relative dielectric constant, strontium titanate crystals sheet (7) relative dielectric constant, sapphire (3);

Then according to the computing formula of resonant cavity frequency-temperature coefficient:

$\frac{\&PartialD;f}{\&PartialD;T}=[\frac{\&PartialD;f}{{\&PartialD;\mathrm{\&epsiv;}}_t}\frac{{\&PartialD;\mathrm{\&epsiv;}}_t}{\&PartialD;T}+\frac{\&PartialD;f}{\&PartialD;d}\frac{\&PartialD;d}{\&PartialD;T}+\frac{\&PartialD;f}{\&PartialD;h_1}\frac{{\&PartialD;h}_1}{\&PartialD;T}+\frac{\&PartialD;f}{\&PartialD;a}\frac{\&PartialD;a}{\&PartialD;T}+\frac{\&PartialD;f}{{\&PartialD;h}_2}\frac{{\&PartialD;h}_2}{\&PartialD;T}]---\left(7\right)$

When Practical Calculation, The approximate Δ f/ Δ ε that replaces to _t, other partial derivative is also replaced after the same method,

Can release formula (8) thus:

τ _f＝(A _r1τ _r1+A _r2τ _r2+A _dτ _α1+A _h1τ _α2+A _aτ _c+A _h2τ _c)(8)

Wherein: τ _fThe temperature coefficient of resonance frequency f, τ _R1, τ _R2, τ _{α 1}, τ _{α 2}, τ _cBe constant all, be respectively sapphire (3) relative dielectric constant temperature coefficient, strontium titanate crystals sheet (7) relative dielectric constant temperature coefficient, the radial and axial thermal coefficient of expansion of sapphire (3), the thermal coefficient of expansion of resonant cavity;

The thickness of strontium titanate crystals sheet (7) and height substitution above-mentioned formula are calculated the frequency-temperature coefficient of resonant cavity, select, determine that strontium titanate crystals sheet (7) thickness is 5mm～7mm according to result of calculation; Strontium titanate crystals sheet (7) is 8～32, and is the even number sheet;

The 3rd step assembling resonant cavity

Strontium titanate crystals sheet (7) evenly is bonded in the upper and lower surface of sapphire (3), and upper and lower surface patch number is identical, and the strontium titanate crystals sheet (7) on upper and lower surface is respectively formed regular polygon; Sapphire (3) screw thread is fixed on resonant cavity bottom (1), and resonant cavity tube (2) is fixed with resonant cavity bottom (1) screw; Piston (4) places sapphire (3) top, and spring (6) places the groove on the piston (4), and six springs (6) are formed regular hexagon, and resonant cavity top cover (5) places on the spring (6), resonant cavity top cover (5) and resonant cavity tube (2) screw;

The frequency-temperature coefficient of the 4th step compensation resonant cavity

When working temperature raise, the resonant cavity volume increased, and it is big that the dielectric constant of sapphire (3) becomes, according to formula (4), (5) and (1), A _a, A _H1And A _R1Become big, and result of calculation is positive number; According to formula (8), the frequency-temperature coefficient of resonant cavity increases; Because strontium titanate crystals sheet (7) is the negative temperature coefficient crystal, so the result of formula (2) is a negative; According to formula (8), strontium titanate crystals sheet (7) dielectric constant is 30 times of sapphire (3) dielectric constant, offsets resonant cavity because the frequency change that sapphire (3) change in dielectric constant causes; When working temperature reduced, the resonant cavity volume reduced, and the dielectric constant of sapphire (3) diminishes, and it is big that the dielectric constant of strontium titanate crystals sheet (7) becomes, and reduced the frequency-temperature coefficient of resonant cavity;

Sapphire (3) resonant cavity temperature coefficient is decided in the 5th pacing

Carry out the measurement of sapphire (3) resonant cavity temperature coefficient, whole resonant cavity is put into high-low temperature chamber, design temperature T ₁, whole resonant cavity reaches hygral equilibrium after 6 hours, and recording current frequency is f ₁Set second temperature T ₂, recording frequency after the resonant cavity hygral equilibrium is f ₂Measure repeatedly with this, utilize the difference computing formula, obtain the temperature coefficient of resonant cavity frequency:

$f{\mathrm{\&tau;}}_f=\frac{\underset{i=2}{\overset{n}{\mathrm{\&Sigma;}}}[(f_i-f_{i-1})/(T_i-T_{i-1})]}{n-1}---\left(9\right)$

The substitution test data, the temperature coefficient that calculates resonant cavity is lower than present-60kHz/ ℃ for-9.7kHz/ ℃.

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