CN101082673A - Method for measuring error with high power microwave under mismatched load eliminated condition - Google Patents

Abstract

The invention discloses an error measuring method of high-power microwave in the mismatch load eliminating condition, which is characterized by the following: analyzing through simplified signal flowchart according to microwave transmitting line theory; obtaining the relationship formula between measured power and real power; analyzing and calculating through writing and compiling program according to the relationship formula; obtaining the quantized error; controlling and protecting the control program according to real power; ensuring safe operation of huge TOKAMAK system; providing reliable safe guard for power measurement and protection under high-power mismatch load.

Description

Eliminate the method for High-Power Microwave measuring error under the mismatch loading condition

Technical field

The invention belongs to High-Power Microwave coupling measurement and data processing technique, specifically is a kind of method of eliminating High-Power Microwave measuring error under the mismatch loading condition.

Background technology

On the full superconducting Tokamak EAST of national big science engineering, will utilize High-Power Microwave (MW magnitude) to drive plasma.The inlet side of microwave transmission line atmospheric side and device is isolated by ceramic window.Be the vacuum environment of assurance device, this requires microwave system to want to turn-off microwave accurately, timely in height reflection and sparking, with the safety of protection ceramic window.Find that in practice carrying out High-Power Microwave by directional coupler measures the very big error of existence.By initial analysis, think it mainly is because the directivity of directional coupler causes inadequately.Because load is the uppity plasma that changes, this brings certain degree of difficulty for the elimination error.

On present domestic and international TOKMAK device; powerful microwave system measurement and protection are still simply obtained incident and reflected power signal by directional coupler and wave detector; send into computer acquisition and directly relatively judge the size of reflection coefficient of power, determine whether to provide the protection cut-off signals according to the coefficient of setting.This method by directional coupler and wave detector is under the condition of miniwatt and high directivity coupling mechanism, and measuring error is very little.But under high power and mismatch condition, if directivity is not high, the error of measurement is very big.According to classical theory, if directivity is D decibel (directivity factor is d), the load terminal reflection coefficient is Г _L.Then the maximum percentage error of incident power measurement is:

ΔP _i＝|Г _L|d ^1/2(2+|Г _L|d ^1/2)×100 (4.1)

In experiment, also verified this point.In the previous experiments of EAST device LHCD system, find that the reflective power that measures can reduce on the contrary when detecting the sparking signal; For under the condition of short circuit, reflective power changes with the difference of short dot position, in some position, even can make reflective power surpass incident power the waveguide terminal people.Power measurement and accurate protection are the lifelines of total system accurately, in case can not in time protect, cause breaking of ceramic window, and whole device can't move.Vacuum, low-temperature superconducting etc. will waste the time of waiting for that microwave system is repaired, bring very big loss to country.

Summary of the invention

The purpose of this invention is to provide a kind of method of eliminating High-Power Microwave measuring error under the mismatch loading condition, obtain the relational expression of microwave power measurement value and the actual actual value of microwave power from simple signal flow graph analysis, by the error between process analysis acquisition measured value and the actual value, obtain microwave power signal accurately by data processing from software correction, protect the normal operation of positive TOKAMAK system.

Main contents of the present invention:

(1) according to the microwave transmission line theory, the analysis by simplifying signal flow diagram obtains measuring the relational expression between power and the real power.

(2) according to the relational expression that obtains in (1), come analytical calculation, obtain the error size that quantizes by coding.

(3) be the needs of security of system, introduce the error analysis algorithm in the lower hybrid wave control program, obtain real watt level, control program is controlled according to real power and is protected.

Technical scheme of the present invention is:

Eliminate the method for High-Power Microwave measuring error under the mismatch loading condition, in the TOKAMAK system, by on wave guide wall, slotting so that dual directional coupler to be installed, its two ends and the butt joint of waveguide coupling, export in coaxial mode, after connect coaxial wave detector, microwave signal can be changed into voltage signal, carry out waveguide power and phase detection, it is characterized in that may further comprise the steps:

(1) according to the microwave transmission line theory, by the relational expression between signal flow diagram acquisition measurement power of simplifying and the real power;

At first, carry out signal analysis in the microwave transmission line:

Each character is defined as follows: V _g, V _i, V _rBe respectively the incident wave voltage signal and the reflection wave voltage signal of source voltage signal, waveguide port; Г _gIt is the source voltage reflection coefficient; Г _LIt is the load voltage reflection coefficient; D is the electrical length of measurement port apart from load; β is a propagation constant; When electrical length d=0, have:

V _g+V _r?Г _g＝V _i (7.1)

V _r＝V _i?Г _L (7.2)

Can solve by formula (7.1), (7.2):

V _i＝V _g/(1-Г _g?Г _L) (7.3)

V _r＝V _i?Г _L (7.4)

In electrical length d ≠ 0 o'clock, to there not being consumption transmission line Г _d=Г _Le ^{-2j β d}, then have:

V _i＝V _g/(1-Г _gГ _Le ^-2jβd) (7.5)

V _r＝V _gГ _Le ^-2jβd/(1-Г? _gГ _Le ^-2jβd) (7.6)

Secondly, directional coupler coupling port signal analysis:

V _i’＝V _g’/(1-Г _g’Г _L’e ^-2jβd’) (7.7)

V _r’＝V _g’Г _L’e ^-2jβd’/(1-Г _g’Г _L’e ^-2jβd’) (7.8)

Wherein, V _i' and V _r' be incident and the reflected voltage signal in the coupling port; Г _g' and Г _L' respectively " source " the end reflection coefficient and the wave detector load reflection coefficient of corresponding coupling port; V _g' be the coupling input signal of coupling port;

Detection power is:

P＝P _i-Pr＝|V _i’| ²-|V _r’| ² (7.9)

(7.7), (7.8) substitution (7.9) can get:

P＝|V _g’|2(1-|Г _L’e ^-2jβd’| ²)/|1-Г _g’Г _L’e ^-2jβd’| ² (7.10)

To same directional coupler and the good wave detector of consistance, can be write as:

P＝K|V _g’| ²，K＝(1-|Г _L’e ^-2jβd’| ²)/|1-Г _g’Г _L’e- ^2jβd’| ² (7.11)

Once more, carry out the microwave power error analysis

The incident port degree of coupling coefficient and the directivity factor of known dual directional coupler are respectively c _i, d _iReflector port degree of coupling coefficient and directivity factor are respectively c _r, d _r,

Incoming signal and reflected signal are provided by (7.5), (7.6) formula respectively in the waveguide, and then incident coupling port signal can be write as:

V _g’ _i＝c _i ^1/2V _g/(1-Г _gГ _Le ^-2jβd)+(c _id _i) ^1/2V _gГ _Le ^-2jβd/(1-Γ _gГ _Le ^-2jβd) (7.12)

Then the power of incident wave detector measurement is:

P _{The i measured value}=K|V _g' _i| ²=c _iK|V _g| ²| 1+d _i ^1/2Г _Le ^{-2j β d}| ²/ | 1-Г _gГ _Le ^{-2j β d}| ²(7.13)

K is the wave detector coefficient;

True incident power is at directional coupler incident port direction D in the waveguide _i=∞ (is d _i=0) P the time _{I is true}

P _{The i actual value}=K|V _g| ²/ | 1-Г _gГ _Le ^{-2j β d}| ²(7.14)

Measured value is got normalized power P to actual value _i, obtain:

P _i=P _{The i measured value}/ P _{The i actual value}=| 1+d _i ^1/2Г _Le ^{-2j β d}| ²(7.15)

So just can obtain measuring the relative error value P of incident power by directional coupler and wave detector _i-1;

Obtaining the incident percentage error by (7.15) formula is:

ΔP _i＝(2|Г _L|d _i ^1/2cos(-2βd _i)+|Г _L| ²d _i)×100 (7.16)

At 2 β d _iDuring=2n π, obtain maximum percentage error and be:

ΔP _i＝|Г _L|d _i ^1/2(2+|Г _L|)×100 (7.17)

Equally, can obtain the reflective power measured value and with the normalized power expression formula of actual value:

(7.18)

The normalization reflective power:

(7.19)

(2) according to the relational expression that obtains in (1), calculate by program, obtain the error size that quantizes:

Concerning a microwave system, if dead load, and size is known, and electrical length and directivity factor all are known, reflection coefficient also is available fixed value, directly so just can calculate power error according to equation (7.14), (7.19);

If load changes, measure simultaneously by incident and reflection spot, set up system of equations and separate:

On the high power waveguide transmission line, measure incident and reflective power respectively at 2 by a, b; A is an incident coupling measurement point, and b is a reflection coupling measurement point; Distance is n λ between a, the b point _g, load is apart from a, b point electrical length d like this _a=d _b=l, l are known;

The incident port a degree of coupling coefficient and the directivity factor of directional coupler are respectively c _i, d _iReflector port b degree of coupling coefficient and directivity factor are respectively c _r, d _rFor pure resistor load,, can obtain reflection coefficient by power measurement to 2 of a, b;

Can obtain by (7.13), (7.18):

(7.20)

(7.21)

L wherein _a=l _b=l;

Then (7.20), (7.21) two formulas are divided by:

$\frac{p_a{c}_r}{p_b{c}_i}=\frac{1+2\sqrt{d_i}{\mathrm{\Γ}}_L\cos (-4\mathrm{\πl}/{\mathrm{\λ}}_g)+d_i{{\mathrm{\Γ}}_L}^2}{d_r+2\sqrt{d_r}{\mathrm{\Γ}}_L\cos (-4\mathrm{\πl}/{\mathrm{\λ}}_g)+{{\mathrm{\Γ}}_L}^2)}$ (7.22)

Abbreviation obtains:

$(1-{\mathrm{nd}}_i){{\mathrm{\&Gamma;}}_{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="A20071001967100151.png"\; state="\{\{state\}\}">L</figure-callout>}}}^2+2\cos \mathrm{\&theta;}(\sqrt{d_r}-n\sqrt{d_i}){\mathrm{\&Gamma;}}_L+d_r-n=0$ (7.23)

Wherein $n=\frac{p_b{c}_i}{p_a{c}_r},$ θ＝4πl/λ _g；

Top equation is except reflectioncoefficient _L, all the other parameters all are known, find the solution and can obtain Г _L(1≤Г _L≤ 0);

Obtained Г _L, just can calculate the waveguide power error by equation (7.14), (7.19);

(3) be the needs of security of system, introduce error analysis algorithm in the step poly-(2) in the lower hybrid wave control program, obtain real watt level, the lower hybrid wave control program is controlled according to real power and is protected.

The invention effect:

The present invention is on the basis of simplifying SFG analysis, obtain the relational expression between HIGH-POWERED MICROWAVES incident and reflected signal measured value and the actual value, by the error that relational expression is come analysis to measure by calculation procedure, obtain to measure the relation of power error and directivity factor and electrical length and reflection coefficient at last.By process analysis of the present invention and calculating, find the best approach of eliminating error, finally come the correct performance number of inverting by computer program, to realize protection accurately, guarantee the safe operation of huge TOKAMAK system.The present invention provides reliable safety guarantee for the power measurement under the load of high power mismatch and protection.

Description of drawings

Fig. 1 is an equivalent signal flow graph in the waveguide transmission line.

Fig. 2 is that the power relative value is to Г _LChange curve P (Г _L).

Wherein: (a): electrical length d=0.68 λ _g(b): electrical length d=0.08 λ _g

Fig. 3 is the change curve P (d) of power relative value to electrical length d.

Wherein: (a): Г _L=-1 (b): Г _L=-0.5

Embodiment

(1) at first according to the microwave transmission line theory, the analysis by simplifying signal flow diagram obtains measuring the relational expression between power and the real power.

Signal analysis (referring to Fig. 1) in a transmission line

Signal flow diagram as shown in Figure 1 in the waveguide transmission line.Dotted line 1 left side equivalence is seen signal in the past from the coupling port of directional coupler to the source; Dotted line 2 the right equivalences are seen signal in the past from transmission-wire terminal to load.When electrical length d=0, have:

V _g+V _r?Г _g＝V _i (7.1)

V _r＝V _iГ _L (7.2)

Can solve by formula (7.1), (7.2):

V _i＝V _g/(1-Г _g?Г _L) (7.3)

V _r＝V _i?Г _L (7.4)

In electrical length d ≠ 0 o'clock, to there not being consumption transmission line Г _d=Г _Le ^{-2j β d}, then have:

V _i＝V _g/(1-Г _g?Г _Le ^-2jβd) (7.5)

V _r＝V _g?Г _Le ^-2jβd/(1-Г _gГ _Le ^-2jβd) (7.6)

The signal analysis of b directional coupler coupling port

Analysis in equally can similar a obtains to the signal of directional coupler coupling port:

V _i’＝V _g’/(1-Г _g’Г _L’e ^-2jβd’) (7.7)

V _r’＝V _g’Г _L’e ^-2jβd’/(1-Г _g’Г _L’e ^-2jβd’) (7.8)

Wherein, V _i' and V _r' be incident and the reflected voltage signal in the coupling port; Г _g' and Г _L' respectively " source " the end reflection coefficient and the wave detector load reflection coefficient of corresponding coupling port; V _g' be the coupling input signal of coupling port.

Detection power is:

P＝P _i-P _r＝|V _i’| ²-|V _r’| ² (7.9)

(7.7), (7.8) substitution (7.9) can get:

P＝|V _g’| ²(1-|Г _L’e ^-2jβd’| ²)/|1-Г _g’Г _L’e ^-2jβd’| ² (7.10)

To same directional coupler and the good wave detector of consistance, can be write as:

P＝K|V _g’| ²，K＝(1-|Г _L’e ^-2jβd’| ²)/|1-Г _g’Г _L’e ^-2jβd’| ² (7.11)

The c power error is analyzed

The incident port degree of coupling coefficient and the directivity factor of known dual directional coupler are respectively c _i, d _iReflector port degree of coupling coefficient and directivity factor are respectively c _r, d _r

Incoming signal and reflected signal are provided by (7.5), (7.6) formula respectively in the waveguide.Then incident coupling port signal can be write as:

V _g’ _i＝c _i ^1/2V _g/(1-Г _gГ _Le ^-2jβd)+(c _id _i) ^1/2V _gГ _Le ^-2jβd/(1-Γ _gГ _Le ^-2jβd) (7.12)

Then the power of incident wave detector measurement is:

P _{The i measured value}=K|V _g' _i| ²=c _iK|V _g| ²| 1+d _i ^1/2Г _Le ^{-2j β d}| ²/ | 1-Г _gГ _Le ^{-2j β d}| ²(7.13)

K is the wave detector coefficient.

True incident power is at directional coupler incident port direction D in the waveguide _i=∞ (is d _i=0) P the time _{I is true}

P _{The i actual value}=K|V _g| ²/ | 1-Г _gГ _Le ^{-2j β d}| ²(7.14)

Measured value is got normalized power P to actual value _i, obtain:

P _i=P _{The i measured value}/ P _{The i actual value}=| 1+d _i ^1/2Г _Le ^{-2j β d}| ²(7.15)

So just can obtain measuring the relative error value P of incident power by directional coupler and wave detector _i-1.

Obtaining the incident percentage error by (7.15) formula is:

ΔP _i＝(2|Г _L|d _i ^1/2cos(-2βd _i)+|Г _L| ²d _i)×100 (7.16)

At 2 β d _iDuring=2n π, obtain maximum percentage error and be:

ΔP _i＝|Г _L|d _i ^1/2(2+|Г _L|)×100 (7.17)

The result who obtains by the simplification SFG analysis is consistent with classical expression formula (4.1) formula.Equally, can obtain the reflective power measured value and with the normalized power expression formula of actual value:

(7.18)

The normalization reflective power:

(7.19)

(2) according to the relational expression that obtains in (1), come analytical calculation, obtain the error size that quantizes by coding.

In the directivity factor of knowing directional coupler and load reflection coefficient, electrical length, can obtain measuring relative errors accurately.And provided under the condition of given reflection coefficient or electrical length the relation curve that relative error changes with electrical length or reflection coefficient.Provide PRELIMINARY RESULTS below.

Arbitrarily fixedly under the situation of electrical length d, calculate according to program, can obtain measuring power relative value P and load reflectioncoefficient _LRelation curve.Provide wherein two representational curve maps below as shown in Figure 2, the normalized power that reflects during the corresponding different directions of 3 curves in top; Below the normalized power of incident during the corresponding different directions of 3 curves.As seen, if Directivity of Directional Coupler is bad, to the relative error bigger (absolute value is also little) of reflection measurement.As can be seen from the figure, if given electrical length has only the directivity that improves coupling mechanism could reduce the relative error value; At total reflection (Г _L=-1) time, if the port direction unanimity, the relative error of incident and reflection is identical; (Г when load is mated fully _L=0), concerning incident, measured value is exactly an actual value, and concerning reflection, because true reflective power is zero, relative error is exactly infinitely great.

At electrical length d=0.68 λ _gThe time, measure power all greater than actual value; At electrical length d=0.08 λ _gThe time, incident is measured power all less than actual value, and reflective power in big reflection all less than actual value, but in little reflection greater than actual value; To different electrical length d, relative power also changes.

At dead load reflectioncoefficient arbitrarily _LSituation under, calculate according to program, can obtain measuring the relation curve of power relative value P and electrical length d.Provide wherein two representational curve maps below as shown in Figure 3.

Provide the dead load reflectioncoefficient among Fig. 3 _L, the relation of normalized power P and electrical length d.(a) load reflection coefficient corresponding in all is-1; (b) load reflection coefficient corresponding in all is-0.5.The normalized power of reflection and incident during the respectively corresponding different directions of 6 curves among the figure.As seen, fixedly the time, normalized power is done periodic the variation with the variation of electrical length at the load reflection coefficient, and period of change is λ _g/ 2.As can be seen from the figure, to different reflectioncoefficients _LWith directivity D, at a λ _gIn 4 point (λ are arranged _g/ 8,3 λ _g/ 8,5 λ _g/ 8,7 λ _g/ 8) normalized power is 1, and promptly measured value and actual value equate, error is zero; At total reflection (Г _L=-1) time, if incident is consistent with the reflector port directivity, the relative error of incident and reflection is identical (incident and reflectivity curve overlap).

(3) control program is controlled according to real power and is protected.In fact obtain accurately reflection coefficient and just can realize safeguard protection.

Concerning a microwave system, if dead load (being example here with the pure resistor load), and size is known, reflection coefficient also is available fixed value, directly so just can calculate power error (electrical length and directivity factor all are known) according to equation (7.14), (7.19).If load changes, want can't solve measuring error by an equation, analyze here by incident and reflection spot and measure simultaneously, set up system of equations and separate.

As shown in Figure 1, on the high power waveguide transmission line, measure incident and reflective power respectively at 2 by a, b.A is an incident coupling measurement point, and b is a reflection coupling measurement point.Distance is n λ between a, the b point _g, load is apart from a, b point electrical length d like this _a=d _b=l, l are known.

The incident port a degree of coupling coefficient and the directivity factor of directional coupler are respectively c _i, d _iReflector port b degree of coupling coefficient and directivity factor are respectively c _r, d _rFor pure resistor load,, can obtain reflection coefficient by power measurement to 2 of a, b.

Can obtain by (7.13), (7.18):

(7.20)

(7.21)

L wherein _a=l _b=l.

Then (7.20), (7.21) two formulas are divided by:

$\frac{p_a{c}_r}{p_b{c}_i}=\frac{1+2\sqrt{d_i}{\mathrm{\&Gamma;}}_L\cos (-4\mathrm{\&pi;l}/{\mathrm{\&lambda;}}_g)+d_i{{\mathrm{\&Gamma;}}_L}^2}{d_r+2\sqrt{d_r}{\mathrm{\&Gamma;}}_L\cos (-4\mathrm{\&pi;l}/{\mathrm{\&lambda;}}_g)+{{\mathrm{\&Gamma;}}_L}^2)}$ (7.22)

Abbreviation obtains:

$(1-n{d}_i){{\mathrm{\&Gamma;}}_{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="A20071001967100151.png"\; state="\{\{state\}\}">L</figure-callout>}}}^2+2\cos \mathrm{\&theta;}(\sqrt{d_r}-n\sqrt{d_i}){\mathrm{\&Gamma;}}_L+d_r-n=0$ (7.23)

Wherein $n=\frac{p_b{c}_i}{p_a{c}_r},$ θ＝4πl/λ _g。

Top equation is except reflectioncoefficient _L, all the other parameters all are known, find the solution and can obtain Г _L(1≤Г _L≤ 0).

Obtained Г _L, just can calculate power error by equation (7.14), (7.19).The protection in according to Г _LJust can realize high reflection safeguard protection accurately.

(4) experimental verification result of calculation

In order to verify the correctness of calculation procedure, this project wishes to verify by little microwave power signal in the laboratory measurement error results of calculating, certainly the directional coupler of using here also is that (about the degree of coupling 67dB of the directional coupler in the EAST microwave system, directivity is 15～20dB) for the not high high-power coupling mechanism of high degree of coupling directivity.

Breadboard microwave measurement system will have isolator (reflection coefficient that guarantees the source is approximately 0) matched load and short-circuiting device fully, can simulate some extreme conditions like this and measure, and obtains a series of data, comes to compare with result calculated.

Under the condition of mating fully, the signal of measuring by the incident directional coupler should be to equate with actual value; Under the condition of terminal short circuit, the performance number that obtains is exactly actual measured value, and the ratio of actual measured value and actual value is exactly the relative error of measuring; Short dot can be measured apart from the some length d of Coupling point, and reflection coefficient is-1, so just can calculate these parameter substitution programs, just can obtain the measuring relative errors that program is calculated.The comparatively validate of these two relative errors the correctness calculated of the analysis of front and program.

Claims (1)

1, eliminates the method for High-Power Microwave measuring error under the mismatch loading condition, in the TOKAMAK system, by on wave guide wall, slotting so that dual directional coupler to be installed, its two ends and the butt joint of waveguide coupling, export in coaxial mode, after connect coaxial wave detector, microwave signal can be changed into voltage signal, carry out waveguide power and phase detection, it is characterized in that may further comprise the steps:

(1) according to the microwave transmission line theory, by the relational expression between signal flow diagram acquisition measurement power of simplifying and the real power;

At first, carry out signal analysis in the microwave transmission line:

Each character is defined as follows: V _g, V _i, V _rBe respectively the incident wave voltage signal and the reflection wave voltage signal of source voltage signal, waveguide port; Г _gIt is the source voltage reflection coefficient; Г _LIt is the load voltage reflection coefficient; D is the electrical length of measurement port apart from load; β is a propagation constant;

When electrical length d=0, have:

V _g+V _rГ _g＝V _i (7.1)

V _r＝V _iГ _L (7.2)

Can solve by formula (7.1), (7.2):

V _i＝V _g/(1-Г _gГ _L) (7.3)

V _r＝V _iГ _L (7.4)

In electrical length d ≠ 0 o'clock, to there not being consumption transmission line Г _d=Г _Le ^{-2j β d}, then have:

V _i＝V _g/(1-Г _gГLe ^-2jβd) (7.5)

V _r＝V _gГ _Le ^-2jβd/(1-Г _gГ _Le ^-2jβd) (7.6)

Secondly, directional coupler coupling port signal analysis:

V _i’＝V _g’/(1-Г _g’Г _L’e ^-2jβd’) (7.7)

V _r’＝V _g’Г _L’e ^-2jβd’/(1-Г _g’Г _L’e ^-2jβd’) (7.8)

Wherein, V _i' and V _r' be incident and the reflected voltage signal in the coupling port; Г _g' and Г _L' respectively " source " the end reflection coefficient and the wave detector load reflection coefficient of corresponding coupling port; V _g' be the coupling input signal of coupling port;

Detection power is:

P＝P _i-P _r＝|V _i’| ²-|V _r’| ² (7.9)

(7.7), (7.8) substitution (7.9) can get:

P＝|V _g’| ²(1-|Г _L’e ^-2jβd’| ²)/|1-Г _g’Г _L’e ^-2jβd’| ² (7.10)

To same directional coupler and the good wave detector of consistance, can be write as:

P＝K|V _g’| ²，K＝(1-|Г _L’e ^-2jβd’| ²)/|1-Г _g’Г _L’e ^-2jβd’| ² (7.11)

Once more, carry out the microwave power error analysis

The incident port degree of coupling coefficient and the directivity factor of known dual directional coupler are respectively c _i, d _iReflector port degree of coupling coefficient and directivity factor are respectively c _r, d _r,

Incoming signal and reflected signal are provided by (7.5), (7.6) formula respectively in the waveguide, and then incident coupling port signal can be write as:

V _g’ _i＝c _i ^1/2V _g/(1-Г _gГ _Le ^-2jβd)+(c _id _i) ^1/2V _gГ _Le ^-2jβd/(1-Г _gГ _Le ^-2jβd) (7.12)

Then the power of incident wave detector measurement is:

P _{The i measured value}=K|V _g' _i| ²=c _iK|V _g| ²| 1+d _i ^1/2Г _Le ^{-2j β d}| ²/ | 1-Г _gГ _Le ^{-2j β d}| ²(7.13)

K is the wave detector coefficient;

True incident power is at directional coupler incident port direction D in the waveguide _i=∞ (is d _i=0) P the time _{I is true}

P _{The i actual value}=K|V _g| ²/ | 1-Г _gГ _Le ^{-2j β d}| ²(7.14)

Measured value is got normalized power P to actual value _i, obtain:

P _i=P _{The i measured value}/ P _{The i actual value}=| 1+d _i ^1/2Г _Le ^{-2j β d}| ²(7.15)

So just can obtain measuring the relative error value P of incident power by directional coupler and wave detector _i-1;

Obtaining the incident percentage error by (7.15) formula is:

ΔP _i＝(2|Г _L|d _i ^1/2cos(-2βd _i)+|Г _L| ²d _i)×100 (7.16)

At 2 β d _iDuring=2n π, obtain maximum percentage error and be:

ΔP _i＝|Г _L|d _i ^1/2(2+|Г _L|)×100 (7.17)

Equally, can obtain the reflective power measured value and with the normalized power expression formula of actual value:

(7.18)

The normalization reflective power:

(7.19)

(2) according to the relational expression that obtains in (1), calculate by program, obtain the error size that quantizes:

Concerning a microwave system, if dead load, and size is known, and electrical length and directivity factor all are known, reflection coefficient also is available fixed value, directly so just can calculate power error according to equation (7.14), (7.19);

If load changes, measure simultaneously by incident and reflection spot, set up system of equations and separate:

On the high power waveguide transmission line, measure incident and reflective power respectively at 2 by a, b; A is an incident coupling measurement point, and b is a reflection coupling measurement point; Distance is n λ between a, the b point _g, load is apart from a, b point electrical length d like this _a=d _b=l, l are known;

The incident port a degree of coupling coefficient and the directivity factor of directional coupler are respectively c _i, d _iReflector port b degree of coupling coefficient and directivity factor are respectively c _r, d _rFor pure resistor load,, can obtain reflection coefficient by power measurement to 2 of a, b;

Can obtain by (7.13), (7.1 8):

(7.20)

(7.21)

L wherein _a=l _b=l;

Then (7.20), (7.21) two formulas are divided by:

$\frac{p_a{c}_r}{p_b{c}_i}=\frac{1+2\sqrt{d_i}{\mathrm{\&Gamma;}}_L\cos (-4\mathrm{\&pi;l}/{\mathrm{\&lambda;}}_g)+d_i{{\mathrm{\&Gamma;}}_L}^2}{d_r+2\sqrt{d_r}{\mathrm{\&Gamma;}}_L\cos (-4\mathrm{\&pi;l}/{\mathrm{\&lambda;}}_g)+{{\mathrm{\&Gamma;}}_L}^2)}$ (7.22)

Abbreviation obtains:

$(1-n{d}_i){{\mathrm{\&Gamma;}}_L}^2+2\cos \mathrm{\&theta;}(\sqrt{d_r}-n\sqrt{d_i}){\mathrm{\&Gamma;}}_L+d_r-n=0$ (7.23)

Wherein $n=\frac{p_b{c}_i}{p_a{c}_r},$ θ＝4πl/λ _g；

Top equation is except reflectioncoefficient _L, all the other parameters all are known, find the solution and can obtain Г _L(1≤Г _L≤ 0);

Obtained Г _L, just can calculate the waveguide power error by equation (7.14), (7.19);

(3) be the needs of security of system, introduce error analysis algorithm in the step poly-(2) in the lower hybrid wave control program, obtain real watt level, the lower hybrid wave control program is controlled according to real power and is protected.

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