CN103884913A - Method for determining parameters of equivalent parallel resistors of Marx generator - Google Patents

Abstract

The invention provides a method for determining parameters of equivalent parallel resistors of a Marx generator. The process for determining the parameters of the resistors and a calculation method are quite simple, the structure, series-parallel connection and nest relations of a complex local discharging loop do not need to be analyzed, total energy consumed on all the resistors can be learnt conveniently only by learning the resistance values of each resistor and the potential difference of the two ends of each resistor and finding out the number of capacitors bridged by each resistor, and the equivalent parallel resistors of the Marx generator can be determined according to energy conservation.

Description

A kind of Marx generator equivalent parallel resistance parameter determination method

Technical field

The invention belongs to Pulse Power Techniques field, be specifically related to Marx generator equivalent parallel resistance parameter determination method.

Background technology

Marx generator is one of modal initial accumulator system in pulse power system, and it is to name with German Irving Marx professor's surname, and Marx is taught in nineteen twenty-three and invented this device.It belongs to capacitor static energy storage mode, can produce amplitude from hundreds of kilovolts to several megavolts, the high-voltage pulse of pulse width from hundreds of nanoseconds to several microseconds, and it is accumulator more satisfactory in contemporary pulse power system.Conventionally people are accustomed to the number of capacitors of composition Marx to be defined as the progression of Marx generator.Its principle of work can be summarised as Parallel-connected Capacitor charging, discharged in series simply.

The primary element of composition Marx generator is mainly high-voltage capacitor, switch, charging resistor, stake resistance and triggering resistance.Charging resistor, stake resistance and triggering resistance play the effect of isolation voltage in the time that Marx generator discharges, and also become the equivalent parallel resistance of Marx generator, and the size of equivalent parallel resistance value directly affects the output efficiency of Marx generator.Therefore need to select suitable resistance value, General Requirements trigger the time constant in the shelf depreciation loop of resistance, charging resistor and stake resistance composition should be much larger than the Time Created of generator and generator the discharge time to load.

Marx generator has the circuit typess such as Z-type, S type, mixed type and leading flip-over type, because the various resistance quantity of Marx generator are many, the quantity of its resistance cross-over connection node of the Marx generator of dissimilar circuit and mode are also different, cause quantity and the structure in shelf depreciation loop very complicated, determine that the process of Marx generator equivalent parallel resistance is also just very complicated.Generally the switch in Marx circuit and electric capacity are considered as to short circuit, the connection in series-parallel relation of analysis circuit, progressively obtains equivalent parallel resistance, and some branch roads exist nest relation, is difficult to analysis and solution and determines.

Summary of the invention

In order to solve the deficiency of existing Marx generator equivalent parallel resistance parameter determination method, patent of the present invention has proposed a kind of Marx generator equivalent parallel resistance parameter determination method based on energy conservation.

Technical solution of the present invention is:

A Marx generator equivalent parallel resistance parameter determination method based on energy conservation, its special character is: comprise the following steps:

(1) measure each positive polarity charging resistor R in the Marx generator that a progression is n _cp, negative polarity charging resistor R _cn, trigger resistance R _twith stake resistance R _gresistance value;

(2), according to Marx generator circuit diagram, determine each positive polarity charging resistor R in Marx generator _cp, negative polarity charging resistor R _cn, trigger resistance R _twith stake resistance R _gthe quantity of flying capcitor device; That is:

Each positive polarity charging resistor R _cpflying capcitor device quantity is a _i, wherein footmark i represents R _cpnumbering, a _irepresent to be numbered the positive polarity charging resistor R of i _cpthe capacitors count of institute's cross-over connection, (i=1,2,3 ..., m ₁),

Each negative polarity charging resistor R _cnflying capcitor device quantity is b _j, wherein footmark j represents R _cnnumbering, b _jrepresent to be numbered the negative polarity charging resistor R of j _cnthe capacitors count of institute's cross-over connection, (j=1,2,3 ..., m ₂),

Each triggering resistance R _tflying capcitor device quantity is c _k, wherein footmark k represents R _tnumbering, c _krepresent to be numbered the triggering resistance R of k _tthe capacitors count of institute's cross-over connection, (k=1,2,3 ..., m ₃),

Each stake resistance R _gflying capcitor device quantity is d _l, wherein footmark l represents R _gnumbering, d _lrepresent to be numbered the stake resistance R of l _gthe capacitors count of institute's cross-over connection, (l=1,2,3 ..., m ₄);

(3) calculate according to the following formula Marx generator equivalent parallel resistance R _p:

$R_p=\frac{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA0000487401890000011.png"\; state="\{\{state\}\}">n</figure-callout>}}^2}{\underset{i=1}{\overset{m_1}{\mathrm{\&Sigma;}}}\frac{a_i^2}{R_{\mathrm{cpi}}}+\underset{j=1}{\overset{m_2}{\mathrm{\&Sigma;}}}\frac{b_j^2}{R_{\mathrm{cnj}}}+\underset{k=1}{\overset{m_3}{\mathrm{\&Sigma;}}}\frac{c_k^2}{R_{\mathrm{tk}}}+\underset{l=1}{\overset{m_4}{\mathrm{\&Sigma;}}}\frac{d_l^2}{R_{\mathrm{gl}}}}$

The invention has the beneficial effects as follows:

The inventive method determine the process of resistance parameter and computing method very simple, do not need to resolve structure, connection in series-parallel and the nest relation in complicated shelf depreciation loop, as long as know the resistance of each resistance and the potential difference (PD) at two ends, and find out the number of each resistance flying capcitor device, just can determine easily the gross energy consuming on all resistance, according to energy conservation, can determine the equivalent parallel resistance of Marx generator.

Accompanying drawing explanation

Fig. 1 is an element circuit schematic diagram of Marx generator.

Embodiment

A kind of Marx generator equivalent parallel resistance parameter determination method based on energy conservation, its principle is: charging resistor, stake resistance and triggering resistance is all electric discharges over the ground in the time that Marx generator is worked, consume the energy of Marx generator system, according to law of conservation of energy, the energy consuming on the energy consuming on all charging resistors, stake resistance and triggering resistance and equivalent parallel resistance equates, Marx generator nominal output voltage is known quantity, can determine thus Marx generator equivalent parallel resistance.Its thinking is: for Marx generator or similar complicated resistance interconnection circuit, by determining each ohmically energy loss, according to output voltage and law of conservation of energy, determine output terminal equivalent parallel resistance.Concrete steps are:

(1) the Marx generator that is n for a progression, accompanying drawing explanation

Figure 1 shows that one of them unit, comprise a positive polarity charging resistor R _cp, a negative polarity charging resistor R _cn, one is triggered resistance R _t, a stake resistance R _g, two storage capacitor C and a switch S.

(2) each positive polarity charging resistor R of survey record _cp, negative polarity charging resistor R _cn, trigger resistance R _twith stake resistance R _gnumerical value.

(3) front what switch of general Marx generator triggers by external trigger, before what setup delay account for the main share of whole Marx generator setup delay, lower owing to bearing voltage on front what resistance, account for energy loss share less, can ignore, therefore can only consider the equivalent parallel resistance after Marx generator is set up.According to above-mentioned thinking, Marx generator is set up the gross energy consuming on rear all resistance and is:

$E_{\mathrm{sum}}=\underset{i=1}{\overset{m_1}{\mathrm{\&Sigma;}}}\frac{U_i^2}{R_{\mathrm{cpi}}}t+\underset{j=1}{\overset{m_2}{\mathrm{\&Sigma;}}}\frac{U_j^2}{R_{\mathrm{cnj}}}t+\underset{k=1}{\overset{m_3}{\mathrm{\&Sigma;}}}\frac{U_k^2}{R_{\mathrm{tk}}}t+\underset{l=1}{\overset{m_4}{\mathrm{\&Sigma;}}}\frac{U_l^2}{R_{\mathrm{gl}}}t---\left(1\right)$

(4), according to Marx generator circuit diagram, determine each positive polarity charging resistor R _cp, negative polarity charging resistor R _cn, trigger resistance R _twith stake resistance R _gthe number of flying capcitor device.Establish each positive polarity charging resistor R herein _cpflying capcitor device quantity is a _i, wherein footmark i represents R _cpnumbering, a _irepresent to be numbered the positive polarity charging resistor R of i _cpthe capacitors count of institute's cross-over connection, i=1,2,3 ..., m ₁; Each negative polarity charging resistor R _cnflying capcitor device quantity is b _j, wherein footmark j represents R _cnnumbering, b _jrepresent to be numbered the negative polarity charging resistor R of j _cnthe capacitors count of institute's cross-over connection, (j=1,2,3 ..., m ₂); Each triggering resistance R _tflying capcitor device quantity is c _k, wherein footmark k represents R _tnumbering, c _krepresent to be numbered the triggering resistance R of k _tthe capacitors count of institute's cross-over connection, (k=1,2,3 ..., m ₃); Each stake resistance R _gflying capcitor device quantity is d _l, wherein footmark l represents R _gnumbering, d _lrepresent to be numbered the stake resistance R of l _gthe capacitors count of institute's cross-over connection, (l=1,2,3 ..., m ₄).

(5) establish Marx generator and set up after voltage on each capacitor equate, be worth for Δ U, output voltage is n Δ U.For the Marx generator of normal operation, the error that this setting brings to equivalent parallel resistance value can be ignored.Formula (1) can be reduced to:

$E_{\mathrm{sum}}=(\underset{i=1}{\overset{m_1}{\mathrm{\&Sigma;}}}\frac{a_i^2}{R_{\mathrm{cpi}}}+\underset{j=1}{\overset{m_2}{\mathrm{\&Sigma;}}}\frac{b_j^2}{R_{\mathrm{cnj}}}+\underset{k=1}{\overset{m_3}{\mathrm{\&Sigma;}}}\frac{c_k^2}{R_{\mathrm{tk}}}+\underset{l=1}{\overset{m_4}{\mathrm{\&Sigma;}}}\frac{d_l^2}{R_{\mathrm{gl}}}){\mathrm{\&Delta;U}}^{2}t---\left(2\right)$

(6) equivalent parallel resistance of establishing after Marx generator is set up is R _p, the energy of equivalent parallel resistance consumption is:

$E_{\mathrm{sum}}=\frac{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA0000487401890000011.png"\; state="\{\{state\}\}">n</figure-callout>}}^2\mathrm{\&Delta;}{U}^{2}t}{R_p}---\left(3\right)$

(7), according to law of conservation of energy, Marx generator equivalent parallel resistance can be expressed as:

$R_p=\frac{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA0000487401890000011.png"\; state="\{\{state\}\}">n</figure-callout>}}^2}{\underset{i=1}{\overset{m_1}{\mathrm{\&Sigma;}}}\frac{a_i^2}{R_{\mathrm{cpi}}}+\underset{j=1}{\overset{m_2}{\mathrm{\&Sigma;}}}\frac{b_j^2}{R_{\mathrm{cnj}}}+\underset{k=1}{\overset{m_3}{\mathrm{\&Sigma;}}}\frac{c_k^2}{R_{\mathrm{tk}}}+\underset{l=1}{\overset{m_4}{\mathrm{\&Sigma;}}}\frac{d_l^2}{R_{\mathrm{gl}}}}---\left(4\right)$

Claims (1)

1. the Marx generator equivalent parallel resistance parameter determination method based on energy conservation, is characterized in that: comprise the following steps:

(1) measure each positive polarity charging resistor R in the Marx generator that a progression is n _cp, negative polarity charging resistor R _cn, trigger resistance R _twith stake resistance R _gresistance value;

(2), according to Marx generator circuit diagram, determine each positive polarity charging resistor R in Marx generator _cp, negative polarity charging resistor R _cn, trigger resistance R _twith stake resistance R _gthe quantity of flying capcitor device; That is:

Each positive polarity charging resistor R _cpflying capcitor device quantity is a _i, wherein footmark i represents R _cpnumbering, a _irepresent to be numbered the positive polarity charging resistor R of i _cpthe capacitors count of institute's cross-over connection, (i=1,2,3 ..., m ₁),

Each negative polarity charging resistor R _cnflying capcitor device quantity is b _j, wherein footmark j represents R _cnnumbering, b _jrepresent to be numbered the negative polarity charging resistor R of j _cnthe capacitors count of institute's cross-over connection, (j=1,2,3 ..., m ₂),

Each triggering resistance R _tflying capcitor device quantity is c _k, wherein footmark k represents R _tnumbering, c _krepresent to be numbered the triggering resistance R of k _tthe capacitors count of institute's cross-over connection, (k=1,2,3 ..., m ₃),

Each stake resistance R _gflying capcitor device quantity is d _l, wherein footmark l represents R _gnumbering, d _lrepresent to be numbered the stake resistance R of l _gthe capacitors count of institute's cross-over connection, (l=1,2,3 ..., m ₄);

(3) calculate according to the following formula Marx generator equivalent parallel resistance R _p:

$R_p=\frac{n^2}{\underset{i=1}{\overset{m_1}{\mathrm{\&Sigma;}}}\frac{a_i^2}{R_{\mathrm{cpi}}}+\underset{j=1}{\overset{m_2}{\mathrm{\&Sigma;}}}\frac{b_j^2}{R_{\mathrm{cnj}}}+\underset{k=1}{\overset{m_3}{\mathrm{\&Sigma;}}}\frac{c_k^2}{R_{\mathrm{tk}}}+\underset{l=1}{\overset{m_4}{\mathrm{\&Sigma;}}}\frac{d_l^2}{R_{\mathrm{gl}}}}$

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