CN103986330A - A resonant step-up DC/DC converter suitable for high-voltage and high-power occasions and its control method - Google Patents

Abstract

The invention discloses a resonant step-up DC/DC converter suitable for high-voltage and high-power occasions and a control method thereof. The converter is connected to a DC input power supply and a load, and includes two primary side diodes, first to fourth switching tubes , a resonant unit, first to second rectifier diodes, two filter capacitors, characterized in that the resonant unit is connected to a bridge arm composed of four switch tubes and a rectifier unit composed of two rectifier diodes and two filter capacitors. The invention can realize near-zero-voltage turn-off of the switch tube and zero-current turn-off of the rectifier diode, can greatly reduce loss, and at the same time, the voltage stress of all switch devices is not greater than one-half of the output voltage. The resonant circuit of the invention can be used in high-power boosting occasions.

Description

A resonant step-up DC/DC converter suitable for high-voltage and high-power occasions and its control method

technical field

The invention relates to the field of direct current converters and can be applied to high-power boosting occasions.

Background technique

Wind power generation is one of the fastest-growing forms of new energy utilization in the world today. Offshore wind power generation is widely valued by coastal countries around the world because it does not occupy land land and has abundant wind energy resources. With the continuous increase of the capacity of offshore wind farms and the increase of offshore distance, the use of high voltage direct current (High Voltage Direct Current, HVDC) power transmission has become an inevitable trend. HVDC power transmission has the advantages of not being affected by capacitive current, adjustable active and reactive power output, etc., but the traditional offshore wind farm system based on the medium-voltage AC busbar needs to use a huge and heavy power frequency step-up transformer, which is very difficult for the wind tower. The construction of the frame and offshore converter station platform puts forward very high requirements. In response to the above shortcomings, research on offshore wind farm systems based on medium-voltage DC bus has emerged in recent years at home and abroad. By using high-voltage and high-power step-up DC converters to replace traditional power frequency step-up transformers, the volume and weight of the system can be greatly reduced. . The high-voltage and high-power step-up DC converter is the key core component of the system, and the electric energy generated by the fan needs to be converted through it for voltage conversion and power transmission loss is high-power transmission.

At present, scholars at home and abroad have carried out some research on the high-voltage and high-power step-up DC converter in this system, and successively proposed a variety of feasible topological circuits. The module combination multilevel DC converter is very suitable for high voltage and high power occasions. This kind of converter connects two module combination multilevel converters through an intermediate frequency transformer. Its main disadvantage is that the manufacture of high power and high voltage intermediate frequency transformers is extremely difficult. difficulty. The document "Multiple module high gain high voltage DC-DC transformers for offshore wind energy systems" proposes a structure in which the input of a Boost converter and a Buck/Boost converter are connected in parallel and the output is in series. The voltage and current stress of the switching device and the diode are relatively decrease. However, due to the hard switching of switching devices and the reverse recovery loss of diodes, the efficiency of the converter is low. The document "Analysis and comparison of medium voltage high power DC/DC converters for offshore wind energy systems" proposes a DC boost converter based on resonant switched capacitors, which can realize soft switching and modular structure of the switching tube, but it not only outputs Voltage regulation is poor and requires a large number of capacitors. Professor Jovcic of the University of Aberdeen proposed a new type of resonant boost converter in the document "Step-up dc-dc converter for megawatt size applications", which can not only realize the soft switching of switching devices and avoid the reverse recovery of diodes Problems, can also achieve a very high boost ratio. However, this type of resonant boost converter also has the following disadvantages: all switching devices need to have reverse voltage blocking capability; the voltage stress of the resonant capacitor, resonant inductor and all switching devices are approximately the output voltage; the resonant inductor is unidirectionally magnetized, The utilization rate of the magnetic core is not high, resulting in a larger volume and weight of the resonant inductor, and a corresponding increase in loss.

Contents of the invention

Purpose of the invention: Aiming at the above-mentioned prior art, a resonant step-up DC/DC converter and its control method suitable for high-voltage and high-power applications are proposed, which not only realizes the output boost but also realizes the near zero-voltage turn-off and rectification of the switching tube The zero-current turn-off of the diode makes the voltage stress of the resonant unit and the switching device not exceed half of the output voltage at the same time.

Technical solution: a resonant step-up DC/DC converter suitable for high-voltage and high-power applications, including a full-bridge inverter circuit, a resonant unit, and a rectifier unit; the input end of the full-bridge inverter circuit is connected to a DC input power supply, and the entire The output end of the bridge inverter circuit is connected to the input end of the rectification unit, the output end of the rectification unit is connected to the load, and the resonance unit is connected in parallel with the output end of the full bridge inverter circuit and the input end of the rectification unit.

As a preferred solution of the present invention, the full-bridge inverter circuit includes one to fourth switch tubes, a first primary side diode and a second primary side diode; the first primary side diode, the first switch tube, the third The switch tubes are sequentially connected in series to form a first branch, and the sequential series connection of the second diode on the primary side, the second switch tube, and the fourth switch tube forms a second branch, and the first branch and the second branch are connected in parallel At both ends of the DC input power supply;

The rectifier unit includes a first rectifier diode, a second rectifier diode, a first filter capacitor, and a second filter capacitor; the first rectifier diode and the second rectifier diode are forwardly connected in series to form a third branch, and the first rectifier diode The filter capacitor and the second filter capacitor are connected in series to form a fourth branch, and the third branch and the fourth branch are connected in parallel at both ends of the load;

The resonant unit is an LC parallel resonant circuit composed of an inductor and a capacitor; one end of the LC parallel resonant circuit is connected to the connecting end of the first switch tube and the third switch tube, and is connected to the first filter capacitor and the third switch tube at the same time. The connecting end of the second filter capacitor; the other end of the LC parallel resonant circuit is connected to the connecting end of the second switching tube and the fourth switching tube, and connected to the first rectifying diode and the second rectifying diode the connecting end.

A control method for a resonant step-up DC/DC converter suitable for high-voltage and high-power applications: one control cycle of the control method is divided into eight consecutive stages, wherein:

The first stage: t ₀ <t<t ₁

At time t ₀ , the first switch tube and the fourth switch tube are turned on, v _Cr =V _in , where v _Cr is the voltage of the capacitor in the resonant unit, V _in is the voltage of the DC input power supply; the current loop at the input terminal is composed of DC The input power supply, _the first diode on the primary side, the first switching tube, the inductor and the _fourth switching tube are composed. The voltage on the inductor is equal to the input voltage V _in . Starting from I ₀ and increasing linearly to I ₁ , the first filter capacitor and the second filter capacitor provide the load output current;

The second stage: t ₁ < t < t ₂

At time t ₁ , the first switching tube and the fourth switching tube are turned off at the same time, and the inductance and capacitor resonate in parallel until v _Cr = -V _o /2 at time t ₂ , where V _o is the output voltage of the converter; the first filter The capacitor and the second filter capacitor provide the load output current;

The third stage: t ₂ < t < t ₃

At time t ₂ , v _Cr =-V _o /2, the first rectifier diode is turned on, and the current in the inductor flows through the first rectifier diode to charge the first filter capacitor and provide load current; within t ₂ ~ t ₃ , v _Cr remains unchanged, and the current on the inductor decreases linearly to zero;

The fourth stage: t ₃ <t<t ₄

At time t ₃ , i _Lr =I ₃ =0, v _Cr =V _o /2, where i _Lr represents the current of the resonant inductor, I ₃ represents the current of the resonant inductor at time t ₃ , the first rectifier diode is turned off, and the inductor Parallel resonance occurs with the capacitor until v _Cr = -V _in ;

The fifth stage: t ₄ < t < t ₅

At time _t4 , the second switch tube and the third switch tube are turned on, v _Cr =-V _in , the current loop at the input terminal is composed of the DC input power supply, the second diode on the primary side, the second switch tube, the inductor and the third switch tube. Composed of switching tubes, the voltage on the inductor is equal to the negative input voltage -V _in , the current of the inductor increases linearly and reversely at time t ₄ ~ t ₅ , and the inductor current increases linearly from -I ₄ to -I ₅ , the first The filter capacitor and the second filter capacitor provide the load output current

The sixth stage: t ₅ <t<t ₆

At time _t5 , the second switch tube and the third switch tube are turned off at the same time, the inductance and the capacitor resonate in parallel until v _Cr =V _o /2, the first filter capacitor and the second filter capacitor provide the load output current;

The seventh stage: t ₆ < t < t ₇

At time t ₆ , v _Cr = V _o /2, the second rectifier diode is turned on, and the current in the inductor flows through the second rectifier diode to charge the second filter capacitor and provide load current; within t ₆ ~ t ₇ , v _Cr remains unchanged, and the current on the inductor decreases linearly to zero;

The eighth stage: t ₇ <t<t ₈

At time t ₇ , i _Lr =I ₇ =0, v _Cr =V _o /2, I ₇ is the current of the resonant inductor at time t ₇ , the second rectifier diode is turned off, and the inductor and capacitor resonate in parallel until v _Cr = V _in .

Beneficial effects: In the resonant step-up DC/DC converter and its control method suitable for high-voltage and high-power occasions of the present invention, the converter has a high voltage gain, and can realize zero-voltage turn-on and approximate zero-voltage turn-off of the switch tube And the zero-current turn-off of the rectifier diode, at the same time, the switching frequency range is small, and the resonant inductor is symmetrically magnetized bidirectionally; the voltage stress of the resonant unit and the switching device of the resonant converter does not exceed one-half of the output voltage; in realizing the boost function At the same time, soft switching is realized for each switching tube and diode, which effectively reduces loss, has high efficiency, and is suitable for high-power transmission.

Description of drawings

Fig. 1 is the topological structure diagram of the LC resonant converter of the cited example;

Fig. 2 is a schematic diagram of the working waveform of the relevant components of the circuit shown in Fig. 1;

Fig. 3 is a schematic diagram of the working mode of the first stage of the circuit shown in Fig. 1;

Fig. 4 is a schematic diagram of the second stage, the fourth stage, the sixth stage, and the eighth stage of the circuit shown in Fig. 1;

Fig. 5 is a schematic diagram of the working mode of the third stage of the circuit shown in Fig. 1;

Fig. 6 is a schematic diagram of the working mode of the fifth stage of the circuit shown in Fig. 1;

FIG. 7 is a schematic diagram of the working mode of the seventh stage of the circuit shown in FIG. 1 .

Detailed ways

The present invention will be further explained below in conjunction with the accompanying drawings.

Fig. 1 is a circuit topology diagram of an example of the present invention. A resonant step-up DC/DC converter suitable for high-voltage and high-power occasions of the present invention includes a full-bridge inverter circuit, a resonance unit and a rectification unit. The input end of the full-bridge inverter circuit is connected to the DC input power supply V _in , the output end of the full-bridge inverter circuit is connected to the input end of the rectification unit, the output end of the rectification unit is connected to the load R, and the resonance unit is connected to the output end of the full-bridge inverter circuit and the input terminals of the rectification unit are connected in parallel. Wherein, the full-bridge inverter circuit includes first to fourth switch tubes Q ₁ -Q ₄ , a first primary diode Di ₁ and a second primary diode Di ₂ . The first diode Di ₁ on the primary side, the first switching tube Q ₁ , and the third switching tube Q ₃ are connected in series in sequence to form the first branch; the second diode Di ₂ on the primary side, the second switching tube Q ₂ , the fourth switching tube Q 2 The switch tubes Q ₄ are sequentially connected in series to form a second branch; the first branch and the second branch are connected in parallel at both ends of the DC input power supply. The rectification unit includes a first rectification diode _DR1 , a second rectification diode _DR2 , a first filter capacitor C ₁ and a second filter capacitor C ₂ . The first rectifier diode _DR1 and the second rectifier diode _DR2 are forwardly connected in series to form the third branch; the first filter capacitor _C1 and the second filter capacitor _C2 are connected in series to form the fourth branch; the third branch and the second The four branches are connected in parallel at both ends of the load. The resonant unit is an LC parallel resonant circuit composed of inductance L _r and capacitor C _r . One end of the LC parallel resonant circuit is connected to the phase terminal of the first switch tube _Q1 and the third switch tube _Q3 , and is connected to the phase terminal of the first filter capacitor _C1 and the second filter capacitor _C2 at the same time; LC parallel resonance The other end of the circuit is connected to the connecting end of the second switching tube _Q2 and the fourth switching tube _Q4 , and is connected to the connecting end of the first rectifying diode _DR1 and the second rectifying diode _DR2 . At the same time, the anode of the first primary diode D _i1 is connected to the positive pole of the DC input power supply, and the cathode is connected to the first switching tube Q ₁ ; the anode of the second primary diode D _i2 is connected to the positive pole of the DC input power supply, and the cathode is connected to the first switching tube Q1. Two switching tubes Q ₂ ; the negative pole of the DC input power supply is connected to the terminal of the third switching tube Q ₃ and the fourth switching tube Q ₄ . The first terminal of the first filter capacitor _C1 is connected to the cathode of the first rectifier diode _DR1 , the second terminal of the first filter capacitor _C1 is connected to one end of the resonant unit; the first terminal of the second filter capacitor _C2 is connected to the second rectifier The anode of the diode D _R2 and the second end of the second filter capacitor _C2 are connected to one end of the resonant unit.

The control method of the resonant step-up DC/DC converter of the present invention suitable for high-voltage and high-power applications will be described in detail below.

As shown in Figure 2 and Figure 3, the first stage: t ₀ <t<t ₁

At time _t0 , the first switching tube _Q1 and the fourth switching tube _Q4 are turned on, v _Cr =V _in , where v _Cr is the voltage of the capacitor in the resonant unit, and _Vin is the voltage of the DC input power supply; the input terminal The current loop is composed of the DC input power supply, the first primary diode Di ₁ , the first switching tube Q ₁ , the inductor L _r and the fourth switching tube Q ₄ , and the voltage on the inductor L _r is equal to the input voltage V _in , t ₀ The current i _Lr of the inductor L _r increases linearly at time ～t _1. This stage is the process of inputting energy to the inductor. The inductor current increases linearly from I ₀ to I ₁ . The first filter capacitor C ₁ and the second filter capacitor C ₂ provides load R _L output current;

As shown in Figure 2 and Figure 4, the second stage: t ₁ <t<t ₂

At time _t1 , the first switching tube _Q1 and the fourth switching tube _Q4 are turned off at the same time, the inductance L _r and the capacitor C _r resonate in parallel until v _Cr = -V _o /2, V _o /2 is the resonant capacitance At the same time, the fourth switch tube Q ₄ reaches its maximum voltage drop V _o /2, the first _switch tube Q ₁ reaches its maximum voltage drop V _in , and the second diode D _i2 on the primary side It reaches its maximum voltage drop V _o /2-V _in , where V _o is the output voltage of the converter; the first filter capacitor C ₁ and the second filter capacitor C ₂ provide the load R _L output current; during this process, the input terminal and There is no energy transmission at the output end, the output current is still provided by the filter capacitor, and the energy is transferred between the inductor and the capacitor, but the total energy on the inductor and capacitor remains unchanged;

As shown in Figure 2 and Figure 5, the third stage: t ₂ <t<t ₃

At time t ₂ , v _Cr =-V _o /2, the first rectifier diode D _R1 is turned on, and the current in the inductor L _r flows through the first rectifier diode D _R1 to charge the first filter capacitor C ₁ and provide the load R _L current; during t ₂ ~ t ₃ , v _Cr remains unchanged, the current on the inductor L _r decreases linearly, and the input energy is transmitted to the load R _L during this period, and this process ends until the inductor current is zero;

As shown in Figure 2 and Figure 4, the fourth stage: t ₃ <t<t ₄

At time t ₃ , i _Lr =I ₃ =0, v _Cr =-V _o /2, where i _Lr represents the current of the resonant inductor L _r , I ₃ represents the current of the resonant inductor at time t ₃ , the first rectifier diode D _R1 is turned off, realizing the zero-current shutdown of the rectifier diode, after which the inductance L _r and the capacitor C _r resonate in parallel until v _Cr = -V _in , during this period, the total energy on the inductance and capacitor remains unchanged;

As shown in Figure 2 and Figure 6, the fifth stage: t ₄ <t<t ₅

At time _t4 , the second switching tube _Q2 and the third switching tube _Q3 are turned on, v _Cr = -V _in , the current loop at the input terminal is composed of the DC input power supply, the second primary diode Di ₂ , the second switch The tube Q ₂ , the inductor L _r and the third switching tube Q ₃ are composed, the voltage on the inductor L _r is equal to the negative input voltage -V _in , and the current i _Lr of the inductor L _r increases linearly and reversely at time t ₄ ~ t ₅ , This stage is the process of inputting energy to the inductor, the inductor current increases linearly from -I ₄ to -I ₅ , the first filter capacitor C ₁ and the second filter capacitor C ₂ provide the load R _L output current;

As shown in Figure 2 and Figure 4, the sixth stage: t ₅ <t<t ₆

At time _t5 , the second switching tube _Q2 and the third switching tube _Q3 are turned off at the same time, at this time the inductance L _r and the capacitor C _r resonate in parallel until v _Cr = V _o /2, at this time the third switching tube Q ₃ has reached its maximum voltage drop V _o /2, the second switch tube Q ₂ has reached its maximum voltage drop V _in , and the first primary diode D _i1 has reached its maximum voltage drop V _o /2-V _in , the first filter capacitor C ₁ and the second filter capacitor C ₂ provide the output current of the load R _L ; in this process, there is no energy transmission between the input terminal and the output terminal, the output current is still provided by the filter capacitor, and the energy is transferred between the inductor and the capacitor transfer, but the total energy on the inductance and capacitance remains unchanged;

The seventh stage: t ₆ < t < t ₇

As shown in Fig. 2 and Fig. ₇ , at time t6, v _Cr = V _o /2, the second rectifying diode _DR2 is turned on, and the current in the inductor L _r flows through the second rectifying diode _DR2 , providing the second filter Capacitor C ₂ charges and provides the load R _L current; during t ₆ ~ t ₇ , v _Cr remains unchanged, the current on the inductor L _r decreases linearly, and the input energy is transmitted to the load during this period, and this process reaches the inductance The current is zero to end;

As shown in Figure 2 and Figure 4, the eighth stage: t ₇ <t<t ₈

At time t ₇ , i _Lr =I ₇ =0, v _Cr =V _o /2, I ₇ is the current of the resonant inductor at time t ₇ , and then the second rectifier diode _DR2 is turned off, realizing the rectification diode _DR2 Zero current is turned off, after which the inductance L _r and the capacitance C _r resonate in parallel until v _Cr =V _in , during this period, the total energy on the inductance and capacitance remains unchanged.

The control method of the resonant step-up direct/direct converter of the present invention, which is suitable for high-voltage and high-power occasions, can realize the step-up function, and each switch tube and diode realizes soft switching, which effectively reduces losses and has high efficiency. Efficiency, suitable for high power transmission.

The above is only a preferred embodiment of the present invention, it should be pointed out that, for those of ordinary skill in the art, without departing from the principle of the present invention, some improvements and modifications can also be made, and these improvements and modifications can also be made. It should be regarded as the protection scope of the present invention.

Claims (3)

1. a resonance step-up DC/DC conversion device that is applicable to high-power occasion, is characterized in that: comprise full bridge inverter, resonant element and rectification unit; The input of described full bridge inverter connects direct-current input power supplying, the output of full bridge inverter connects the input of described rectification unit, the output of described rectification unit connects load, and the output of described resonant element and full bridge inverter and the input of rectification unit are connected in parallel.

2. a kind of resonance step-up DC/DC conversion device that is applicable to high-power occasion according to claim 1, is characterized in that: described full bridge inverter comprises first to fourth switching tube (Q ₁～Q ₄), the first former limit diode (Di ₁) and the second former limit diode (Di ₂); Described former limit the first diode (Di ₁), the first switching tube (Q ₁), the 3rd switching tube (Q ₃) be followed in series to form the first branch road, described former limit the second diode (Di ₂), second switch pipe (Q ₂), the 4th switching tube (Q ₄) be followed in series to form the second branch road, described the first branch road and the second branch circuit parallel connection are at direct-current input power supplying two ends;

Described rectification unit comprises the first rectifier diode (D _r1), the second rectifier diode (D _r2), the first filter capacitor (C ₁) and the second filter capacitor (C ₂); Described the first rectifier diode (D _r1) and the second rectifier diode (D _r2) forward is connected in series and forms the 3rd branch road, described the first filter capacitor (C ₁) and the second filter capacitor (C ₂) being connected in series formation the 4th branch road, described the 3rd branch road and the 4th branch circuit parallel connection are at load two ends;

Described resonant element is by inductance (L _r) and electric capacity (C _r) the LC antiresonant circuit that forms; One end of described LC antiresonant circuit is connected in described the first switching tube (Q ₁) and the 3rd switching tube (Q ₃) the end that joins, be connected in the first filter capacitor (C simultaneously ₁) and the second filter capacitor (C ₂) the end that joins; The other end of described LC antiresonant circuit is connected in described second switch pipe (Q ₂) and the 4th switching tube (Q ₄) the end that joins, be connected in described the first rectifier diode (D simultaneously _r1) and the second rectifier diode (D _r2) the end that joins.

3. a kind of control method that is applicable to the resonance step-up DC/DC conversion device of high-power occasion described in claim 1, is characterized in that: a control cycle of described control method is divided into eight continuous stages, wherein:

First stage: t ₀< t < t ₁

At t ₀constantly, the first switching tube (Q ₁) and the 4th switching tube (Q ₄) conducting, v _cr=V _in, v wherein _crfor the voltage of the electric capacity in resonant element, V _involtage for direct-current input power supplying; Input current circuit is by direct-current input power supplying, former limit the first diode (Di ₁), the first switching tube (Q ₁), inductance (L _r) and the 4th switching tube (Q ₄) form inductance (L _r) on voltage equal input voltage V _in, t ₀～t ₁moment internal inductance (L _r) electric current (i _lr) being linear increase, inductive current is from I ₀start linearity and be increased to I ₁, the first filter capacitor (C ₁) and the second filter capacitor (C ₂) load (R is provided _l) output current;

Second stage: t ₁< t < t ₂

At t ₁constantly, the first switching tube (Q ₁) and the 4th switching tube (Q ₄) turn-off inductance (L simultaneously _r) and electric capacity (C _r) there is parallel resonance, until v _cr=-V _o/ 2, V wherein _ofor converter output voltage; The first filter capacitor (C ₁) and the second filter capacitor (C ₂) load (R is provided _l) output current;

Phase III: t ₂< t < t ₃

At t ₂constantly, v _cr=-V _othe/2, first rectifier diode (D _r1) conducting, inductance (L _r) in electric current flow through the first rectifier diode (D _r1) to the first filter capacitor (C ₁) charging, and load (R is provided _l) electric current; At t ₂～t ₃in, v _crremain unchanged, inductance (L _r) cleanliness that powers on is reduced to zero;

Fourth stage: t ₃< t < t ₄

At t ₃constantly, i _lr=I ₃=0, v _cr=V _o/ 2, i wherein _lrrepresent resonant inductance (L _r) electric current, I ₃represent that resonant inductance is at t ₃electric current constantly, the first rectifier diode (D _r1) turn-off inductance (L _r) and electric capacity (C _r) there is parallel resonance, until v _cr=-V _in;

Five-stage: t ₄< t < t ₅

At t ₄constantly, second switch pipe (Q ₂) and the 3rd switching tube (Q ₃) conducting, v _cr=-V _in, input current circuit is by direct-current input power supplying, former limit the second diode (Di ₂), second switch pipe (Q ₂), inductance (L _r) and the 3rd switching tube (Q ₃) form inductance (L _r) on voltage equal negative input voltage-V _in, t ₄～t ₅moment internal inductance (L _r) electric current (i _lr) be linear inverse and increase, inductive current is from-I ₄start be increased to-I of reverse linear ₅, the first filter capacitor (C ₁) and the second filter capacitor (C ₂) load (R is provided _l) output current;

The 6th stage: t ₅< t < t ₆

At t ₅constantly, second switch pipe (Q ₂) and the 3rd switching tube (Q ₃) turn-off inductance (L simultaneously _r) and electric capacity (C _r) there is parallel resonance, until v _cr=V _othe/2, first filter capacitor (C ₁) and the second filter capacitor (C ₂) load (R is provided _l) output current;

The 7th stage: t ₆< t < t ₇

At t ₆constantly, v _cr=V _othe/2, second rectifier diode (D _r2) conducting, inductance (L _r) in electric current flow through the second rectifier diode (D _r2), give the second filter capacitor (C ₂) charging, and load (R is provided _l) electric current; At t ₆～t ₇in, v _crremain unchanged, inductance (L _r) cleanliness that powers on is reduced to zero;

The 8th stage: t ₇< t < t ₈

At t ₇constantly, i _lr=I ₇=0, v _cr=V _o/ 2, I ₇for resonant inductance is at t ₇electric current constantly, the second rectifier diode (D _r2) turn-off inductance (L _r) and electric capacity (C _r) there is parallel resonance, until v _cr=V _in.