CN203352440U - Tri-state DC/DC converter - Google Patents

Abstract

The utility model discloses a tri-state DC/DC converter. The converter comprises a switching tube VT1, a switching tube VT2, a diode D1, a diode D2, an energy storage inductor L, a filter capacitor C, and connection wires among all the above-mentioned elements. The connection wires is combined to form three operation modes of the converter with the aid of power-on and power-off of the switching tubes VT1 and VT2. The three operation modes are an inductor current linear rising mode, an inductor current linear declining mode, and an inductor current inertial afterflow mode. Due to the inertial afterflow mode, the converter has larger flexibility, can achieve independent control of input voltages and currents, and acquires a converter pseudo continuous conduction mode and superior dynamic response. The converter circuit can be applied to a general DC/DC conversion control system to achieve conversion from DC to DC, and further applied to a DC/DC conversion circuit having power factor correction.

Description

A Three-State Direct/Direct Converter

technical field

The utility model belongs to the technical field of pseudo-continuous conduction mode conversion circuits, in particular to a three-state direct/direct converter. the

Background technique

At present, in the traditional uncontrolled rectification circuit, because of the harmonics in the input current of the power grid, it will cause serious pollution to the power system and affect the stable and efficient operation of the power system. In order to reduce the harmonic pollution caused by the rectifier load to the power system and improve the quality of power transmitted by the power system, it is necessary to use a conversion circuit with power factor correction after the rectifier circuit, or directly use a fully controlled rectifier circuit with power factor adjustment. But no matter what, the uncontrolled rectification circuit is deeply loved by the public and widely used because of its simple structure, reliable operation, and low cost. the

The conversion circuit widely used in power factor correction is mainly Boost boost conversion circuit, and there is also a two-tube Back-Boost conversion circuit to realize power factor correction of the input circuit. Among them, the boost converter with average current control has become the preferred structure for power factor correction because of its good stability and insensitivity to noise. In the power factor correction control process, the current control methods include continuous current mode (CCM), discontinuous current mode (DCM), and pseudo continuous conduction mode (PCCM). Compared with the DCM converter, the PCCM converter has a larger load capacity and is better than the dynamic response speed of the CCM and DCM. Therefore, the pseudo-continuous conduction mode has attracted everyone's attention. the

Document 1 [Three-state Power Factor Correction Converter with Fast Dynamic Response, Journal of Electrical Machinery and Control, January 2011, Vol.15No.1:13-19] introduced the power of Boost three-state step-up conversion applied to rectifier circuits Factor correction, literature 2 [Two-switch pseudo-continuous conduction mode Back-Boost power factor correction converter, Chinese Journal of Electrical Engineering, March 2012, Vol.32No.9:56-64] introduces a two-switch Back-Boost conversion circuit Realize the power factor correction of the rectifier circuit. the

Utility model content

Purpose of the utility model: Aiming at the deficiencies in the prior art, the purpose of the utility model is to provide a three-state DC/DC converter, which realizes power factor correction of the rectifier circuit through a pseudo-continuous conduction mode conversion circuit. the

Technical solution: In order to realize the purpose of the above-mentioned utility model, the technical solution adopted in the utility model is as follows:

A three-state direct/direct converter, including two switch tubes VT ₁ and switch tube VT ₂ , two diodes D ₁ and diode D ₂ , energy storage inductance L and filter capacitor C; the anode of the input circuit is connected to the switch tube VT ₁ The collector is connected, the emitter of the switch tube _VT1 is connected to the cathode of the diode _D1 , the anode of the diode _D1 is connected to the negative pole of the output circuit; the negative pole of the input circuit is connected to the anode of the diode _D2 , and the cathode of the diode _D2 is connected to the positive pole of the output circuit connected; one end of the energy storage inductor L is connected to the common end of the emitter of the switch tube VT ₁ and the cathode of the diode D ₁ , and the other end is connected to the common end of the negative pole of the input circuit and the anode of the diode D ₂ ; the filter capacitor C is connected to the positive pole of the output circuit and the negative pole; the emitter of the switch tube _VT2 is connected to the common end of the anode of the diode _D1 and the filter capacitor C, and the collector of the switch tube _VT2 is connected to the common end of the anode of the diode _D2 and the negative pole of the input circuit.

The anode of the input circuit is connected to the collector of the switching tube _VT1 , the emitter of the switching tube _VT1 is connected to the cathode of the diode _D1 , and the anode of the diode _D1 is connected to the negative pole of the output circuit; the negative pole of the input circuit is connected to the positive pole of the output circuit; One end of _the energy storage inductance L is connected to the common end of the emitter of the switch tube VT ₁ and the cathode of the diode D ₁ , and the other end is connected to the negative pole of the input circuit; the filter capacitor C is connected between the positive pole and the negative pole of the output circuit; The collector is connected to the common end of the energy storage inductance L and the filter capacitor C, the emitter of the switch tube _VT2 is connected to the anode of the diode _D2 , and the cathode of the diode _D2 is connected to the common end of the emitter of the switch tube _VT1 and the cathode of the diode _D1 end.

The utility model forms a three-state direct-to-direct converter by means of two switch tubes, two diodes, an energy storage inductance and a filter capacitor to realize the rising and falling conversion of the input voltage, and the output polarity of the voltage is opposite to that of the input voltage. There are three working modes, namely, the linear rise of the inductor current, the linear drop of the inductor current, and the inertial freewheeling mode of the inductor current. When the input switch tube is turned on, the input power is applied to both ends of the inductor, and under the excitation of the input power voltage, the current of the energy storage inductor increases linearly. The output load voltage is maintained by the output capacitor voltage to supply power to the load. In this mode, no matter whether the switch tube controlling the inertial maintenance of the energy storage inductor is on or off, the working state of the converter in which the current of the energy storage inductor increases linearly remains unchanged. When the input switching tube is turned off, the switching tube that controls the inertial maintenance of the energy storage inductor is turned off, and the electric energy in the energy storage inductor continues to flow through the two diodes to supply power to the load and charge the output filter capacitor at the same time. As the inductor releases energy to the load, the inductor current decreases linearly. When the input switching tube is turned off, the switching tube controlling the inertial maintenance of the energy storage inductor is turned on, and the converter enters the inertial freewheeling (maintaining) mode of the inductor current. the

In the utility model, the input switching tube is turned off, and the switching tube controlling the inertial maintenance of the energy storage inductor is turned on, and the inductor current continues to flow through the switched switching tube and the diode. Because the loop impedance is small, the inertial maintenance of the inductor current is maintained. The output load voltage is maintained by the output filter capacitor voltage to supply power to the load. the

A control method of the three-state direct/direct converter, comprising the following:

1) The deviation between the output voltage set by the converter and the actual output voltage is output by the voltage regulator to output the control voltage. The control voltage is compared with the triangular wave signal to obtain the control signal of VT ₁ , which is driven by the drive circuit to VT ₁ ;

2) The set value of the converter control current and the inductor current output the control signal of VT ₂ through the hysteresis comparator, and drive the VT ₂ through the drive circuit; the comparator sets the hysteresis to improve the reliability of the circuit.

3) The driving signal of VT ₂ needs to be synchronized with the working cycle of VT ₁ to ensure the coordinated control of the two switches; use the driving signal of VT ₁ as the gating signal of the VT ₂ control signal, and open VT ₂ when VT ₁ is off drive signal;

4) In each switching cycle, as soon as VT ₁ is turned on, VT ₂ will be turned off, the freewheeling process ends, and the inductor current rises under the action of the input power supply voltage; when VT ₂ is turned on again, the inductor current is lower than the set current At this time, the freewheeling process of the inductor current begins.

The set inductor current lower limit changes according to the sinusoidal law within half a power frequency cycle, and the input voltage also changes according to the sinusoidal law. In each control cycle, the peak value of the inductor current also changes according to the sinusoidal law, and the average value of the inductor current naturally also Change according to the sine law. the

In the utility model, if the inertial maintenance current of the control converter and the input voltage change according to the sinusoidal law within half a power frequency cycle, the inductor current also changes according to the sinusoidal half-wave law. Therefore, the conversion circuit can be applied to a direct/direct conversion circuit with power factor correction in addition to being applied to a general direct/direct conversion control system to implement direct current/direct conversion. the

Compared with the buck-boost DC/DC converter, the utility model has greater flexibility due to the existence of the inertial mode, can realize independent control of input voltage and current, and obtain the pseudo-continuous conduction mode of the converter , can be applied to a direct/direct conversion circuit with power factor correction. the

Beneficial effects: Compared with the prior art, the utility model has a three-state DC/DC converter and its control method. Because of the existence of the inertial mode, the utility model has greater flexibility in the converter circuit and can realize input voltage , The independent control of the current obtains the pseudo-continuous conduction mode of the converter and obtains superior dynamic response. Set the freewheeling current of the inertia mode to change according to the sinusoidal law, and the sinusoidal changing law of the inductor current can be obtained. Therefore, the conversion circuit can not only be applied to the general DC/DC conversion control system to implement DC to DC conversion, but also can be applied to the DC/DC conversion circuit with power factor correction. the

Description of drawings

Figure 1 is the first schematic diagram of the three-state DC converter;

Figure 2 is a schematic diagram of the VT ₁ on and VT ₂ off intervals (0-t ₁ );

Figure 3 is a schematic diagram of the off interval (t ₁ ~ t ₂ ) of VT ₁ and VT ₂ ;

Figure 4 is a schematic diagram of the interval (t ₂ ~ T) between VT ₁ off and VT ₂ on;

Fig. 5 is circuit working waveform diagram;

Fig. 6 is the second schematic diagram of the three-state DC converter;

Fig. 7 is a three-state DC converter control circuit diagram;

Fig. 8 is a three-state DC converter control signal diagram;

Fig. 9 is a waveform diagram of the voltage and current of each element of the three-state DC converter. the

Detailed ways

Below in conjunction with specific embodiment the utility model is described further. the

As shown in Figure 1, the three-state DC converter consists of two switch tubes VT ₁ and switch tube VT ₂ , two diodes D ₁ and diode D ₂ , energy storage inductor L and filter capacitor C and the connection circuit between them composition. In the figure, VT ₁ , L, D ₁ , and C form a buck-boost chopper circuit, VT ₂ provides an inertial circuit for the continuous flow of the inductor current, and D ₂ prevents the short-circuit discharge of the capacitor during the continuous flow of the inductor current. According to VT ₁ , VT ₂ 's turn-on and turn-off combinations constitute four working combinations of the converter circuit, which are:

①VT ₁ : ON, VT ₂ : ON;

_②VT1 : ON, _VT2 : OFF;

_③VT1 : OFF, _VT2 : ON;

④ VT ₁ : OFF, VT ₂ : OFF;

Among these four working combinations, the working modes of the two working combination circuits ① and ② are the same, and they are attributed to one working mode, that is, the linear rise mode of the inductor current. At this stage, the input power supplies energy to the inductor through the turned-on switch tube VT1, and the inductor current increases. Due to the small loop impedance and the high operating frequency of the converter circuit, the inductor current rises almost linearly, which can be called linear growth of the inductor current. stage. During this phase, the load voltage is maintained by the capacitor, which discharges to the load. the

In the working combination ④, it is the mode of the linear decrease of the inductor current, and the VT ₁ tube at the input end is turned off. The inductor current continues to flow through D ₁ and D ₂ , and while supplying power to the load, it charges the output filter capacitor. As the inductor supplies power to the load and charges the capacitor, the inductor current decreases exponentially. Due to the large loop time constant (large capacitance), the switching frequency of the circuit is high, and the inductor current decreases almost linearly, which can be called the linear decline stage of the inductor current.

In the working combination ③, it is the inertial freewheeling mode of the inductor current, and the VT ₁ tube at the input end is turned off. The inductor current continues to flow through D ₁ and VT ₂ , and the inductor current basically remains unchanged because of the small loop impedance. In this phase, the load voltage at the output is maintained by the capacitor, which discharges to the load.

According to the working mode of the circuit, the utility model analyzes the relationship between the input and output of the converter circuit as follows:

$\frac{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; in</span>}}}{{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="d"\; filenames="130529111007.png"\; state="\{\{state\}\}">d</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="d"\; filenames="130529111007.png"\; state="\{\{state\}\}">d</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}}$

In the formula: U _o and U _i are the input and output voltages of the converter circuit, I _in and I _o are the input and output currents of the converter circuit, d ₁ , d ₂ and d ₃ are the current rise, fall and inertia of the converter circuit The ratio of the time to maintain the three intervals to the control period.

According to the working principle of the converter circuit, the control of the circuit is carried out in this way. The deviation between the output voltage set by the converter and the actual output voltage is output by the voltage regulator to control the voltage, and the control voltage is compared with the triangular wave signal to obtain the control signal of VT _1. The width of the signal depends on the set output voltage and the actual output voltage deviation. The control signal of VT ₁ is driven to VT ₁ through the driving circuit. The converter control current setting value and the inductor current output the control signal of VT ₂ through the hysteresis comparator, and drive the VT ₂ through the driving circuit. The comparator sets the hysteresis, the purpose is to improve the reliability of the circuit work. The driving information of VT ₂ needs to be synchronized with the working cycle of VT ₁ to ensure the coordinated control of the two switches.

In order to realize the cycle synchronization controlled by VT ₂ and VT ₁ , the driving signal of VT ₁ is used as the gate control signal of the VT ₂ control signal, and the driving signal of VT ₂ is only opened when VT ₁ is turned off. In each switching cycle, as soon as VT ₁ is turned on, VT ₂ is turned off, the freewheeling process ends, and the inductor current rises under the action of the input power supply voltage. The re-opening of VT ₂ is the moment when the inductor current is lower than the set current, and at this moment, the freewheeling process of the inductor current begins.

If the set lower limit current changes according to the sinusoidal law within half a power frequency cycle, the input voltage also changes according to the sinusoidal law, and the peak value of the inductor current in each control cycle also changes according to the sinusoidal law, and the average value of the inductor current will naturally also change. Change according to the sine law. In the actual control process, the reference current is set as a half-sine wave, and the final result of the control is that the inductor current also changes according to the half-sine wave rule in the half cycle of the power frequency. Therefore, the conversion circuit can not only be applied to the general DC/DC conversion control system to implement DC to DC conversion, but also can be applied to the DC/DC conversion circuit with power factor correction. the

Embodiment 1 Composition and working principle of three-state DC converter

The schematic diagram of the three-state DC converter is shown in Figure 1, the working mode of the converter is shown in Figures 2, 3, and 4, and the driving and inductor voltage and current operating waveforms are shown in Figure 5. the

In Figure 1, VT ₁ and VT ₂ can realize the transformation of input and output voltage according to a certain working combination, and the combination methods can be as follows:

①VT ₁ : OFF, VT ₂ : OFF;

_②VT1 : ON, _VT2 : OFF;

_③VT1 : OFF, _VT2 : ON;

④ VT ₁ : ON, VT ₂ : ON;

Figure 2 corresponds to the working combination mode ②. In this mode, VT ₁ is turned on to connect the input circuit, the power supply stimulates the inductance to increase the magnetization, the electric energy of the inductance increases, the output voltage is maintained by the capacitor, and the electric energy is supplied to the load, and the circuit is in the inductive current rising mode. In this working combination mode, when VT ₁ is turned on, VT ₂ is turned on or turned off, and the circuit working status is the same. Therefore, the two modes ④ and ② are the same. During this phase, the inductor current rises linearly.

Figure 3 corresponds to the working combination mode ①. In this mode, both VT ₁ and VT ₂ are turned off, and the inductor current continues to flow through D ₁ and D ₂ to provide current to the capacitor and the load. Part of the inductor current is supplied to the load, and part of it is charged to the capacitor. The circuit is in the inductor current drop mode. state. During this phase, the inductor current decreases linearly.

Figure 4 corresponds to the working combination mode ③. In this mode, VT ₁ is turned off, VT ₂ is turned on, the inductor current continues to flow, and the circuit enters the inductor current inertial mode. During this phase, the inductor current remains constant.

Explanation: The circuit is in the rising stage of the inductor current in Figure 2 and the falling stage of the inductor current in Figure 3, the inductor current should rise and fall according to the law of the index, but because the converter has a high operating frequency, the loop resistance value is small, for the convenience of analysis , in the switching control period, the change of the inductor current can be analyzed according to the linear law. the

Observing the waveform in Figure 5, the three periods of circuit operation are d ₁ T, d ₂ T, and d ₃ T respectively, and the relationship between them is as follows:

d ₁ +d ₂ +d ₃ =1

d ₁ =t ₁ /T

d ₂ =(t ₂ −t ₁ )/T

d ₃ =(Tt ₂ )/T (0)

If the components in the figure are regarded as ideal components, then in the interval from 0 to t ₁ , VT ₁ is turned on, VT ₂ is turned off, the power supply charges the inductor, and the output capacitor discharges the load. Under the power supply voltage, the inductor current increases from i _Lmin to i _Lmax . The working state of the circuit is shown in Figure 2. The input circuit voltage equation is:

${\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; L</span>}\frac{{\mathrm{<span\; class="notranslate">\; di</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

In the interval between t ₁ and t ₂ , VT ₁ is turned off, VT ₂ is turned off, the inductor discharges through diodes D ₁ and D ₂ , part of the discharge current charges the capacitor, and part of it supplies power to the load, and the inductor current gradually decreases. The working state of the circuit is shown in Figure 3. The output circuit voltage equation is:

${\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; L</span>}\frac{{\mathrm{<span\; class="notranslate">\; di</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

As the discharge progresses, the inductor current gradually decreases. When the inductor current decreases to i _Lmin , the control circuit drives VT ₂ to conduct, and the inductor current continues to flow through VT ₂ and D, and the interval is t ₂ ~T. In this interval, the inductor current remains unchanged, the working state of the circuit is shown in Figure 4, and the output voltage is maintained by the capacitor.

Assuming that the input and output voltages u _i =U _i , u _o =U _o remain unchanged, and the resistance of the input circuit and output circuit of the converter is ignored, the inductor current will change linearly in the rising and falling stages. For equation (1):

${\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; L</span>}\frac{{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}\mathrm{<span\; class="notranslate">\; min</span>}}}{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

For equation (2):

${\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; L</span>}\frac{{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}\mathrm{<span\; class="notranslate">\; min</span>}}}{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

From equations (3) and (4):

$\frac{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="d"\; filenames="130529111007.png"\; state="\{\{state\}\}">d</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="d"\; filenames="130529111007.png"\; state="\{\{state\}\}">d</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

According to the inductor voltage in Figure 5, the weekly average value is zero, and the formula (5) can also be obtained. The calculation method is as follows:

${\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}\mathrm{<span\; class="notranslate">\; dt</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; (</span>{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; dt</span>}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}^{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}\mathrm{<span\; class="notranslate">\; dt</span>}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; 0</span>}\mathrm{<span\; class="notranslate">\; dt</span>}<span\; class="notranslate">\; )</span>$

U _L ＝U _i d ₁ +U _o d ₂ =0

That is, formula (5). the

Embodiment 2 Analysis of input and output current characteristics of three-state DC converter

1. Time average equivalent method

According to the time-averaged equivalent method, assuming that the inductor current and capacitor voltage remain unchanged during the switching process (this assumption requires that the values of the inductor and capacitor be large), the time-average value of the input current and the average value of the capacitor current are calculated respectively, and the following can be obtained:

$\begin{array}{c}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; in</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; in</span>}}\mathrm{<span\; class="notranslate">\; dt</span>}\\ <span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; (</span>{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}\mathrm{<span\; class="notranslate">\; dt</span>}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; T</span>}}^{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="d"\; filenames="130529111007.png"\; state="\{\{state\}\}">d</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; 0</span>}\mathrm{<span\; class="notranslate">\; dt</span>}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; \&Integral;</span>}_{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="d"\; filenames="130529111007.png"\; state="\{\{state\}\}">d</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; T</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; 0</span>}\mathrm{<span\; class="notranslate">\; dt</span>}<span\; class="notranslate">\; )</span>\end{array}$

I _in = d ₁ I _L (7)

$\begin{array}{c}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}\mathrm{<span\; class="notranslate">\; dt</span>}\\ <span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; (</span>{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}\mathrm{<span\; class="notranslate">\; dt</span>}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; T</span>}}^{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="d"\; filenames="130529111007.png"\; state="\{\{state\}\}">d</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; dt</span>}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; \&Integral;</span>}_{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="d"\; filenames="130529111007.png"\; state="\{\{state\}\}">d</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; T</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}\mathrm{<span\; class="notranslate">\; dt</span>}<span\; class="notranslate">\; )</span>\end{array}$

I _C ＝d ₂ I _L -I _o (8)

When the circuit works stably, the average value of the capacitor current is zero. From formulas (7) and (8), we get:

$\frac{{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}{{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; in</span>}}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

$\frac{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; in</span>}}}{{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="d"\; filenames="130529111007.png"\; state="\{\{state\}\}">d</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="d"\; filenames="130529111007.png"\; state="\{\{state\}\}">d</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span>$

From the analysis here, it can be seen that the three-state DC converter can realize the input voltage and current conversion, and has the properties of a DC transformer. However, because of the effect of VT ₂ , that is, the existence of the inertial mode of the inductor, the charging mode of the inductor is different from that of the capacitor. The charging mode (inductance discharging mode) is separated. After the control period is determined, the charging mode of the inductor and the charging mode of the capacitor can be independently controlled.

2. The inductor current is analyzed according to the law of linear change

Considering the actual situation, without loss of generality, the following analysis is made. the

在t₁～t₂区间，电感电流线性减小，其斜率为

有（注：以下公式，所有符号量均按其数值代入，极性在公式中已经考虑）：  If the existence of a large output filter capacitor is considered in the analysis, the output current is regarded as a constant value during the switching cycle, and the inductor current changes as shown in Figure 5, that is, the current increases linearly during the rising phase of the inductor current, and according to the current during the decreasing phase of the inductor current. The linear law decreases. Assuming that the initial value of the inductor current is I _x , then the inductor current increases linearly in the interval from 0 to t ₁ , and its slope is

In the interval between t ₁ and t ₂ , the inductor current decreases linearly, and its slope is

Yes (Note: In the following formula, all symbols are substituted according to their values, and the polarity has been considered in the formula):

${\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{\mathrm{<span\; class="notranslate">\; L</span>}}\mathrm{<span\; class="notranslate">\; t</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; T</span>}\\ {\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{\mathrm{<span\; class="notranslate">\; L</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}{\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; )</span>& {\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; \&le;</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="d"\; filenames="130529111007.png"\; state="\{\{state\}\}">d</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; T</span>}\\ {\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}& <span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="d"\; filenames="130529111007.png"\; state="\{\{state\}\}">d</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; T</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 11</span>}<span\; class="notranslate">\; )</span>$

In the interval from 0 to t ₁ , the power supply provides electric energy to the inductor, VT ₂ is turned off in the interval from t ₁ to t ₂ to T, the input current is zero, and the average value of the input current is:

$\begin{array}{c}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; in</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}\mathrm{<span\; class="notranslate">\; dt</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{\mathrm{<span\; class="notranslate">\; L</span>}}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; dt</span>}\\ <span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="u\; i\; d"\; filenames="130529111007.png"\; state="\{\{state\}\}">u</figure-callout></span><figure-callout\; id="1"\; label="u\; i\; d"\; filenames="130529111007.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{}_{}^{}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; L</span>}}\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 12</span>}<span\; class="notranslate">\; )</span>$

In the interval from 0 to t ₁ , the voltage at the output terminal is maintained by the capacitor and outputs current; in the interval from t ₁ to t ₂ , part of the discharge current of the inductor charges the capacitor, and part of it is supplied to the load; in the interval from t ₂ to T, the inductor continues to flow, and the output voltage The current is maintained and output by the capacitor. The capacitor current is expressed as:

${\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; T</span>}\\ {\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{\mathrm{<span\; class="notranslate">\; L</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}{\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; )</span>& {\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; \&le;</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="d"\; filenames="130529111007.png"\; state="\{\{state\}\}">d</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; T</span>}\\ <span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}& <span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="d"\; filenames="130529111007.png"\; state="\{\{state\}\}">d</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; T</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 13</span>}<span\; class="notranslate">\; )</span>$

Assuming that the output voltage remains constant throughout the working range, the average value of the capacitor current can be expressed as:

${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; [</span>{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}\mathrm{<span\; class="notranslate">\; dt</span>}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; \&Integral;</span>}_{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; T</span>}}^{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="d"\; filenames="130529111007.png"\; state="\{\{state\}\}">d</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{\mathrm{<span\; class="notranslate">\; L</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}{\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; dt</span>}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; \&Integral;</span>}_{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="d"\; filenames="130529111007.png"\; state="\{\{state\}\}">d</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; T</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}\mathrm{<span\; class="notranslate">\; dt</span>}<span\; class="notranslate">\; ]</span>$

${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; [</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; T</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}\mathrm{<span\; class="notranslate">\; T</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; T</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; T</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{\mathrm{<span\; class="notranslate">\; L</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="L\; d"\; filenames="130529111007.png"\; state="\{\{state\}\}">L</figure-callout></span><figure-callout\; id="2"\; label="L\; d"\; filenames="130529111007.png"\; state="\{\{state\}\}">\; </figure-callout>}}{\mathrm{<span\; class="notranslate">\; </span>}}_{}^{}{\mathrm{<span\; class="notranslate">d</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 14</span>}<span\; class="notranslate">\; )</span>$

The average value of the capacitor current should be zero within a week, so:

$<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="d"\; filenames="130529111007.png"\; state="\{\{state\}\}">d</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="d"\; filenames="130529111007.png"\; state="\{\{state\}\}">d</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{\mathrm{<span\; class="notranslate">\; L</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="L\; d"\; filenames="130529111007.png"\; state="\{\{state\}\}">L</figure-callout></span><figure-callout\; id="2"\; label="L\; d"\; filenames="130529111007.png"\; state="\{\{state\}\}">\; </figure-callout>}}{\mathrm{<span\; class="notranslate">\; </span>}}_{}^{}{\mathrm{<span\; class="notranslate">d</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 15</span>}<span\; class="notranslate">\; )</span>$

From formulas (0), (12), and (15), and considering formula (5) (input and output voltages are calculated by value):

${\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; in</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="d"\; filenames="130529111007.png"\; state="\{\{state\}\}">d</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}$

There is a relationship between input current and output current:

$\frac{{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}{{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; in</span>}}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 16</span>}<span\; class="notranslate">\; )</span>$

This formula is the same as formula (9). the

The circuit in Fig. 1 can also be in the form of Fig. 6. The charging stage of the inductor is the same. The difference from Fig. 1 is that the route of the inductance discharging stage in Fig. 6 is: power supply - → D ₁ → L → power supply +, and the route of the current freewheeling stage is : L→VT ₂ →D ₂ →L, the current path of the inductor discharge stage has only one diode voltage drop, and D ₁ does not participate in the freewheeling process. Due to the large current in the discharge phase of the inductor, both D ₁ and D ₂ participate in Figure 1, but only D ₁ participates in Figure 6; in the freewheeling phase of the inductor current, D ₁ participates and D ₂ does not. Therefore, the overall loss in Figure 1 is larger than that in Figure 6, but their control process is the same.

Embodiment 3 Control of three-state DC converter

In order to realize the control of the three-state DC converter, the control circuit diagram of the design system is shown in Figure 7. In the figure, u _ref and u _o are the output voltage set by the converter and the actual output voltage, Δu is the deviation value between u _ref and u _o , and the voltage regulator outputs the control voltage u _k , which is obtained by comparing the control voltage with the triangular wave signal The control signal of VT ₁ is driven to VT ₁ through the driving circuit. i _ref is the set value of the converter control current, which and the inductor current output the control signal of VT ₂ through the hysteresis comparator, and drive VT ₂ through the drive circuit. The setting purpose of the comparison hysteresis is to reduce the high-frequency action of the control switch VT ₂ when the inductor current is close to _Ix during the current control process, and improve the working reliability of the circuit. The driving circuit of VT ₂ needs to be synchronized with the working cycle of VT ₁ to ensure the coordinated control of the two switches. Its control signal is shown in Figure 8.

In the actual control process, in order to realize the periodic synchronization of VT ₂ and VT ₁ control, the driving signal of VT ₁ is used as the gate control signal of the VT ₂ control signal, and the driving signal of VT ₂ is only opened when VT ₁ is turned off. Then in each switching cycle, as soon as VT ₁ is turned on, VT ₂ is turned off, the freewheeling process ends, and the inductor current rises under the action of the input power supply voltage. The re-opening of VT ₂ is the moment when the inductor current is lower than _Ix , at this time, the freewheeling process of the inductor current begins. Although VT ₁ is turned on and VT ₂ is turned off is the time starting point of each control cycle, and the circuit enters the stage of increasing the inductor current, because it takes time for the two switches to be turned on and off, there will be an overlapping area of common conduction between them, but The structure of the circuit guarantees that even if the two tubes VT ₁ and VT ₂ are turned on at the same time, the circuit still enters the stage of increasing the inductor current, just as explained in the analysis of the circuit principle.

The previous analysis is the conclusion obtained under the assumption that I _x is constant. If I _x changes according to the sinusoidal law within half the power frequency period, that is:

I _x ＝|I _m |sinωt (17)

After the conversion circuit works stably, VT ₁ is turned on in one switching cycle, and after d ₁ T time, the inductor current reaches the peak value of this cycle, and its value in the current peak value of the i-th switching cycle can be expressed as:

${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; mi</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; xi</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{\mathrm{<span\; class="notranslate">\; L</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&omega;</span>}{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{\mathrm{<span\; class="notranslate">\; L</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 18</span>}<span\; class="notranslate">\; )</span>$

If the input voltage u _i also changes according to the sinusoidal law, in each control cycle, the peak value of the inductor current also changes according to the sinusoidal law, and the average value of the inductor current naturally also changes according to the sinusoidal law. Then, in the actual control process, the reference current is set as half-sine wave, and the final result of the control is that the inductor current also changes according to the law of half-sine wave. Therefore, the conversion circuit can not only be applied to the general DC/DC conversion control system to implement DC to DC conversion, but also can be applied to the DC/DC conversion circuit with power factor correction.

Embodiment 4 Determination of the parameters of the three-state DC converter

The current flowing through each component of the converter and the voltage borne by both ends are shown in Figure 9. According to the working conditions of each component in Figure 9, the rated parameters of each component can be determined. the

VT ₁ : I _c1 =(1.5～2)I _m , U _ce1 =(2～3)×(U _im +U _om );

VT ₂ : I _c2 =(1.5～2)I _x , U _ce2 =(2～3)×U _om ;

D ₁ : I _D1 =(1.5～2)I _m , U _D1 =(2～3)×U _im ;

D ₂ : I _D2 =(1.5～2)I _m , U _D2 =(2～3)×U _om ;

L: I _Lm ≥ I _m ;

C: U _Cm ≥ U _om .

Claims (2)

1. a tri-state DC/DC conversion device, is characterized in that: comprise two switching tube VT ₁with switching tube VT ₂, two diode D ₁with diode D ₂, energy storage inductor L and filter capacitor C; Input circuit positive pole and switching tube VT ₁collector electrode is connected, switching tube VT ₁emitter and diode D ₁negative electrode be connected, diode D ₁anode with the output circuit negative pole, be connected; Input circuit negative pole and diode D ₂anode be connected, diode D ₂anodal being connected of negative electrode and output circuit; The end of energy storage inductor L is connected to switching tube VT ₁emitter and diode D ₁the common end of negative electrode, the other end is connected to input circuit negative pole and diode D ₂the common end of anode; Filter capacitor C is connected between the positive pole and negative pole of output circuit; Switching tube VT ₂emitter be connected to diode D ₁the common end of anode and filter capacitor C, switching tube VT ₂collector electrode be connected to diode D ₂the common end of anode and input circuit negative pole.

2. tri-state DC/DC conversion device according to claim 1, is characterized in that: described input circuit positive pole and switching tube VT ₁collector electrode is connected, switching tube VT ₁emitter and diode D ₁negative electrode be connected, diode D ₁anode with the output circuit negative pole, be connected; The input circuit negative pole is connected with output circuit is anodal; The end of energy storage inductor L is connected to switching tube VT ₁emitter and diode D ₁the common end of negative electrode, the other end is connected to the input circuit negative pole; Filter capacitor C is connected between the positive pole and negative pole of output circuit; Switching tube VT ₂collector electrode be connected to the common end of energy storage inductor L and filter capacitor C, switching tube VT ₂emitter and diode D ₂anode is connected, diode D ₂negative electrode is connected to switching tube VT ₁emitter and diode D ₁the common end of negative electrode.

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