CN111478600A - Control method for double-active bridge type single-stage AC-DC converter - Google Patents
Control method for double-active bridge type single-stage AC-DC converter Download PDFInfo
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- CN111478600A CN111478600A CN202010266503.9A CN202010266503A CN111478600A CN 111478600 A CN111478600 A CN 111478600A CN 202010266503 A CN202010266503 A CN 202010266503A CN 111478600 A CN111478600 A CN 111478600A
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
- H02M7/00—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output
- H02M7/02—Conversion of ac power input into dc power output without possibility of reversal
- H02M7/04—Conversion of ac power input into dc power output without possibility of reversal by static converters
- H02M7/06—Conversion of ac power input into dc power output without possibility of reversal by static converters using discharge tubes without control electrode or semiconductor devices without control electrode
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
- H02M3/00—Conversion of dc power input into dc power output
- H02M3/22—Conversion of dc power input into dc power output with intermediate conversion into ac
- H02M3/24—Conversion of dc power input into dc power output with intermediate conversion into ac by static converters
- H02M3/28—Conversion of dc power input into dc power output with intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode to produce the intermediate ac
- H02M3/325—Conversion of dc power input into dc power output with intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode to produce the intermediate ac using devices of a triode or a transistor type requiring continuous application of a control signal
- H02M3/335—Conversion of dc power input into dc power output with intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode to produce the intermediate ac using devices of a triode or a transistor type requiring continuous application of a control signal using semiconductor devices only
- H02M3/33569—Conversion of dc power input into dc power output with intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode to produce the intermediate ac using devices of a triode or a transistor type requiring continuous application of a control signal using semiconductor devices only having several active switching elements
- H02M3/33576—Conversion of dc power input into dc power output with intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode to produce the intermediate ac using devices of a triode or a transistor type requiring continuous application of a control signal using semiconductor devices only having several active switching elements having at least one active switching element at the secondary side of an isolation transformer
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
- H02M1/00—Details of apparatus for conversion
- H02M1/0003—Details of control, feedback or regulation circuits
- H02M1/0012—Control circuits using digital or numerical techniques
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
- H02M1/00—Details of apparatus for conversion
- H02M1/0048—Circuits or arrangements for reducing losses
- H02M1/0054—Transistor switching losses
- H02M1/0058—Transistor switching losses by employing soft switching techniques, i.e. commutation of transistors when applied voltage is zero or when current flow is zero
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02B—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO BUILDINGS, e.g. HOUSING, HOUSE APPLIANCES OR RELATED END-USER APPLICATIONS
- Y02B70/00—Technologies for an efficient end-user side electric power management and consumption
- Y02B70/10—Technologies improving the efficiency by using switched-mode power supplies [SMPS], i.e. efficient power electronics conversion e.g. power factor correction or reduction of losses in power supplies or efficient standby modes
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- Engineering & Computer Science (AREA)
- Power Engineering (AREA)
- Dc-Dc Converters (AREA)
Abstract
The invention provides a control method for a double-active-bridge single-stage AC-DC converter, solves the technical problems of complex drive, continuous mode switching and complex control strategy calculation in the traditional topology of an active double-bridge single-stage AC-DC converter, and belongs to the technical field of isolated high-frequency power conversion direction in power electronics. According to the method, the primary side level, the secondary side level duty ratio and the primary and secondary side voltage phase shift angle of the transformer are controlled in a full digital mode, and neither an inner current loop nor table lookup is needed. In addition, the method does not need to switch between modes, and ensures the continuity of the control strategy. Meanwhile, soft switching of all switching tubes can be realized in a wide range, the efficiency of the converter is improved, and the double-active bridge can work in an extremely wide power range and voltage range. Compared with the traditional two-stage alternating current-direct current converter scheme, the method has the characteristics of high efficiency, high power density and high reliability.
Description
Technical Field
The invention relates to a control method for a double-active bridge type single-stage AC-DC converter, and belongs to the technical field of isolation high-frequency power conversion directions in power electronics.
Background
The AC-DC converter is widely applied to the fields of electric vehicles, L ED power supply, communication power supply systems, digital centers and the like.
In order to achieve electrical isolation, a conventional AC-DC converter generally adopts a two-stage structure, that is, a PWM rectifier is used to convert AC power into DC power at a front stage, and a DC-DC converter with high-frequency isolation is used to output DC voltage at a rear stage. Although this two-stage configuration can be used in various applications with a rich topology, it does not have a high power density because it requires a high-voltage bus capacitor. Also, the two-stage configuration also results in a reduction in efficiency.
Therefore, a single-stage AC-DC converter using a Dual Active Bridge (DAB) topology is proposed in the literature. Compared with a traditional two-stage structure, the double-active bridge type single-stage AC-DC converter has the advantages of zero voltage switching-on (ZVS), simple structure and the like while ensuring electrical isolation, and improves power density and efficiency.
The single-stage AC-DC converter adopting a double-active-bridge (DAB) topology is essentially characterized in that a certain commutation device is added on the traditional voltage source type DAB topology. Therefore, for the voltage source type DAB, the essential requirement is to realize energy conversion from steamed bread waves to direct currents. DAB of voltage source type, it is made up of two active full bridges and a high-frequency transformer. In dc applications, a number of DAB control methods of voltage supply type have been proposed in the literature. Under the condition that the traditional single phase-shift control is matched with voltage, zero-voltage turn-off of all switching tubes can be realized, and under the condition that double phase-shift control and triple phase-shift control are applied to unmatched voltage, further optimization of a current effective value and soft switching conditions can be realized.
Compared with the DC-DC conversion occasion, the control method of the active double-bridge topology has an extremely wide gain range in the AC-DC application occasion. Based on this, some documents have proposed a control method thereof. However, in these approaches, whether for full-bridge or half-bridge topologies, three control variables need to be introduced to optimize the converter's soft switching conditions and peak currents while achieving very wide gains. Furthermore, existing control strategies require switching between different operating modes, which can lead to complexity of the control strategy and distortion of the current waveform at certain operating points. Since these control strategies require complex calculations to provide the control variables, most of the practical applications use table lookup methods, which results in the influence on the dynamic performance of the system and the continuity of the control.
Disclosure of Invention
The invention aims to solve the technical problems of complex driving, continuous mode switching and complex control strategy calculation in the traditional topology of an active double-bridge type single-stage AC-DC converter, and creatively provides a control method for the double-active bridge type single-stage AC-DC converter.
According to the method, the primary side level, the secondary side level duty ratio and the primary and secondary side voltage phase shift angle of the transformer are controlled in a full digital mode, and neither an inner current loop nor table lookup is needed. In addition, the method does not need to switch between modes, and ensures the continuity of the control strategy. Meanwhile, soft switching of all switching tubes can be realized in a wide range, and the efficiency of the converter is improved.
Specifically, the phase shift angle of the primary side and the secondary side is obtained by giving an output voltage and detecting the output voltage. And obtaining the duty ratio of the low voltage of the secondary side through the phase shift angle and the phase of the input alternating voltage. The duty ratio of the primary side full bridge is determined by inputting and outputting voltage and the number of turns of the transformer, so that the soft switching of the primary side switching tube in an extremely wide range and the soft switching of the secondary side switching tube in a certain power range are realized while the power factor correction is realized, and the conversion efficiency of the converter is improved.
The invention is realized by the following technical scheme.
A control method for a dual active bridge single stage AC-DC converter.
The double-active bridge type single-stage AC-DC converter comprises a main circuit and a control circuit.
The main circuit comprises an uncontrolled rectifier bridge, a primary side full bridge circuit, a high-frequency transformer and a secondary side full bridge circuit.
The primary side full-bridge circuit, the high-frequency transformer and the secondary side full-bridge circuit form an active double-bridge structure of the main circuit. The primary side full bridge circuit comprises four switching tubes (Q)1，Q2，Q3，Q4) The secondary side full bridge circuit comprises four switching tubes (Q)5，Q6，Q7，Q8). The uncontrolled rectifier bridge is in a full-bridge structure and is composed of four diodes.
Specifically, the main circuit is connected with the input side series inductor LacA low-pass filter is formed and then is connected with an uncontrolled rectifier bridge formed by four diodes. The output side of the uncontrolled rectifier bridge is connected with the input side of the double active bridges and is connected with a high-frequency capacitor C in parallelrecTo absorb the high frequency ripple of the dual active bridge. The input side of the double active bridge is composed of four switching tubes (Q)1，Q2，Q3，Q4) The output side of the formed full bridge is composed of four switching tubes (Q)5，Q6，Q7，Q8) Forming a full bridge, and passing a high-frequency transformer T between the two bridgesrConnection resonant inductor LrAnd the transformer is connected in series and is responsible for power transmission. Output side of double active bridge and a high-frequency capacitor CohIn parallel to absorb current ripple in the switching frequency. An electrolytic capacitor ColIn parallel with the output side of the dual active bridge to reduce the voltage ripple at low frequencies.
The control circuit comprises a controller, a driving circuit and a sampling circuit.
Specifically, the controller takes the DSP as a core and is used for converting the input-side and output-side voltage sampling signals sampled by the sampling circuit. Obtaining a control signal according to an error closed loop of a given output voltage and an actual output voltage
Namely the phase shift angle of the original secondary side, and the secondary side duty ratio control signal D is obtained through the phase and the phase shift angle of the input voltage2According to the optimized soft switching conditions, from D2Phase shift angle control signal of primary and secondary side
Calculating the duty ratio control signal D of the primary side1. And generating a PWM driving signal according to the control signal to control the on and off of the eight switching tubes.
The drive circuit is used for receiving the PWM signal from the DSPAfter over-isolation and power amplification, the power amplifier is composed of eight switching tubes (Q) in the main circuit1、Q2、Q3、Q4、Q5、Q6、Q7、Q8) A driving voltage is provided.
The sampling circuit is used for sampling to obtain voltage sampling signals of the input side and the output side of the double-active bridge.
The control method for the double-active bridge type single-stage AC-DC converter comprises the following steps:
the method comprises the following steps: sampling converter input voltage vinInstantaneous value of (a). For an input ac voltage, the real-time phase σ of the input voltage is obtained by a digital phase locked loop in the DSP.
Step two: sampling converter output voltage voInstantaneous value of (a). Will output a voltage voIs filtered (possibly by means of a danger filter) and a given output voltage value vrefMaking difference, and making the output voltage error pass through PI regulator to obtain original secondary side phase-shifting angle control signal
Step three: real-time phase sigma and primary and secondary side phase shift angle control signals of input voltage obtained according to digital phase-locked loop
Obtaining a secondary side duty ratio control signal D2The calculation formula is as follows:
step four: for the converter to realize soft switching with less circulating current cost, the primary side duty ratio control signal D is applied1And (6) optimizing. With IZVS1The minimum current required by soft switching of the primary side switching tube and the primary side duty ratio control signal D1The following constraints are satisfied:
wherein v isrecInput voltage for a double active bridge, LrIs the inductance value of the resonant inductor, TsIn order to be the switching period of the switch,
the phase shift angle control signal of the original secondary side; according to the transformer transformation ratio 1: n, M is defined as the gain of the double active bridge, and the expression is as follows:
M＝nvrec/vo(3)
where vo is the output voltage.
Step five: and generating a PWM driving signal according to the control signal, and controlling the on and off of eight switching tubes in the main circuit to realize the control of the converter.
Advantageous effects
1. The method provided by the invention aims at the double-active bridge type single-stage AC-DC converter, has the characteristic of high-frequency isolation, and has the characteristics of high efficiency, high power density and high reliability compared with the traditional two-stage AC-DC converter scheme.
2. The method is applied to AC-DC conversion occasions, so that the conversion range of the double-active-bridge topology and the input voltage is extremely large. The control strategy of the present invention enables a dual active bridge topology to operate over an extremely wide voltage gain range. Meanwhile, the input instantaneous power is changed from zero, so the working mode and the control strategy of the invention can ensure that the double active bridge works in an extremely wide power range and voltage range.
3. Compared with the existing double-active bridge type single-stage alternating current-direct current converter, the method has the advantage that the control strategy is further simplified. By modeling and analyzing the proposed working mode, different control variables are extracted to perform decoupling control on the output voltage and the input current. Under the condition of ensuring power factor correction and output voltage closed-loop control, the control variable is given without complex calculation and switching among different modes, so that the relation between the control variable and a controlled object is clear and definite, and the method has high practical value.
4. The method can realize soft switching in a wider range at low circulating current cost. By optimizing the duty ratio of the primary side, the switching tube of the primary side can realize soft switching within an extremely wide voltage gain range and a power range with minimum cost. Through the analysis of the secondary side control variable under the control strategy, the secondary side switching tube can realize soft switching under the condition of medium and light load. Therefore, the double-active bridge type single-stage alternating current and direct current converter is low in switching loss, and efficiency is improved.
Drawings
FIG. 1 is a main circuit of a dual active bridge single stage AC-DC converter;
FIG. 2 is a control block diagram of a main circuit of a dual active bridge type single-stage AC-DC converter;
fig. 3 is a waveform of the primary and secondary side levels, the leakage inductance current, and the dual active bridge input current in one switching period.
Fig. 4 is a waveform of an envelope of an ac input current and a leakage inductance current under different loads.
Detailed Description
The present invention will be described in detail with reference to the accompanying drawings and embodiments, and technical problems and advantages solved by the technical solutions of the present invention will be described, wherein the described embodiments are only intended to facilitate understanding of the present invention, and do not limit the present invention in any way.
Example 1
In the embodiment, a 220V power grid is used as an alternating current input power supply, the output voltage is 60V direct current voltage, the rated power is 1400W, the unit power factor correction can be realized, and the device can be used for data center power supply or an electric vehicle charger.
Main circuit structure of double active bridge type single-stage AC-DC converter, as shown in FIG. 1, wherein the low-pass filter has an inductor LacComposition, sensory value in the example is 50 μ H. The uncontrolled rectifier bridge is composed of four common frequency diodes. Since the diode operates in the common frequency state and the dual active bridge operates in the high frequency state, a high frequency capacitor C is requiredrecTo absorb the high frequency ripple of the dual active bridge. Due to CrecThe value of (A) is too large to cause the waveform distortion rate of the input current to rise, and C is selected in the case where the waveform distortion rate is less than 5%recThe capacitance value of the active bridge is 2.5 mu F, the switching tubes in the full bridge at the input side of the double active bridges all use SiC devices, the switching tubes in the full bridge at the output side of the active bridges all use low-voltage high-current MOSFETs, &lTtT transfer = L "&gTt L/T &gTtrFor the resonant inductor, responsible for the power transfer, in order to guarantee a maximum power transfer of 1.4kW, the inductance of the resonant inductor must not be greater than 55.67 muh, in the example the inductance of the resonant inductor L r is 50 muhoh) The parallel connection is carried out to absorb the current ripple in the switching frequency, and the capacity value is 100 mu F; and an electrolytic capacitor (C)ol) And then connected in parallel to reduce the voltage ripple at low frequency, with a capacitance of 20 mF. The outputs of the two bridges are connected through a high-frequency transformer Tr, and the turn ratio is 1: 0.15. in this embodiment, the digital controller is a TMS320F28335 chip.
FIG. 2 is a control block diagram of the dual active bridge type single-stage AC-DC converter disclosed in this embodiment, wherein Gv(s) is a regulator consisting of proportional and integral regulation to achieve a quiet regulation of the output voltage. Since the output voltage of the rectifier includes a second harmonic component, a notch filter H is requiredo(s) for the effect of second harmonics in the output voltage on the regulator control.
The control method of the embodiment comprises the following steps:
the method comprises the following steps: sampling converter input voltage vinInstantaneous value of (a). For an input ac voltage, the real-time phase σ of the input voltage is obtained by a digital phase locked loop in the DSP.
Step two: sampling converter output voltage voInstantaneous value of (a). Will output a voltage voIs filtered (possibly by means of a danger filter) and a given output voltage value vrefMaking difference, and making the output voltage error pass through PI regulator to obtain original secondary side phase-shifting angle control signal
Thirdly, obtaining a real-time phase sigma of the input voltage and a phase shift angle control signal of the original secondary side according to the digital phase-locked loop (P LL)
Obtaining a secondary side duty ratio control signal D2The calculation formula is as follows:
step four: for the converter to realize soft switching with less circulating current cost, the primary side duty ratio control signal D is applied1And (6) optimizing. With IZVS1The minimum current required by soft switching of the primary side switching tube and the primary side duty ratio control signal D1The following constraints are satisfied:
wherein v isrecInput voltage for a double active bridge, LrIs the inductance value of the resonant inductor, TsIn order to be the switching period of the switch,
the phase shift angle control signal of the original secondary side; according to the transformer transformation ratio of 1:0.15, IZVS1The minimum current required for realizing soft switching for the primary side switching tube is 1A; m is defined as the gain of the dual active bridge, and the expression is as follows:
M＝nvrec/vo(3)
where vo is the output voltage.
Fig. 4 shows the relationship between the input ac voltage of 220V and the leakage current at the ac frequency at the load of 0.36kW to 1.44kW, respectively, and it can be seen that the waveform distortion rate of the input current is low and is in phase with the ac voltage.
Step five: and generating a PWM driving signal according to the control signal, and controlling the on and off of eight switching tubes in the main circuit to realize the control of the converter.
The above detailed description is intended to illustrate the objects, aspects and advantages of the present invention, and it should be understood that the above detailed description is only exemplary of the present invention and is not intended to limit the scope of the present invention, and any modifications, equivalents, improvements and the like within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (3)
1. A control method for a dual active bridge single stage AC-DC converter,
the double-active bridge type single-stage AC-DC converter comprises a main circuit and a control circuit, wherein the main circuit comprises an uncontrolled rectifier bridge, a primary side full bridge circuit, a high-frequency transformer and a secondary side full bridge circuit, and the control circuit comprises a controller, a driving circuit and a sampling circuit;
the primary side full-bridge circuit, the high-frequency transformer and the secondary side full-bridge circuit form an active double-bridge structure of the main circuit; the primary side full-bridge circuit comprises four switching tubes, and the secondary side full-bridge circuit comprises four switching tubes; the uncontrolled rectifier bridge is in a full-bridge structure and consists of four diodes;
the control process comprises the following steps:
the method comprises the following steps: sampling converter input voltage vinThe instantaneous value of (2) is obtained by a digital phase-locked loop in the DSP according to the input alternating voltage;
step two: sampling converter output voltage voWill output a voltage voIs filtered and compared with a given output voltage value vrefMaking difference, and making the output voltage error pass through PI regulator to obtain original secondary side phase-shifting angle control signal
Step three: real-time phase sigma and primary and secondary side phase shift of input voltage obtained according to digital phase-locked loopAngle control signal
Obtaining a secondary side duty ratio control signal D2：
Step four: duty ratio control signal D to primary side1Optimizing; with IZVS1The minimum current required by soft switching of the primary side switching tube and the primary side duty ratio control signal D1The following constraints are satisfied:
wherein v isrecInput voltage for a double active bridge, LrIs the inductance value of the resonant inductor, TsIn order to be the switching period of the switch,
the phase shift angle control signal of the original secondary side is used as the control signal; according to the transformer transformation ratio 1: n, M is defined as the gain of the double active bridge, and the expression is as follows:
M＝nvrec/vo(3)
wherein vo is the output voltage;
step five: and generating a PWM driving signal according to the control signal, and controlling the on and off of eight switching tubes in the main circuit to realize the control of the converter.
2. The control method for the dual active bridge single-stage AC-DC converter according to claim 1, wherein the connection relationship of the main circuit is:
from input side series inductance LacA low-pass filter is formed and then is connected with an uncontrolled rectifier bridge formed by four diodes; the output side of the uncontrolled rectifier bridge is connected with the input side of the double active bridges and is connected with a high-frequency capacitor C in parallelrecTo absorb two kinds ofHigh frequency ripple of the source bridge; the input side of the double-active bridge is a full bridge consisting of four switching tubes, the output side of the double-active bridge is a full bridge consisting of four switching tubes, and a high-frequency transformer T is arranged between the two bridgesrConnection, resonant inductance LrThe transformer is connected in series and is responsible for power transmission; output side of double active bridge and a high-frequency capacitor CohParallel connection to absorb current ripple in the switching frequency; an electrolytic capacitor ColIn parallel with the output side of the dual active bridge to reduce the voltage ripple at low frequencies.
3. A control method for a dual active bridge single stage AC-DC converter as claimed in claim 1, wherein:
the controller takes the DSP as a core and is used for converting voltage sampling signals of an input side and an output side, which are obtained by sampling of the sampling circuit;
the driving circuit is used for receiving the PWM signal from the DSP, and providing driving voltage for eight switching tubes in the main circuit after isolation and power amplification;
the sampling circuit is used for sampling to obtain voltage sampling signals of the input side and the output side of the double-active bridge.
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| CN112671250A (en) * | 2021-01-07 | 2021-04-16 | 中国科学院电工研究所 | Power electronic transformer switch control system based on direct current side capacitance resonance |
| CN112701917A (en) * | 2020-12-17 | 2021-04-23 | 大唐可再生能源试验研究院有限公司 | Method and device for reducing reactive power of converter |
| CN112803783A (en) * | 2021-03-17 | 2021-05-14 | 北京动力源科技股份有限公司 | Digital control-based direct current converter gain modulation system |
| CN112910264A (en) * | 2021-01-25 | 2021-06-04 | 深圳市斯康达电子有限公司 | Five-degree-of-freedom modulation method of double-active bridge type DC-DC converter |
| CN114977872A (en) * | 2022-05-26 | 2022-08-30 | 上海交通大学 | Bidirectional double-active-bridge micro inverter and power modulation mode switching method and system |
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| CN112803783B (en) * | 2021-03-17 | 2022-07-26 | 北京动力源科技股份有限公司 | Digital control-based direct current converter gain modulation system |
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