CN107482912A - A Method of Improving the Stability of Buck Circuit in Peak Current Mode Based on K Factor - Google Patents
A Method of Improving the Stability of Buck Circuit in Peak Current Mode Based on K Factor Download PDFInfo
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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
- H02M3/02—Conversion of DC power input into DC power output without intermediate conversion into AC
- H02M3/04—Conversion of DC power input into DC power output without intermediate conversion into AC by static converters
- H02M3/10—Conversion of DC power input into DC power output without intermediate conversion into AC by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
- H02M3/145—Conversion of DC power input into DC power output without intermediate conversion into AC by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal
- H02M3/155—Conversion of DC power input into DC power output without intermediate conversion into AC by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only
- H02M3/156—Conversion of DC power input into DC power output without intermediate conversion into AC by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only with automatic control of output voltage or current, e.g. switching regulators
- H02M3/158—Conversion of DC power input into DC power output without intermediate conversion into AC by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only with automatic control of output voltage or current, e.g. switching regulators including plural semiconductor devices as final control devices for a single load
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Abstract
基于k因子提高峰值电流模式的Buck电路稳定性的方法，涉及提高Buck电路稳定性的方法，为了解决采用峰值电流模式的Buck电路的稳定性低不能满足实际需求的问题。该方法包括以下步骤：基于MATLAB仿真Buck电路的补偿网络，得到伯德图；根据实际需求，基于k因子在伯德图中添加零点和极点；基于MATLAB得到补偿网络的传递函数；根据传递函数计算补偿网络中各元件的参数；根据所得参数设计补偿网络。本发明适用于提高峰值电流模式的Buck电路的稳定性。
A method for improving the stability of a Buck circuit in a peak current mode based on a k factor relates to a method for improving the stability of a Buck circuit, in order to solve the problem that the stability of a Buck circuit using a peak current mode is low and cannot meet actual needs. The method comprises the following steps: simulating the compensation network of the Buck circuit based on MATLAB to obtain a Bode diagram; adding zeros and poles to the Bode diagram based on the k factor according to actual needs; obtaining the transfer function of the compensation network based on MATLAB; calculating according to the transfer function The parameters of each component in the compensation network; design the compensation network according to the obtained parameters. The invention is suitable for improving the stability of the Buck circuit in the peak current mode.
Description
技术领域technical field
本发明涉及提高Buck电路稳定性的方法。The invention relates to a method for improving the stability of a Buck circuit.
背景技术Background technique
在家用电器及工业生产等场合，需要将工频交流电转换成直流电然后加以利用。非隔离式Buck电路作为DC-DC的基本拓扑，由于结构简单，成本低廉，在以上场合有着广泛的应用。采用峰值电流控制Buck电路，相比于平均电流模式，它具有能有效防止偏磁、补偿网络简单、稳定性强等优点。电流型Buck电路包含两个反馈环：由接受输出电压采样信号的误差放大器构成的电压外环和一个由接收回路峰值电流采样信号的PWM比较器构成的电流内环。与电压模式不同的是，电流模式Buck电路直接对输出电流峰值进行控制，具有响应快，防止偏磁导致磁饱和，补偿网络简单等优点。但是采用峰值电流模式的Buck电路的稳定性制约了其发展，如何提高采用峰值电流模式的Buck电路的稳定性成为亟需解决的问题。In occasions such as household appliances and industrial production, it is necessary to convert power frequency alternating current into direct current and then utilize it. As the basic topology of DC-DC, the non-isolated Buck circuit is widely used in the above occasions due to its simple structure and low cost. Using the peak current control Buck circuit, compared with the average current mode, it has the advantages of effectively preventing bias, simple compensation network, and strong stability. The current mode Buck circuit contains two feedback loops: the voltage outer loop formed by the error amplifier receiving the output voltage sampling signal and the current inner loop formed by the PWM comparator receiving the loop peak current sampling signal. Different from the voltage mode, the current mode buck circuit directly controls the peak value of the output current, which has the advantages of fast response, preventing magnetic saturation caused by bias magnetism, and simple compensation network. However, the stability of the Buck circuit using the peak current mode restricts its development, and how to improve the stability of the Buck circuit using the peak current mode has become an urgent problem to be solved.
发明内容Contents of the invention
本发明的目的是为了解决采用峰值电流模式的Buck电路的稳定性低不能满足实际需求的问题，从而提供基于k因子提高峰值电流模式的Buck电路稳定性的方法。The purpose of the present invention is to solve the problem that the stability of the Buck circuit using the peak current mode is low and cannot meet the actual demand, thereby providing a method for improving the stability of the Buck circuit in the peak current mode based on the k factor.
本发明所述的基于k因子提高峰值电流模式的Buck电路稳定性的方法，该方法包括以下步骤：The method for improving the stability of the Buck circuit of the peak current mode based on the k factor of the present invention comprises the following steps:
基于MATLAB仿真Buck电路的补偿网络，得到伯德图；Based on the MATLAB simulation of the compensation network of the Buck circuit, the Bode diagram is obtained;
根据实际需求，基于k因子在伯德图中添加零点和极点；According to actual needs, add zeros and poles in the Bode diagram based on the k factor;
基于MATLAB得到补偿网络的传递函数；The transfer function of the compensation network is obtained based on MATLAB;
根据传递函数计算补偿网络中各元件的参数；Calculate the parameters of each component in the compensation network according to the transfer function;
根据所得参数设计补偿网络。Design the compensation network according to the obtained parameters.
优选的是，补偿网络包括电阻R1、电阻R2、电容C1、电容C2和误差放大器；Preferably, the compensation network includes a resistor R1, a resistor R2, a capacitor C1, a capacitor C2 and an error amplifier;
电阻R1的一端作为电压反馈信号输入端，电阻R1的另一端与电阻R2的一端和电容C2的一端相连，电阻R1、电阻R2、电容C2的公共端与误差放大器的反相输入端相连，电阻R2的另一端与电容C1的一端相连，电容C1的另一端、电容C2的另一端和误差放大器的输出端相连，并作为误差信号的输出端，误差放大器的同向输入端接+2.5V电压。One end of resistor R1 is used as the input end of the voltage feedback signal, the other end of resistor R1 is connected to one end of resistor R2 and one end of capacitor C2, the common end of resistor R1, resistor R2, and capacitor C2 is connected to the inverting input end of the error amplifier, and the resistor The other end of R2 is connected to one end of capacitor C1, the other end of capacitor C1 and the other end of capacitor C2 are connected to the output end of the error amplifier, and are used as the output end of the error signal, and the same input end of the error amplifier is connected to +2.5V voltage .
本发明所述的基于k因子提高峰值电流模式的Buck电路稳定性的方法，基于MATLAB仿真软件，通过在伯德图中添加零点和极点，得到元件的参数，最终得到满足需要的Buck电路稳定性，本发明的方法操作简单、便于实现。The method for improving the stability of the Buck circuit in the peak current mode based on the k factor of the present invention is based on MATLAB simulation software, by adding zeros and poles in the Bode diagram to obtain the parameters of the components, and finally obtain the stability of the Buck circuit that meets the needs , the method of the present invention is simple and easy to implement.
本发明适用于提高峰值电流模式的Buck电路的稳定性。The invention is suitable for improving the stability of the Buck circuit in the peak current mode.
附图说明Description of drawings
图1是具体实施方式一所述的基于k因子提高峰值电流模式的Buck电路稳定性的方法的流程图；Fig. 1 is the flow chart of the method for improving the Buck circuit stability of the peak current mode based on the k factor described in the first embodiment;
图2是具体实施方式一中未校正时得到的伯德图；Fig. 2 is the Bode diagram obtained when not corrected in the specific embodiment one;
图3是具体实施方式一中校正后得到的伯德图；Fig. 3 is the Bode diagram obtained after correction in the specific embodiment one;
图4是具体实施方式二中的补偿网络的结构示意图。Fig. 4 is a schematic structural diagram of the compensation network in the second embodiment.
具体实施方式detailed description
具体实施方式一：结合图1至图3具体说明本实施方式，本实施方式所述的基于k因子提高峰值电流模式的Buck电路稳定性的方法，该方法包括以下步骤：Embodiment 1: This embodiment is specifically described in conjunction with FIGS. 1 to 3 . The method for improving the stability of a Buck circuit in peak current mode based on the k factor described in this embodiment includes the following steps:
基于MATLAB仿真Buck电路的补偿网络，得到伯德图；Based on the MATLAB simulation of the compensation network of the Buck circuit, the Bode diagram is obtained;
根据实际需求，基于k因子在伯德图中添加零点和极点；According to actual needs, add zeros and poles in the Bode diagram based on the k factor;
基于MATLAB得到补偿网络的传递函数；The transfer function of the compensation network is obtained based on MATLAB;
根据传递函数计算补偿网络中各元件的参数；Calculate the parameters of each component in the compensation network according to the transfer function;
根据所得参数设计补偿网络。Design the compensation network according to the obtained parameters.
k因子指出了由补偿网络产生的零点频率和极点频率之间需要分开的距离，然后通过选择期望的截止频率fc和fc处所需的相位裕度，k因子自动放置零点和极点，使fc等于零点频率和极点频率的几何平均值，并在fc处有最高的相位提升。k因子法中，交叉频率处产生的相位提升会随k值的不同而不同。k＝1时，极点和零点占据同一位置，相位提升为0。k增加，极点和零点的距离增加，在fc处提供的相位提升也随之增加。增加相位提升值是以降低直流增益为代价的。The k-factor indicates the distance that needs to be separated between the zero frequency and the pole frequency produced by the compensation network, then by selecting the desired cutoff frequency fc and the required phase margin at fc, the k-factor automatically places the zero and pole such that fc equals zero The geometric mean of the dot and pole frequencies, with the highest phase boost at fc. In the k-factor method, the phase boost produced at the crossover frequency varies with the value of k. When k=1, the pole and zero occupy the same position, and the phase is raised to 0. As k increases, the distance between poles and zeros increases, and so does the phase boost provided at fc. Increasing the phase boost value comes at the expense of decreasing DC gain.
假设零点频率为fc/k，极点频率为kfc，则在fc处得相位提升Boost为：Assuming that the zero frequency is fc/k and the pole frequency is kfc, then the phase boost Boost at fc is:
其中fz0为零点频率，fp0为极点频率；Where f z0 is the zero frequency and f p0 is the pole frequency;
由三角函数关系可知：From the relationship of trigonometric functions, we know that:
由上式得到：Obtained from the above formula:
Boost＝arctan(k)-90°+arctan(k)＝2*arctan(k)-90° (3)Boost＝arctan(k)-90°+arctan(k)＝2*arctan(k)-90° (3)
由此得到：From this we get:
系统的相对稳定性通常通过相角裕度r以及增益裕度Kg来衡量。一般相角裕度在30度至60度之间，增益裕度应大于6dB。中频宽与超调量有关，中频宽h越大，超调量越小。低频增益K决定了稳态误差，低频增益越大，稳态误差越小。截止频率fc决定了系统的响应速度，fc越大，系统响应越快。The relative stability of the system is usually measured by the phase angle margin r and the gain margin Kg. Generally, the phase angle margin is between 30 degrees and 60 degrees, and the gain margin should be greater than 6dB. The intermediate bandwidth is related to the overshoot, the larger the intermediate bandwidth h, the smaller the overshoot. The low-frequency gain K determines the steady-state error, the larger the low-frequency gain, the smaller the steady-state error. The cut-off frequency fc determines the response speed of the system, the larger the fc, the faster the system response.
本实施方式中开关频率fs为80kHz，为避免开关器件带来的高频噪声，系统带宽应小于fs/10，即8kHz。通常要求截止频率要大于系统有效信号的5～10倍。另外，Buck电路输出滤波电容与电感构成滤波器的谐振In this embodiment, the switching frequency fs is 80 kHz. In order to avoid high-frequency noise caused by switching devices, the system bandwidth should be less than fs/10, that is, 8 kHz. Usually the cutoff frequency is required to be 5 to 10 times greater than the effective signal of the system. In addition, the Buck circuit output filter capacitor and inductor constitute the resonance of the filter
通常设计截止频率要大于10f0，f0为谐振频率，所以系统带宽合理的取值范围为1.6kHz<fc<8kHz，选为4kHz。 Usually the design cut-off frequency is greater than 10f0, and f0 is the resonant frequency, so the reasonable value range of the system bandwidth is 1.6kHz<fc<8kHz, and 4kHz is selected.
在伯德图中添加零点和极点后，得到相应状态下补偿网络的传递函数。After adding zeros and poles in the Bode diagram, the transfer function of the compensation network in the corresponding state is obtained.
由图2可知，未进行校正时，系统带宽仅为20Hz。频率4kHz处，系统增益为-32dB，相位裕度为-18.7°。由图3可知，校正后，系统带宽为3.93kHz，系统截止频率为4kHz，相位裕度为80°，中频宽h为11.6，系统增益大大提高，校正后满足了设计需求。图2和图3的坐标相同，横坐标均为频率(Hz)，纵坐标分别为幅值(dB)和相角(°)。It can be seen from Figure 2 that the system bandwidth is only 20Hz without correction. At a frequency of 4kHz, the system gain is -32dB and the phase margin is -18.7°. It can be seen from Figure 3 that after correction, the system bandwidth is 3.93kHz, the system cutoff frequency is 4kHz, the phase margin is 80°, the intermediate frequency width h is 11.6, the system gain is greatly improved, and the design requirements are met after correction. The coordinates in Fig. 2 and Fig. 3 are the same, the abscissa is frequency (Hz), and the ordinate is amplitude (dB) and phase angle (°) respectively.
具体实施方式二：结合图4具体说明本实施方式，本实施方式是对具体实施方式一所述的基于k因子提高峰值电流模式的Buck电路稳定性的方法作进一步说明，本实施方式中，补偿网络包括电阻R1、电阻R2、电容C1、电容C2和误差放大器；Specific embodiment two: This embodiment is described in detail in conjunction with FIG. 4. This embodiment is a further description of the method for improving the stability of the Buck circuit in peak current mode based on the k factor described in specific embodiment one. In this embodiment, the compensation The network includes resistor R1, resistor R2, capacitor C1, capacitor C2 and error amplifier;
电阻R1的一端作为电压反馈信号输入端，电阻R1的另一端与电阻R2的一端和电容C2的一端相连，电阻R1、电阻R2、电容C2的公共端与误差放大器的反相输入端相连，电阻R2的另一端与电容C1的一端相连，电容C1的另一端、电容C2的另一端和误差放大器的输出端相连，并作为误差信号的输出端，误差放大器的同向输入端接+2.5V电压。One end of resistor R1 is used as the input end of the voltage feedback signal, the other end of resistor R1 is connected to one end of resistor R2 and one end of capacitor C2, the common end of resistor R1, resistor R2, and capacitor C2 is connected to the inverting input end of the error amplifier, and the resistor The other end of R2 is connected to one end of capacitor C1, the other end of capacitor C1 and the other end of capacitor C2 are connected to the output end of the error amplifier, and are used as the output end of the error signal, and the same input end of the error amplifier is connected to +2.5V voltage .
补偿网络的传递函数为 The transfer function of the compensation network is
其中，R1为电阻R1的阻值、R2为电阻R2的阻值、C1为电容C1的电容值、C2电容C2的电容值，该补偿网路在系统附加了一个零点与一个极点，通过积分的作用提高了稳态增益。Among them, R 1 is the resistance value of resistor R1, R 2 is the resistance value of resistor R2, C 1 is the capacitance value of capacitor C1, and C 2 is the capacitance value of capacitor C2. This compensation network adds a zero point and a pole to the system , which increases the steady-state gain through the action of the integral.
对于本领域技术人员而言，显然本发明不限于上述示范性实施例的细节，而且在不背离本发明的精神或基本特征的情况下，能够以其他的具体形式实现本发明。因此，无论从哪一点来看，均应将实施例看作是示范性的，而且是非限制性的，本发明的范围由所附权利要求而不是上述说明限定，因此旨在将落在权利要求的等同要件的含义和范围内的所有变化囊括在本发明内。It will be apparent to those skilled in the art that the invention is not limited to the details of the above-described exemplary embodiments, but that the invention can be embodied in other specific forms without departing from the spirit or essential characteristics of the invention. Accordingly, the embodiments should be regarded in all points of view as exemplary and not restrictive, the scope of the invention being defined by the appended claims rather than the foregoing description, and it is therefore intended that the scope of the invention be defined by the appended claims rather than by the foregoing description. All changes within the meaning and range of equivalents of the elements are embraced in the present invention.
虽然在本文中参照了特定的实施方式来描述本发明，但是应该理解的是，这些实施例仅仅是本发明的原理和应用的示例。因此应该理解的是，可以对示例性的实施例进行许多修改，并且可以设计出其他的布置，只要不偏离所附权利要求所限定的本发明的精神和范围。应该理解的是，可以通过不同于原始权利要求所描述的方式来结合不同的从属权利要求和本文中所述的特征。还可以理解的是，结合单独实施例所描述的特征可以使用在其他所述实施例中。Although the invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely illustrative of the principles and applications of the invention. It is therefore to be understood that numerous modifications may be made to the exemplary embodiments and that other arrangements may be devised without departing from the spirit and scope of the invention as defined by the appended claims. It shall be understood that different dependent claims and features described herein may be combined in a different way than that described in the original claims. It will also be appreciated that features described in connection with individual embodiments can be used in other described embodiments.
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| 姜述国: "一种用于短距离无线接收系统的多模式降压PWM调整直流变换器的设计", 《中国优秀硕士学位论文全文数据库 工程科技Ⅱ辑》 * |
| 张实: "一种高效率的电流型Buck DC-DC变换器的分析与设计", 《中国优秀硕士学位论文全文数据库 工程科技Ⅱ辑》 * |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111669050A (en) * | 2019-03-05 | 2020-09-15 | 东南大学 | Compensation method, device and Buck circuit for Buck circuit |
| CN111669050B (en) * | 2019-03-05 | 2023-05-23 | 东南大学 | Compensation method and device for Buck circuit and Buck circuit |
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Application publication date: 20171215 |