Topology of switching power supply (IV)

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Topology of switching power supply (IV) [Copy link]

Power unit operating mode

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In all the power topologies discussed so far, it is assumed that the current in the magnetic components flows continuously during the operation of the switch tube. However, this is not always the case. Going back to the simple single-switch Buck circuit, there are three different current conduction modes, as shown in the figure below.

The Buck circuit in this figure depicts the waveforms of the inductor current in three conditions, that is, the three current conduction modes. In a specific design, the inductor current is a function of the output load.

Now we know that the inductor current increases during the on-time of the switch tube, and decreases when the switch tube is turned off and the rectifier tube is freewheeling. The output capacitor averages this ramp current to provide a relatively constant current to the load. If the input voltage is fixed, the rising slope of the inductor current is also fixed, and if the output voltage is unchanged, its falling slope is also fixed. These waveforms are all drawn with the load current as a variable.

The top waveform has a relatively high average current value, with current always flowing, and it alternately rises to _{ILMAX and then falls to ILMIN} . Of course _, this mode of operation is called "continuous conduction mode," or CCM for short.

The middle current waveform is a special form of CCM, which occurs when the load current decreases to a lower value, causing I _LMIN to reach zero. This is still CCM, but since it is a special form, we give it a different name, namely "critical conduction mode" (CRM) or "transition mode" because it characterizes the transition between continuous and discontinuous modes.

This brings us to the third state, “discontinuous conduction mode” (DCM), where the load current drops to a lower average value. Here, the downward slope of the inductor current has reached zero and remains for a period of time, forming a dead zone, hence the name “discontinuous”.

The voltage regulator is a control system with closed-loop feedback. To keep the circuit stable under all operating conditions, including load changes, the operating characteristics of CCM and DCM are different. When the circuit operates in CCM mode, the duty cycle is a linear function of the input voltage, and the control loop can perform continuous control:

But when the circuit enters DCM, the inductor current and the voltage across the inductor both reach zero, and the loop no longer works. The duty cycle relationship now becomes a nonlinear relationship:

The practical result is that the system may become unstable when crossing the DCM boundary, or, equally problematically, the low control gain severely degrades the responsiveness to rapid load changes. To ensure that the system always operates in CCM, a fixed minimum load should always exist, and the critical load current needs to be as follows:

We will further discuss the case of using synchronous rectifiers in later chapters.

But on the other hand, for DCM circuits, the state is known at the beginning of each cycle, so feedback compensation is much easier. Therefore, there is a class of circuits designed to always remain in DCM, usually with fixed on-time and variable frequency, so they have natural stability. This control method, at light load, can reduce the switching frequency and switching loss because the off time can be extended, thereby achieving high efficiency.

Before leaving this topic, there is another type of circuit designed to operate in critical conduction mode (CRM), where the control circuit detects the inductor current and turns on the switch tube immediately when the inductor current reaches zero. The advantage provided by CRM is that when the inductor current becomes zero, the current in the rectifier diode is also zero, so the transient reverse recovery current of the diode is minimized. However, the need to control the on and off time at the same time makes it impossible to maintain a constant switching frequency, which will cause other design problems.

Right half plane zero

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We will discuss the definition and significance of poles and zeros in more detail later in the chapter on closed-loop feedback, but there is a term that is often used in relation to power topologies: the "right half plane zero" (RHPZ). In small signal frequency compensation, poles and zeros are usually located in the left half of the complex plane. A left half plane pole will cause gain reduction and phase lag, while a zero will do the opposite, causing gain increase and phase advance. The problem with an RHPZ is that its effect is to increase gain (similar to a traditional zero), but with a phase lag. This characteristic is troublesome to compensate for (and is generally difficult to compensate for), and it usually causes the overall loop gain to roll off at relatively low frequencies.

RHPZ does not occur in the Buck series circuit, it only appears in the Boost and Flyback topologies, and only when the circuit operates in continuous conduction mode (CCM) and constant switching frequency. This is caused by the half-cycle delay of energy transfer from input to output (energy needs to be stored before release), which can be simply explained by the following two pictures:

In both topologies, when the switch is turned on, energy is first stored in the inductor for a period of time DxT , and when the switch is turned off, energy is transferred to the output (and output capacitor) for a period of time (1-D)×T . Considering CCM operation, the inductor current is continuous. If our load current suddenly increases slightly, the first response is that the input end will increase energy, which will increase the duty cycle (D) by a certain amount (d), as shown in the waveform shown in the figure below.

Although the increase in duty cycle will increase the average inductor current in the first few switching cycles, the initial result is that as D increases, (1-D) decreases accordingly, so that the energy actually output through the diode is reduced. After a few switching cycles, the increased inductor current will eventually cause the average output current to reach the new required value, and even if the inductor current responds immediately in a positive direction, there will be a lag.

Mathematically, it can be deduced that RHPZ is a nonlinear function on the frequency curve, which is related to the duty cycle and load impedance. Specifically:

Remember that RHPZ is a problem specific to CCM. In DCM, all the energy stored in the inductor is delivered to the load in every cycle, so the average output current always corresponds to the peak value of each pulse.