“Loop control is an important part of switching power supply design. However, for a variety of reasons, research is often left behind at the end of the project after major elements have been selected. Through simple trial and error analysis, we sometimes feel that if a design achieves acceptable transient response on an oscilloscope, the design is ready for production, but this thinking is very unwise and can lead to Expensive.

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Loop control is an important part of switching power supply design. However, for a variety of reasons, research is often left behind at the end of the project after major elements have been selected. Through simple trial and error analysis, we sometimes feel that if a design achieves an acceptable transient response on an oscilloscope, the design is ready for production, but this thinking is very unwise and can lead to Expensive. This is because most components used in converters are affected by stray components, the extensive effects of which are hidden during the prototyping stage. Without a thorough analysis based on simulation and loop measurements, you won’t know what the phase and gain margins look like and how reliable they are. Such loosely designed converters are likely to fail in production or shortly after powering up in the field. To avoid this, this article reviews some of the tools available today that allow you to calculate, simulate, and measure your prototypes before you start production, ensuring that production runs safely and smoothly.

**I. Introduction**

In a switching converter, the output of the power stage is controlled by a voltage variable. This type of voltage variable is referred to herein as Verr or Vc, and is provided by the compensation module responsible for maintaining the converter output within a specified range. For a converter operating at a fixed switching frequency Fsw, the control variable is the duty cycle D. But this is not always the case, some converters are controlled by a variable frequency (e.g. resonant converters such as LLC) or by a variable on or off time. This article will focus on the types of converters that operate at a fixed switching frequency.

The error voltage Verr can directly control the duty cycle, what we are talking about here is voltage mode control (VM) or direct duty cycle control. On the other hand, in current mode control (CM), the control voltage Vc fixes the Inductor peak current periodically through the sense resistor, and indirectly sets the duty cycle. However, when using an oscilloscope to Display the waveforms of a converter operating in VM or CM, you cannot tell whether the converter is operating in current mode control or voltage mode control. This is because the power stages of the two architectures are very similar, only the way the duty cycle is specified has changed: when the buck converter uses a 10V supply to supply 5V to the load, whether the system is in voltage mode control or in current mode Operating under control, the converter will theoretically have a 50% duty cycle.

As power supply designers, our goal is to build stable converters that provide precisely regulated voltage (or current), but are insensitive to operating conditions (input source changes, ambient temperature changes, different load conditions, etc.). In addition to these practical requirements, designers must also ensure that their converters will remain stable and functional throughout their lifetime. You must also account for natural production errors or component degradation due to aging. What will the margin, which is good now, look like in 5 years? If my buyer friend showed me a newer, more affordable capacitor selected from the factory, how confident would I be of my choice? “Hi Anaximander, can you confirm that a new batch of 1 million adapters will work properly if the output capacitors were selected from the B brand instead of the currently stocked A brand?” Can you answer this question boldly? If you did your homework and carefully studied the effect of parasitic capacitance on crossover frequency and phase margin, etc., then you really can. But if you didn’t do that and just turned the R and C knobs of the compensator in the lab and watched the step response, you can wipe the sweat off your forehead and you’re sure to be working late for the next few days to correct mistakes and avoid catastrophic results.

One way to avoid this dilemma is to play by the book and start with power level response. This is the only place to start: before considering possible control strategies, you need to characterize the system you want to control. What you need is to determine how the output variable responds to changes in the control input. In other words, you need the control-to-output transfer function of the buck or boost converter you are building: how Vout dynamically responds to the excitation specified in Verr (Figure 1). That is, how does the device respond?

Figure 1: We want the dynamic response of the power stage.

Once you have the transfer function amplitude-phase diagram, you can consider compensation strategies (ie, placing poles, zeros, and gain (or attenuation) at different frequency locations) to meet your design goals. This is the example shown in Figure 2. D1

When building a compensator, there are several approaches to follow, as shown in Figure 3. The classical approach, which is abundantly described in the literature, uses an op amp to build the filter, since the compensator is an active filter. However, the TL431 is primarily used in the industry, and you can find traces of it in the vast majority of adapters sold on the market today. I’ll admit it’s unsurpassed by other methods in terms of simplicity or cost: you can get an op amp with a moderately high open-loop gain (55 dB) and an accurate 2.5 V reference for just a few cents, and the TLV version’s Vref is as low as 1.24 V. The part is available in a number of different packages, and some versions can accept voltages up to 36 V. However, choosing this device brings other issues related to fast and slow channels.

Figure 2: You insert poles and zeros through a compensator and create the desired frequency response.

Alternatively, a transconductance operational amplifier (OTA) can be used for compensation purposes. IC designers prefer to use OTAs because they take up less silicon area than their op amp counterparts. I personally don’t like OTA very much because op amp based compensators provide virtual ground while OTA based ones don’t. In addition, the resistor divider ratio also affects the pole/zero placement.

Figure 3: There are a variety of active components to choose from when designing a compensator.

OTA is popular in power factor correction (PFC) applications and is ideal for implementing compensators with modest phase margin boost. If you intend to use it for applications that require high phase margin boost, you may hit an upper limit on the Vout/Vref ratio.

The phase margin boost is the amount of extra phase that the compensator compensates for to meet the phase margin goal, typically a number greater than 45°. From Figure 4, you can see that the power stage has a phase lag of 90° or 145° at some selected frequencies f1 and f2. If the loop is closed using a standard integrator with a fixed 270° hysteresis, the sum of the hysteresis of these two factors at the f1 frequency is -360° or 0°: the signal returns in phase at the injection point and the condition for continuous oscillation is satisfied . This is not what you want unless your goal is to build an oscillator. Now, if you force a crossover at f2, the phase margin is negative, that is, the closed-loop pole is on the right half-plane: the system is unstable. You can solve this problem by implementing phase margin boosting at the f1 or f2 frequencies. By placing the poles and zeros in the compensator, you can adjust its phase response so that it is no longer fixed at -270°, but lower. When combined with the device response, the total parameter or phase will now be less than -360°, resulting in the phase margin required for stabilization.

Figure 4: The device phase is added to the compensator phase so that the total phase lag is below -360°.

We can identify three types of compensators, called types 1, 2, and 3, as shown in Figure 5. Type 1 contains the origin pole: it is the integrator represented by the following transfer function:

There is no phase margin boost, and the phase is the phase of the inverting op amp structure (-180°) plus the phase of the origin pole (-90°), so the final parameter is -270° or 90°.

The second type is commonly found in current-mode control designs where the desired phase margin boost is less than 90°. It contains the origin pole as well as a pole and a zero. In theory, the origin pole (s=0) can eliminate the static error (the deviation between the target DC supply and the DC supply when the loop is closed). This pole is present in the vast majority of compensators, but there are also techniques (such as so-called output resistor shaping) that deliberately ignore this pole and accept a small deviation.

Figure 5: You can implement compensation strategies using these three configurations.

In type 2, the zeros are located before the poles, causing the phase to increase with frequency. The pole comes later, and the phase margin is lifted back to zero. By spreading the zeros and poles, you can adjust the phase margin boost as needed, up to 90°. Note that if the pole and zero coincide, the compensator becomes Type 1 again, with the phase margin raised to 0°.

The transfer function described in this structure is as follows:

You can see that there is an inverse zero in the numerator, so factoring by G0 with a gain dimension.

Finally, Type 3 compensators add another pair of pole-zeros to Type 2 and can boost phase up to 180°. This can be described by the following expression:

If we now use a circuit of type 3 for G(s), instead of the pure integrator in the example of Figure 4, and boost the phase by 125°, the total loop phase is now offset by 0° or -360°, And we would have a 70° margin (Figure 6).

From the power stage lag and the required phase margin, jm, we can derive a formula that relates to the amount of phase margin boost required. We all know that an inverting op amp and a pole at the origin cause a 270° lag, plus the phase of the power stage characterized by the chosen crossover frequency fc. Adding these numbers together should give the result a phase margin away from the -360° limit. Therefore, we can write:

By solving for the lift value, we get:

From this number, we can deduce the type of compensator to use:

1. No Lifting Required: Type 1. Applies to discontinuous conduction mode converters and, to some extent, PFC stages as well.

2. Up to 90°: Type 2. Commonly used in current-mode control converters (eg, flyback and PFC stages).

3. Over 90° but less than 180°: Type 3. Typically used for voltage mode controlled converters operating in continuous conduction mode (CCM).

Figure 6: The phase margin is currently 70°, so consider a 3rd type of compensator.

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