Switching power supplies can be categorized into different types based on various standards. When classified by output voltage, we generally recognize buck circuits (step-down), boost circuits (step-up), and buck-boost circuits (step-up/down). The flexible step-up and step-down capabilities are actually one of the major advantages switching power supplies have over linear power supplies. This article discusses the relationship between the input and output voltage regulation in switching power supplies.

The core components of a switching power supply are essentially the following four elements: active switches (MOSFET), passive switches (diodes), energy storage inductor L, and filter capacitor C. By arranging these components in different configurations, the goal of arbitrarily stepping up or down the voltage is achieved. This voltage conversion, operating in PWM mode, fundamentally alters the magnitude of voltage step-up or step-down based on the duty cycle of the switches. Below, we examine the relationship between these types of input duty cycles and the output voltage.

For many newcomers to the principles of switching power supplies, clearly describing the changes in I-t and V-t across each component at different times can be challenging. However, determining the precise output voltage magnitude from the input voltage and duty cycle is the ultimate goal of power supply design. In circuit analysis, various forms of circuits follow fundamental principles or laws, such as Ohm's Law and Kirchhoff's Laws. In the analysis of switching power supplies, the law used is the Volt-Second Balance Law.

The following describes this law: We establish the following simple circuit model to illustrate it. The switch has a duty cycle of 70%, and by adjusting the values of RLC, the stabilized waveform obtained is as follows:

According to

, it is obtained that: during the conduction period, there is

Launch

During the cutoff period there is

, introducing

According to the steady state there must be

(equal in magnitude and opposite in direction), otherwise the inductor current would trend towards increasing in one direction, making it impossible to reach a steady state. Thus, we obtain

Finally, we derive

In the above circuit, there is 0.705V * 3ns ≈ 0.301V * 7ns (with minor decimal point rounding errors). This is known as the volt-second balance law of switching power supplies, describing the relationship between voltage and conduction time during inductor turn-on and turn-off periods under steady-state conditions.

With this law, we can bypass tedious qualitative and quantitative analysis to directly obtain the output voltage of various types of switching circuits.

Below, we will analyze and verify the relatively complex buck-boost circuit, whose general form is as follows:

When the MOSFET S is turned on, since Vg will flow through the inductor to ground to store energy (the diode direction blocks the voltage), the on-time volt-second product is obtained as: Vg*Ton.

When the MOSFET S is turned off, since L releases energy to the capacitor and R (the EMF of the inductor is positive at the bottom and negative at the top), due to the direction of the diode, the voltage across the inductor is: -V0*Toff. (The negative sign indicates the opposite direction.)

According to the volt-second balance law, we have Vg*Ton=-V0*Toff, derived from the duty cycle.

Finally, the output voltage of the buck-boost circuit is obtained.

From the formula, it can be seen that when the duty cycle is less than 50%, it functions as a step-down circuit; when equal to 50%, the input and output amplitudes are the same; and when greater than 50%, it acts as a step-up circuit. Additionally, it's important to note that, regardless of the duty cycle, the directions of the output voltage and input voltage are opposite.

We can set up a rough circuit simulation with a duty cycle of 25%.

According to the formula calculation, the output voltage should be -0.25/(1-0.25)*10V=-3.33V

The simulation results are as follows: meeting the requirements

Alright, that concludes the analysis of the relatively most challenging buck-boost circuit's output voltage.