Power Supply Design: How to Use Bode Plots to Meet Dynamic Control Behavior Requirements

[Introduction]This article describes how to use the Bode plot to quickly assess whether your power supply design meets the dynamic control behavior requirements. The power supply usually maintains a fixed output voltage through a control loop. This control loop may or may not be stable; it may adjust quickly or slowly. In most cases, a Bode plot can be used to describe a control loop. By using the Bode plot, you can see the speed of the control loop, especially its regulation stability.

Power Supply Design: How to Use Bode Plots to Meet Dynamic Control Behavior Requirements

Figure 1. Example of a switching regulator that uses a control loop (shown in green) to regulate its output voltage

Figure 1 shows a typical switching regulator in a buck topology. It converts a higher input voltage to a lower output voltage. The goal is to regulate the output voltage VOUT as accurately as possible. To do this, a control loop is integrated into the circuit through the feedback (FB) pin. It can detect the voltage change of VOUT. The control loop should respond quickly to always regulate VOUT as accurately as possible. Whenever the input voltage or load current changes, the output voltage must be re-regulated.

Power Supply Design: How to Use Bode Plots to Meet Dynamic Control Behavior Requirements

Figure 2. Bode plot showing control loop gain (at ~80 kHz, 0 dB crossover point is reached)

Figure 2 shows the gain curve of the control loop in the Bode plot, which provides two important pieces of information. The frequency at which the gain is equal to 1 (ie 0 dB) can be obtained. For the control loop shown in Figure 2, this so-called crossover frequency occurs at about 80 kHz. As a rule of thumb, this frequency should not exceed one tenth of the set switching frequency of a switched mode power supply. Otherwise, circuit instability may result. The second important piece of information shown in the graph is the area under the gain curve, the integral of the function. The higher the DC gain and crossover frequency, the better the control loop can keep the output voltage constant.

Power Supply Design: How to Use Bode Plots to Meet Dynamic Control Behavior Requirements

Figure 3. Phase Curve of Control Loop with 60° Phase Margin

Figure 3 shows the phase curve in a Bode plot. The most important parameter value that can be read from this graph is the phase margin. The stability of the control loop can be judged by this value. The phase margin can be read from the crossover frequency in the gain plot (see Figure 2). In the example shown, the crossover frequency is 80 kHz. Therefore, the phase margin in Figure 3 is about 60°. Phase margins below about 40° are considered unstable. The control loop is well set up when the phase margin is between 40° and 70°. Within this range, the adjustment speed and stability can be better taken into account. When the phase margin is higher than 70°, the system is very stable, but the regulation speed is very slow.

Bode plots are generally not available in switching regulator data sheets. The reason is that Bode plots depend heavily on circuit design. The switching frequency used, the choice of external components (such as inductors and output capacitors), and the respective operating conditions (such as input voltage, output voltage, and load current) all have a huge impact. Therefore, Bode plots are typically generated using computational tools (eg LTpowerCAD®) or simulation tools (eg LTspice®). With the help of these tools to generate Bode plots, you can quickly determine whether the designed circuit can meet the dynamic control behavior requirements.

About the Author

Frederik Dostal studied Microelectronics at the University of Erlangen, Germany. He started his career in 2001 in the power management business and has held various applications engineer positions and spent 4 years in Phoenix, Arizona working on switch mode power supplies. He joined Analog Devices in 2009 and worked as a power management field applications engineer at Analog Devices in Munich. Contact: [email protected]

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