Add a single-pole and single-zero PI compensation network

The PI compensation network with a single pole and a single zero is called a single pole and a single zero compensation network in some literature. Figure 1 (a) shows the circuit diagram of the PI network with a single pole and a single zero. In the figure, Z1 (s) = R1, z2 (s) = (1/sC ∥ CR2 + 1/sC2). The symbol ∥ indicates parallel connection. Therefore, the transfer function of the PI compensation network with a single pole and a single zero is

In addition to the pole s=0 generated by the integrator 1/s, there is a zero point -1/TZ and a pole -1/TP, both located in the left half S plane.

Figure 1 (b) shows the amplitude-frequency and phase-frequency characteristics of the PI network with a single pole and a single zero. In the example, the zero frequency fz is 505Hz and the pole frequency fp is 50kHz.

Figure 1: PI compensation network with single pole and single zero added

Figure 2 shows the effect of compensation using this network (whose amplitude-frequency characteristic is |Κ|). The object of adjustment is a Buck switch taking into account the capacitor ESR.

Figure 2 Bode diagram of Buck switching power supply after compensation using single-pole, single-zero PI compensation network

The converter has an ESR zero point. After adding a single-pole and single-zero Pi network, the open-loop transfer function T of the Buck switching power supply has an ideal amplitude-frequency characteristic |T0|. The low-frequency band has high gain, the mid-frequency band crosses the 0dB line at a rate of -1 to ensure system stability, and the high-frequency band decays rapidly.