Ing. Cristoforo Baldoni

In this article we ‘ll see how to find the output power stage transfer function H(s), called the Control-to-Output function, of the most switching power supplies: **BUCK, BOOST, BUCK-BOOST, HALF-BRIDGE, FULL BRIDGE**, both in voltage mode control and current mode control. In spite of the complexity of the different types of power supplies that use one or more output feedback, the output power transfer function H(s), can be reduced to a few schematic categories of general validity. We’ ll see when it’s the case to consider the effects of the **RHPZ**, the Right Half Plane Zero, and what it means in practical terms.

Once the components for the specific power supply have been sized, we can estimate with good approximation the transfer function which describes mathematically the output power stage. As seen in the article about the determination of **POLES** and **ZEROS** by inspection, we ‘ll identify immediately the **POLES** and **ZEROS** which characterize the different switching categories.

We ‘ll draw the Bode plots of these functions with PSpice, and, according to their characteristics, we ‘ll choose the most suitable compensator G(s), implementing the compensation network with the operational amplifiers embedded in the microcontrollers. The SPICE simulation of the open loop transfer function G(s)*H(s), will allows us to evaluate the results for the system stability. Finally, we ‘ll apply this method in two real switching power supply: a low power flyback converter and an off-line, half-bridge switching.

This method allows us to speed up the design of the compensator G(s) in the prototyping phase before the physical measurement with the instrumentation.

It’s strongly recommended the reading of these articles:

Accessing this article you can download the following SPICE simulation files about switching power supply compensation design:

-Forward function example

-Flyback function example

-Flyback function example with a Right Half Plane ZERO

-Origin POLE compensator

-Origin POLE Transfer function implementation

-Forward function compensated example

-One ZERO two POLES compensator

-One ZERO two POLES Transfer Function Implementation

-Flyback with RHPZ compensated

-Three POLES two ZEROS compensator

-Three POLES two ZEROS Transfer Function

-Transfer function of a real Flyback converter

-Compensator for the flyback converter

-Overall compensated transfer function of the flyback converter

-Transfer function of a real Forward converter

-Compensator for the Forward converter

-Transfer function of compensator for the Forward converter

-Overall compensated transfer function of the Forward converter