Straightforward Method to Design and Simulate with SPICE the Loop Compensation Controller for All Switching Power Supplies.

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

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Find Poles and Zeros of Circuit by Inspection

 Ing. Cristoforo Baldoni

 

In this article we ‘ll see how to recognize the number of poles and zeros of a transfer function simply by inspection, also of a large linear network, avoiding to calculate the analytical expression of the transfer function.  After reading this article, you ‘ll be able to determine the number of poles at first glance . Once set the output, you ‘ll also be able to determine the number of zeros by inspection and calculate the exact symbolic transfer function, the exact values of zeros and poles with simple software tool available for free. Using the SPICE analysis, we ‘ll verify the results found. The purpose of this article is to explore the concept of poles and zeros of a transfer function, their phisical meaning, and provide useful analysis tool for analog circuit designers and control systems engineers.

 

How many poles has the following network?

 

polesnetworkBig

and what about this High-Pass filter?

fiveorderHPfilter

if your answer to the first question is 9 or 8 , or you don’t recognize a fifth order filter (five poles) in the filter’s picture you should read this article.

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