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?



and what about this High-Pass filter?


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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Control System Theory and SPICE Simulation

Ing. Cristoforo Baldoni

This article provides the principles for the design and analysis of Feedback and Control Systems. The Control Systems are everywhere in the modern industrial technological world, in the laser positioning of a CD Reader,  in the very high precision positioning system of an hard disk head, and even our body has a large number of biological control systems. After introducing the basic concepts, we’ll see how easily evaluate the Open loop Transfer Function with PSPice.




1.  Processes, Open Loop and Closed Loop Control Systems (Feedback Systems)


2. Generic closed loop schematic of Feedback Systems


3. Physycal Processes Modeling, differential equations and calculations simplification with Laplace transform


4. Transfer Function, Poles and Zeros of a Transfer Function, phisical meaning


5. Natural and Forced Response, calculating Residues, when it’s possible simplify identical Zeros and Poles, dominant poles


6. Process Stability


7. Steady State Error, Type of Systems


8. Study of Transfer Function with Bode diagram. Study the Open Loop Transfer Function with SPICE.


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