# Find Poles and Zeros of a Circuit by Inspection

Ing. Cristoforo Baldoni

In this article, focused on ‘Poles and Zeros of a Circuit‘, we will explore the technique of identifying the count of poles and zeros within a transfer function, including those in complex linear networks, solely through visual inspection. This method obviates the need for calculating the analytical expression of the transfer function. By the conclusion of this article, you will have the capability to swiftly determine the number of poles upon initial examination.

Once the output is established, this approach also enables you to ascertain the quantity of zeros through inspection and subsequently compute the precise symbolic form of the transfer function. Additionally, you can calculate the exact values of both zeros and poles employing user-friendly software tools readily accessible for free. We will validate the findings using SPICE analysis.

The primary objective of this article is to delve into the concepts of poles and zeros within a transfer function, elucidating their physical significance. Furthermore, we aim to furnish valuable analytical tools to aid analog circuit designers and control systems engineers in their endeavors.

How many POLES does this circuit have?

And how many does this high-pass filter have?

If your response to the initial question is 9 or 8, or if you do not identify a fifth-order filter (with five poles) in the filter’s illustration, then you should proceed to read this article.

# Control Systems using SPICE Simulation.

Ing. Cristoforo Baldoni

Exploring the domain of Control Systems using SPICE Simulation, this article offers essential principles for designing and analyzing Feedback and Control Systems. Control Systems theory, a cornerstone of engineering and automation, involves the study of dynamic systems and their manipulation to achieve desired outcomes. These systems are omnipresent in our modern industrial technological world, seamlessly integrated into everyday devices. They play a vital role in processes as diverse as the precise positioning of a Reader’s laser, the intricate control of a hard disk head’s movement, and even the numerous biological control systems orchestrating our bodily functions.

Control Systems theory involves understanding how systems respond to various inputs and disturbances, and how to design controllers that shape these responses to achieve desired goals. These goals can include stability, accuracy, speed, and overall performance optimization. Whether it’s managing the temperature of an oven, stabilizing the flight of an aircraft, or controlling the speed of a motor, the principles of Control Systems theory provide the framework to analyze, design, and optimize these dynamic processes.

As we navigate through this article, we’ll begin by introducing the basic concepts that underpin Control Systems theory. From there, we’ll seamlessly transition into exploring how these theories come to life through the application of SPICE simulation. Our journey includes the evaluation of the Open Loop Transfer Function using the versatile tool of PSPice, providing hands-on insights into the practical implementation of control strategies. Whether you’re a novice eager to comprehend the foundations or an enthusiast seeking to refine your expertise, this article offers a holistic perspective on the symbiotic relationship between Control Systems theory and the power of SPICE Simulation.

Topics Covered:

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 Laplace Transform Simplification.

4. Transfer Function: Understanding Poles, Zeros and their Phisical Significance.

5. Natural and Forced Response: Residues Calculation, Simplification of identical Zeros and Poles, Dominant Poles.

6. Process Stability.

7. Steady State Erro and Systems Types.

8. Transfer Function through Bode Diagram Analysis. Examination of the Open Loop Transfer Function using SPICE Simulation.