## Feedback Loops Made Easy

Feedback loops are everywhere and are necessary to make circuits and systems behave the way we want them to.  Understanding feedback loops and how to stabilize them is a subject many relegate to the "black arts" of engineering.  Venable Instruments has spent the last forty years demystifying the subject, so that anyone can understand what is going on with their system and compensate it (create a feedback loop) that results in a system that performs as desired.

Venable has primarily worked with power supply designers and engineers, providing solutions tailored to their needs.  In reality, anyone that is trying to design and implement a feedback loop will benefit from Venable's Frequency Response Analyzers and Stability Analysis Software.  Venable's K Factor Analysis is a straightforward method for specifying and acheiving desired closed loop performance.

## Breaking It Down

#### The Plant

Understanding the plant (Modulator) to be compensated is the first step. Venable Instruments' Frequency Response Analyzers will reveal the plant's transfer function as a graph of gain versus frequency (Bode plot).

#### Type 1, 2 or 3 Compensation?

Once the plant is revealed, the designer can choose the type of compensation required and specify the gain and phase margins.  From there, Venable's Stability Analysis Software will generate the feedback circuit, including specifying component values.

#### Simulate it!

Now that the feedback circuit is designed, simulate the closed loop performance.  Venable's Stability Analysis Software uses the measured plant transfer function and newly created compensation to show the overall loop gain.

#### Validation

The final step is to validate the plant and compensation performance by measuring the physical implementation.  Venable's FRA and Stability Analysis Software allows you to compare the simulated loop gain to that which has been measured.

## The K Factor: A New Mathematical Tool for Stability Analysis and Synthesis

This paper presents a new mathematical concept that is simple but powerful.  The techniques described allow synthesis of a feedback amplifier circuit (for plant compensation) with a few algebraic equations to obtain any desired crossover frequency and phase margin (within reason) on the first try.