Frequency-coordinate vector diagram

From the standpoint of circuit synthesis as well as for a fundamental comprehension of circuit behavior, it is desirable to be able to visualize the response of a circuit over an extended frequency range by means of a geometrical construction. Mathematically, the response of a circuit can be expressed with the La Place transform theory as a function of the complex frequency variable, p = α + jωw, in which a is the decrement and ω is the “real” angular frequency. Physically, the nature of the real-frequency response is usually not discernible by casual inspection of the mathematical function. This paper develops a means of visualizing this frequency response readily through the construction of a vector diagram from the response function.