This demonstration shows how a first order zero expressed as:

$$1+\frac{s}{\omega_0}=1+j\frac{\omega}{\omega_0},$$is displayed on a Bode plot. To change the value of ω_{0}, you can either enter a new value in the text box, below, or drag the vertical line showing ω_{0} on the graphs to the right. The exact values of magnitude and phase are shown as black dotted lines and the asymptotic approximations are shown with a thick magenta line. The value of ω_{0} is constrained such that 0.1≤ω_{0}≤10 rad/second.

Enter a value for ω_{o}:

The asymptotic magnitude plot starts (at low frequencies) at 0 dB and stays at that level until it gets to ω_{0} (1 rad/sec). At that point the gain starts rising with a slope of +20 dB/decade.

The asymptotic phase plot starts (at low frequencies) at 0° and stays at that level until it gets to 0.1·ω_{0} (0.1 rad/sec). At that point the phase starts rising at +45°/decade until it gets to +90° at 10·ω_{0} (10 rad/sec), at which point it becomes constant at +90° for high frequencies. Phase goes through +45° at ω=ω_{0}.

© Copyright 2005 to 2019 Erik Cheever This page may be freely used for educational purposes.

Erik Cheever Department of Engineering Swarthmore College