# Asymptotic Bode: First Order Pole

This demonstration shows how a first order pole expressed as:

$$\frac{1}{1+\frac{s}{\omega_0}}=\frac{1}{1+j\frac{\omega}{\omega_0}},$$

is displayed on a Bode plot. To change the value of ω0, you can either change the value in the text box, below, or drag the vertical line showing ω0 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 ω0 is constrained such that 0.1≤ω0≤10 rad/second.

Enter a value for ωo:

The asymptotic magnitude plot starts (at low frequencies) at 0 dB and stays at that level until it gets to ω0 (1 rad/sec). At that point the gain starts dropping 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·ω0 (0.1 rad/sec). At that point the phase starts dropping at -45°/decade until it gets to -90° at 10·ω0 (10  rad/sec), at which point it becomes constant at -90° for high frequencies. Phase goes through -45° at ω=ω0.

References