What’s on the Poles & Zeros poster
A definition and 6 facts worth remembering.
Poles are the roots of the denominator of H(s); zeros are the roots of its numerator.
- A pole in the right half plane means instability
- Poles on the imaginary axis oscillate forever
- Distance from the origin sets natural frequency
- Angle from the real axis sets the damping
- A zero shapes the response but cannot destabilise
- Complex poles always come in conjugate pairs
- Damping ratio 1 — Critically damped
- Below 1 — Overshoot and ringing
- Above 1 — Slow, no overshoot
- A pole pair at −1 ± j10 rings near 1.6 Hz and decays with a one-second time constant.
Stability rests on the poles alone. Zeros change the shape of the response, never whether it converges.
Questions about the Poles & Zeros poster
- What’s on the Poles & Zeros poster?
- A definition and 6 facts worth remembering. Poles are the roots of the denominator of H(s); zeros are the roots of its numerator. A pole in the right half plane means instability; Poles on the imaginary axis oscillate forever; Distance from the origin sets natural frequency; Angle from the real axis sets the damping; A zero shapes the response but cannot destabilise; Complex poles always come in conjugate pairs; Damping ratio 1 — Critically damped; Below 1 — Overshoot and ringing; Above 1 — Slow, no overshoot; A pole pair at −1 ± j10 rings near 1.6 Hz and decays with a one-second time constant.. Stability rests on the poles alone. Zeros change the shape of the response, never whether it converges.
- Who is the Poles & Zeros poster for?
- Poles & Zeros belongs to the Electrical Engineering section rather than to a school year, because engineering is not something one grade owns. Anyone learning signals & systems can pin it up — a beginner, a student mid-course, or someone revising years later.
- When should you use the Poles & Zeros poster?
- Read a pole-zero plot and you know the response before computing anything. A wall chart earns its place by being glanceable from where the work is happening, so Poles & Zeros belongs on the wall where that engineering work actually happens, within glancing distance, rather than filed away.
- What other posters go with Poles & Zeros?
- Filter Responses, Bode Plots and Convolution sit alongside Poles & Zeros in the Electrical Engineering section. Printed together they make a wall rather than a single sheet, which is how a reference set actually gets used.Filter ResponsesBode PlotsConvolution
- Is the Poles & Zeros poster free to download and print?
- Yes. Poles & Zeros downloads as a free PDF with no account, no email and no watermark, like everything else in the Electrical Engineering section. Print as many copies as you like for a home, a classroom, a library or a tutoring group; reselling the file is the only thing the licence rules out.Read the licence
- What size does the Poles & Zeros poster print at?
- Poles & Zeros is a vector PDF laid out for US Letter, and prints on A4 with Fit to page — the same file, no separate download. Because every mark on it is drawn rather than photographed, it stays sharp enlarged to A3, A2 or A1 at a copy shop. Colour carries emphasis only, so a greyscale print of Poles & Zeros loses nothing.Printing guide
Related posters
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