# Why $s/(1-s) = 1$ at $s=1$ in bode plot?

Wolfram plot of $\frac{s}{1-s}$ is $\pm\infty$ at $s=1$. But, bode plot of $\frac{s}{1-s}$ results in $1$ at $s=1$. Obviously, this is wrong. Why?

• You could look at what a bode plot is. – Peter Shor May 27 '13 at 18:43
• @PeterShor I think the asker's question is valid. Even from reading the wiki article, it's not entirely clear what's happening here if you're new to Bode plots and frequency domain. – Ataraxia May 27 '13 at 18:47

The x-axis in the Bode plot isn't $s$, but $\omega$. Remember that $s=j\omega$, so what you're seeing in the Bode plot is as follows:
$$20\log|H(j1)|=20\log|\frac{j1}{1-j1}|=20\log|\frac{j(1+j)}{2}|$$
• @Val Most likely $\omega=1$ will prove the most useful. See, the difference between $s$ and $j\omega$ is $s$ is a complex number, whereas $j\omega$ is only an imaginary number. The real component of $s$ is what is known as the damping frequency, whereas the imaginary part is the frequency that most of us are familiar with: the periodicity. The chances are, if you're looking at a Bode plot, you're more interested in the latter. – Ataraxia May 27 '13 at 19:09