# how capacitor in series with resistor to gnd forms a pole or zero ?

#### sneha rayala

##### Newbie level 4
How Does connecting a resistor in series with capacitor form zero. can someone please elaborate. Got this doubt when I was studying compensation of LDO using ESR resistance .2
Thank you

#### sutapanaki

Imagine the frequency behavior of the series combination of R and C. For low frequencies it is the cap impedance that dominates. At high frequencies it is the R. This can be decomposed as an integrator type of responce from the cap only and a response that has a zero at 1/RC as in the drawing.

#### BigBoss

$Z=R+\frac{1}{sC}=\frac{1+sRC}{sC}$

When $s=j\omega$

$f_z=\frac{1}{2\pi RC}$

Taking BigBoss's Z expression

Z = {s + 1/RC} / s/R so the pole is at 0 and the zero is at -1/RC

So if you are walking around the complex plane the zero is in LHP and
the pole at 0,0. So exponentially decaying response.

Regards, Dana.