# Find same modulus z plane poles of over damped system

I am asked to find two poles of a second order discrete over damped system that have the same magnitude (0.4, to be exact) in the Z plane. From what I understand, that is not possible since over damped systems have two distinct negative real poles at the S plane and, using $$z=e^{sT}$$ , the two poles in S become two real, distinct and positive poles in Z. This means that poles z1 and z2

are:

z1,z2=a,b with a≠b, a,b>0 and a,b∈R

So they can't both have length 0.4. Am I missing something here?

• I think you're correct, overdamped necessarily means two real unequal poles. What does "same length" of a pole mean? Do they mean same magnitude? Exactly equal? Why "step response poles"? Something may be lost in translation here... The rest of this exercise just sounds like they just want you to do a bilinear transform. May 10 at 14:32
• @PeteW edited the question a bit, but that pretty much answers it May 10 at 15:10