Finding impedance that is unit step function

[anol1258]

Homework Statement

Consider the following circuit which uses ideal components. Prior to t=0 switch S is open. Then suddenly at t=0 switch S is closed. Find the impedance $Z_{2}$ such that the system output is a unit step function of voltage. Be certain to show all components used to construct $Z_{2}$ and their connections along with component values of your design.
Z1 is Given
circuit:

Homework Equations

KVL, KCL, V=IR,

The Attempt at a Solution

Nothing yet. Just wanted to get this up here for now.

 

[rude man]

The output will not be a UNIT step function unless the input voltage is > 1V.

The solution furthermore is not unique. You can say pick any R2, then X2 is defined as is the voltage gain < 1.
Where Z1 = R1 + jX1 and Z2 = R2 + jX2.

 

[anol1258]

Ok I understand why the input voltage has to be > 1V. So how should I start this out? Can I connect the two grounds and do a loop equation?

 

[rude man]

Ok I understand why the input voltage has to be > 1V. So how should I start this out? Can I connect the two grounds and do a loop equation?

The two grounds are already connected, by definition.

Let Z1 = R1 + jX1, Z2 = R2 + jX2, then you have a voltage divider Vout/Vin = Z1/(Z1 + Z2). In terms of the real vs. the imaginary components of that transfer function, what has to be true to make the transfer function independent of frequency?

 

[anol1258]

real and imaginary must be equal?

 

[anol1258]

or reactance is 0?

 

[rude man]

or reactance is 0?

Much better! Come up with a Z2 such that the transfer function Z1/(Z1 + Z2) has no frequency sensitivity.