Finding impedance that is unit step function

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Homework Help Overview

The discussion revolves around finding the impedance Z2 in a circuit that will yield a unit step function of voltage as the output when a switch is closed at t=0. The circuit involves ideal components and includes a given impedance Z1.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • Participants discuss the conditions under which the output can be a unit step function, noting the requirement for the input voltage to exceed 1V. There is exploration of the relationship between the components of the circuit, particularly the voltage divider formed by Z1 and Z2. Questions arise regarding the setup of loop equations and the implications of connecting grounds.

Discussion Status

Participants have raised several points about the nature of the impedance and its components, with some suggesting that the real and imaginary parts must be equal or that reactance should be zero to achieve a transfer function independent of frequency. Guidance has been offered regarding the formulation of Z2 to meet these criteria.

Contextual Notes

There is an emphasis on showing all components and their connections, as well as component values, which may influence the design of Z2. The discussion also reflects on the non-uniqueness of the solution and the implications of varying component values.

anol1258
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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:
9.jpg


Homework Equations



KVL, KCL, V=IR,

The Attempt at a Solution



Nothing yet. Just wanted to get this up here for now.
 
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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.
 
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?
 
anol1258 said:
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?
 
real and imaginary must be equal?
 
or reactance is 0?
 
anol1258 said:
or reactance is 0?

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

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