Is it possible to build a phase shifter from RLC components?

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Kfir Dolev
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Say you have a circuit component with impedence Z(\omega). Is it possible combine it in some way to resistors, capacitors, and inductors, so as to shift the phase of the impedance by a constant?
 
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Do you mean the polar angle of the impedance, that is, the angle when Z is expressed in polar form? In that case, simply changing the reactance or the resistance using the formula tan(θ) = X/R will do that (where X is the reactance and R is the resistance), using the relevant form of X according to whether you are using capacitors or inductors.
 
Kfir Dolev said:
Say you have a circuit component with impedence Z(\omega). Is it possible combine it in some way to resistors, capacitors, and inductors, so as to shift the phase of the impedance by a constant?
If you require a fixed phase shift over a band of frequencies, there are some circuits to do this. But you cannot obtain a fixed phase shift over the entire frequency spectrum.