Explore BrainMass

Explore BrainMass

    LCR Circuit analysis using complex impedances

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Please refer to the attachment for questions complete with circuit diagrams, and provide full answers.

    1a) Derive an expression for the transfer function Vout/Vin of the circuit below (assume that no current flows to the output terminals AB).

    1b) State whether the circuit can be made to produce an output signal with zero phase shift. If a zero phase shift is possible, describe the conditions under which it occurs.

    2a) Calculate the Thevenin's equivalent e.m.f. and impedance as seen between terminals AB (assume C2 is the load at AB).

    2b) Using the Thevenin's equivalent circuit derived in Part a above, calculate the voltage VOUT.

    © BrainMass Inc. brainmass.com March 4, 2021, 10:39 pm ad1c9bdddf
    https://brainmass.com/physics/emf/lcr-circuit-analysis-complex-impedances-349945

    Attachments

    Solution Preview

    1a) Lets work out the impedance of the || combination of the resistance (R) and the inductance (L) at an angular frequency w. Lets call this impedance Z(out) which is given by the || impedance rule as

    1/Z(out) = 1/R + 1/jwL (1) {where w is angular frequency of operation}

    We will substitute s = jw in (1) so

    1/Z(out) = 1/R + 1/sL

    Z(out) = sLR/{R + sL} (2)

    Impedance of the series capacitor is given by

    Z(cap) = 1/jwC = 1/sC (3)

    Total impedance of the circuit is given by Z(tot) where

    Z(tot) = Z(cap) + Z(out) (4)

    Putting in expressions for Z(out) & Z(cap) as obtained in (2) & (3) into (4) we get

    Z(tot) = 1/sC + sLR/{R + sL}

    Z(tot) = ({R + sL} + (s^2)*LCR)/sC(R + sL) (5)

    Now by the voltage divider rule we can say that the transfer function
    Av = V(out)/V(in) = Z(out)/Z(tot) (6)

    Av = Z(out)/{Z(tot)} (7)

    Av = sLR/{R + sL}*sC(R + sL)/({R + sL} + s^2*LCR)

    Av = sLR*sC*(R + sL)/(R +sL)*({R + sL} + s^2*LCR) (8)

    Reducing to

    Av = s^2*LCR/({R + sL} + s^2LCR) ...

    Solution Summary

    An LCR circuit is presented and the transfer function of Vout/Vin is determined based on known passive values. An expression for the phase is determined and questions about zero phase are asked and answered. The Thevenin equivalent circuit is deduced and the Thevenin emf and input impedance worked out

    $2.49

    ADVERTISEMENT