1 Eeng224 Chapter 9 Sinusoids and Phasors  Delta-to-wye and wye-to-delta conversions  Phase Sifters.  AC Bridges.  Problem Solutions Huseyin Bilgekul Eeng224 Circuit Theory II Department of Electrical and Electronic Engineering Eastern Mediterranean University

2 Eeng224 Y-Δ and Δ-Y Equivalent Circuits  Y-Δ and Δ-Y type equivalent conversions will be most useful when considering Three Phase circuits.  Impedances Z 1, Z 2 and Z 3 are are Y connected.  Impedances Z a, Z b and Z c are Δ connected.  Y and Δ forms can be eqivalently converted from one form to the other.  Y-Δ and Δ-Y conversions are valid for impedances as well as resistive circuits.

3 Eeng224 Y-Δ and Δ-Y Equivalent Circuits  Y-Δ and Δ-Y type equivalent conversions will be useful when considering Three Phase circuits in Chapter 12.

4 Eeng224 Balanced Y-Δ and Δ-Y Equivalent Circuits  A delta (Δ) or Y (wye) circuit is balanced if it has equal impedances in all three branches.  Y-Δ and Δ-Y conversions is very simple for balanced circuits.

5 Eeng224 Converting Δ Connection to Y form, we obtain Find I in the circuit given? Converting to Y form, we can simplify the circuit by combining the parallel and series elements Z

6 Eeng224 P.P.9.12 Continued

7 Eeng224 Phase Shifters (Leading Output) Output Leads the input  Phase shifting is employed to correct undesirable phase shift of the AC voltage. Leading Output.

8 Eeng224 Phase Shifters (Lagging Output) Lagging Output. Output Lags the input  Phase shifting is employed to correct undesirable phase shift of the AC voltage.

9 Eeng224 P.P.9.13 Design an RC circuit that provide 90° lagging phase shift. Find the output voltage if 10 Volt is applied.

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11 Eeng224  The AC bridge is Balanced when no current flows through the meter. AC bridges are used in measuring inductance and capacitance values. AC Bridges A general AC bridge circuit

12 Eeng224 AC Bridges AC Bridge for measuring LAC Bridge for measuring C.  Unknown capacitance and inductances C x and L x are measured in terms of the known standard values C s and L s

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14 Eeng224 Chapter 9, Problem 41.

15 Eeng224 Chapter 9, Problem 51.

16 Eeng224 Ch 9, Prob 55. Find Z in the network given that

17 Eeng224 Chapter 9, Problem 77a) Calculate the phase shift at 2 Mhz. b) Calculate the frequency at which phase shift is 45 degree.

18 Eeng224 Chapter 9, Problem 77a) Calculate the phase shift at 2 Mhz. b) Calculate the frequency at which phase shift is 45 degree.