2) Make a PSpice (or MultiSim) model for this simple circuit and a) verify the answers you calculated for parts (c) through (g) above. In addition, b) Plot the input impedance to the transformer (both real and imaginary parts) as well as the power delivered to the load impedance from 100 Hz to 100,000 Hz. c) What happens when you change the load from real to reactive? (That is to say: When you change the load from a resistor to either an inductor or capacitor.) d) Extra Credit: Plot the amount of power deposited in the transformer itself for both a real load (8.2 Ohm resistor) and for a reactive load from 100 to 100,000 Hz. Your model should look something like this in PSPICE: R3 VOFF = 0 1000 VAMPL = 10 FREQ=0.1kV3 AC=1 TX1 220 R2 8.2 w You will have to modify the transformer model (TX1) using the "Schematic" in OrCAD Capture CIS - Lite to give it the correct inductances and coupling factor. Bias Value Power COUPLING Graphic Ow 0.99925 XFRM_LINEAR.Normal 650mH L1_VALUE L2_VALUE 4.92mH Name INS2039 Part Reference TX1 Source Part Value XFRM_LINEAR.Normal XFRM_LINEAR In PSPICE one can specify an equation for a trace using the "Add Trace" feature in PSPICE A/D - Lite. One can plot either the real or imaginary part of the input impedance (V/I) using the R() and IMG() functions. For the diagram above, the following equations could be used to plot the reactive and real impedances: IMG(V(R3:2)/I(R3)) and R(V(R3:2)/I(R3)). Consider the following transformer circuit assuming an ideal transformer. In this circuit the signal generator will provide a 10-Volt peak-to-peak sinusoidal signal at a frequency of 1.0 kHz. Assume that L₁ = 0.65 H, L2 = 0.00492 H (=4.92 mH) and that the coupling constant = 0.99925. + VG1( R1 1k N1:N2 11.5:1 12 V1 N1 N2 V2 R2 8.2 1) Find the following using the theory presented in the prelab reading: a) Start with Equations (2) of the prelab reading and show that the input impedance to an ideal transformer is given by the equation for Z1 (=V1/11) in Equations (4) of the prelab reading. Equations (2) are: V₁ = joLI₁ + jœMI₂ and V₂ = j@MI₁ +j@L₂I₂ The equation for the input impedance is: Z₁ = 1½ = jwL₁ + (WM)² jwL₂+ZL b) Assuming that Z is a real impedance, find the equations for the real and imaginary parts of Z1. c) Use your equations from part (b) to calculate the value of the input impedance (Z) at an operating frequency of 200 Hz. Assume that the load impedance is 8.2 Ohms (characteristic of an audio speaker) and completely real. Find both the real and imaginary parts of Z1. d) Repeat part (c) at an operating frequency of 5 kHz e) Calculate the voltages V1 and V2 at 5 kHz f) Calculate the currents 11 and 12 at 5 kHz g) Calculate the amount of power supplied by the signal generator, VG1, and the amount of power dissipated in each of the two resistors in the circuit at 5 kHz.

2) Make a PSpice (or MultiSim) model for this simple circuit and a) verify the answers you calculated for parts (c) through (g) above. In addition, b) Plot the input impedance to the transformer (both real and imaginary parts) as well as the power delivered to the load impedance from 100 Hz to 100,000 Hz. c) What happens when you change the load from real to reactive? (That is to say: When you change the load from a resistor to either an inductor or capacitor.) d) Extra Credit: Plot the amount of power deposited in the transformer itself for both a real load (8.2 Ohm resistor) and for a reactive load from 100 to 100,000 Hz. Your model should look something like this in PSPICE: R3 VOFF = 0 1000 VAMPL = 10 FREQ=0.1kV3 AC=1 TX1 220 R2 8.2 w You will have to modify the transformer model (TX1) using the "Schematic" in OrCAD Capture CIS - Lite to give it the correct inductances and coupling factor. Bias Value Power COUPLING Graphic Ow 0.99925 XFRM_LINEAR.Normal 650mH L1_VALUE L2_VALUE 4.92mH Name INS2039 Part Reference TX1 Source Part Value XFRM_LINEAR.Normal XFRM_LINEAR In PSPICE one can specify an equation for a trace using the "Add Trace" feature in PSPICE A/D - Lite. One can plot either the real or imaginary part of the input impedance (V/I) using the R() and IMG() functions. For the diagram above, the following equations could be used to plot the reactive and real impedances: IMG(V(R3:2)/I(R3)) and R(V(R3:2)/I(R3)). Consider the following transformer circuit assuming an ideal transformer. In this circuit the signal generator will provide a 10-Volt peak-to-peak sinusoidal signal at a frequency of 1.0 kHz. Assume that L₁ = 0.65 H, L2 = 0.00492 H (=4.92 mH) and that the coupling constant = 0.99925. + VG1( R1 1k N1:N2 11.5:1 12 V1 N1 N2 V2 R2 8.2 1) Find the following using the theory presented in the prelab reading: a) Start with Equations (2) of the prelab reading and show that the input impedance to an ideal transformer is given by the equation for Z1 (=V1/11) in Equations (4) of the prelab reading. Equations (2) are: V₁ = joLI₁ + jœMI₂ and V₂ = j@MI₁ +j@L₂I₂ The equation for the input impedance is: Z₁ = 1½ = jwL₁ + (WM)² jwL₂+ZL b) Assuming that Z is a real impedance, find the equations for the real and imaginary parts of Z1. c) Use your equations from part (b) to calculate the value of the input impedance (Z) at an operating frequency of 200 Hz. Assume that the load impedance is 8.2 Ohms (characteristic of an audio speaker) and completely real. Find both the real and imaginary parts of Z1. d) Repeat part (c) at an operating frequency of 5 kHz e) Calculate the voltages V1 and V2 at 5 kHz f) Calculate the currents 11 and 12 at 5 kHz g) Calculate the amount of power supplied by the signal generator, VG1, and the amount of power dissipated in each of the two resistors in the circuit at 5 kHz.

Power System Analysis and Design (MindTap Course List)

6th Edition

ISBN:9781305632134

Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Chapter2: Fundamentals

Section: Chapter Questions

Problem 2.1MCQ: The rms value of v(t)=Vmaxcos(t+) is given by a. Vmax b. Vmax/2 c. 2Vmax d. 2Vmax

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