Find V1 and V2 in the ideal transformer circuit of Fig. 13.56, using PSpice.

Question

Find [latex]\pmb{V_1}[/latex] and [latex]\pmb{V_2}[/latex] in the ideal transformer circuit of Fig. 13.56, using PSpice.

Accepted Answer

1. Define. The problem is clearly defined and we can proceed to the next step.

2. Present. We have an ideal transformer and we are to find the input and the output voltages for that transformer. In addition, we are to use PSpice to solve for the voltages.

3. Alternative. We are required to use PSpice. We can use mesh analysis to perform a check.

4. Attempt. As usual, we assume ω = 1 and find the corresponding values of capacitance and inductance of the elements:

[latex] j 10=j \omega L \quad \Rightarrow \quad L=10 H \ \space \ -j 40=\frac{1}{j \omega C} \quad \Rightarrow \quad C=25 mF [/latex]

Figure 13.57 shows the schematic. For the ideal transformer, we set the coupling factor to 0.99999 and the numbers of turns to 400,000 and 100,000. The two VPRINT2 pseudocomponents are connected across the transformer terminals to obtain [latex]\pmb{V_1} \text{ and } \pmb{V_2}[/latex]. As a single-frequency analysis, we select Analysis/Setup/AC Sweep and enter Total Pts = 1, Start Freq =  0.1592, and Final Freq =  0.1592. After saving the schematic, we select Analysis/Simulate to simulate it. The output file includes:

FREQ VM($N_0003,$N_0006) VP($N_0003,$N_0006)
1.592E-01 9.112E+01 3.792E+01
FREQ VM($N_0006,$N_0005) VP($N_0006,$N_0005)
1.592E-01 2.278E+01 -1.421E+02

This can be written as

[latex] V _1=\pmb{91.12 \underline{/37.92^{\circ}} V} \quad \text { and } \quad V _2=\pmb{22.78 \underline{/-142.1^{\circ}} V}[/latex]

5. Evaluate. We can check the answer by using mesh analysis as follows:

[latex]\text{Loop 1 }\quad -120 \underline{/30^{\circ}}+(80-j 40) I_1+V_1+20\left(I_1-I_2\right)=0 \ \space \ \text{Loop 2 }\quad 20\left(-I_1+I_2\right)- V _2+(6+j 10) I_2=0 \ \space [/latex]

But [latex]V_2 = −V_1/4 \text{ and } I_2 = −4I_1[/latex]. This leads to

[latex] -120 \underline{/30^{\circ}}+(80-j 40) I_1+V_1+20\left(I_1+4 I_1\right)=0 \ \space \(180-j 40) I_1+V_1=120 \underline{/ 30^{\circ}} \ \space \ 20\left(-I_1-4 I_1\right)+V_1 / 4+(6+j 10)\left(-4 I_1\right)=0 \ \space \(-124-j 40) I_1+0.25 V_1=0 \quad \text { or } \quad I_1=V_1 /(496+j 160) [/latex]

Substituting this into the first equation yields

[latex] (180-j 40) V_1 /(496+j 160)+V_1=120 \underline{/30^{\circ}} \ \space \ \left(184.39 \underline{/-12.53^{\circ}} / 521.2 \underline{/ 17.88^{\circ}}\right) V_1+V_1 \ \space \ =\left(0.3538 \underline{/-30.41^{\circ}}+1\right) V_1=(0.3051+1-j 0.17909) V_1=120 \underline{/30^{\circ}} \ \space \ V_1=120 \underline{/ 30^{\circ}} / 1.3173 \underline{/-7.81^{\circ}}= \pmb{9 1 . 1 \underline{/ 3 7 . 8 1 ^ { \circ }} V} \quad \text { and } \ \space \ V_2=\pmb{22.78 \underline{/-142.19^{\circ}} V} [/latex]

Both answers check.

6. Satisfactory? We have satisfactorily answered the problem and checked the solution. We can now present the entire solution to the problem.

Question 13.14: Find V1 and V2 in the ideal transformer circuit of Fig. 13.5...

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