What's wrong with this calculation simplified transformation circuit?

In summary, the homework statement is trying to find the equivalent current source and parallel-connected impedance for a circuit with a voltage source and series-connected impedance. The first step is to simplify the voltage source into a current source. Then the current source and resistor are combined to get a new current source, and the new current source and inductor are combined to get the equivalent impedance. The problem stated that the equivalent impedance is complex and that you need to add the impedance of the resistor to the parallel impedances of the other two components.
  • #1
pokie_panda
37
0

Homework Statement



Use source transformation on the voltage source and series-connected impedance for the circuit shown here to find the equivalent current source and parallel-connected impedance. Continue the simplification by combining the two parallel current sources into an equivalent current source, and by combining the three parallel impedances into a single equivalent impedance.

Homework Equations



1/((1/Zr)+(1/Zl))
I=V/R

The Attempt at a Solution



First we simplify the voltage source into a current source
I=V/R
30<-90/15
=2<-90 A
to find the new current source we have I1+I2
=2<-90 A+4<90
=6<0A
Now to combine the resistor with the inductor
1/((1/Zr)+(1/Zl))
Therefore the new Z is
3+j9
 

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  • #2
pokie_panda said:

Homework Statement



... to find the new current source we have I1+I2
=2<-90 A+4<90
=6<0A

That is not the correct addition. Express the two current sources as complex numbers and add per the rules of complex addition.
Now to combine the resistor with the inductor
1/((1/Zr)+(1/Zl))
Therefore the new Z is
3+j9

What happened to the 15 ohm resistor?
 
  • #3
Because we are simplifying we combine the resistor 15
Using 15 + (ZR*ZL)/(ZL+ZR)
 
  • #4
pokie_panda said:
Because we are simplifying we combine the resistor 15
Using


15 + (ZR*ZL)/(ZL+ZR)

" ... and by combining the three parallel impedances into a single equivalent impedance." That's what the problem said. So it gave you a hint right there.

The 15 ohm resistor is now in parallel with the 30 ohm and the inductor, so why are you adding its impedance to the parallel impedance of the other two components?
 
  • #5
so is this correct calculation

30V<-90 = I * 15 ohms
I = 2A<-90

The 15 ohm || 30 ohm = 10 ohms,

the 2A<-90 || 4A<90 = -j2 +j4 = j2 = 2<90

the 10 ohm || +j10 ohm = ((10) * (+j10)) / (10 +j10) = (+j100) / (10 +j10) = 5 +j5
 
Last edited:
  • #6
pokie_panda said:
30V<-90 = I * 15 ohms
I = 2A<-90

The 15 ohm || 30 ohm = 10 ohms,

the 2A<-90 || 4A<90 = -j2 +j4 = j2 = 2<90

the 10 ohm || +j10 ohm = ((10) * (+j10)) / (10 +j10) = (+j100) / (10 +j10) = 5 +j5

Ah, much better.
 

Related to What's wrong with this calculation simplified transformation circuit?

1. What is a simplified transformation circuit?

A simplified transformation circuit is a type of electronic circuit that is used to change the voltage or current levels of a signal. It typically consists of resistors, capacitors, and inductors arranged in a specific configuration to achieve the desired transformation.

2. Why is it important to identify what's wrong with a calculation in a simplified transformation circuit?

Identifying errors in a calculation for a simplified transformation circuit is crucial because even small mistakes can result in significant errors in the output signal. This can lead to malfunctions or damage to the circuit and the devices connected to it.

3. What are some common mistakes made in calculations for simplified transformation circuits?

Some common mistakes in calculations for simplified transformation circuits include using incorrect values for component parameters, forgetting to account for the effects of parasitic elements, and using the wrong equation for the desired transformation.

4. How can errors in a simplified transformation circuit calculation be corrected?

Errors in a simplified transformation circuit calculation can be corrected by carefully double-checking all input values and equations, using simulation software to verify the results, and consulting with other experts in the field.

5. What measures can be taken to prevent errors in simplified transformation circuit calculations?

To prevent errors in simplified transformation circuit calculations, it is important to use reliable and accurate component values, carefully follow the correct equations and procedures, and use simulation software or prototyping to test the circuit before implementing it in a final design.

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