Simple electronic circuit analysis 
I have to find a substitute for this circuit. (The substitution is on the right) 
The arrows in one circle are perfect voltage sources. 
The arrows in two circles are perfect current sources. 
It seems easy but the concept of ideal current sources baffles me, I can't seem to know what voltage is on it because it theoretically has no resistance. 
Could anybody give me some steps to solve this problem? 
 A: 
I can't seem to know what voltage is on it because it theoretically
  has no resistance.

Be careful here!  The ideal current source has infinite internal resistance and "no resistance" typically means zero resistance.
Regardless, the voltage across an ideal current source is whatever it must be so that the circuit equations are satisfied.  So, for example, the current $I_4$ is what it is regardless of the voltage across the source and this implies that you can disregard all the circuit elements to the left of source $I_4$ in your calculation of the Thevenin voltage $E_Z$ and resistance $R_Z$.
In other words, the open-circuit voltage and short-circuit current for the output port can only depend on $I_4$, $E_3$, and $R_3$.
A: Here are some hints:


*

*This kind of problem can usually (and in this case it can) be solved by finding the open circuit voltage and short-circuit current of the original circuit.

*Because of the presence of $J_4$, circuit elements $E_1$, $R_1$, and $J_2$ won't affect the output voltage or current, and can be ignored when solving the problem. 
