Electrical – Are there any cases that Source Transformation method can not be applied

Write the expression for the current through R1 + R2: (V+ - V-)/(R1+R2)

Now find the voltage drop across R2: R2*(V+ - V-)/(R1+R2)

Now find the open circuit Vth at the base connection point:

From ground: V- + (V+ - V-)*R2/(R1+R2)

(The drop across V- plus the drop across R2 is the voltage at the base connection point with respect to ground.)

There are several ways to reduce a net of sources and resistors to its Thevenin equivalent. One way is like what you started to do. Find the open circuit voltage and the short circuit current.

Another way is to keep simplifying the circuit in steps. Take a source and two resistors and find its Thevenin equivalent on its own. Then replace the three parts with the two Thevenin equivalent parts in the circuit. Keep doing this until the circuit is a single voltage source in series with a single resistor.

However, in all cases you should start by drawing the circuit in a comprehensible way. Problems like this are often deliberately drawn to obscure the circuit. Never let that get in your way. Redraw the schematic properly with power voltages descending down the page, logical flow left to right, etc. That should be your first step here too.

You should always draw circuits properly before asking others to look at them. This web site is no exception.