The circuit below contains two dependent sources: a voltage controlled voltage source and a voltage controlled current source.
Figure 3-1
The circuit elements have the following values: Vin=15V, R1=0.5Ω, R2=1.5Ω, R3=5Ω, A=2V/V and B=1.5A/V.
1.13
To analyze the circuit, we can use the concept of superposition.
First, let's consider the effect of the voltage controlled voltage source (VCVS). The VCVS has a gain of A=2V/V, which means that the output voltage is twice the input voltage.
1. Replace the VCVS with a short circuit (0V) to find the contribution of the VCVS to the circuit. This means connecting the positive and negative terminals of the VCVS together.
Now we have a circuit with two independent sources: Vin and the voltage controlled current source (VCCS) with a gain B=1.5A/V.
2. Analyze the circuit with only Vin and the VCCS. The VCCS generates a current that is proportional to Vin with a gain of B=1.5A/V. The current generated by the VCCS can be calculated as I = B * Vin.
Using Ohm's Law, we can calculate the voltage across each resistor:
- The voltage across R1 is given by V1 = I * R1 = (B * Vin) * R1.
- The voltage across R2 is given by V2 = I * R2 = (B * Vin) * R2.
- The voltage across R3 is given by V3 = I * R3 = (B * Vin) * R3.
Finally, we can calculate the total voltage across the load resistor RL by summing up the contributions from each resistor:
Vout = V1 + V2 + V3.
3. Once we have the voltage Vout, we can reapply the effect of the VCVS by multiplying Vout with the gain A=2V/V.
Therefore, the final output voltage Vout of the circuit can be calculated as follows:
Vout = A * (V1 + V2 + V3) = A * ((B * Vin) * R1 + (B * Vin) * R2 + (B * Vin) * R3).
Substituting the given values Vin=15V, R1=0.5Ω, R2=1.5Ω, R3=5Ω, A=2V/V, and B=1.5A/V into the equation will give you the numerical value for Vout.