In the circuit shown in the figure, Assume that the output voltag
In the circuit shown in the figure, Assume that the output voltage saturation level of Vo = ±12 V. Determine the range of Va for linear operation.
A. V<sub>o</sub> > 10.7V
B. 10.7 < V<sub>a</sub> < 10.7 V
C. 2.67 < V<sub>a</sub> < 10.7 V
D. V<sub>a</sub> > 2.67 V
Please scroll down to see the correct answer and solution guide.
Right Answer is: C
SOLUTION
Concept:
The output of an Op-Amp in inverting configuration is given by:
\(V_o=(-\frac{R_2}{R_1})V_{in}\)
Also, the superposition theorem can be applied for multiple input sources, i.e. the output because of individual sources is calculated and the net output is obtained by simply adding the individual output responses.
Application:
Since the given configuration is an inverting one, the output voltage with only 10 V acting will be:
\(V_{o1}=(-\frac{12}{6})10~V\)
Similarly, the output voltage with only Va acting alone will be:
\(V_{o2}=(-\frac{12}{4})V_a\)
The net output voltage will be:
V0 = V01 + V02
\({V_o} = - \left[ {\frac{{12}}{4}{V_a} + \frac{{12}}{6}\left( { - 10} \right)} \right]\)
Linear operation means that the output is not saturated, i.e. |V0| ≤ 12, i.e.
± 12 = -3 Va + 20
\(∴ {V_a} = \frac{{20 \pm 12}}{3} \)
Va = 10.7 and 2.67
∴ For linear operation, Va must be lie between 2.67V < Va < 10.7 V