Question

Given V1 = 8 vpp, R1 = 6 kΩ, V2 = 5 vpp, R2 = 3 kΩ, V3 = 10 vpp, R3 = 3 kΩ, and Rf = 14 kΩ, find Vout. Vout = vpp. (Round your answer to 2 decimal places.) In phasor notation, Vout = at an angle of o vpp.

Answer 1

Vout= 93.3V

Step-by-step explanation:

For this question, consider circuit in the attachment 1.

This is the circuit of an inverting amplifier. In an inverting amplifier

Vout/Vin= -Rf/Rin

To calculate the Vout, we must find Rin and Vin. For this we must solve the input circuit (attachment 2) using Thevinine theorem. Thevnine theorem states that all voltage sources in a circuit can be replaced by an equivalent voltage source Veq and and all resistances can be replaced by an equivalent resistance Req. To find out Req all voltage sources must be short circuited (attachment 3)

1/Req= 1/R1+1/R2+1/R3

1/Req=1/6+1/3+1/3

Req=6/5

To find out Veq consider circuit in attachment 4. We will solve this circuit using nodal analysis. In nodal analysis, we use the concept that sum of currents entering a node is equal to the sum of currents leaving a node. So,

I1= I2+I3

(10-Veq)/6= (Veq-5)/3+(Veq-10)/3

Veq=8V

Now the input circuit can be simplified as shown in attachment 5. Solve for Vout using equation

Vout/Veq= -Rf/Req

Vout/8= -14/(6/5)

Vout= - 93.3

It is at an angle of 180° from Veq