Determine the expression of output voltage for inverting summing amplifier consisting of four internal resistors? (Assume the value of internal resistors to be equal)

To determine the expression of the output voltage for an inverting summing amplifier consisting of four internal resistors, we can follow these steps:

Step 1: Assign variables to the input voltages and the internal resistors. Let's denote the input voltages as V1, V2, V3, and V4, and the internal resistors as R1, R2, R3, and R4.

Step 2: Apply Kirchhoff's current law (KCL) at the inverting input terminal of the operational amplifier. Since the inverting input is a virtual ground, the sum of currents entering the node is equal to zero. This gives us the equation:

(V1/R1) + (V2/R2) + (V3/R3) + (V4/R4) = 0

Step 3: Apply Ohm's law to express the currents in terms of the input voltages and the internal resistors. The current flowing through each resistor is equal to the voltage across it divided by its resistance. This gives us the following equations:

V1/R1 = I1 V2/R2 = I2 V3/R3 = I3 V4/R4 = I4

Step 4: Substitute the expressions for the currents (I1, I2, I3, and I4) into the KCL equation from Step 2. This gives us:

(I1) + (I2) + (I3) + (I4) = 0

Step 5: Substitute the expressions for the currents (I1, I2, I3, and I4) from Step 3 into the KCL equation from Step 4. This gives us:

(V1/R1) + (V2/R2) + (V3/R3) + (V4/R4) = 0

Step 6: Rearrange the equation to solve for the output voltage (Vout). Since it is an inverting amplifier, the output voltage is given by the negative sum of the input voltages multiplied by the ratio of the feedback resistor (Rf) to the input resistor (Rin). In this case, since the internal resistors are equal, we can simplify the expression to:

Vout = -((V1 + V2 + V3 + V4) * (Rf/R1))

Therefore, the expression for the output voltage of the inverting summing amplifier with four equal internal resistors is -((V1 + V2 + V3 + V4) * (Rf/R1)).

To determine the expression of the output voltage for an inverting summing amplifier consisting of four internal resistors, we can follow these steps:

Step 1: Assign variables to the input voltages and the internal resistors. Let's denote the input voltages as V1, V2, V3, and V4, and the internal resistors as R1, R2, R3, and R4.

Step 2: Apply Kirchhoff's current law (KCL) at the inverting input terminal of the operational amplifier. Since the inverting input is a virtual ground, the sum of currents entering the node is equal to zero. This gives us the equation:

(V1/R1) + (V2/R2) + (V3/R3) + (V4/R4) = 0

Step 3: Apply Ohm's law to express the currents in terms of the input voltages and the internal resistors. The current flowing through each resistor is equal to the voltage across it divided by its resistance. This gives us the following equations:

V1/R1 = I1 V2/R2 = I2 V3/R3 = I3 V4/R4 = I4

Step 4: Substitute the expressions for the currents (I1, I2, I3, and I4) into the KCL equation from Step 2. This gives us:

(I1) + (I2) + (I3) + (I4) = 0

Step 5: Substitute the expressions for the currents (I1, I2, I3, and I4) in terms of the input voltages and the internal resistors into the equation from Step 4. This gives us:

(V1/R1) + (V2/R2) + (V3/R3) + (V4/R4) = 0

Step 6: Rearrange the equation from Step 5 to solve for the output voltage (Vout). This gives us:

Vout = -((V1/R1) + (V2/R2) + (V3/R3) + (V4/R4))

Therefore, the expression for the output voltage of the inverting summing amplifier with four equal internal resistors is -((V1/R1) + (V2/R2) + (V3/R3) + (V4/R4)).