Ideal Op-Amp: Voltage Gain Formula | R1, R2, R4

[spoonjabba]

Derive a symbolic expression (i.e., a formula containing symbols R1, R2, ..., etc., andarithmetic operators instead of numerical values) for the voltage gain of the amplifier

What I am stuck at is the two nodes on each side of R4

I initially disregarded the node to the right of R4, which was wrong. since there is a virtual sc at the input of the op amp terminals what would i consider the node on the right of r4?

 

[lewando]

Since no current is flowinginto either -/+ terminal as well, the voltage at the + terminal is 0V.

 

[rude man]

Derive a symbolic expression (i.e., a formula containing symbols R1, R2, ..., etc., andarithmetic operators instead of numerical values) for the voltage gain of the amplifier

What I am stuck at is the two nodes on each side of R4

I initially disregarded the node to the right of R4, which was wrong. since there is a virtual sc at the input of the op amp terminals what would i consider the node on the right of r4?

You just said to consider the node on the right of R4 to be a sc which I assume must mean short circuit or, as we call it, ground. The problem?

 

[uart]

Derive a symbolic expression (i.e., a formula containing symbols R1, R2, ..., etc., andarithmetic operators instead of numerical values) for the voltage gain of the amplifier

What I am stuck at is the two nodes on each side of R4

I initially disregarded the node to the right of R4, which was wrong. since there is a virtual sc at the input of the op amp terminals what would i consider the node on the right of r4?

You could also replace Vi, R3 and R1 with their Thevenin's equivalent and then just analyze it as a standard inverting amplifier.

 

[rezeew]

I understand your confusion regarding the nodes on either side of R4 in the ideal op-amp circuit. However, it is important to note that in an ideal op-amp, the input impedance is infinite, meaning that no current can flow into or out of the input terminals. Therefore, the node on the right of R4 can be considered as a virtual short circuit, and can be disregarded in the calculation of voltage gain.

To derive a symbolic expression for the voltage gain of the amplifier, we can use Kirchhoff's Current Law (KCL) at the inverting input terminal of the op-amp. This states that the sum of currents entering and leaving a node is equal to zero.

Applying KCL at the inverting input terminal, we can write:

(Vin - Vx)/R1 + (Vx - Vout)/R2 = 0

Where Vin is the input voltage, Vx is the voltage at the inverting input terminal, and Vout is the output voltage.

Solving for Vout/Vin, we get:

Vout/Vin = -R2/R1

However, this is only the voltage gain for the inverting configuration of the op-amp. To consider the non-inverting configuration, we can use the voltage divider rule at the non-inverting input terminal, which states that the output voltage is equal to the input voltage multiplied by the ratio of the resistors in the feedback loop.

Therefore, for the non-inverting configuration, we can write:

Vout/Vin = 1 + R2/R1

Combining both expressions, we get the final symbolic expression for voltage gain as:

Vout/Vin = -R2/R1 for the inverting configuration
Vout/Vin = 1 + R2/R1 for the non-inverting configuration

I hope this helps in deriving the symbolic expression for the voltage gain of the ideal op-amp circuit. Please feel free to ask any further questions or clarifications.