Homework about a simple inverting amplifier

[Learner123]

Homework Statement

The picture is an closed loop amplifier, the question is simple: find the closed-loop voltage amplifier of the circuit

Homework Equations

Av = v0/v in = - (R2/R1)

The Attempt at a Solution

If R2 is just simply a bunch of resistors connecting crazily, then it is no problem to me, but in here, R2 is partly connected to the ground (2 connected to the ground), so if anyone could explain how the part connecting to the ground affecting the closed loop formula, i would very thankful.

 

[vk6kro]

Give each resistor the same value and assume an output voltage.
I assumed 10K for the resistors and 10 volts output.

Because the output is positive and this is an inverting amplifier, the input must be negative.

The other thing we know is that the inverting input is at ground potential, even though there is no current flowing into this input.

Start at the input of the opamp and take the series 10 K and the 10 K to ground in parallel. (the inverting input is at ground potential, remember).
so, that is 5 K in series with the next 10 K ie 15 K to the left of the RH T junction.

Continue like this to get the total impedance connected to the output.

Then work out the total current using the 10 V figure.

Then it splits with 10 K to ground and 15 K to the left.

When you have all the currents, the last one is the current going towards the -Ve input. This continues into the input resistor and the negative signal source.

Knowing the size of the series resistor, you can work out the input voltage and hence the gain because this voltage is causing the 10 volts output.

I have a set of answers when you try this. The gain is an integer number.