An ideal operational-amplifier circuit is shown in the diagram below.
State where the virtual earth point is located in this circuit, and show that the closed-loop voltage gain is given by:
VoutVin=−RfRin\frac{V_{\text{out}}}{V_{\text{in}}} = -\frac{R_{\text{f}}}{R_{\text{in}}}VinVout=−RinRf
Explain clearly any assumptions made about the ideal operational amplifier in your derivation.
The input signal VinV_{\text{in}}Vin is a sine wave with a peak value of 800 mV800\text{ mV}800 mV.
If Rin=15 kΩR_{\text{in}} = 15\text{ k}\OmegaRin=15 kΩ, Rf=120 kΩR_{\text{f}} = 120\text{ k}\OmegaRf=120 kΩ, and the operational amplifier is powered by ±6.0 V\pm 6.0\text{ V}±6.0 V power-supply rails, describe the key features of the resulting output voltage waveform VoutV_{\text{out}}Vout and state its maximum and minimum values.
A student modifies the circuit to construct an adder (summing amplifier) that combines two input signals, V1V_1V1 and V2V_2V2, to produce an output voltage calculated by:
Vout=−(4.0V1+0.25V2)V_{\text{out}} = -(4.0V_1 + 0.25V_2)Vout=−(4.0V1+0.25V2)
If the feedback resistor is chosen to be Rf=60 kΩR_{\text{f}} = 60\text{ k}\OmegaRf=60 kΩ, calculate the required values of the input resistors R1R_1R1 and R2R_2R2.