To calculate the output voltage of an inverting operational amplifier (op-amp) amplifier, you need to consider the circuit's feedback configuration and apply the ideal op-amp assumptions. The output voltage in an inverting op-amp amplifier can be determined using the following formula:
Vout = -(Rf / Rin) * Vin
where:
Vout is the output voltage of the amplifier.
Rf is the feedback resistor (resistor connected from the output to the inverting input terminal of the op-amp).
Rin is the input resistor (resistor connected to the inverting input terminal of the op-amp).
Vin is the input voltage applied to the inverting input terminal of the op-amp.
Here are the steps to calculate the output voltage:
Apply the ideal op-amp assumptions:
The input impedance at the inverting terminal is infinite (no current flows into the terminal).
The voltage at the inverting and non-inverting terminals is equal (virtual short circuit).
Calculate the input current (I_in) at the inverting terminal:
Since the input impedance at the inverting terminal is infinite, no current flows into this terminal. Therefore, I_in is equal to zero.
Apply Kirchhoff's current law (KCL) at the inverting terminal:
Since I_in is zero, the current flowing through the input resistor (Rin) is also zero.
Apply KCL at the output terminal:
Since the voltage at the inverting and non-inverting terminals is equal (virtual short circuit), the current flowing through the feedback resistor (Rf) is the same as the current flowing through the input resistor (I_in = 0).
Apply Ohm's law to calculate the output voltage (Vout):
Since the current through Rf is the same as the current through Rin, we can use Ohm's law to calculate Vout:
Vout = -I_in * Rf
Since I_in is zero, the output voltage simplifies to:
Vout = 0
As a result, the output voltage (Vout) of an ideal inverting op-amp amplifier is zero. However, in real-world scenarios, there might be some minor offsets and limitations, so the output voltage may not be exactly zero, but it will still be close to it under normal operating conditions.