Derive an expression for the gain Vout/Vin. Express your answer in the form of A+jB.
A basic non inverting operational amplifier with a capacitor connected in series with the resistor at the bottom.
To derive the expression for the gain (Vout/Vin) of a non-inverting operational amplifier with a capacitor connected in series with the resistor, you can follow these steps:
1. Identify the circuit configuration: The given circuit description suggests you have a non-inverting amplifier with feedback components consisting of a resistor (R) and a capacitor (C) in series.
2. Draw the circuit diagram: Sketch the circuit, labeling the input voltage (Vin), output voltage (Vout), resistor (R), and capacitor (C) in their appropriate locations. Make sure to indicate the correct direction of current flow.
3. Apply the ideal op-amp assumption: Assuming an ideal op-amp, you consider that the input impedance of the op-amp is infinite and the output impedance is zero.
4. Analyze the circuit: Apply Kirchhoff's voltage law (KVL) and Kirchhoff's current law (KCL) to the circuit to derive equations relating the input and output voltages, along with the resistor and capacitor currents.
5. Develop the transfer function: The transfer function provides the relationship between the input and output voltages. In this case, it corresponds to the gain (A) of the amplifier. To develop the transfer function, you can take the Laplace transform of the circuit equations derived in the previous step.
6. Express the transfer function in the complex form: The transfer function can be expressed as a complex number in the form A+jB, where A is the real part and B is the imaginary part.
By following these steps, you can derive the expression for the gain (Vout/Vin) of the described non-inverting operational amplifier circuit with a capacitor connected in series with the resistor.