# Op Amp AC Circuit

Op Amp ac circuit can also be analyzed with the same method with dc sources.

The main idea is still the same as the other techniques, such as :
1. Transform the circuit to the phasor or frequency domain.
2. Solve the problem using circuit techniques
1. Kirchhoff,
2. Nodal,
3. Mesh,
4. Superposition,
5. Source Transformation, and
6. Thevenin and Norton
3. Transform the resulting phasor to the time domain.

Make sure to read what is ac circuit first.

And its applications:

## Op Amp AC Circuits

Please remember, we will use ideal op amps here to ease the explanation. Take notice on the key of analyzing op-amp circuits those are :

1. No current enters either of its input terminals
2. The voltage across its input terminals is zero

Let us review the examples below :
1. Determine vo(t) for the op amp in Figure.(1a) if vs = 3 cos 1000t V. Figure 1. For example 1 : (a) the original circuit in the time domain, (b) its frequency domain

Solution :
We first transform the circuit to the frequency domain, as drawn in Figure.(1b), where Vs = 3∠0oω = 1000 rad/s. Applying KCL at node 1 we get

or (1.1)

At node 2, KCL gives (1.2)

Substituting Equations.(1.2) to (1.1) gives

Thus

2. Compute the closed-loop gain and phase shift for the circuit in Figure.(2). Assume that R1 = R2 = 10 kΩ, C1 = 2 uF, C= 1 uF, and ω = 200 rad/s. Figure 2

Solution :
The feedback and input impedances are calculated as

Since the circuit in Figure.(2) is an inverting amplifier, the closed-loop gain is given by

Substituting the given values of R1, R2, C1, C2, and ω, we get

Hence, the closed-loop gain is 0.434 and the phase shift is 130.6o.

Read also : voltage division rule