Op Amp ac circuit can also be analyzed with the same method with dc sources.
- Transform the circuit to the phasor or frequency domain.
- Solve the problem using circuit techniques
- Source Transformation, and
- Thevenin and Norton
- Transform the resulting phasor to the time domain.
Make sure to read what is ac circuit first.
Make sure to read:
- What is phasor
- Impedance and admittance
- Kirchhoff’s laws for ac circuit
- Power calculation in ac circuit
- Three phase circuit
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 :
- No current enters either of its input terminals
- 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|
We first transform the circuit to the frequency domain, as drawn in Figure.(1b), where Vs = 3∠0o, ω = 1000 rad/s. Applying KCL at node 1 we get
At node 2, KCL gives
which leads to
Substituting Equations.(1.2) to (1.1) gives
2. Compute the closed-loop gain and phase shift for the circuit in Figure.(2). Assume that R1 = R2 = 10 kΩ, C1 = 2 uF, C2 = 1 uF, and ω = 200 rad/s.
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.