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Op Amp AC Circuits

Op Amp can also be analyzed when it is connected with ac sources. The main idea is still the same with 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.
Op Amp AC Circuits

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.
Op Amp AC Circuits
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
Op Amp AC Circuits
or
Op Amp AC Circuits
(1.1)
At node 2, KCL gives
Op Amp AC Circuits
which leads to
Op Amp AC Circuits
(1.2)
Substituting Equations.(1.2) to (1.1) gives
Op Amp AC Circuits
Thus
Op Amp AC Circuits

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.
Op Amp AC Circuits
Figure 2
Solution :
The feedback and input impedances are calculated as
Op Amp AC Circuits
Since the circuit in Figure.(2) is an inverting amplifier, the closed-loop gain is given by
Op Amp AC Circuits
Substituting the given values of R1, R2, C1, C2, and ω, we get
Op Amp AC Circuits
Hence, the closed-loop gain is 0.434 and the phase shift is 130.6o

Untuk Bahasa Indonesia baca Rangkaian AC Op Amp
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