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The open-loop gain (G_{V}) of an op-amp has the same frequency characteristics as a first-order RC lowpass filter as shown in Figure 2-3. At frequencies higher than the corner frequency (f_{C}) at which the open-loop gain is 3 dB lower than the DC gain, the open-loop gain decreases at a rate of 6 dB per octave (20 dB per decade). In this frequency range, the decibel open-loop gain of the op-amp (G_{V}) decreases by 6 dB (i.e., the linear open-loop gain (A_{V}) halves) when the frequency doubles. Hence:

f_{c} × A_{V} = constant

The frequency at which the gain is equal to 1 (0 dB) is called the unity gain cross frequency (f_{T}). Therefore, the above equation can be restated as follows. This is called the gain-bandwidth product (designated as GBWP, GBW, GBP, or GB).

f_{c} × A_{V} = f_{T}

Note that this equation is true in the frequency range in which the open-loop gain decreases at a rate of 6 dB per octave.

The input (V_{in}) and the output (V_{out}) have the following relationship. This relationship is called a closed-loop gain (represented as G_{CL} in dB scale and A_{CL} in linear scale). The 20 log rule is used to convert a linear voltage gain into a decibel voltage gain: G = 20 × log A.

V_{out} / V_{in} = A_{CL} = A_{V} / (1 + A_{V} × B)

= 1 / {B (1 + 1 / A_{V} × B)}

where A_{V} is the open-loop gain of an amplifier and B is the feedback factor. (A_{V} × B) is called the loop gain. The denominator, (1 + A_{V} × B), is called the amount of feedback. In the case of negative feedback, A_{V} × B < 0. An op-amp has a very high A_{V}. Hence, | A_{V} x B | >> 1. Therefore, the amount of feedback is calculated as (1 + A_{V} × B) ≈ A_{V} × B (loop gain). Hence, the above equation can be simplified as follows:

V_{out} / V_{in} = A_{CL} = 1/B

Figure 2-5 shows this relationship. The op-amp has a bandwidth of f_{C}. With negative feedback, its closed-loop bandwidth expands to f_{CL}. f_{CL} is calculated as follows from the gain-bandwidth product equation:

f_{CL} = f_{T} / A_{CL}

_{CL}) or the bandwidth (f_{CL}) is insufficient, it is necessary to select an op-amp with high f_{T}.

2. Using an op-amp

2.1. Feedback (positive and negative feedback)

2.3. Oscillation

2.4. Basic op-amp applications

2.5. Virtual short (virtual ground)

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