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Frequency Response— Voltage Feedback Op amps, Gain-Bandwidth Product

previous Op Amp Frequency Response
The open-loop frequency response of a voltage feedback op amp is shown in Figure 1-59 below. There are two possibilities: Fig. 1-59A shows the most common, where a high DC gain drops at 6dB/octave from quite a low frequency down to unity gain. This is a classic single pole response. By contrast, the amplifier in Fig. 1-59B has two poles in its response—gain drops at 6dB/octave for a while, and then drops at 12dB/octave. The amplifier in Fig. 1-59A is known as an unconditionally stable or fully compensated type and may be used with a noise gain of unity. This type of amplifier is stable with 100% feedback (including capacitance) from output to inverting input.
Frequency response of voltage feedback op amps
Figure 1-59: Frequency response of voltage feedback op amps
Compare this to the amplifier in Fig 1-59B. If this op amp is used with a noise gain that is lower than the gain at which the slope of the response increases from 6 to 12dB/octave, the phase shift in the feedback will be too great, and it will oscillate. Amplifiers of this type are characterized as "stable at gains ≥ X" where X is the gain at the frequency where the 6dB/12dB transition occurs. Note that here it is, of course, the noise gain that is being referenced. The gain level for stability might be between 2 and 25, typically quoted behavior might be "gain-of-five-stable," etc. These decompensated op amps do have higher gain-bandwidth products than fully compensated amplifiers, all other things being equal. So, they are useful, despite the slightly greater complication of designing with them. But, unlike their fully compensated op amp relatives, a decompensated op amp can never be used with direct capacitive feedback from output to inverting input.
The 6dB/octave slope of the response of both types means that over the range of frequencies where this slope occurs, the product of the closed-loop gain and the 3dB closed-loop bandwidth at that gain is a constant —this is known as the gain-bandwidth product (GBW) and is a figure of merit for an amplifier.
For example, if an op amp has a GBW product of X MHz, then its closed-loop bandwidth at a noise gain of 1 will be X MHz, at a noise gain of 2 it will be X/2 MHz, and at a noise gain of Y it will be X/Y MHz (see Figure 1-60 below). Notice that the closed-loop bandwidth is the frequency at which the noise gain plateau intersects the open-loop gain.
Gain-bandwidth product for voltage feedback op amps
Figure 1-60: Gain-bandwidth product for voltage feedback op amps
In the above example, it was assumed that the feedback elements were resistive. This is not usually the case, especially when the op amp requires a feedback capacitor for stability.
Figure 1-61 below shows a typical example where there is capacitance, C1, on the inverting input of the op amp. This capacitance is the sum of the op amp internal capacitance, plus any external capacitance that may exist. This always-present capacitance introduces a pole in the noise gain transfer function.
Bode plot showing noise gain for voltage feedback op amp with resistive and reactive feedback elements
Figure 1-61: Bode plot showing noise gain for voltage feedback op amp with resistive and reactive feedback elements
The net slope of the noise gain curve and the open-loop gain curve, at the point of intersection, determines system stability. For unconditional stability, the noise gain must intersect the open-loop gain with a net slope of less than 12dB/octave (20dB per decade). Adding the feedback capacitor, C2, introduces a zero in the noise gain transfer function, which stabilizes the circuit. Notice that in Fig. 1-61 the closed-loop bandwidth, fcl, is the frequency at which the noise gain intersects the open-loop gain.
The Bode plot of the noise gain is a very useful tool in analyzing op amp stability. Constructing the Bode plot is a relatively simple matter. Although it is outside the scope of this section to carry the discussion of noise gain and stability further, the reader is referred to Reference 1 for an excellent treatment of constructing and analyzing Bode plots. Second-order systems related to noise analysis are discussed later in this section.
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