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Effects of Feedback Capacitance in Op Amps

previous Current Feedback (CFB) Op Amps
It is quite common to use a capacitor in the feedback loop of a VFB op amp, to shape the frequency response as in a simple single-pole lowpass filter shown in Figure 1-113A below. The resulting noise gain is plotted on a Bode plot to analyze stability and phase margin. Stability of the system is determined by the net slope of the noise gain and the open-loop gain where they intersect.
Noise gain stability analysis for VFB and CFB op amps with feedback capacitor
Figure 1-113: Noise gain stability analysis for VFB and CFB op amps with feedback capacitor
For unconditional stability, the noise gain plot must intersect the open-loop response with a net slope of less than 12dB/octave. In this case, the net slope where they intersect is 6dB/octave, indicating a stable condition. Notice for the case drawn in Fig. 1-113A, the second pole in the frequency response occurs at a considerably higher frequency than fu.
In the case of the CFB op amp (Fig. 1-113B), the same analysis is used, except that the open-loop transimpedance gain, T(s), is used to construct the Bode plot.
The definition of noise gain (for the purposes of stability analysis) for a CFB op amp, however, must be redefined in terms of a current noise source attached to the inverting input as shown in Figure 1-114 on the following page. This current is reflected to the output by an impedance, which we define to be the "current noise gain" of a CFB op amp:
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Now, return to Fig. 1-113B, and observe the CFB current noise gain plot. At low frequencies, the CFB current noise gain is simply R2 (making the assumption that Ro is much less than Z1 or Z2. The first pole is determined by R2 and C2. As the frequency continues to increase, C2 becomes a short circuit, and all the inverting input current flows through RO (again refer to Fig. 1-114).
Current "noise gain" definition for CFB op amp for use in stability analysis
Figure 1-114: Current "noise gain" definition for CFB op amp for use in stability analysis
A CFB op amp is normally optimized for best performance for a fixed feedback resistor, R2. Additional poles in the transimpedance gain, T(s), occur at frequencies above the closed-loop bandwidth, fcl, (set by R2). Note that the intersection of the CFB current noise gain with the open-loop T(s) occurs where the slope of the T(s) function is 12dB/octave. This indicates instability and possible oscillation.
It is for this reason that CFB op amps are not suitable in configurations which require capacitance in the feedback loop, such as simple active integrators or lowpass filters.
The Sallen-Key filter configuration
Figure 1-115: The Sallen-Key filter configuration
They can, however, be used in certain active filters such as the Sallen-Key configuration shown in Figure 1-115 above, which do not require capacitance in the feedback network.
On the other hand, VFB op amps, do make very flexible active filters. A multiple feedback 20MHz lowpass filter example using an AD8048 op amp is shown below in Figure 1-116.
In general, an active filter amplifier should have a bandwidth that is at least ten times the bandwidth of the filter, if problems due to phase shift of the amplifier are to be avoided. (The AD8048 has a bandwidth of over 200MHz in this configuration).
Multiple feedback 20MHz lowpass filter using the AD8048 VFB op amp
Figure 1-116: Multiple feedback 20MHz lowpass filter using the AD8048 VFB op amp
Design details of the filter design can be found on the AD8048 data sheet. Further discussions on active filter design will be discussed later.
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