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(Part 1 of this article provides an overview of basic current-mode control (CMC) circuits and demonstrates the need for slope compensation).
Evaluating peak CMC waveforms
Let's assume a typical application where Vout and L are fixed, and determine how the value of Vin affects slope compensation. Analyzing the problem with time plots of steady-state inductor and control signals provides us with a good vehicle for visualizing the operation of slope compensation in specific applications.
In Figure 11, the inductor current waveforms are shown for three values of Vin. Note that the downward slope of the inductor current, Sd, is constant for a fixed value of inductor and Vout, independent of Vin. The dotted lines represent the values of (Icontrol - Islope) referenced to their respective inductor current waveform. Any change in Iload causes this cluster of waveforms to simply shift together up or down.
There is no apparent change in these waveforms within the CMC loop with Iload. However, the load does have an effect on the converter's output pole (Co, Ro from Fig. 1) and the overall gain of the CMC modulator. These two parameters are components that enter into the overall compensation of the system loop. The waveforms in Fig. 11 assume a low value of linear slope compensation. The downward slope of (Icontrol - Islope), Se, is of significantly lower magnitude than Sd. From the previous series of plots illustrating the settling of perturbed current, it is probable that the Vin = 3 condition will be unstable with this low level of slope compensation.
Also note that, with this low value of Se, a small disruption of the control signal results in relatively large change of duty cycle. Greater Se therefore results in much lower system sensitivity to injected noise.
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Fig. 11: Inductor and control waveforms, linear slope compensation, Se/Sd= 0.2
We assume the same set of operating conditions in Fig. 12. Here, Se is greater. This illustrates a special case of slope compensation. The slope of Se is equal to one half of the downward slope of the inductor current. The three (Icontrol - Islope) waveforms nearly lie on top of each other. That is, changes in Vin, which result in a simultaneous change of duty cycle and peak inductor current, require no change in the (Icontrol - Islope) signal.
Thus no change is required in the error amplifier's output or feedback or control voltage. There is no systematic source of line-regulation error, even with finite error amp gain. Also note Se/Sd = 0.5 is the minimum value of Se that assures stability for all duty cycles.
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Fig. 12: Inductor and control waveforms, linear slope compensation, Se/Sd = 0.5
Another special value for slope compensation is observed in Fig. 13. Here we have Se/Sd = 1, and the special case of 'deadbeat' is achieved for all values of Vin. Because the slope of (Icontrol - Islope) matches the downward slope of the inductor current, the inductor current will recover from a disruption at the first PWM termination. The inductor's downward slope will instantaneously align to the desired steady state value. For linear slope compensation, if deadbeat is achieved for a particular Vout and L, it is achieved for all values of Vin.
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Fig. 13: Inductor and control waveforms, linear slope compensation, Se/Sd = 1
Let's increase the downward slope (Fig. 14). The general trend is that the magnitude of the control current, i.e., the value of (Icontrol - Islope) at the start of the switch cycle, must increase as Se increases. The drawback is the dynamic range of the control is compressed toward the high end of the signals' range. No additional benefit in stability is gained with excessive Se. In fact, in the extreme, the loop approaches a hysteretic mode of operation and the benefits of CMC are lost.
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Fig. 14: Inductor and control waveforms, linear slope compensation, Se/Sd = 2
Next, we plot the same current waveforms for the same series of set applications (fixed output voltages) for nonlinear slope compensation (Fig. 15). Ideally, Se changes linearly with duty cycle as Vout is changed so a more constant Se/Sd ratio is maintained with change in Vout. The magnitude of Islope is derived by integrating this ideal Se which is a linear function of duty cycle. So the resultant nonlinear Islope increases with the square of the duty cycle before it is subtracted from Icontrol.
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Fig. 15: Inductor and control waveforms, nonlinear slope compensation, Se/Sd = 0.2
In Fig. 15, a low value of nonlinear slope compensation is applied and all of the observations discussed in reference to Fig. 11, where a low value of linear slope compensation is applied, still hold true. Instability will probably occur for Vin = 3 because this level of Se is marginal compensation for higher values of duty cycle. The sensitivity to noise is still greater than that for larger Se. Therefore these waveforms represent an inadequate level of slope compensation.
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