Current capacitor

Since discovering and making use of the piezoelectric effect in naturally occurring crystals such as quartz and Rochelle salts, scientists have produced a wide range of piezoelectric materials in the laboratoi y. An early example is barium titanate, used in an electrical component called a capacitor. Currently, most piezoelectric materials are oxide materials based on lead oxide, zirconate oxide, and titanium. These very hard piezoelectric materials are termed piezoceramics. 

Capacitors, circuit breakers and HRC fuses must be selected with care for use with capacitor circuits, with contractors chosen on the basis that the capacitor current can rise by 25 per cent above nominal line current. Equally, HRC fuses for capacitor applications should be de-rated by a factor of 1.5. 

Therefore, if we plot the current waveform we realize that during the OFF time, the capacitor current must be sitting at a steady -0.67A (Block 3). This is the capacitor charging (refresh) current. 

However, the entire capacitor current waveform is simply equivalent to taking the switch waveform and translating it down vertically, by an amount exactly equal to the DC value of the switch waveform. Doing so effectively subtracts the DC component from the switch waveform and provides the required AC component to the capacitors. 

Therefore, the total height (peak to peak) of the capacitor current waveform (measured to the center of the ramp) is still 1A, which is also the case for the switch waveform from which it is derived. 

That means 1A - 0.67A = 0.33A is the average value of the capacitor current during the switch ON time (Block 3). In other words, although the capacitor cannot provide net DC (over the full cycle), it can and does provide the missing current of I0 x (1 - D) during the ON time. 

We pick the OFF time for the following calculation since the capacitor current is relatively fixed during this interval (and so we can therefore truly apply the equation I = CdV7d/). 

Figure 12-13 Input Capacitor Current Possibilities for Dual Channel Out-of-phase Buck Switchers...

We would like to plot the capacitor current. Select PSpice, Markers, and then Current Into Pin. A marker with an I will become attached to the mouse pointer ... 

Note that the Maximum Step Size has not been specified, allowing PSpice to take as much time between simulation points as possible. If we run the circuit and plot the capacitor current, we obtain the plot ... 

When we run the simulation and plot the capacitor current, we obtain the plot ... 

This plot agrees with what we expect the capacitor current to look like. However, the simulation does take longer to run. 

FIGURE 3.5 Capacitor voltage and capacitor current with time. 

Now let us repeat the same experiment, but with the capacitor replaced by an inductor (L), as also shown in Figure 1-3. Interviewees usually get the charging part (switch-closed phase) of this question right too. They are quick to point out that the current in the inductor behaves just as the voltage across the capacitor did during the charging phase. And the voltage across the inductor decays exponentially, just as the capacitor current did. They also seem to know that the time constant here is t = L/R, not RC. 

Note that in Figure 2-6, though we have used the buck topology as an example, the energy curve in particular is exactly the same for any topology. The capacitor current curves though, may not be identical to those of the buck, but are similar, and so the conclusions above still apply. 

For a buck — peak to peak capacitor current is Io x tdmin- This is the same point at which the general inductor design procedure would have been carried out, and so rDMiN is already known. 

For the buck and the boost, the worst-case input RMS capacitor current occurs at D = 0.5. 

The rule-of-thumb is to pick an output capacitor with a ripple current rating equal to or greater than the worst-case RMS capacitor current calculated above. Its voltage rating is usually picked to be at least 20 to 50% higher than what it will see in the application (i.e. Vin.max for all topologies). The input voltage ripple of the converter is also usually a concern because a small part of it does get transmitted to the output. There can also be EMI considerations involved. In addition, every control IC has a certain (usually unspecified) amount of input noise and ripple rejection, and it may misbehave if the ripple is too much. Typically, the input ripple needs to be kept down to less than 5% to 10% of the input... 

For a boost — peak to peak capacitor current at the worst-case point for this parameter (i.e. D = 0.5) is equal to 2 x Iq x rso where... 

Note that if the input range does not include the D = 0.5 point, we need to look for the input voltage end closest to D = 0.5. Then we can use the general equation for the peak to peak input capacitor current... 

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