The decay of charge in a capacitor is similar to the decay of a radioactive nuclide. It is exponential decay. If we discharge a capacitor, we find that the charge decreases by half every fixed time interval - just like the radionuclides activity halves every half life.
The voltage, current, and charge all decay exponentially during the capacitor discharge. We can charge up the capacitor and then flip the switch and record the voltage and current readings at regular time intervals and plot the data, which gives us the exponential graphs below. The half life of the decay is independent of the starting voltage.
Objective of compensation is to achieve stable operation when negative feedback is applied around the op amp. Miller - Use of a capacitor feeding back around a high-gain, inverting stage. Miller capacitor only Miller capacitor with an unity-gain buffer to block the forward path through the compensation capacitor. Can eliminate the RHP zero.
A capacitor can be mechanically destroyed or may malfunction if it is not designed, manufactured, or installed to meet the vibration, shock or acceleration requirement within a particular application. Movement of the capacitor within the case can cause low I.R., shorts or opens.
In addition to these failures, capacitors may fail due to capacitance drift, instability with temperature, high dissipation factor or low insulation resistance. Failures can be the result of electrical, mechanical, or environmental overstress, "wear-out" due to dielectric degradation during operation, or manufacturing defects.
The state of health, or life, of these capacitors depends on stress factors like temperature, voltage, ripple current, charge- discharge, and humidity. Various degradation measures such as capacitance, equivalent series resistance, dissipation factor, and insulation resistance have been used to monitor the degradation state of capacitors.