Time domain response capacitor

Experimental Methods.— The initial fleeting excursions from frequency domain into time domain (for example, ref. S) appear to have been made because, at that time, steady-state measurements at very low frequencies ( 10 Hz) were unsatisfactory. Step-up, step-down, and ramp voltages were variously applied to capacitors containing dielectric samples, and the tranaent current i(/), or charge q t), responses monitored over a wide range of times such approaches have been reviewed. Although it is now quite feasible to make steady-state measurements at very low frequencies. 

If we have a circuit (or network) constituted only of resistors, the voltage at any point in it is uniquely defined by the applied voltage. If the input varies, so does this voltage — instantly, and proportionally so. In other words, there is no lag (delay) or lead (advance) between the two. Time is not a consideration. However, when we include reactive components (capacitors and/or inductors) in any network, it becomes necessary to start looking at how the situation changes over time in response to an applied stimulus. This is called time domain analysis. ... 

In actual practice, all filters have a distributed cutoff frequency so that none are infinitely sharp, and the way in which the attenuation "rolls off" with frequency affects the attainable S/N. The world of electrical engineering knows of many different filters (such as the Bessel and the Butterworth) which are characterized by different amplitude rolloff and phase characteristics near the cutoff frequency. A commonly used filter is the RC filter because of its ease of implementation. It consists simply of a capacitor C and a resistor R. It has the time constant RC (check it it has the unit of time) and this simply means that it will not respond to signals that change appreciably in times shorter than RC so it is a low pass filter. Its response to a step function in time is exponential so that the rolloff in the frequency domain, i.e., its Fourier transform, is a Lorentzian and the cutoff is very broad. 

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