the integrator and the differentiator

clock signal
A typical square wave (clock)
Differentiator
Differentiator signal
Integrator increase in R
Integrator with increase in R, now acting as a low pass filter
sawtooth
Integrator signal (sawtooth) and at a different frequency can be more of a ramp generator
Differentiator increase in R
Differentiator with increase in R
ROUNDING CLOCK WAVE
Rounding of a clock wave not quite integrating due to the values of R.C

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Two circuit modules Arranged in a way containing a resistor and capacitor form the basis for an Integrator and a Differentiator, and depending on the waveform put in, also act as low pass filter or a high pass filter.  And the most basic type is a passive network arrangement containing these two components., which draw on the signal provided to them. The other type is an active component arrangement, using op-amps with a dc supply for support.                         The oscilloscope wave forms above, show clock signals at the inputs and the resultant output wave forms, using a resistor and capacitor.

rcint
Passive and Active networks

The product of R and C in these networks are called the  RC time constant, as t=r.c. The integrator can function as a low pass filter allowing low frequencies to pass, and the differentiator can function as a high pass filter allowing only high frequencies to pass.  rc1111

 

And like the two branches of calculus, The integrator deals with the area under a graph (integral calculus) and the slope of this wave form describes the increase in area beneath the input signal.  And the differentiator  deals with the rate of change at its input to find some point or derivative (differential calculus)on the slope of the wave form at its output, like the output voltage.                                                               In Maths if a fourier analysis was performed on say, a complex  wave form, this would show it’s constituent parts which go to making the wave form up, it would show the fundamental component, which could be a sine wave, and integer multiples of this fundamental frequency  like 2f, 3f, 4f,….nth, where 2f is 2x the fundamental frequency and so on, and when summed together this produces such waveforms we see on an oscilloscope, or what the load in a circuit  sees.  These integer multiples can be out of phase and of different amplitudes and frequencies, and contain odd or even harmonics (depending on the type of waveform).

harmonicsynthesis
Resultant waveform of the addition of even harmonics (integer multiples) of the fundamental frequency

 

7/4/2016/Led Labs