15-01-2013, 04:22 PM
Passive integrator and differentiator circuits
[attachment=47050]
The resistor is called a shunt because it is designed to produce a voltage proportional to current, for the
purpose of a parallel (”shunt”)-connected voltmeter or oscilloscope to measure that current. Ideally, the shunt
resistor is there only to help us measure current, and not to impede current through the capacitor. In other
words, its value in ohms should be very small compared to the reactance of the capacitor (Rshunt << XC).
Suppose that we connect AC voltage sources with the following wave-shapes to the input of this passive
differentiator circuit. Sketch the ideal (time-derivative) output waveform shape on each oscilloscope screen,
as well as the shape of the actual circuit’s output voltage (which will be non-ideal, of course):
The technician suggests you build a passive differentiator circuit for his application. You have never
heard of this circuit before, but you probably know where you can research to find out what it is! He tells
you it is perfectly okay if the circuit generates negative voltage pulses when the switch is de-actuated: all he
cares about is a single positive voltage pulse to the computer each time the switch actuates. Also, the pulse
needs to be very short: no longer than 2 milliseconds in duration.
Given this information, draw a schematic diagram for a practical passive differentiator circuit within
the dotted lines, complete with component values.
As the robotic arm rotates up and down, the potentiometer wire moves along the resistive strip
inside, producing a voltage directly proportional to the arm’s position. A voltmeter connected between
the potentiometer wiper and ground will then indicate arm position. A computer with an analog input port
connected to the same points will be able to measure, record, and (if also connected to the arm’s motor drive
circuits) control the arm’s position.
If we connect the potentiometer’s output to a differentiator circuit, we will obtain another signal
representing something else about the robotic arm’s action. What physical variable does the differentiator
output signal represent?
One of the fundamental principles of calculus is a process called integration. This principle is important
to understand because it is manifested in the behavior of inductance. Thankfully, there are more familiar
physical systems which also manifest the process of integration, making it easier to comprehend.
If we introduce a constant flow of water into a cylindrical tank with water, the water level inside that
tank will rise at a constant rate over time:
[attachment=47050]
The resistor is called a shunt because it is designed to produce a voltage proportional to current, for the
purpose of a parallel (”shunt”)-connected voltmeter or oscilloscope to measure that current. Ideally, the shunt
resistor is there only to help us measure current, and not to impede current through the capacitor. In other
words, its value in ohms should be very small compared to the reactance of the capacitor (Rshunt << XC).
Suppose that we connect AC voltage sources with the following wave-shapes to the input of this passive
differentiator circuit. Sketch the ideal (time-derivative) output waveform shape on each oscilloscope screen,
as well as the shape of the actual circuit’s output voltage (which will be non-ideal, of course):
The technician suggests you build a passive differentiator circuit for his application. You have never
heard of this circuit before, but you probably know where you can research to find out what it is! He tells
you it is perfectly okay if the circuit generates negative voltage pulses when the switch is de-actuated: all he
cares about is a single positive voltage pulse to the computer each time the switch actuates. Also, the pulse
needs to be very short: no longer than 2 milliseconds in duration.
Given this information, draw a schematic diagram for a practical passive differentiator circuit within
the dotted lines, complete with component values.
As the robotic arm rotates up and down, the potentiometer wire moves along the resistive strip
inside, producing a voltage directly proportional to the arm’s position. A voltmeter connected between
the potentiometer wiper and ground will then indicate arm position. A computer with an analog input port
connected to the same points will be able to measure, record, and (if also connected to the arm’s motor drive
circuits) control the arm’s position.
If we connect the potentiometer’s output to a differentiator circuit, we will obtain another signal
representing something else about the robotic arm’s action. What physical variable does the differentiator
output signal represent?
One of the fundamental principles of calculus is a process called integration. This principle is important
to understand because it is manifested in the behavior of inductance. Thankfully, there are more familiar
physical systems which also manifest the process of integration, making it easier to comprehend.
If we introduce a constant flow of water into a cylindrical tank with water, the water level inside that
tank will rise at a constant rate over time: