A logic system is one that anything it does can be translated to a true
or false, present or absent, high or low, in other words, two opposite
and contrasting states where the system can only be at one of them at
any one time. Digital electronics use only two voltage levels to work
with, one to represent a true, 1 or high (usually 3v or 5v) and another
to represent false, 0 or low (a connection to ground, which is at 0v),
which make the basis of any logic system.
But what does a true represent in a logic circuit? anything you can
think of, it depends on what you are using it to model. One of the most
used introductory digital systems is that of a car key alarm, where if
the door is open while the key is still in the ignition, a buzzer alarm
will sound alerting you not to let the key inside the car when you close
it.
To construct a digital circuit for this alarm, you use one input to
represent whether the door is open (will be true when it is open, false
when closed) and another to represent whether the key is in the ignition
(will be true when in the ignition, false when not). For this circuit
we want the buzzer to sound when both conditions are true: the door is
open and the key is in the ignition.
A digital system is not concerned if the key is only half in, at the on
or off position or if the car is only half open or it didn't close
correctly; all of these situations are either forced to one state of the
other, or switching between both at a very high rate, but it must have
one of only two values.
As you can see, we have modeled a fairly complex situation (an alarm
controlled by a door and a key) to only two inputs that take only two
values. This is what makes digital circuits very useful, they are
dependable (a half closed door is an open door, just as a slightly open
door).
Reactive Voltage Divider schematic with explation
Another method to create active filters using opamps is to create a
voltage divider with a resistance & a reactance (from a capacitor).
This approach has some advantages over the previously mentioned filters:
they are easy to build, easy to understand, & have "programmable"
gain.
In the reactive voltage divider, the input is applied to the non inverting input of the opamp. This is so that it can be used as a simple non inverting amplifier, the gain being set by extra resistors that do not interfere or need to be considered much in the filter's working; they are just there to set the amplifier feedback's gain.
The signal is applied in series with one of the components & taken at the input in parallel with the second. The choice of which component is in series & which in paralel with the non inverting input has direct consequences in the functioning of the filter.
If the series component is chosen to be a resistor, then the voltage at the capacitor will determine the signal to be amplified. Since the reactance of the capacitor gets lower with frequency, the higher the frequency the lower the signal available at the opamp input (remember the voltage divider formula: (Vin*R2)/(R1 + R2), in this case, it becomes (Vin*Xc)/(Xc + R) where Xc is the capacitive reactance); This configuration gives us a low pass filter.
With the capacitor being the series component, the voltage at the resistor now determines the signal available at the opamp input. As the frequency gets higher, the capacitor's reactance lowers, up to the point where it acts almost as just a wire; this means that the higher the frequency the more signal available to the opamp. This configuration gives us a high pass filter.
These two main types of voltage divider filters can be cascaded (The output of the first used the the input of the second) in a single stage (one opamp, multiple voltage dividers) or multiple stages (one opamp per voltage divider), the latter having better characteristics due to the opamp's compensating mechanisms.
In the reactive voltage divider, the input is applied to the non inverting input of the opamp. This is so that it can be used as a simple non inverting amplifier, the gain being set by extra resistors that do not interfere or need to be considered much in the filter's working; they are just there to set the amplifier feedback's gain.
The signal is applied in series with one of the components & taken at the input in parallel with the second. The choice of which component is in series & which in paralel with the non inverting input has direct consequences in the functioning of the filter.
If the series component is chosen to be a resistor, then the voltage at the capacitor will determine the signal to be amplified. Since the reactance of the capacitor gets lower with frequency, the higher the frequency the lower the signal available at the opamp input (remember the voltage divider formula: (Vin*R2)/(R1 + R2), in this case, it becomes (Vin*Xc)/(Xc + R) where Xc is the capacitive reactance); This configuration gives us a low pass filter.
With the capacitor being the series component, the voltage at the resistor now determines the signal available at the opamp input. As the frequency gets higher, the capacitor's reactance lowers, up to the point where it acts almost as just a wire; this means that the higher the frequency the more signal available to the opamp. This configuration gives us a high pass filter.
These two main types of voltage divider filters can be cascaded (The output of the first used the the input of the second) in a single stage (one opamp, multiple voltage dividers) or multiple stages (one opamp per voltage divider), the latter having better characteristics due to the opamp's compensating mechanisms.
