Schmitt which is a comparator with hysteresis introduced due

Schmitt
Trigger

All circuits we have discussed so far are having an op-amp in
open loop operation at its core. Since open loop gain is very high, even for a
small Vd , output will change. This means that a steady signal
hovering around (just above or below) threshold may trigger the circuit many
times due to noise. For example, in a zero-crossing detector, input sine wave
may have HF noise superimposed on it. So, during the expected zero crossing of
input, due to noise, actual amplitude may cross zero more than once. This will
trigger the circuit more than once, something that we don’t wish for as we are
interested only in  the number of times
the signal cross zero. A solution to this problem is to implement a circuit
which has some kind of memory. Such a zero- crossing detector circuit will
change output only if input is sufficiently high (more than some positive
voltage, say V) while increasing and only if input is sufficiently small ( less
than a negative voltage, say -V) while decreasing. If this V is more than the
amplitude of noise (which is the usual case), only actual zero crossings by the
signal trigger the circuit.

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Schmitt trigger is one such circuit which is a comparator
with hysteresis introduced due to positive (regenerative) feedback.

Inverting
Schmit trigger

Consider the basic Inverting Schmitt trigger circuit
given in the left page for explanation purpose.

Here,   = ?Vout

Let the saturation levels of the op-amp be  VCsat = L+ and -VCsat
= L- . When the input is largely negative, VN

Given in
Fig 4 b is a circuit which  have
different magnitudes of VTH and VTL.

Here, we
use resistors R and mR for positive feedback and nR to set the desired value
for VP . Operation is straightforward as we have seen in the case of
simple circuit discussed above. Only difference is in the design procedure
which is mentioned below:

We can
write VP in terms of VCC and Vout using
superposition as follows

For getting the desired
VTH and VTL ,
replace VP with VTH ( or VTL) and Vout
with L+ ( or L- ) and solve for m and n. Choose resistor
by assuming a suitable value of R, say 3.3 k? .

Non –
Inverting Schmitt Trigger

This also similar to
the previous case but the main difference is that input is given to inverting
terminal. Consider Fig 5 a .

This is the simplest
Non Inverting Schmitt Trigger circuit. Here also, we use the same notations we
used in the inverting case. The main thing to note here is that VP
is not fixed. Using superposition, we can write VP­ as follows:

It should be noted that
output switches its state when VP cross zero in either direction.

Consider the input to
be largely negative.  This means that
output will be at L- . When we increase Vin , VP
also strart to become less negative. At one particular input voltage, VP
cross zero. Corresponding input voltage is denoted as VTH­ . Once VP
goes positive, Vout becomes L+
, increasing VP further. This means that for further
rise in Vin , there is no change in Vout ( Even if Vin
is kept as 0 just after output has changed, Vout won’t trip back to
L- as VP is still positive due to feedback) .

Putting VP =
0 , Vout = L- and Vin = VTH in the
above eqn, we get

When we go in the other
direction, Vout will remain as L+ until VP
cross zero. This crossing occur at an input voltage of VTL . Once Vi
decrease below VTL , output becomes L- , which further
decrease VP which ensure output won’t change for further decrease in
Vin. ( Even if Vin is kept as 0 just after output has
changed, Vout won’t trip back to L+ as VP is
still negative due to feedback)

Using equation x , we
get

As we have seen for the
inverting case, to shift the switching levels, we use external voltage .  Fig 5 b is a Non Inverting Schmitt Trigger in
which we can design threshold levels. Ra and Rb are used for setting
VN and R1 and R2 are used as feedback
resistors. Working is similar to the simple case but with different threshold
voltages. Design can be done using the following equations.

For switching, VP
should cross VN  where

i.e., (Using
superposition)

Or

Substitute Vin
= VTH ( or VTL ) and Vout = L- ( or
L+ ) to obtain  expressions
for threshold voltages as given below :

And

Solve for R1
, R2 ,Ra  and R4
using above expressions ( Assume some parameters to get remaining )

x

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