Dear Larry,
Could you please explain how hysteresis can be used in digital circuits?
Colin E.
Colin, I would be more than happy to go over the topic of hysteresis.
Hysteresis, in relation to a logic device, is the property of the circuit that causes its output to switch between its two states at two different input voltages. This is the main feature of a Schmitt Trigger. The 74xxx14 is a common device used in digital circuits today. The advantage of this type of circuit is that it is less susceptible to noise. The following discussion attempts to explain how hysteresis works using a standard operational amplifier powered by a single supply.
In the circuit of Figure 1, the op-amp is a comparator with positive feedback.
The following can be stated due to the characteristics of an ideal operational amplifier:
- (1)
- (2)
- (3) if Vp > Vm then Vo = Vdd
- (4) if Vp < Vm then Vo = 0
In order to simplify the resulting equations, let’s also define that R2 = N * R1
The equation for I becomes: 
This allows us to now write the equation for Vp as: 
Which reduces to: 
Which further reduces to equation (5): 
This is the general equation showing the relationships among all the variables. For the sake of the following examples we will use these “real world” values:
N = 4, Vm = 2.4 and Vdd = 5.0 V
We will now use equation (5) to derive equation (6):
In order to determine the significant values for Vin we will first define an initial condition of Vo = 0.
Equation (6a) then becomes: Vp = 0.8 * Vin
Now, using equation (4), we have: 0.8 * Vin < Vm or Vin < Vm / 0.8
If Vm is 2.4V then in order for Vo to be 0, Vin must be less than 3.0V.
Now let’s do the same thing when the initial condition is Vo = 5V.
Equation (6b) is: 
Now, using equation (3), we have:
0.8 * Vin + 1 > Vm or Vin > (Vm - 1) / 0.8
Since Vm is 2.4V then in order for Vo to be 5V, Vin must be greater than 1.75V
What these results tell us is that the logic 0 (Vo=0V) to 1 input transition voltage is 3.0V and the logic 1 (Vo=5V) to 0 input transition voltage is 1.75V.
Figure 2, often called a B-H curve since it was originally used to describe a property of magnetic materials, shows the results. The heavy dotted line is the input voltage. The solid lines are the output voltage. The arrowheads on the output voltage indicate the direction that the input voltage is transitioning to achieve the indicated output.
Without the positive feedback, the output voltage will switch when Vin is within millivolts of the reference voltage at Vm. This would be a noise immunity approaching 0V. The hysteresis band in this example gives the circuit a noise immunity of 1.25V. Once the output voltages switches from one state to the other it will require an input voltage change of at least 1.25V to achieve the original output state.
A similar technique can be applied to a CMOS non-inverting logic element. The following are some restrictions:
- Vm is the CMOS switching point – nominally Vdd / 2
- The “idle” voltage of Vp should never be within the band VILmax and VIHmin. For some devices this range is from .3Vdd to .7Vdd. The above sample violates this rule.
The equations and descriptions in this explanation allows you to design a relatively noise immune circuit using a standard operational amplifier. You should be able to customize the transition voltages based on your particular requirements. I hope this explanation of hysteresis has been useful.
- Larry C.
Larry Cicchinelli is Rabbit Semiconductor’s Technical Support Manager. He has 30 years of embedded experience, and is considered one of the foremost authorities on Rabbit products. Larry and his staff offer comprehensive technical support to Rabbit customers.
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