In its most general sense; hysteresis is a property that means a device behaves differently when its input is increasing from the way it behaves when its input is decreasing. In the context of a voltage comparator, hysteresis means that the output will switch when the input increases to one level but will not switch back until the input falls below a different level. In some applications, hysteresis is a desirable characteristic because it prevents the comparator from switching back and forth in response to random noise fluctuations in the input. For is near o V, and if the input offset voltage is 1 mY, then noise voltages on the order of 1 mV will cause random switching of the comparator output. On the other hand, if the output will switch to one state only when the input rises past -1 V, and will switch to the other state only when the input falls below + 1 V, then only a very .arge (2- V) noise voltage will cause it to switch states when the input is in:l.~the ‘;(.mity of one of these “trigger” points.
(a) shows how hysteresis can be introduced into comparator operation. In this case, the input is connected to the inverting terminal and a voltage divider is connected across the nonin /erting terminal between u; and a fixed reference
voltage VREF (which may be 0). Figure 15-5(b) shows the resulting transfer characteristic (called a hysteresis loop). This characteristic shows that the output switches to + VmlU when Vi. falls below a lower trigger level (L TL), but will not switch to – Vma.r unless VI. rises past an upper trigger level (UTL). The arrows indicate the portions of the characteristic followed when the input is increasing (upper line) and when it is decreasing (lower line). A comparator having thi<; characteristic is called a Schmitt trigger.
We can derive expressions for UTL and LTL using the superposition principie. Suppose first that the comparator output is shorted to ground. Then
IMG
In these equations. of V”,”,is the maximum positive output voltage (a’positive number) and – VHloU is the maximum negative output voltage (a negative number). The magnitudes of these quantities may be different; for example, +Vnuu = +10 V and – VIII”‘” = -5 V
Quantitatively, the hysteresis of a Schmitt trigger is defined to be the difference between the input trigger levels. From =quations 15-4 and 15-5,
IMG
1. Find the upper and lower trigger levels and the hysteresis of the Schmitt trigger
shown in Figure 15-6. Sketch the hyster sis loop. The output switches between ±15 V.
2. Repeat (1) if VREF = 0 V.
3. Rep-st (1) if VREF = 0 V and the output switches between 0 V and +15 V.
The comparator we have discussed is called an inuerting Schmitt trigger because the output is high when the input is low, and vice versa, as can be seen in Figure 15-7. Figure 15-8 shows a noninverting Schmitt trigger. For this circuit, the lower and upper trigger levels are.
Notice that these equations permit the magnitudes of +V” and – V,/UU to be different values. For example, if R, = 10 kO and R2 , 20 kf], and if the put switches between +10 V and -5 V, then LTL = -(0.5)(10 V) := -5 V and: TL = 0.51-5 Vi = +2.5 V. The derivation of equations 15,-8 and 15-9 is an exercise at the end of this chapter.