# 4.4 Comparators – Pulse and Digital Circuits

##### 4.4 COMPARATORS

An amplitude comparator is a circuit that tells the time instant at which the input amplitude has reached a reference level. A comparator is shown in Fig. 4.24.

Ideally, in this comparator:

vo = 0 for t < t1

vo = V for tt1

The amplitude of the output abruptly rises from 0 to V at t = t1, t1 is the time instant at which vi reaches VR.

#### 4.4.1 Diode Comparators

In this section, we discuss two types of diode comparators—pick-off and break-away diode comparators.

Pick-off Diode Comparators. A simple diode comparator circuit is shown in Fig. 4.25. A base clipper is used as a comparator. The input now is a ramp and VR is the reference voltage. The circuit is required to tell the time instant at which the input reaches VR. FIGURE 4.24 A comparator FIGURE 4.25 A pick-off diode comparator

Using an ideal diode, as long as, vi < VR, vo = VR. If viVR, vo = vi. Upto t = t1, vo = VR and the slope of the output is 0. At t = t1, output suddenly rises as the input (the slope at the output has changed) and this is the time instant at which the input reaches the reference level VR. The point P where the slope changes when the diode conducts is called the break point. The diode in this case is called a “pick-off” diode.

As is evident from the Fig. 4.25, there is a sudden change in the slope of the output at the instant the input reaches VR. However, due to ageing and temperature variations, the diode may not switch from OFF to ON at exactly t = t1 (break point, P). It may switch state at any instant after t1 and before t2 (see Fig. 4.26). FIGURE 4.26 The input and output of the diode comparator

Hence, the break point (the point at which the device D changes state) may not exactly be at t1. Instead, there is a break region (t1 to t2), within which, at any instant the device may switch state. Therefore, there is a large region of uncertainty. After the break point, the output follows the input—it has the same slope as the input. If this region of uncertainty is to be reduced to know precisely at which time instant the input reaches the reference level, the break region should be sharp. To achieve this, an amplifier may be placed before or after the comparator.

Consider the response of the comparator circuit shown in Fig. 4.25. To the left of the break point, the diode is OFF. Hence, the reverse incremental resistance of the diode is significantly larger when compared to R. To the right of the break point, the forward incremental resistance of the diode is much smaller than R. If the break point is located at a point where the incremental resistance of the diode, (r) is equal to the resistance (R) then the incremental change in the output voltage (Δvo) for a corresponding change at the input (Δvi) is calculated using Fig. 4.27. If r = R:  FIGURE 4.27 The circuit to calculate the incremental change in the output voltage

This relation tells that Δvi = 2Δvo. That is, for a larger incremental change in the input, there is a smaller incremental change in the output. The region of uncertainty is larger.

A device is connected at the output of the comparator, and is required to be activated when the diode current is say, I and has a drop across R as IR. If, now an amplifier is connected at the output of the comparator to reduce the region of uncertainty, the output of this amplifier activates the device (see Fig. 4.28). Let the amplifier have a gain A. During Δt = t2t1, the output changes by Δvo = V2VR, see Fig 4.26, the delay in the response is reduced to Δt/A or (t2t1)/A.

Let the amplifier only amplify the change in the comparator input but not the reference voltage. The device to be activated is activated only when the drop across R is IR. However, now I = I/A. Hence, the device is activated when the drop across R is RI/A since the diode current is amplified by A and the dynamic diode resistance, r = (η VT/I), varies inversely with current. Therefore, it is evident that, the device to be activated by the comparator will respond at a current corresponding to r = RA. As A→ ∞, → 1

Without an amplifier, Δvovi (the transmission gain) was half and with an amplifier connected as in Fig. 4.29, Δvovi is one; i.e., there is no marked improvement in the response of the comparator arrangement of Fig. 4.28.

Now, consider a comparator circuit where the amplifier precedes a comparator and the output of the comparator is directly connected to the device to be actuated. Let the amplifier have a gain A and Δvi be the incremental change in the input needed to actuate the device when the output is directly connected to the device. With a pre-amplifier with gain A connected to the comparator, Δvi/A is now the incremental change in the input needed to make the output change as in the previous case. As Δvi/A is small, the break region is reduced. Thus, this is a better comparator. FIGURE 4.28 The output of the comparator connected to an amplifier FIGURE 4.29 The output of the amplifier drives a comparator

Break-away Diode Comparators. Consider the circuit in Fig. 4.30. If the input to the circuit is a negative ramp, then the output is as shown. The diode in this case is called a “break-away” diode. Here:

As long as vi > VR, D is ON and vo = VR. When viVR, D is OFF and vo = vi.

The Op-amp as a Comparator. Consider the op-amp comparator as shown in Fig. 4.31(a). The voltage at the inverting input is VR. When vi > VR, vo = +Vsat (VCC ≈ 15 V, the positive supply voltage). Alternatively, when vi < VR, vo = −Vsat (VEE ≈ −15 V, the negative supply voltage). The output thus jumps from +Vsat to −Vsat and vice versa when the input reaches VR, as shown in Fig. 4.31(b). As we see in this comparator, the variation of the signal at the input has no relevance to the output, which is a pulse. This pulse can actuate a device. FIGURE 4.30 Break-away diode comparator FIGURE 4.31(a) Op-amp as a comparator FIGURE 4.31(b) Input and output waveforms of the op-amp comparator

#### 4.4.2 The Double Differentiator as a Comparator

In any comparator, if the output activates a device, the comparator output should reach the device to be activated just at the moment of comparison. Once the device has been activated by the output of the comparator, it is also desirable that the signal is not present. A double differentiator [see Figs. 4.32(a) and (b)] does these twin jobs.

Let the input to the comparator be a ramp. The output of the diode comparator is a step voltage VR up to t and is a ramp beyond this time instant. As long as the input to the first differentiator is a step, its output is zero in no time because C1 blocks dc. At t, the input to the high-pass circuit is ramp; hence, its output is an exponential. This signal is then connected to an amplifier with gain A and the resultant output, which is an exponential, is applied as an input to another high-pass circuit. The output of this is now a pulse whose amplitude and duration can be controlled. FIGURE 4.32(a) A double differentiator as a comparator

In a double differentiator comparator, the device to be activated receives the signal only when the input reaches a reference level. Soon after, as the amplitude of the pulse dies down, no signal reaches the device to be activated. This could be called a practical comparator. FIGURE 4.32(b) The waveforms of a double differentiator