##### 15.4 A MONOSTABLE MULTIVIBRATOR AS A DIVIDER

A monostable multivibrator can be used for synchronization with frequency division [see Fig. 15.9(a)] and the waveforms are shown in Fig. 15.9(b). Here, the positive pulse train is applied at *B*_{1} through a small capacitance from a low impedance source.

The positive pulse train applied at *B*_{1} gets quasi-differentiated as discussed earlier in the Section 15.3.4. The negative spikes at the trailing edge of the pulses are amplified and inverted and appear as the positive spikes at *B*_{2}. As a result, positive spikes due to the second pulse will prematurely terminate the time period resulting in synchronization with the frequency division of 2:1. On the other hand, if the amplitude of the pulses is large enough, pulse 1 may prematurely terminate the time period, thereby changing the counting ratio from 2 to 1.

#### 15.4.1 A Relaxation Divider that Eliminates Phase Jitter

When a pulse train is applied to a divider, there could be a small time delay by the time it appears at the respective bases to cause a possible premature change in the state of the devices. This delay is called the phase delay. Also, as the pulse train is coupled to the divider circuit through an *RC* circuit, it could result in pulses having a finite rise time, Further the divider may have a certain response time which is liable to change with the frequency of the sync signals and the time constants associated with the circuit. As a result, this signal can influence the instant at which the base waveform would drive the device OFF. The phase delay could also be due to the variations in the device characteristics, supply voltages and the noise in the circuit. The phase delay that varies due to the cumulative effect of all these factors is termed as phase jitter. The frequency division without the phase jitter can be implemented using the schematic arrangement shown in Fig. 15.10.

**FIGURE 15.8** The synchronization of both the portions of astable multivibrators with positive pulses applied at *B*_{1} through a small capacitor and low impedance source

The waveforms are shown in Fig. 15.11. The input to the divider is a train of pulses. The divider is an *n*:1 divider, i.e., for every *n* pulses, the *n*^{th} pulse is obtained at the output of the divider. This *n*^{th} pulse is applied as a trigger to the monostable multivibrator which generates a gated output, that is, a pulse of duration *T*. This pulse of duration *T* controls the sampling gate. A sampling gate is one which transmits the input to its output as long the enabling signal (the gating signal) is present. For the rest of the duration, there is no output for the sampling gate. As only the output of the divider (*n*^{th} pulse) triggers the monostable multivibrator, a pulse of duration *T* occurs only at the end of the *n*^{th} pulse. Though a sequence of pulses is present at the input of the sampling gate, only the pulse marked 1 is transmitted to the output, as during the occurrence of this pulse the sampling gate is enabled. The output consists of the pulses labeled 1 only. By adjusting the pulse width of the gating signal such that *T _{p} < T <* 2

*T*

_{p}, we can ensure that the

*n*

^{th}pulse does not pass to the output of the sampling gate. Thus, phase jitter can be eliminated.

**FIGURE 15.9(a)** A monostable multivibrator

**FIGURE 15.9(b)** The waveform at *B*_{2}

**FIGURE 15.10** The frequency division without the phase jitter

**FIGURE 15.11** The waveforms of the divider that eliminates the phase jitter

**Stability of the Relaxation Divider.** In a frequency divider, due to phase jitter, if the *n*^{th} pulse is required to prematurely terminate a sweep cycle, it is possible that either the (*n* − 1)^{th} pulse or even the (*n* − 2)^{nd} pulse may terminate a sweep cycle. This accounts for the instability of the natural timing period of the oscillator, which in turn may cause a loss of synchronization or an incorrect division ratio. The typical voltage variation at the base of an astable multivibrator is shown in Fig. 15.12.

In order to calculate the time period of a monostable multivibrator, we use the relation: *v _{o}*(

*t*) =

*v*

_{f}− (

*v*−

_{f}*v*)

_{i}*e*

^{−t/τ}where,

*v*

_{i}is the initial voltage from which the charge on the capacitor discharges and

*v*

_{f}is the final voltage to which the capacitor would discharge, if allowed to discharge, as

*t*→ ∞. Assuming that

*τ*remains fairly constant, it is the changes in

*v*

_{i}and

*v*

_{f}and

*v*

_{C}(=

*V*) that could be responsible for the instability of the natural period. Let us consider the influence of these factors on the natural time period of the monostable multivibrator:

_{γ}(i) The parameters of the transistor are likely to change due to temperature variations. Also, if the existing transistor is replaced by another for some reason the transistor parameters may be affected. This could influence *v*_{i} and *v*_{C}, the voltage at which the period terminates. *v*_{C} can be the cut in the voltage of a transistor (*V _{γ}*) and

*v*

_{f}can change due to loading. Normally, a regulated power supply with sufficient current rating is used for

*v*

_{f}. Hence, the instability of the time period

*T*

_{o}due to the variation of

*v*

_{f}can be minimized or eliminated. The time period

*T*

_{o}can now mainly change due to the variations in

*v*

_{i}and

*v*

_{C}. However, the choice of

*v*

_{f}may influence the natural time period.

ii) Let us consider the case when *v*_{f} is a large value, say, *v*_{f1} (curve 1). Then the variation between *v*_{i} and *v*_{C} can be approximately linear. Consequently, the change in *T*_{o} due to variation in *v*_{C} can be minimized to some extent. However, in curve 1, if *v*_{i} changes by a larger amount than *v*_{C} (with the same *τ*), then choosing a larger value of *v*_{f} may again give rise to instability of the time period.

iii) On the contrary, if *v*_{f} is reduced to *v*_{f2}, the variation of the voltage between *v*_{i} and *v*_{C} is exponential in nature and hence, non-linear. Now if *v*_{i} varies, then a given percentage change in (*v*_{C} − *v*_{i}) could cause a lesser percentage change in *T*_{o} (curve 2).

**FIGURE 15.12** The factors that account for the instability of a relaxation divider

Hence, the variation in *T*_{o} i.e., instability of the time period, can be minimized by the proper choice of *v*_{f}, depending on whether the instability has occurred either due to the variation in *v*_{C} or *v*_{i}.