# 15.2 Pulse Synchronization of Relaxation Devices – Pulse and Digital Circuits

##### 15.2 PULSE SYNCHRONIZATION OF RELAXATION DEVICES

We are going to consider synchronization of the output of a UJT sweep generator using a pulse train. Consider a circuit where a capacitor charges during a finite time interval and the sweep is terminated abruptly by the discharge (relaxation) of the condenser. Such a circuit is called a relaxation circuit. Some relaxation circuits that we have already considered include sweep generators, blocking oscillators and multivibrators. Let us consider a UJT relaxation oscillator shown in Fig. 15.1(a).

Here, the UJT is simply used as a switch. Initially, let the capacitor be uncharged. When the switch is open the capacitor tries to charge to VBB. The moment the voltage across C reaches VP(peak voltage or the breakdown voltage of the UJT), the switch closes, allowing the charge on the capacitor C to discharge almost instantaneously. Again, when the voltage across C reaches VV (valley voltage of the UJT), the switch opens, once again the capacitor charges. This process is repeated, resulting in a waveform as shown in Fig. 15.1(b).

FIGURE 15.1(a) The UJT relaxation oscillator

FIGURE 15.1(b) The output waveform

It is now required to synchronize the output of this relaxation oscillator with an external signal, called the sync signal. This sync signal, which is essentially a negative pulse train, is connected to the UJT circuit such that it changes its peak voltage VP. Thus, in a UJT circuit, the sync signal (negative pulses) is applied at B2 to lower VP, as shown in Fig. 15.2. The resistances RB1 and RB2 are added in series with B1 and B2 respectively.

Let us try to visualize the situation when the synchronizing pulses are applied. As already mentioned, the effect of the sync pulses is to lower the peak or breakdown voltage of the UJT. A repetitive pulse train, having a certain amplitude is shown in Fig. 15.3(a), starting at t = 0. For the first few cycles the sweep generator runs at its natural frequency fo(= 1/To) with Vp = Vo as its amplitude. The sweep signal and the pulse train run at different frequencies and no synchronization is established. At time t = T, the negative pulse reduces the peak of the natural sweep and the relaxation device switches ON, thereby terminating the sweep prematurely. This results in a new sweep time of Ts, which is the same as the spacing between the successive sync pulses, Tp and has the amplitude Vs which is smaller than Vo. From now onwards, the sweep generator output and the pulse train run in synchronism, as shown in Fig. 15.3(a).

FIGURE 15.2 The synchronization of a relaxation device with external pulses

FIGURE 15.3(a) The synchronization takes place after a few cycles

Thus, initially the two generators are not synchronized. However, the unsynchronized generators run in synchronism after a few cycles (from t = T onwards). The synchronization takes place only when the sync pulses occur at the time when they would terminate the sweep cycle prematurely. This means that for synchronization to be possible, the interval between the pulses, Tp must be less than the sweep duration To. Once synchronization takes place the sweep duration changes to Ts and the sweep amplitude to Vs. Now consider a case where Tp > To, as shown in Fig. 15.3 (b).

Here, Tp > To and sync pulses occur at such instants of time that they will not be able to prematurely terminate the sweep cycle. Hence, no synchronization is possible between these two waveform generators. Obviously, synchronization cannot take place if Tp is greater than To. Let us consider another situation where Tp < To, but the amplitude of the sync pulses is small, as shown in Fig. 15.3(c).

It is said that synchronization is possible when Tp < To. However, in the present case, as the amplitude of the sync pulses is small, they will not be able to prematurely terminate the sweep cycle. Hence, here again, no synchronization is possible. Thus, it may be inferred from this discussion that for synchronization to take place: (a) Tp must be less than or equal to To, and (b) the amplitude of the sync pulses should be large enough to bridge the gap between the quiescent breakdown voltage VP and the sweep voltage vc.

FIGURE 15.3(b) There is no synchronization for Tp > To

FIGURE 15.3(c) No synchronization is possible if the amplitude of the sync pulses is small

#### 15.2.1 Frequency Division in a Sweep Circuit

Consider Fig. 15.4(a) in which Tp < To. We see that the first two pulses (marked 2 and 1) do not have sufficient amplitude so as to lower Vp and terminate the sweep cycle. Hence, there is no synchronization. However, the third pulse marked 2 though has the same amplitude as pulses marked 1, but occurs at such a time instant so as to be able to prematurely terminate the sweep cycle. The next sweep is initiated at this instant. However, the next pulse once again marked 1 may still have the same amplitude as the rest of the pulses, but will not be able to terminate the sweep. Once again the next pulse marked 2 occurs at such an instant that its amplitude may still be sufficient enough to prematurely terminate the sweep. Thus, we see that only pulses marked 2 will be able to terminate sweep cycle and not the pulses marked 1. For every two sync pulses there is one sweep cycle and these two generators are seen to be running in synchronization. The sweep generator is now called a divider–the division being by a factor 2. There is one sweep cycle for every two sync pulses, i.e., Ts/Tp = 2, because Ts = 2Tp, where Ts is the sweep duration after synchronization and Tp is the spacing between the sync pulses.

Consider Fig. 15.4(b) where pulses marked 1 and 2 are not large enough to terminate the sweep cycle prematurely. Only when the amplitude of the pulse 1 is as large as V1 and that for pulse 2, it is they will be able to terminate the cycle prematurely to effect synchronization. However, pulses marked 3, though have the same amplitude, occur at such instants that they will be able to effect synchronization. Hence, for every three sync pulses the sweep generator completes one cycle. Therefore, the two generators are said to be synchronized with the frequency division being by a factor 3.

FIGURE 15.4(a) Frequency division by 2

FIGURE 15.4(b) Frequency division by 3 in a sweep generator

We can infer from the previous conditions that:

(i) No synchronization is possible for pulses of smaller amplitude.

(ii) For a pulse amplitude large enough to prematurely terminate the sweep cycle, as Tp/Ts progressively decreases from 1 to 0, 1:1 synchronization holds, followed by 2:1 synchronization and then 3:1 synchronization and so on. TS/Tp is called the counting ratio.

(iii) For a pulse amplitude that is very large, synchronization is always possible. As Tp/Ts decreases from 1 to 0, the division, however, changes from 1:1 to 2:1 to 3:1 and so on.