# 8.4 Commutating Condensers – Pulse and Digital Circuits

##### 8.4 COMMUTATING CONDENSERS

In the initial stable state Q2 is ON and in saturation, Q1 is OFF. Once a trigger is applied [see Fig. 8.3] to change the state of the devices in the monostable multivibrator, because of the stray capacitances of the devices they may not go into the next state immediately. This is a problem which needs to be overcome.

Now, let a negative pulse be applied at the base Q2 to drive it into the OFF state and consequently Q1 into the ON state. Prior to the application of this trigger the voltage at the second collector was VCE(sat). On the application of a trigger at t = 0, as Q2 goes into the OFF state, the voltage at its collector rises from VCE(sat) to VCC. Let the change in voltage at the second collect be vi, a step voltage. That is,

This voltage change at the second collector is coupled to the first base through R1 and R2, as shown in Fig. 8.9(a). As a result, Q1 is expected to switch into the ON state.

If the attenuator is a simple resistive attenuator as seen in Fig. 8.9(a), the moment Q2 switches into the OFF state, Q1 quickly switches into the ON state. However, between the input terminals of Q1 if a stray capacitance Ci is present, then the attenuator circuit in Fig. 8.9(a) gets modified as shown in Fig. 8.9(b).

FIGURE 8.9(a) A simple resistive attenuator

FIGURE 8.9(b) An attenuator considering the stray capacitance

To reduce this two loop network into a single loop network, let us Thévenise the circuit.

where

and

Then the circuit shown in Fig. 8.9(b) reduces to that shown in Fig. 8.9(c).

Now, only when the voltage at B1 rises to 90 per cent of its final value, the device Q1 is assumed to switch from the OFF state into the ON state. This time interval is the rise-time of the circuit.

As an example, if R1 = R2 = 1 MΩ, Rth = 0.5 MΩ and if Ci = 10 nF then:

tr = 2.2 × 0.5 × 106 × 10 × 10−9 = 11 ms

Having applied a trigger at t = 0 so as to switch Q2 into the OFF state and consequently Q1 into the ON state, it is understood that Q1 will not go into the ON state unless a time period of 11 ms elapses from the instant the trigger is applied, which is a large time delay and is not acceptable. Such an attenuator is called uncompensated attenuator. From the above discussion, it is evident that conduction is transferred from Q2 to Q1 after a finite time interval (11 ms) from the instant the trigger is applied. This time delay is called the transition time. Transition time is, therefore, defined as the time taken for conduction to be transferred from one device to the other. This means that transition time is the time interval from the instant the trigger is applied at the base of Q2 which is ON to the instant when Q1 switches ON. To reduce this transition time condenser C1 is connected in shunt with resistor R1, as shown in Fig. 8.9(d).

Then the attenuator circuit shown in Fig. 8.9(d) is redrawn as shown in Fig. 8.9(e).

The circuit shown in Fig. 8.9(e) is in the form of a bridge comprising of four arms—R1, C1, R2 and Ci. The bridge is said to be balanced when R1C1 = R2Ci. If this condition is satisfied, then the current in the loop XY is zero and it appears as though there is no physical connection between X and Y, as shown in Fig. 8.9(f). The net result is that the output is calculated independently, either by considering the capacitance combination or the resistance combination.

As discussed in section 3.4.1, at t = 0+, C1 and Ci decides the output and at t = ∞, R1 and R2 decide. As the voltage at the base of Q1 abruptly rises, Q1 goes into the ON state almost instantaneously. Therefore, with this arrangement the moment a trigger is applied, conduction is transferred from Q2 to Q1. Obviously, transition time is drastically reduced by using a compensated attenuator, as shown in Fig. 8.9(f). If the output at vo(0+) = vo(∞) then this attenuator is a perfect attenuator. Here C2 is the collector of Q2 and B1 is the base of Q1.

FIGURE 8.9(c) An attenuator circuit with Thévenin source and its internal resistance

FIGURE 8.9(d) An attenuator circuit with condenser C1 in shunt with resistor R1

FIGURE 8.9(e) The redrawn circuit of Fig. 8.9(d)

FIGURE 8.9(f) The compensated attenuator

FIGURE 8.9(g) The collector-coupled monostable multivibrator using commutating condenser

As the capacitor C1 is connected in shunt with resistor R1 it helps in reducing the transition time, this capacitor is called the speed-up capacitor, commutating condenser or transpose capacitor. The collector-coupled monostable multivibrator using commutating condenser is shown in Fig. 8.9(g).

#### 8.4.1 Calculation of the Value of the Commutating Condenser

If C1 is the commutating condenser then,

where, Ci is the stray capacitance at the input of the transistor and using Eq. (8.49), C1 can be calculated. In the absence of any specification of Ci, R1C1 is typically chosen as 1 µs.

#### 8.4.2 A Monostable Multivibrator as a Voltage-to-time Converter

A monostable multivibrator can be used as a voltage-to-time converter, in which the time duration is a function of voltage, as shown in Fig. 8.10(a). The time, T for which Q1, in the quasi-stable state, is ON and Q2 is OFF is calculated. Now, consider the voltage variations at B2, as shown in Fig. 8.10(b).

FIGURE 8.10(a) The monostable multivibrator as a voltage-to-time converter

FIGURE 8.10(b) Voltage variation at B2

VB2(t) = vf − (vfvi)et/τ      vf = V      vi = VσI1RC

If Q1 is in saturation,

At t = T,

VB2(t) = Vγ      Vγ = V − [VVσ + VCCVCE(sat)]eT/τ

As Vγ, Vσ and VCE(sat) are small when compared to V and VCC,

Thus, to change T, V can be varied. As the pulse width is a function of V, the monostable multivibrator is called a voltage-to-time converter.