# 6.4 Switching Times of a Transistor – Pulse and Digital Circuits

##### 6.4 SWITCHING TIMES OF A TRANSISTOR

Instead of a step, if a pulse is applied to the transistor switch, how does the device respond? To understand this, we consider the switching times of a transistor (see Fig. 6.24).

Let the input to the transistor switch be a pulse of duration T. When a pulse is applied, because of stray capacitances, collector current will not reach the steady-state value instantaneously. To know exactly when the device switches into the ON state and also into the OFF state, we define the following switching times of the transistor. FIGURE 6.24 Switching times of the transistor

#### 6.4.1 The Turn-on Time of a Transistor

Turn-on time of the transistor is the time taken by the transistor from the instant the pulse is applied to the instant the transistor switches into the ON state and is the sum of the delay time and rise time. To find out the turn-on time of the transistor, the delay time and rise time have to be calculated.

Delay Time (td). It is the time taken for the collector current to reach from its initial value to 10 per cent of its final value.

If the rise of the collector current is linear, the time required to rise to 10 per cent IC(sat) is 1/8 the time required for the current to rise from 10 per cent to 90 per cent IC(sat).

It is given as: where, tr is the rise time.

Rise Time. Rise time, tr is the time taken for the collector current to reach from 10 per cent of its final value to 90 per cent of its final value. From Fig. 6.24 it is seen that the moment input pulse is zero, the collector current is expected to fall to zero. However, because of the stored charges, the current remains unaltered for sometime interval ts1 and then begin to fall. The time taken for this current to fall from its initial value at ts1 to 90 per cent of its initial value is ts2. The sum of these ts1 and ts2 is approximately ts1 = ts and is called the storage time. To calculate the rise time, consider the transistor switch as shown in Fig. 6.25.

Let IB be the base current pulse that drives the transistor into saturation at IB1 and into OFF state at IB2. If RS is large when compared to hie, The response of the transistor to the current step IB1 is given by: If RS is large, where f2 = Upper 3-dB frequency of the low-pass RC circuit. where, τ is the time constant.

Substituting Eq. (6.35) in Eq. (6.34),  FIGURE 6.25 A transistor switch

If the device does not go into saturation, iC would have increased as shown by the dashed line in Fig. 6.26 and would have reached a value hFEIB1 as t → ∞. The gain bandwidth product of a transistor amplifier in which the transistor is replaced by an ideal current source hFEIB(since (1/hoe) ≈ ∞) is given as: where, fT is the frequency at which the short circuit common emitter current gain has a value 1 and CTC is the collector diode transition capacitance.

From Eq. (6.37): Therefore: The variation of the collector current iC is plotted in Fig. 6.26 using Eq. (6.36).

When in saturation Eq. (6.36) is written as: As If N1 > 1, the transistor is in saturation (over-driven transistor). Hence,  FIGURE 6.26 Variation of iC (i) when the device is in saturation (ii) when the device is not in saturation and (iii) when the device switches into OFF state

At t = t1, 1/N1 is 0.1/N1 Similarly t = τ ln  We know that ln (1 + x) =  For N1 >> 1, considering only the 1st term From Eq. (6.39), The rise time tr, is inversely proportional to IB1. Therefore, if the turn-on time is to be small it is desirable to have a larger base current drive (over-driven transistor).

##### EXAMPLE

Example 6.8: Consider the switch in Fig. 6.27, CTC = collector transition, capacitance = 7 pF, hFE = 100 and fT = 10 MHz. Calculate the turn-on time of the transistor. FIGURE 6.27 The given transistor switch

Solution:

To calculate the turn-on time, we have to calculate tr and td.

From Fig. 6.27, we have, In the quiescent state the voltage at B is -4 V. However, when a pulse of 10 V appears at the input this voltage at B is 6 V. We have from Eq. (6.39),  Hence, N1 ≥ 1. Equation (6.41) is valid when the overdrive factor N1 ≥ 1. ωT is the radial frequency at which the current gain is unity. The rise time tr is calculated using Eq. (6.41) as, and from Eq. (6.38), where τ is the time constant.

Using Eq. (6.42) From Eq. (6.41) tturn−on = tr + td = 184 + 23 = 207 ns.

##### EXAMPLE

Example 6.9: A transistor has fT = 50 MHz, hFE = 50, CTC = 5 pF, (CTC = collector transition capacitance) and the supply voltage VCC = 10 V, RC = 0.5 kΩ. Initially the transistor is operating in the neighbourhood of the cut-in point. What base current must be applied to drive the transistor into saturation in 1µs?

Solution:

We have Also ωT = 2πfT = 2 × π × 50 × 106= 314 × 106 radians

CTCRC = 5 × 10−12 × 0.5 × 103 = 2.5 × 10−9 s tr = 1 × 10−6 A transistor is said to be switched from the OFF state into the ON state only when the collector current is 90 per cent of its final value. Thus we see that even though the transistor is expected to switch from OFF to ON at t = 0 when vi = V, the device switches actually into the ON state only when a finite time elapses and we call this time interval as the turn-on time of the transistor. From Example 6.8:

tturn-on = td + tr = 23 + 184 = 207 ns

#### 6.4.2 The Turn-off Time of a Transistor

Again at t = T (at the end of the pulse), the transistor is required to switch into the OFF state instantaneously. But this is not going to happen. Once the device is driven hard into saturation, because of large number of stored charges on either side of the junction, the collector current is not going to fall to a smaller value instantaneously. To calculate the turn-off time we have to calculate the storage time and the fall time.

Storage Time (ts). Storage time, ts, is the time taken for the collector current to fall from its initial value to 90 per cent of its initial value. IB1 is the base current, when the pulse amplitude is V = 10 V and IB2 is the base current, when the pulse amplitude is zero, (see Fig. 6.27).

Here  where, αI and αN are the inverted mode and normal mode current gains in terms of Ebers–Moll parameters. αN0 is the normal direction current gain and its 3-dB frequency is ωN. αI0 is the inverted mode current gain and the 3-dB frequency is ωI.

##### EXAMPLE

Example 6.10: From Fig. 6.27, calculate the storage time if hFE = 100, αN0 = 0.99, αI0 = 0.5, fN = 1.2 fT fT = 1.2 × 1 × 106 = 1.2 MHz, fI = 1MHz

Solution:

From Eq. (6.44): If V = 10 V Using Eq. (6.43): Further, the transistor is said to be switched from the ON state to OFF state only when the collector current falls to 10 per cent of its initial value. This is the fall time.

Fall Time. Fall time, tf, is the time taken for the collector current to fall from 90 per cent of its initial value to 10 per cent of its initial value. To calculate the fall time, consider Fig. 6.28 when the base current is IB2.

The fall time calculation is similar to the rise time calculation. Here, IB2 flows in the opposite direction. The device returns from saturation to active region where the collector current is hFEIB2. As IB2 flows in the opposite direction N2 is positive. We have, From Fig.6.26 at t = t3, 1/N2 is 0.9/N2  FIGURE 6.28 Base current is IB2 Similarly, t4 = τ ln  Fall time, tf again is inversely proportional to IB2. If the turn-off time is to be small, IB2 should be relatively large.

It is given as: Equation (6.47) is valid when N2 > 1.

##### EXAMPLE

Example 6.11: For the circuit in Fig. 6.27, calculate the fall time.

Solution: From Eq. (6.47), we have, Therefore, from the calculations made in Examples 6.10 and 6.11, we have the turn-off time of the transistor as,

tturn-off = ts + tf = 447 + 274 = 721ns.

The major concern now in switching applications is – how quickly can we drive a transistor from one state to the other. This switching speed obviously depends on the switching times of the transistor.