Transistors are widely used in digital logic circuits and switching applications similar to those described in Chapter 3. Recall that the waveforms encountered in those applications periodically alternate between a “low” and a “high” voltage, such as o Y and +5 Y. The fundamental transistor circuit used in switching applications is called an inverter, the NPN version of which is shown in FigureA-42. Note in the figure that the transistor is in a common-emitter configuration, !fut there is no bias voltage connected to the base through a resistor, as in the CE bias circuits studied earlier. Instead, a resistor Ru is connected in. series with the base and then directly to a square or pulse-type waveform that serves as the inverter’s input. In the circuit shown, Vn and the “high” level of the input are both +5 Y. The output is the voltage K!tween collector and emitter (VnJ. as usual.

When the input to the inverter is high (+5 V). the base-emitter junction ‘is forward biased and current flows through Ru into the base, The values of RII and R; are chosen (designed) so that the amount of base current flowing is enough to saturate the transistor. that is, to drive it into the saturation region of its output characteristics, Figure 4-43 shows a load line plotted on a set of CE output characteristics and identifies the point on the load line where saturation occurs. Note that the value of Vu. corresponding to this point, called VO:(sat), is very nearly 0 (typically – about 0.1 V). The current at the saturation point is called Iq…,) and is very nearly equal to the intercept of the load line of the Ie-axis, namely, VcclRc. When the transistor is saturated, it is said to be ON. This analysis has shown that a high input to the ;~1V(‘rtcr (+5 Y) results In a low output (= 0 V).

When the input to the transistor is low, i.e., 0 Y, the base-emitter junction has no forward bias applied to it, so no base current, and hence no collector current,

flows. There is. therefore. no voltage drop across Rc. and it follows that Va must be the same as Va’; +5 V. This fact is made evident by substituting Ie = 0 in the’ equation for V”l (cquati :l 4-24); V~K = Vcc – feR, = VeL – (O)(Rc) = Vcc. In this situation. the transistor is in the cutoff region of its output chai acteristics. as shown in Figure 4-43, and is said to be OFF. A low input to the inverter results in a high output. and it is now obvious why this circuit is called an inverter. In designing and analyzing transistor inverters. it ic l,’m’llly assumed that 1C(.,m) = VcclRc and that VC£(‘OI) = 0 V. These are very good approximations and lead to results that are valid for most practical applications. Under these assumptions. we can easily derive the voltage-current relations in a transistor inverter. Since the transistor is cut off when the input is low. regardless of the values of RB and Rc. the equations we will study are those that apply when the input is high. Actually. these equations are precisely those we have already derived fo.r a CE transistor. for the special case Ie =- Iq,al)’ Thus.

**Inverter Design**

To design a transistor inverter we must have criteria for specifying the values of RB and Re. Typically, one of the two is known (or chosen arbitrarily), and the value of the other is derived from the first. Using equations 4-33 and 4-34, we can obtain the following relationships between RB and Re

Equation 4-35 can be used to find RIJ when Re is known, and equation 4-36 to find Re when Ro is known. However, since these equations are valid only for a specific value of f3, they are not entirely practical. We have already discussed the fact that the {3of a transistor of a given type is liable to vary over a wide range. If the actual value of f3 is smaller than the one used in the design equations, the transistor -vill not saturate. For this reason, the f3 used in the design equations should always be the smallest possible value that might occur in a given application. In other words, equations 4-35 and 4-36 arc more practical when expressed in the form of inequalities, as follows

These inequalities should hold for the entire range of f3-values that transistors used in the inverter may have. This will be the case if the minimum possible f3-value ‘t used.

We should note that when a transistor has a higher value of f3 than the~me for which the inverter circuit is designed, a high input simply drives it deeper into saturation. This overdriuing of the transistor creates certain new problems, including the fact that it slows the speed at which the device can switch from ON to OFF, but the output is definitely low in the ON state .

**Solution**

Using equation 4-35 with {3 = (3(lIIill) = 80, we find

**The Transistor, as a Switch**

transistor inverter is often called a transistor switch. This terminology is appropriate because the ON and OFF stales of the transistor correspond closely to the closing and opening of a switch connected between the collector and the emitter. When the transistor is ON, or saturated, the voltage between collector and emitter is nearly 0, as it would be across a closed switch, and the current is the maximum possible, Vcel Re. When the transistor is OFF, zero current flows from collector to emitter and the voltage is maximum, as it would be across an open switch. The switch is opened or closed by the input voltage: a high input closes it and a low input opens it. Figure 4-45 illustrates these ideas.

In many switching applications, the emitter may be connected to another circuit, or to another voltage source, instead of to ground. When analyzing such complex digital circuits, it is quite helpful to think of the transistor as simply a switch, for then-it is easy to understand circuit operation in terms of the collector circuit being

connected to or disconnected from the e~.~er circuit. For example, Ii’ the emitter in the hasic inverter circuit were conn ctcd to -5 V instead 01 ground, then the output would clearly switch between +.5 V and -.5 V mstcad of between -!.5 V and () V,