431/531 Class Notes 5
5 Transistors and Transistor Circuits
Although I will not follow the text in detail for the discussion of transistors, I will follow the text's philosophy. Unless one gets into device fabrication, it is generally not important to understand the inner workings of transistors. This is dicult, and the descriptions which one gets by getting into the intrinsic properties are not particularly satisfying. Rather, it is usually enough to understand the extrinsic properties of transistors, treating them for the most part as a black box, with a little discussion about the subtleties which arise from within the black box.
In practice, one usually confronts transistors as components of pre-packaged circuits, for example in the operational amplier circuits which we will study later. However, I have found that it is very useful to understand transistor behavior even if one rarely builds a transistor circuit in practice. The ability to analyze the circuit of an instrument or device is quite valuable.
We will start, as with Chapter 2 of the text, with bipolar transistors. There are other common technologies used, particularly FET's, which we will discuss later. However, most of what you know can be carried over directly by analogy. Also, we will assume npn type transistors, except where it is necessary to discuss pnp. For circuit calculations, one simply reverses all signs of relevant currents and voltages in order to translate npn to pnp.
5.1 Connections and Operating Mode
Below we have the basic connection denitions for bipolar transistors as taken from the text. As indicated in the gure, and as you determined in lab, the base-emitter and base-collector pairs behave somewhat like diodes. Do not take this too literally. In particular, for the base- collector pair this description is far o the mark. We will refer to the transistor connections as C, B, and E.
Figure 16: Bipolar transistor connections.
5.1.1 Rules for Operation
Let's start by stating what needs to be done to a transistor to make it operate as a transistor. Suppose we have the following:
1. VC > VE, by at least a few 0:1 V.
2. VB > VE
3. VC > VB
4. We do not exceed maximum ratings for voltage dierences or currents.
When these conditions are not met, then (approximately) no current ows in or out of the transistor. When these conditions are met, then current can ow into the collector (and out the emitter) in proportion to the current owing into the base:
IC = hFEIB = IB (19)
where hFE = is the current gain. (We will use the notation in these notes.) The value of the current gain varies from transistor type to type, and within each type, too. However, typically 100. Unless otherwise specied, we will assume = 100 when we need a number. From Figure 17 below and Kircho's rst law, we have the following relationship among the currents:
IE = IB + IC = IB + IB = ( + 1)IB IC (20)
As we will see below, the transistor will \try" to achieve its nominal . This will not always be possible, in which case the transistor will still be on, but IC < IB. In this case, the transistor is said to be \saturated".
Figure 17: Transistor currents.
Because 1, the main utility of the transistor becomes evident: We are able to control a large current IC IE with a small current IB. The simplest such control is in the form of a switch. Note that in our second condition above we require that the base-emitter \diode" be forward biased, i.e. that VBE VB VE be positive. In fact, the base-emitter pair does behave much like a diode. So when it is forward biased, current can easily ow, and the voltage drop quickly reaches its asymptotic value of 0:6 V. Unless otherwise noted, we will generally assume that, when the transistor is in operation, we have
VBE VB VE 0:6Volts (21)
5.1.2 Transistor Switch and Saturation
From the preceding discussion, the most straightforward way to turn the transistor \on" or \o" is by controlling VBE. This is illustrated by the circuit below which was introduced in Lab 2. We will follow the lab steps again here.
Figure 18: A transistor switch.
First, letR = 10 k . When the switch is open, IC = IB = 0, of course. When the switch is closed, then VBE becomes positive and VB = VE + 0:6 = 0:6 V. IB = (5 0:6)=104 = 0:44 mA. Hence, IC = IB = 44 mA. Then, assuming negligible voltage drop across the LED, VC = 5 33 0:044 = 3:5 V. So, VCE > 0 and VCB > 0. So this should work just ne.
Substituting R = 1 k gives IB = 4:4 mA and IB = 440 mA. Setting this equal to IC would give VC = 9:5 V. This is not possible. In order to stay in operation VCE must be positive, and depending upon the transistor species, usually can only go as low as 0:2 V. (Appendix K of the text, pages 1066-1067, gives data for a typical model.) Hence, IC is limited to a maximum value of IC = (5 0:2)=33 150 mA. So, eectively, the current gain has been reduced to = IC=IB = 150=4:4 = 34. In this mode of operation, the transistor is said to be saturated. It turns out that for high-speed switching applications, for example in computers, the transistors are generally operated in a partially saturated mode, for reasons discussed in Section 2.02 of the text.
We will now look at some other typical transistor congurations, including the emitter follower, the current source, and the common-emitter amplier. But rst we need to set some notation. We will often be considering voltages or currents which consist of a time varying signal superposed with a constant DC value. That is,
V (t) = V0 + v(t) ; I(t) = IO + i(t)
where V0 and I0 are the DC quantities, and v or i represent time-varying signals. Hence,
V = v ; I = i
Typically, we can consider v or i to be sinusoidal functions, e.g. v(t) = vo cos(!t + ), and their amplitudes vo and io (sometimes also written as v or i when their is no confusion) are small compared with V0 or I0, respectively.
5.3 Emitter Follower
The basic emitter follower conguration is shown below in Figure 19. An input is fed to the base. The collector is held (by a voltage source) to a constant DC voltage, VCC. The emitter connects to a resistor to ground and an output. As we shall see, the most useful characteristic of this circuit is a large input impedance and a small output impedance.
Figure 19: Basic emitter follower.
For an operating transistor we have Vout = VE = VB 0:6. Hence, vout = vE = vB. From this, we can determine the voltage gain G, equivalent to the transfer function, for the emitter follower:
G vout=vin = vE=vB = 1 (22)
From Eqn. 20, IE = (+1)IB ) iE = (+1)iB. Therefore, we see that the follower exhibits \current gain" of output to input equal to + 1. Assuming the output connection draws negligible current, we have by Ohm's Law iE = vE=R. Using this in the previous expression and solving for iB gives iB = iE=( + 1) = (vB=R)=( + 1). Now we can dene the input impedance of the follower:
Zin = vin=iin = vB=iB = R( + 1) (23)
By applying the Thevenin denition for equivalent impedance, we can also determine the output impedance of the follower:
Zout = vin=iE = vin
( + 1)iB = Zsource + 1
where Zsource is the source (i.e. output) impedance of the circuit which gave rise to vin. Hence, the emitter follower eectively increases input impedance (compared to R) by a factor + 1 100 and reduces output impedance, relative to that of the source impedance of the previous circuit element, by a factor + 1 100. We will return to this point next time.