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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 imp ortant to understand the inner workings of transistors. This is dicult, and the descriptions which one gets by getting into the intrinsic prop erties are not particularly satisfying. Rather, it is usually enough to understand the extrinsic prop erties of transistors, treating them for the most part as a black b ox, with a little discussion ab out the subtleties which arise from within the black b ox. In practice, one usually confronts transistors as comp onents of pre-packaged circuits, for example in the op erational ampli er circuits which we will study later. However, I have found that it is very useful to understand transistor b ehavior 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 bip olar transistors. There are other common technologies used, particularly FET's, which we will discuss later. However, most of what you know can b e carried over directly by analogy. Also, we will assume npn typ e 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 Op erating Mo de
Below we have the basic connection de nitions for bip olar transistors as taken from the text. As indicated in the gure, and as you determined in lab, the base-emitter and base-collector pairs b ehave somewhat like dio des. Do not take this to o 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: Bip olar transistor connections.
5.1.1 Rules for Op eration
Let's start by stating what needs to b e done to a transistor to make it op erate as a transistor. Supp ose we have the following:
- VC > VE , by at least a few 0 : 1 V.
- VB > VE
- VC > VB
- We do not exceed maximum ratings for voltage di erences 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 prop ortion to the current owing into the base:
IC = hFE IB = 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 typ e to typ e, and within each typ e, to o. However, typically 100. Unless otherwise sp eci ed, we will assume = 100 when we need a numb er. From Figure 17 b elow 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 b elow, the transistor will \try" to achieve its nominal. This will not always b e p ossible, in which case the transistor will still b e on, but IC < IB. In this case, the transistor is said to b e \saturated".
I C
IE
IB
Figure 17: Transistor currents.
Because 1, the main utility of the transistor b ecomes 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 ab ove we require that the base-emitter \dio de" b e forward biased, i.e. that VBE VB VE b e p ositive. In fact, the base-emitter pair do es b ehave much like a dio de. 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 op eration, we have
VBE VB VE 0 :6Volts (21)
Typically, we can consider v or i to b e 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 V 0 or I 0 , resp ectively.
5.3 Emitter Follower
The basic emitter follower con guration is shown b elow 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 imp edance and a small output imp edance.
Vin
Vout
R
Vcc
Figure 19: Basic emitter follower.
For an op erating 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 de ne the input imp edance of the follower:
Zin = vin =iin = vB =iB = R( + 1) (23)
By applying the Thevenin de nition for equivalent imp edance, we can also determine the output imp edance of the follower:
Zout = vin =iE =
vin ( + 1)iB
Zsource
where Zsource is the source (i.e. output) imp edance of the circuit which gave rise to vin. Hence, the emitter follower e ectively increases input imp edance (compared to R) by a factor + 1 100 and reduces output imp edance, relative to that of the source imp edance of the previous circuit element, by a factor + 1 100. We will return to this p oint next time.
