Lecture Notes for Analog Electronics - The Electronic Universe ...

We see that IC is not intrinsically a function of IB, but rather is controlled by VBE. For
this reason, and others, it is often stated that transistor gain is really a transconductance
gain. This means that it takes a voltage input and converts it to a current output. So we
write, in general,
gm = iout/vin
as the transconductance gain. We then recover voltage gain by multiplying gm by the resistor
at the output which converts the output current to a voltage. For example, for the commonemitter
amplifier we have iout = −vin/RE and
G = gmRC = −RC/RE
as before.
The base-emitter “diode” implies a relationship between IB and VBE of the form VBE =
V0 ln(IB/I0), where V0 ≈ 0.6 VandI0is a constant. If this form for VBE is plugged into Eqn.
31, we recover our previous relationship IC = βIB, where the current gain β is a combination
of the various factors which are slowly-varying functions of temperature and currents.
Another consequence of Ebers-Moll equation is that we see where the intrinsic emitter
resistance re, which we introduced last time, comes from. By definition,
1/re = iE/vBE ≈ iC/vBE = dIC
From Eqn. 31, the derivative is simply IC/VT .Sowehave
where VT is again as above.
5.9.2 The Current Mirror
re=VT/IC
dVBE
Figure 28 shows a very commonly used current source circuit known as the current mirror.
Understanding its principle of operation requires the Ebers-Moll equation. The “programming
current” IP defines the collector current of the left-hand transistor. (The base
currents should be negligibly small.) From the Ebers-Moll equation, this collector current
then uniquely determines VBE. The collector-base connection transfers this well-defined base
voltage to the collector, thus maintaining the voltage drop across the programming resistor.
The right-hand transistor is “matched” to the left-hand one. That is, the pair were manufactured
together to have nearly identical properties. So this right-hand transistor assumes
a nearly identical collector current to that which is programmed. Thus the load current
becomes IL = IP . Besides transferring the program current to a load at another point of
the circuit, the current mirror also has the advantage of having a larger range of compliance
than the standard single-transistor current source we studied earlier.
5.9.3 Other Non-ideal Effects
The following represent some of the important departures from ideal transistor behavior:
• VBE = VBE(T ). As discussed above, the base-emitter “diode” includes a Boltzmann
factor temperature dependence. This can be linearized, as given in the text, to yield
approximately
∆VBE
∆T ≈−2.1×10−3 V/ ◦ C
32
.
(32)