rare to need more than two iterations (including the one driven by the initial guess) when the values
of
are large. The exceptions to this rule are (of course) low
transistors, and configurations where
the value of
is large, regardless of
. Overall, one can see that this is a very simple method
–
we
did not even need to solve a system of equations.
One-Shot Solution
This circuit can also (relatively) easily be solved using a single-stage solution. This process becomes
exponentially more difficult as the circuit complexity increases. We would begin our process in the
same manner as the previous solution, by writing a node equation for
, and re-arranging to yield
the same update equation as before:
(1)

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234
From here, we need to either replace
with a term using
, or vice versa. Typically, it is easier to
replace the current, as it often has alternate equations due to resistors elsewhere in the circuit
(typically emitter resistors or collector resistors). In this case, we trace the path of
through both
transistors to the resistor
before finding an alternate equation. Working backwards, we see a
similar path as in the iterative solution:
(2)
Substituting and solving yields a direct solution for
:
(3)
Confirming BJT operating modes:
(4)

235
The answer is identical to what we obtained after iterating. In general, both methods entail roughly
the same set of steps, though the iterative method typically makes these sequential so that we do not
need to solve the circuit all at once. Many people find it easier to work through in this way, but the
choice is yours. This ends the basic examples on BJT DC calculations. More examples are available
in the solutions to the past exams. I will also provide one additional extremely difficult (challenge)
problem; as before, if you can solve this, you are very prepared for this section. Our last work for the
course will cover the BJT small signal model. As we will see, it is very similar to the MOSFET
model. The only addition will be a resistor from base (formerly gate) to emitter (formerly source).
Otherwise, everything will be basically identical. This means that all of the small-signal circuit
knowledge you have from MOSFET circuits will still apply.
Source:
LAST YEAR’S EXAM
In-Class Break
–
Exam Art

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This set of notes provides an extra practice problem for BJTs at DC.
Current Topics: More DC BJT Examples
Next Topics: SS Model, SS Analysis
The following example is significantly more complex than you would find on a test or exam. If you
are comfortable with this example, then you should have no problem with anything in an actual test
situation.
BJT DC Example 3
The following is the output stage of a large-signal BJT amplifier. It is actually part of a 20W audio
amplifier which you can easily build yourself, if interested. The only other major component is an op-
amp and some resistors.

- Spring '17