day02

Easy bipolar transistor circuits are easy to analyze

Figure 1. Simple BJT circuit

1. Reading

Read Art of Electronics from §2.1 (page 71) through the end of §2.2.3 (page 82), you may skip §2.2.2 (that was 340’s topic).

2. Introduction

The in-class part of this activity is on paper (engineering paper is recommended for helping make nice drawings, but not required).^[1] However, you will need the hardware of Table 1 to complete the related out-of-classtime activities.

Table 1. Homework hardware requirements
Equipment	Parts
(AD2 is A-OK) 5 V power supply 0-5 V variable voltage source voltmeter	(all in your Analog Parts Kit) NPN transistor (e.g. 2N3904) small valued resistor (1-10 Ω range) 1 kΩ resistor 2.2 kΩ resistor

3. BJT circuit analysis at DC

There are a few simple rules analyzing a BJT circuit by hand which work quite well 80% of the time.^[2] This is good news!

Tourbook: Bipolar transistor operation works through the general characteristics of a BJT and continues into a directed discussion about the full Ebers-Moll model and some reasonable approximations in Section 3.4.3.

Make a note-to-self to read that section!

In a way, it is a little easier to understand what triode mode in a MOSFET is about, which is the analogous “ON switch” mode — there is a channel on both the drain and source sides of the device and it behaves somewhat like a small-value resistor.

Ever confused about what is happening in saturation mode for a BJT? Carefully and slowly read Tourbook Section 3.4.3.3. to develop an accurate intuition of what is really going on in a BJT in saturation mode. Remeber that this means that both pn junctions are forward-biased.

But for right now in class, please read Tourbook Section 3.4.4. Hand-calculation models, including §3.4.4.1. Example 1 analysis.

I’ll wait :)

Remember: Only escalate to more complicated models if you need the accuracy and/or have enough time — this is a decision that you as an engineer need to make in the context of your goals.

BJT hand analysis rules

Guess the transistor’s mode of operation {cutoff, active, saturation}.
Substitute the transistor symbol with the appropriate Hand-calculation model.
Solve the rest of the circuit using your linear circuit analysis skills..
Check that the computed voltages and currents are consistent with the chosen mode.
- No? Then make a different guess and try again.

For our hand calculations, use the following “constants:”

V_BE = 0.6 V
V_CEsat = 0.1 V
I_B ≈ 0 μA

3.1. Case A

Set R_C to zero so it acts like a short circuit.
Set R_E to 1 kΩ

Take some paper and draw Figure 1, replace R_C with a wire to emphasize that it is 0 Ω. If you are physically building this, use a 2N3904 or PN2222A transistor and use a small-valued resistor for R_C (≪ R_E, like 1 Ω).

Draw a voltage source between the base node and 0 V and set this voltage source to 1.0 V.
Eyeball the circuit and “guess” that the transistor is in (forward) active mode.
In this (active) mode, we take v_BE to always be 0.6 V (even though it’s not in reality). Therefore, V_E is simply __.
V_C should be really easy to figure out :)
Ohm’s law gives us I_E.
The simple hand analysis model says that the base current is zero. What is the collector current I_C?
CHECK THE VALUES to be sure the results are consistent with the assumptions of the model.
Select another row in the table (suggest 2.0 V) and work out the values for the rest of the row.

\(V_B\)	mode	\(V_E\)	\(V_C\)	\(I_C\)	\(I_E\)
0.0
0.4 (^2nd)
0.8
1.0 (^1st)
2.0
3.0
4.0
5.0

3.2. Case B

Set R_C to 1 kΩ
Set R_E to 1 kΩ

Same circuit, Figure 1. Set the base voltage (via attaching a phantom voltage source) to a value in the table and compute.

\(V_B\)	mode	\(V_E\)	\(V_C\)	\(I_C\)	\(I_E\)
0.0
0.4
0.8
1.0 (^3rd)
2.0
3.0
4.0 (^4th)
5.0

3.3. Case C

Set R_C to 2.2 kΩ
Set R_E to 1 kΩ

\(V_B\)	mode	\(V_E\)	\(V_C\)	\(I_C\)	\(I_E\)
0.0
0.4
0.8 (^5th)
1.0
2.0
3.0
4.0
5.0

4. DBM-01 package

Figure 2. Three legs of circuit understanding

This is the first element of your first DBM package, the analysis part. (Not all of these DBM packages will involve design, especially near the beginning of the course, despite the cute acronym)

Next (class time), you will simulate this same circuit,
then you will build and measure this circuit.

You turn in the package for instructor evaluation after you’ve completed all three phases, and corrected whatever issues with them until all three results match. That “report” will be scored using Syllabus: Grading: EMRN marks.

Electronics are “self-checking” — our hand analysis is only useful if it corresponds to real circuit behavior under real conditions! Many times we make lots of assumptons about those conditions so that the analysis yields some intuition about the circuit’s behavior. Then we use simulation and physical hardware to fill in the details of other characteristics.

1. The paper sold by the Hesse Center is a good price and even my favorite brand. Roaring Spring, Engineer Calculation Pad, green, #95582

2. see the Pareto principle