Quote of the Day
The power of instruction is seldom of much efficacy except in those happy dispositions where it is almost superfluous.
— Gibbon. I think this quote is a bit harsh, but not off too much. I recently have been taking some online classes where I work problems and can ask the instructor questions if I have issues. In this case, there really is no instruction – I am just reading the book and getting the opportunity to ask an expert questions. It works.
I thought Dennis' post was good because it (1) provided a very clean demonstration of the use of Thevenin and beta transform equivalent circuits for analysis, and (2) it also provide me a good demonstration for how to use a computer-algebra system to help you design a circuit.
I am always looking for good Mathcad reference applications for my staff. In this post, I illustrate the the basic circuit transformation and then use Mathcad to determine component values and predict circuit performance. I also simulate the circuit using LTSpice (Appendix A).
I should point out that even though this circuit is simple, the algebra can get overwhelming. The gods of electronics work by simple rules, but they have no fear of algebra.
I am always looking for simple power conversion circuits to use for my home projects. I like to see current-limited power sources for safety reasons. The performance of this circuit is not great, but there are ways to improve it – I will cover these later.
This circuit really operates in two modes (see Appendix A for simulation details):
- Q1 Saturated
When not limiting the output current, Q1 is saturated. As such, Q1 dissipates relatively little power.
- Q1 Active
When limiting the output current, Q1 is in the active region and is dissipating significant power.
Circuit with Beta Transformation
Figure 3 shows the circuit of Figure 2 using a beta transformation.
Derivation of Formulas for the RI and RB Values
Figure 4 shows how to analyze the circuit in Figure 3 for RE and RB. Note how I grabbed an intermediate term to determine the constraint for a positive RE value.
Derivation of Constraint on RE
Figure 5 shows how to derive the constraint on RB that ensures positive RE.
Derivation of RE Equation
Figure 6 shows to derive the expression for RE. I start with the expression shown in Figure 4 with the bubble numbered 1.
Figure 7 shows the example worked on the blog post.
This was a good illustration of the capabilities of a computer algebra system for a simple electronic circuit. This current-limited voltage source served that purpose well.
Appendix A: LTSpice Simulation
I captured the circuit in LTSpice (Figure 8).
Figure 9 shows my simulation result. The values are in the range I would expect for this circuit.