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DO YOU EXCEL IN ELECTRONICS?

Part 3: The Bottom Line
by Aubrey Kagan

Start ı Calculating The Odds ı Strange Occurrences ı Can You Relate? ı Nothing Up My Sleeve ı Source and PDF

CALCULATING THE ODDS

Letıs consider the simple circuit of the TL431 adjustable voltage reference, which consists of three resistors (see Figure 1). Strictly speaking, all Iım interested in is the generated reference voltage, V_ka. However, there are some constraints that can be placed. First, the current through the TL431 must be ³ 1 mA. Secondly, I would like the current through the programming resistor divider network to be low, say <0.5 mA. And finally, I would like the power dissipated in the voltage-dropping resistor (R3) to be < 0.125 W.

Figure 1ıThe reference voltage for a TL431 circuit is decided by the ratio of R1:R2. However, there are other constraints to the design such as the minimum current required to flow through the TL431 to maintain regulation.

Enter the calculations for V_ka, the current through the TL431 and programming resistors, and the power dissipated in R3 in terms of the values of R1, R2, and R3. This has been done in Example5a.xls (download Excel files). You seed the spreadsheet with some values just to see that the calculations are working correctly. There is another implicit constraint that all of the resistors must be positive. This can be entered for each individual resistor, but there is a blanket option setting to cover this.

Invoke the Solver function by clicking on Tools and then Solver. Choose Options from the Solver dialog box and check the "Assume Non-Negative" option. This forces all of the cells being changed to positive. Description of the effects of the other options can be found in Excelıs Help function. Return to the Solver dialog and enter the cell selections as shown in Photo 1. Run the Solver function and make a note or save the results. Change the values of R1 through R3 to one and run Solver again. Note that two totally different results are generated.

Now, run the Solver function and set V_ka to three. Solver cannot find a solution because the constraints are too tight. If you edit the power dissipation in R3 to 0.25 W, the Solver function will find a solution.

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