Introduction

The Art of Electronics (AoE) book is full of tips and tricks that make the process of designing a circuit quicker and more intuitive. The entire left column of page 6 is

Most of these questions are quick and review. The last two require using your reference materials (Razavi and slides) to get the information you need.

1. Questions

1.1. AoE Exercise 1.1

Found on book page 5.

1.2. AoE Exercise 1.2

Also on page 5.

1.3. AoE Exercise 1.4

Page 6.

Equation (1.5) works for any number of resistors in parallel. The “parallel resistor equation” you remember is just this formula with two resistors and simplified to a single fraction — do that 40 seconds of algebra to show this to yourself.

Do this “show” (proof) exercise by first drawing a schematic of 3 or more resistors in parallel. Then do circuit analysis to find the equivalent resistance of the network without using a parallel resistor formula, e.g. using equations generated from Ohm’s law, KCL, and KVL.

1.4. AoE Exercise 1.5

Page 6.

Power rating of a resistor

The maximum power that the resistor can absorb (and therefore increase in temperature) under “rated” conditions.

This is usually at the maximum ambient temperature specified for the resistor, but may have other and more conditions. For example, a 1/4 W resistor can absorb much more power if it is submerged in ice water.

1.5. AoE 1.5 followup

The resistors in your “Analog Parts Kit” that you received in the package with your Analog Discovery 2 have 1/8 W ratings.

  • If your power supply outputs up to 10 V maximum, what is the smallest value of resistor that is guaranteed to never exceed its 1/8 W power rating in any connection arrangement across this supply?

Another way to think of this problem is: below what resistor value do you need to concern yourself with the resistor possibly getting too hot?

Req Review

Remember that the fundamental way of determining an equivalent resistance is finding a single resistor value whose V/I relationship exactly matches the V/I for the two-terminal network.

Figure 1 shows how you can attach an independent voltage or current source to the terminals of an unknown network and measure either:

  • The current Ix that flows in response to Vforce (obviously: Vx == Vforce), or

  • the voltage Vx that is developed in response to Iforce (clearly: Ix == Iforce).

equivalent resistance model
Figure 1. Using an independent source to detect apparent resistances.

 

1.6. ni vs temp for silicon

Find the values of the intrinsic carrier concentration, ni, for silicon at the temperatures in the table. Also, at each temperature, what fraction of the atoms are ionized?  (A silicon crystal has about 5x1022 atoms/cm3).

When you need values for constants, use values you find in the Razavi book first.  The values are not as "constant" as you might wish and you will therefore get different numbers depending on your source. Such constants depend on many other factors, including even atmospheric pressure (!).
Temp \((^\circ C)\) ni (#/cm3) #ionized / #atoms

125

75

20

0

-55

1.7. ni for GaAs

Calculate the value of ni for gallium arsenide (GaAs) at T=300 K.

The material constant for GaAs is \(B = 3.56 \times 10^{14}\) cm-3 K-3/2

2. Submission

Submit your 7 problem solutions as a single PDF file with all your work.

  • It is preferable for each problem to begin at the top of a new page. Use your judgement for when it is reasonable to have multiple problems on a page.

  • Doing this on engineering paper is even better. The College sells the best stuff at-cost, see Tina in the CoE office.