Unless otherwise specified, all electrical parameters in the following problems are as in Examples 5.1 and 5.2.

5.1

A simple passive filter has a cutoff frequency f _c given by f _c = 1(2 ? RC), where R is the resistance of a poly resistor and C is the capacitance of a metal-poly capacitor. The nominal values of R and C are 10 k ? and 50 pF, respectively, at room temperature. Find the worst-case (extreme) values of f _c at room temperature, assuming tolerances of 20 percent for the resistor and 10 percent for the capacitor. Also, find the worst-case values of the nominal f _c at 0 and 70 C, assuming temperature coefficients of 500 ppm/ C for the resistor and 25 ppm/ C for the capacitor.

5.2

The temperature coefficient of a capacitor C ₁ is 25 ppm/ C; that of a neighboring capacitor C ₂ is 23 ppm/ C. What is the temperature coefficient of the ratio C ₁/ C ₂?

5.3

A well resistor (Fig. 5.8f) has a zero-bias sheet resistance of 1 k ?/ ? 20 percent, a temperature coefficient of 6000 ppm/ C, and a voltage coefficient of 10,000 ppm/V. The length and width tolerances are 0.3 ?m. When it is connected in a circuit, one end of the resistor is at 5 V and the other at 2 0.2 V. The resistor is laid out...