TABLE OF CONTENTS An important inductor class is a single layer of wire wound in the form of a cylindrical solenoid with an air core. A rigorous mathematical solution for the inductance of even this simple structure is involved. The inductance is modeled to about 1% by the popular Wheeler [5] formula if the length-to-diameter ratio exceeds 0.33.
| (18) |  |
where n is the number of turns, r is the radius in inches to the wire center and 1 is the solenoid length (wire center to wire center) in inches. This model of the solenoid is ideal in that Q u and parasitics are not considered. A practical inductor model is given in Figure 3-2 where L is given by the above expression.
The series resistor, R s, and the solenoid Q u are related by equation (6).
From equation (2) we see that the reactance and therefore Q u should increase linearly with frequency and from equation (15) we see that conductor ac resistance increases with the square root of frequency. Although equation (15) is valid only for an isolated conductor, we may hypothesize a similar relationship as a function of frequency for the solenoid. We would therefore expect Q u to increase as the square root of frequency. As it turns out, the unloaded Q of a single-layer copper-wire air solenoid has been empirically found [6] to...
