Reactive Components

very high, so these factors can be ignored at low frequencies. At radio frequencies, however, these residuals become noticeable, and the capacitor functions as a complex RLC circuit. Most of these effects can be greatly minimized by keeping the capacitor leads very short. This problem is mostly eliminated by using the newer chip capacitors, which have no leads as such.

Capacitance is generally added to a circuit by a capacitor of a specii c value, but capacitance can occur between any two conductors separated by an insulator. For exam- ple, there is capacitance between the parallel wires in a cable, between a wire and a metal chassis, and between parallel adjacent copper patterns on a printed-circuit board.

These are known as stray, or distributed, capacitances. Stray capacitances are typically small, but they cannot be ignored, especially at the high frequencies used in communica- tion. Stray and distributed capacitances can signii cantly affect the performance of a circuit.

Inductors.

An inductor, also called a coil or choke, is simply a winding of multiple turns of wire. When current is passed through a coil, a magnetic i eld is produced around the coil. If the applied voltage and current are varying, the magnetic i eld alternately expands and collapses. This causes a voltage to be self-induced into the coil winding, which has the effect of opposing current changes in the coil. This effect is known as inductance.

The basic unit of inductance is the henry (H). Inductance is directly affected by the physical characteristics of the coil, including the number of turns of wire in the induc- tor, the spacing of the turns, the length of the coil, the diameter of the coil, and the type of magnetic core material. Practical inductance values are in the millihenry (mH510²³ H), microhenry (µH510²⁶ H), and nanohenry (nH510²⁹ H) regions.

Fig. 2-9 shows several different types of inductor coils.

● Fig. 2-9(a) is an inductor made of a heavy, self-supporting wire coil.

● In Fig. 2-9(b) the inductor is formed of a copper spiral that is etched right onto the board itself.

● In Fig. 2-9(c) the coil is wound on an insulating form containing a powdered iron or ferrite core in the center, to increase its inductance.

● Fig. 2-9(d) shows another common type of inductor, one using turns of wire on a toroidal or doughnut-shaped form.

● Fig. 2-9(e) shows an inductor made by placing a small ferrite bead over a wire; the bead effectively increases the wire’s small inductance.

● Fig. 2-9(f) shows a chip inductor. It is typically no more than ¹⁄8 to ¹⁄4 in long.

A coil is contained within the body, and the unit is soldered to the circuit board with the end connections. These devices look exactly like chip resistors and capacitors.

In a dc circuit, an inductor will have little or no effect. Only the ohmic resistance of the wire affects current l ow. However, when the current changes, such as during the time the power is turned off or on, the coil will oppose these changes in current.

When an inductor is used in an ac circuit, this opposition becomes continuous and constant and is known as inductive reactance. Inductive reactance X_L is expressed in ohms and is calculated by using the expression

X_L52πf L

For example, the inductive reactance of a 40-µH coil at 18 MHz is XL56.28(18310⁶) (40310²⁶)54522 V

In addition to the resistance of the wire in an inductor, there is stray capacitance between the turns of the coil. See Fig. 2-10(a). The overall effect is as if a small capac- itor were connected in parallel with the coil, as shown in Fig. 2-10(b). This is the equivalent circuit of an inductor at high frequencies. At low frequencies, capacitance  may  be Stray (or distributed) capacitance

Inductor (coil or choke)

Inductance

Inductive reactance

ignored,  but at radio frequencies, it is sufi ciently large to affect circuit operation. The coil then functions not as a pure inductor, but as a complex RLC circuit with a self- resonating frequency.

Any wire or conductor exhibits a characteristic inductance. The longer the wire, the greater the inductance. Although the inductance of a straight wire is only a fraction of Figure 2-9

Types of inductors. (a) Heavy self-supporting wire coil. (b) Inductor made

as copper pattern. (c) Insulating form. (d) Toroidal inductor. (e) Ferrite bead inductor. (f) Chip inductor.

(a)

Printed circuit (PC) board

Component lead or wire

(e) Ferrite

bead Insulating

form

Core moves in or out to vary inductance

Powdered iron or ferrite

core

(c)

(b)

PC board

Toroidal inductor

Turns of wire (d)

(f) Toroidal

core

Body

Solder connection

Figure 2-10

Equivalent circuit of an inductor at high frequencies. (a) Stray capacitance between turns. (b) Equivalent circuit of an inductor at high frequencies.

Stray capacitance between turns

Winding (coil) resistance

L ⫽ inductor

C ⫽ stray capacitance

(a) (b)

R

a microhenry, at very high frequencies the reactance can be signii cant. For this reason, it is important to keep all lead lengths short in interconnecting components in RF circuits.

This is especially true of capacitor and transistor leads, since stray or distributed induc- tance can signii cantly affect the performance and characteristics of a circuit.

Another important characteristic of an inductor is its quality factor Q, the ratio of inductive power to resistive power:

Q5 I ²XL

I ²R 5 XL

R

This is the ratio of the power returned to the circuit to the power actually dissipated by the coil resistance. For example, the Q of a 3-µH inductor with a total resistance of 45V at 90 MHz is calculated as follows:

Q5 2πf L

R 56.28(90310⁶) (3310²⁶)

45 5 1695.6

45 537.68

Resistors.

At low frequencies, a standard low-wattage color-coded resistor offers nearly pure resistance, but at high frequencies its leads have considerable inductance, and stray capacitance between the leads causes the resistor to act as a complex RLC circuit, as shown in Fig. 2-11. To minimize the inductive and capacitive effects, the leads are kept very short in radio applications.

The tiny resistor chips used in surface-mount construction of the electronic circuits preferred for radio equipment have practically no leads except for the metallic end pieces soldered to the printed-circuit board. They have virtually no lead inductance and little stray capacitance.

Many resistors are made from a carbon-composition material in powdered form sealed inside a tiny housing to which leads are attached. The type and amount of carbon material determine the value of these resistors. They contribute noise to the circuit in which they are used. The noise is caused by thermal effects and the granular nature of the resistance material. The noise contributed by such resistors in an amplii er used to amplify very low level radio signals may be so high as to obliterate the desired signal.

To overcome this problem, i lm resistors were developed. They are made by depos- iting a carbon or metal i lm in spiral form on a ceramic form. The size of the spiral and the kind of metal i lm determine the resistance value. Carbon i lm resistors are quieter than carbon-composition resistors, and metal i lm resistors are quieter than carbon i lm resistors. Metal i lm resistors should be used in amplii er circuits that must deal with very low level RF signals. Most surface-mount resistors are of the metallic i lm type.

Skin Ef ect.

The resistance of any wire conductor, whether it is a resistor or capacitor lead or the wire in an inductor, is primarily determined by the ohmic resistance of the wire itself. However, other factors inl uence it. The most signii cant one is skin effect, the tendency of electrons l owing in a conductor to l ow near and on the outer surface Quality factor Q

Resistor

Skin effect

Figure 2-11

Equivalent circuit of a resistor at high (radio) frequencies.

Resistor Lead inductance

Stray capacitance

of the conductor frequencies in the VHF, UHF, and microwave regions (Fig. 2-12). This has the effect of greatly decreasing the total cross-sectional area of the conductor, thus increasing its resistance and signii cantly affecting the performance of the circuit in which the conductor is used. For example, skin effect lowers the Q of an inductor at the higher frequencies, causing unexpected and undesirable effects. Thus many high-frequency coils, particularly those in high-powered transmitters, are made with cop- per  tubing. Since current does not l ow in the center of the conductor, but only on the surface, tubing provides the most efi cient conductor. Very thin conductors, such as a copper pattern on a printed-circuit board, are also used. Often these conductors are sil- ver- or gold-plated to further reduce their resistance.