## Nonideal Wires And Transmission Lines

In circuit analysis, wires are usually considered to be ideal short circuits. All wires have resistance, which can be a problem at any frequency if the wire gauge (or trace width in the case of printed circuit traces) is not chosen properly. In addition, all wires have inductance. At low frequencies, the inductance can usually be ignored. At high frequencies, the inductance greatly affects how the wires carry signals. Furthermore, all circuits use at least two wires to deliver the signal from source to load. Typically one wire is designated for the source current and the other is designated for the return current and is often grounded.

Figure 7.6 A) Frequency response of a ferrite-core, 100nH surface-mount inductor (Cp = 1 pF; RDC = 0.26ohm). Above about 80 MHz, the ESR increases dramatically due to ferrite losses in the core. The self-resonant frequency occurs at about 500 MHz. Above the self-resonant frequency, the device acts like a ~1 pF capacitor.

Apparent Inductance
 . ■ ■ . • 1 ' idiri'r^fcir'T.V.i" 1 ! . :: ; ,' r. ■ i i Î ■ : j*|T: —---- ' ; ' .1 : \ i * ¡ X T. J.T {.. * "4. * J.. j ; . ''''-V ; ; ;. j r ; -V'A':" "'""' :" V:'*: [ •3 If : ; ••. . j—
 •1 C-r: . : ; rr- fir.'.y.'.i" „ A ..Ü _ - ■ " A \

Like any two conductors, these two wires have a capacitance between them. A simple circuit is shown in Figure 7.7, showing the parasitic elements of the wires.

To make the problem of parasitic inductance and capacitance manageable at high frequencies, transmission lines are used. A transmission

Figure 7.6 B) Frequency response of an air-core, 100nH surface-mount inductor (Cp = 0.25 pF; RDC = 0.38ohm). The self-resonant frequency occurs at about 1 GHz. Above the self-resonant frequency, the device approaches the behavior of a ~0.25 pF capacitor.

Impedance

Impedance

103 [Hz] 10"

Apparent Inductance

Apparent Inductance

109 [Hz] 10"

Apparent Capacitance

Apparent Capacitance

10e io5 m io"

line is a set of conductors with uniform spacing. Some examples are coaxial cable (used for cable TV and lab instruments), twisted pair cable (used for telephone lines and computer network cables), ribbon cables (used to connect circuit boards inside computers), twin lead cables (used for TV antennas), microstrip and stripline (used on printed circuit boards). Transmission lines serve to guide the electromagnetic signals predictably and to reduce radiation.

Figure 7.7 A) A simple circuit consisting of a voltage source connected to a load resistor. B) The hidden schematic for the wires includes resistance (Rwlre), inductance (Lwlre), and parasitic capacitance (Cp).

Figure 7.7 A) A simple circuit consisting of a voltage source connected to a load resistor. B) The hidden schematic for the wires includes resistance (Rwlre), inductance (Lwlre), and parasitic capacitance (Cp).

## Solar Panel Basics

Global warming is a huge problem which will significantly affect every country in the world. Many people all over the world are trying to do whatever they can to help combat the effects of global warming. One of the ways that people can fight global warming is to reduce their dependence on non-renewable energy sources like oil and petroleum based products.

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