transmission media and antenna

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

Transmission Media and Transmission Media and Antenna SystemsAntenna Systems

Principles of Electronic Communication Systems –Louis Frenzel

Electronic Communication SystemsWayne Tomasi

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

Transmission Lines

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

Topics CoveredTopics Covered

13-1: Transmission-Line Basics 13-2: Characteristic Impedance

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

Electric field Produced by the presence of electrically charged particles, and gives rise to the electric force.

Magnetic fieldProduced by the motion of electric charges, or electric current, and gives rise to the magnetic force associated with magnets.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

13-1: Transmission-Line Basics13-1: Transmission-Line Basics

Transmission lines in communication carry telephone signals, computer data in LANs, TV signals in cable TV systems, and signals from a transmitter to an antenna or from an antenna to a receiver.

Their electrical characteristics are critical and must be _____________to the equipment for successful communication to take place.

Transmission lines are also _______.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

13-1: Transmission-Line Basics13-1: Transmission-Line Basics

The two primary requirements of a transmission line are:1. The line should introduce __________ attenuation to

the signal.

2. The line should _______ radiate any of the signal as radio energy.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

13-1: Transmission-Line Basics13-1: Transmission-Line Basics

Types of Transmission Lines Parallel-wire line is made of two _________conductors

separated by a space of _____inch to ______inches.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

13-1: Transmission-Line Basics13-1: Transmission-Line Basics

Types of Transmission Lines Parallel-wire line

300-Ω twin-lead

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

13-1: Transmission-Line Basics13-1: Transmission-Line Basics

Types of Transmission Lines Twisted-pair cable uses two insulated solid _________

wires covered with insulation and loosely twisted together.

Two types of twisted-pair cable are (UTP) cable (STP) cable

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

13-1: Transmission-Line Basics13-1: Transmission-Line Basics

Types of Transmission Lines Coaxial Cable. It consists of a solid center conductor

surrounded by a _________ material, usually a plastic insulator such as Teflon.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

13-1: Transmission-Line Basics13-1: Transmission-Line Basics

Types of Transmission Lines A second conducting shield made of fine wires

covers the insulator, and an outer plastic sheath insulates the braid.

Coaxial cable comes in sizes from ________to several inches in diameter.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

13-1: Transmission-Line Basics13-1: Transmission-Line Basics

Balanced Versus Unbalanced Lines Transmission lines can be balanced or unbalanced. A balanced line is one in which _________ wire is

connected to ground. The signal on each wire is referenced to__________. In an unbalanced line, _________conductor is

connected to ground.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

13-1: Transmission-Line Basics13-1: Transmission-Line Basics

Figure 13-1: Common types of transmission lines. (a) Open-wire line. (b) Open-wire line called twin lead. (c) Coaxial cable (d) Twisted-pair cable.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

13-1: Transmission-Line Basics13-1: Transmission-Line Basics

Figure 13-2: (a) Balanced line. (b) Unbalanced line.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

13-1: Transmission-Line Basics13-1: Transmission-Line Basics

Balanced Versus Unbalanced Lines Balanced-line wires offer significant protection from

noise pickup and cross talk. Coaxial cables are unbalanced lines. Coaxial cable and shielded twisted-pair provide

significant but not complete protection from noise or cross talk.

Unshielded lines may pick up signals and cross talk and can even radiate energy, resulting in an undesirable loss of signal.

A device called a balun is used to convert from balanced to unbalanced lines and vice versa.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

Transmission-Line BasicsTransmission-Line Basics

1. Determine the characteristic impedance for an air dielectric two wire parallel transmission line with a D/r ratio = 12.22

2. Determine the characteristic impedance for an RG-59A coaxial cable with the following specifications: L= 0.118 µH/ft, C = 21pF/ft, d = 0.025 in., D = 0.15 in. , and € = 2.23.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

SummarySummary

1. The input impedance of an infinitely long line at RF is resistive and equal to Zo.

2. The ratio of voltage to current at any point along the line is equal to Zo.

3. In a non resonant line – TEM travels without reflection

4. Line losses are minimum in a non resonant line

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

5. A Tx line terminated in a purely resistive load equal to Zo acts as if it were an infinite line.

a. Zi = Zob. There are no reflected wavesc. V and I are in phased. There is maximum power transfer from

source to load

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

13-1: Transmission-Line Basics13-1: Transmission-Line Basics

Velocity Factor The speed of the signal in the transmission line is

________ than the speed of a signal in free space. The velocity of propagation of a signal in a cable is

_________ the velocity of propagation of light in free space by a fraction called the velocity factor (VF).

VF = Vp/Vc

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

Transmission-Line BasicsTransmission-Line Basics

1. For a given length of RG-8A/U coaxial cable with a distributed capacitance of C = 241.56 nH/m, a distributed inductance of L = 241.56 nH/m and a dielectric constant of €r = 2.3 determine the velocity of propagation and the velocity factor.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

13-1: Transmission-Line Basics13-1: Transmission-Line Basics

Wavelength of Cables The electrical length of conductors is typically

_____compared to 1 wavelength of the frequency they carry.

A pair of current-carrying conductors is not considered to be a transmission line unless it is at least _______ long at the signal frequency.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

13-1: Transmission-Line Basics13-1: Transmission-Line Basics

Connectors Most transmission lines terminate in some kind of

connector, a device that connects the cable to a piece of equipment or to another cable.

Connectors are a common failure point in many applications.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

13-1: Transmission-Line Basics13-1: Transmission-Line Basics

Connectors: Coaxial Cable Connectors Coaxial cables are designed not only to provide a

convenient way to attach and disconnect equipment and cables but also to maintain the physical integrity and electrical properties of the cable.

The most common types are the PL-259 or UHF, BNC, F, SMA, and N-type connectors.

The PL-259, also referred to as a UHF connector, can be used up to low UHF frequencies (less than 500 MHz.)

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

13-1: Transmission-Line Basics13-1: Transmission-Line Basics

Figure 13-3: UHF connectors. (a) PL-259 male connector. (b) Internal construction andconnections for the PL-259. (c) SO-239 female chassis connector.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

13-1: Transmission-Line Basics13-1: Transmission-Line Basics

Connectors: Coaxial Cable Connectors BNC connectors are widely used on 0.25 inch coaxial

cables for attaching test equipment. In BNC connectors the center conductor of the cable is

soldered or crimped to a male pin and the shield braid is attached the body of the connector.

The least expensive coaxial connector is the F-type, which is used for TV sets, VCRs, DVD players, and cable TV.

The RCA phonograph connector is used primarily in audio equipment.

The best performing coaxial connector is the N-type, which is used mainly on large coaxial cable at higher frequencies.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

13-1: Transmission-Line Basics13-1: Transmission-Line Basics

Figure 13-4: BNC connectors. (a) Male. (b) Female. (c) Barrel connector. (d) T connector.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

13-1: Transmission-Line Basics13-1: Transmission-Line Basics

Figure 13-6: The F connector used on TV sets, VCRs, and cable TV boxes.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

13-1: Transmission-Line Basics13-1: Transmission-Line Basics

Figure 13-7: RCA phonograph connectors are sometimes used for RF connectors up to VHF.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

13-1: Transmission-Line Basics13-1: Transmission-Line Basics

Figure 13-8: N-type coaxial connector.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

13-1: Transmission-Line Basics13-1: Transmission-Line Basics

Time Delay Because the velocity of propagation of a transmission

line is less than the velocity of propagation in free space, any line will slow down or delay any signal applied to it.

A signal applied at one end of a line appears some time later at the other end of the line.

This is called the time delay or __________. A transmission line used specifically for the purpose of

achieving delay is called a delay line.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

13-1: Transmission-Line Basics13-1: Transmission-Line Basics

Figure 13-11: The effect of the time delay of a transmission line on signals. (a) Sine wave delay causes a lagging phase shift. (b) Pulse delay.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

13-1: Transmission-Line Basics13-1: Transmission-Line Basics

Transmission-Line Specifications Attenuation is _____________ proportional to cable

length and increases with frequency. A transmission line is a _________ filter whose cutoff

frequency depends on distributed inductance and capacitance along the line and on length.

It is important to use larger, low-loss cables for longer runs despite cost and handling inconvenience.

A gain antenna can be used to offset cable loss.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

13-1: Transmission-Line Basics13-1: Transmission-Line Basics

Figure 13-14: Attenuation versus length for RG-58A/U coaxial cable. Note that both scales on the graph are logarithmic.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

Transmission-Line BasicsTransmission-Line Basics

1. A 165 ft. RG-8A/U at 100 MHZ is being used to connect a tx to an antenna. Its attenuation for 100ft at 100 MHz is 5.3 dB. Its input power from a transmitter is 100 W. What are the total attenuation and the output power to the antenna?.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

13-1: Transmission-Line Basics13-1: Transmission-Line Basics

Transmission-Line Specifications Many coaxial cables are designated by an

alphanumeric code beginning with the letters RG or a manufacturer’s part number.

Primary specifications are characteristic impedance and attenuation.

Other important specifications are maximum breakdown voltage rating, capacitance per foot, velocity factor, and outside diameter in inches.

The attenuation is the amount of power lost per 100 ft of cable expressed in decibels at 100 MHz.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

1.A 150 ft. length RG-62A/U coaxial cable is used as a transmission line. Find

a. the load impedance that must be terminated to avoid reflections

b. inductance per foot c. the time delay introduced by the cable

d. phase shift that occurs on a 2.5 MHz sine wave

e. total attenuation in decibels

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

13-2: Standing Waves13-2: Standing Waves

When a signal is applied to a transmission line, it appears at the other end of the line some time later because of the propagation _______.

If the load on the line is an _______, the signal is converted into electromagnetic energy and radiated into space.

If the load at the end of the line is an open or a short circuit or has an impedance other than the characteristic impedance of the line, the signal is _______fully absorbed by the load.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

13-2: Standing Waves13-2: Standing Waves

When a line is not terminated properly, some of the energy is ____________ and moves back up the line, toward the generator.

This reflected voltage adds to the forward or incident generator voltage and forms a composite voltage that is distributed along the line.

The pattern of voltage and its related current constitute what is called a ___________________.

Standing waves are not desirable.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.Figure 13-15: How a pulse propagates along a transmission line.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

13-2: Standing Waves13-2: Standing Waves

Matched Lines A _________________is one terminated in a load that

has a resistive impedance equal to the characteristic impedance of the line.

Alternating voltage (or current) at any point on a matched line is a constant value. A correctly terminated transmission line is said to be __________.

The power sent down the line toward the load is called_____________.

Power not absorbed by the load is_____________.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

13-2: Standing Waves13-2: Standing Waves

Figure 13-16: A transmission line must be terminated in its characteristic impedance forproper operation.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

13-2: Standing Waves13-2: Standing Waves

Calculating the Standing Wave Ratio The magnitude of the standing waves on a transmission

line is determined by the ratio of the maximum current to the minimum current, or the ratio of the maximum voltage to the minimum voltage, along the line.

These ratios are referred to as the standing wave ratio (SWR).

SWR =Imax

Imin

=Vmax

Vmin

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

An RG-11/U foam coaxial cable has a maximum voltage standing wave of 52 V and a minimum voltage of 17 V. Find (a) SWR, (b) the reflection coefficient, and (c) the value of the resistive load (d) disregarding attenuation due to length if the line input to the cable is 30 solve for the output power.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

13-3: Transmission Lines 13-3: Transmission Lines as Circuit Elementsas Circuit Elements

The standing wave conditions resulting from open- and short-circuited loads must usually be avoided when working with transmission lines.

With quarter- and half-wavelength transmissions, these open- and short-circuited loads can be used as resonant or reactive circuits.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

Review: Tuned CircuitsReview: Tuned Circuits

Tuned Circuits and Resonance A tuned circuit is made up of inductance and

capacitance and resonates at a specific frequency, the___________________.

The terms tuned circuit and resonant circuit are used interchangeably.

Tuned circuits are ________________and respond best at their resonant frequency.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

Review : Tuned CircuitsReview : Tuned Circuits

Tuned Circuits and Resonance: Series Resonant Circuits A series resonant circuit is made up of inductance,

capacitance and resistance connected in series. Series resonant circuits are often referred to as LCR or

RLC circuits. Resonance occurs when inductive and capacitive

reactances are _____.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

2-2: Tuned Circuits2-2: Tuned Circuits

Tuned Circuits and Resonance: Series Resonant Circuits

Example:

What is the resonant frequency of a 2.7-pF capacitor and a 33-nH inductor?

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

2-2: Tuned Circuits2-2: Tuned Circuits

Tuned Circuits and Resonance: Series Resonant Circuits The _______________ of a series resonant circuit is the

narrow frequency range over which the current is highest. ________________are the current levels at which the

frequency response is 70.7% of the peak value of resonance.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

2-2: Tuned Circuits2-2: Tuned Circuits

Example:

What value of inductance will resonate with a 12 – pF capacitor at 49 Mhz?

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

2-2: Tuned Circuits2-2: Tuned Circuits

Figure 2-13: Series RLC circuit.

Figure 2-14 Variation of reactance with frequency.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

2-2: Tuned Circuits2-2: Tuned Circuits

Figure 2-16: Bandwidth of a series resonant circuit.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

2-2: Tuned Circuits2-2: Tuned Circuits

Tuned Circuits and Resonance: Parallel Resonant Circuits A parallel resonant circuit is formed when the inductor

and capacitor of a tuned circuit are connected in parallel with the applied voltage.

A parallel resonant circuit is often referred to as a LCR or RLC circuit.

Resonance occurs when inductive and capacitive reactances are equal.

The resonant frequency (fr) is inversely proportional to inductance and capacitance.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

2-2: Tuned Circuits2-2: Tuned Circuits

Figure 2-19: Parallel resonant circuit currents. (a) Parallel resonant circuit. (b) Currentrelationships in parallel resonant circuit.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

2-2: Tuned Circuits2-2: Tuned Circuits

Tuned Circuits and Resonance: Parallel Resonant Circuits At resonance, a parallel tuned circuit appears to

have infinite resistance draw no current from the source have infinite impedance act as an open circuit.

However, there is a high circulating current between the inductor and capacitor, storing and transferring energy between them.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

Review: FiltersReview: Filters

A filter is a frequency-selective circuit. Filters pass certain frequencies and reject others. _______________are created using components

such as: resistors, capacitors, and inductors that do not amplify.

_______________use amplifying devices such as transistors and operational amplifiers.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

Attenuation ____________________________________________

Figure 2-3: A voltage divider introduces attenuation.

Review: Gain, Attenuation,Review: Gain, Attenuation,and Decibelsand Decibels

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

2-3: Filters2-3: Filters

Figure 2-24: RC low-pass filter. (a) Circuit.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

2-3: Filters2-3: Filters

Figure 2-28: (a) RC high-pass filter. (b) RL high-pass filter.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

2-3: Filters2-3: Filters

Figure 2-29: RC notch filter.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

13-3: Transmission Lines 13-3: Transmission Lines as Circuit Elementsas Circuit Elements

Resonant Circuits and Reactive Components Shorted and open quarter wavelengths act like

________ tuned or resonant circuits at the reference frequency.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

13-3: Transmission Lines 13-3: Transmission Lines as Circuit Elementsas Circuit Elements

Resonant Circuits and Reactive Components With an open line, a one-quarter wavelength line looks

like a _____ resonant circuit to the generator, and a one-half wavelength line looks like a _______ resonant circuit, just the opposite of a shorted line.

If the line is less than one-quarter wavelength(open), the generator sees a __________.

If the line is between one-quarter and one-half wavelength(open), the generator sees an _________.

These characteristics repeat for lines that are some multiple of one-quarter or one-half wavelengths.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

Figure 13-25: Summary of impedance and reactance variations of shorted and open lines for lengths up to one wavelength.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

13-3: Transmission Lines 13-3: Transmission Lines as Circuit Elementsas Circuit Elements

Stripline and Microstrip Special transmission lines constructed with copper

patterns on a printed circuit board (PCB), called microstrip or stripline, can be used as tuned circuits, filters, phase shifters, reactive components, and impedance-matching circuits at high frequencies.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

13-3: Transmission Lines 13-3: Transmission Lines as Circuit Elementsas Circuit Elements

Stripline and Microstrip Microstrip is a flat conductor separated by an

insulating dielectric from a large conducting ground plane.

The microstrip is usually a quarter or half wavelength long.

The ground plane is the circuit common and is equivalent to an unbalanced line.

The characteristic impedance of microstrip is dependent on its physical characteristics.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

13-3: Transmission Lines 13-3: Transmission Lines as Circuit Elementsas Circuit Elements

Figure 13-26: Microstrip. (a) Unbalanced. (b) Balanced.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

A microstrip transmission line is to be used as a capacitor of 4 pF at 800 MHz. The PCB dielectric is 3.6. The microstrip dimensions are h = 0.0625 in; w = 0.13 in ; and t = 0.002 in. What are the (a) characteristic impedance of the line and (b) the reactance of the capacitor?

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

13-3: Transmission Lines 13-3: Transmission Lines as Circuit Elementsas Circuit Elements

Stripline and Microstrip Stripline is a flat conductor sandwiched between two

ground planes. It is more difficult to make than microstrip; however, it

does not radiate as microstrip does. The length is one-quarter or one-half wavelength at the

desired operating frequency. Shorted lines are more commonly used than open lines.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

13-3: Transmission Lines 13-3: Transmission Lines as Circuit Elementsas Circuit Elements

Figure 13-28: Stripline.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

A stripline transmission line is to be used as a reactance circuit. The PCB dielectric is 4.5. The stripline dimensions are h = 0.0125 in; w = 0.13 in; d = 0.2 in ; and t = 0.004 in. What are the (a) characteristic impedance of the line?

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

13-4: The Smith Chart13-4: The Smith Chart

The mathematics required to design and analyze transmission lines is complex, whether the line is a physical cable connecting a transceiver to an antenna or is being used as a filter or impedance-matching network.

This is because the impedances involved are complex ones, involving both resistive and reactive elements.

The impedances are in the familiar rectangular form, R + jX.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

13-4: The Smith Chart13-4: The Smith Chart

The Smith Chart is a sophisticated graph that permits visual solutions to transmission line calculations.

Despite the availability of the computing options today, this format provides a more or less standardized way of viewing and solving transmission-line and related problems.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

13-4: The Smith Chart13-4: The Smith Chart

The horizontal axis is the pure resistance or zero-reactance line.

The point at the far left end of the line represents zero resistance, and the point at the far right represents infinite resistance. The resistance circles are centered on and pass through this pure resistance line.

The circles are all tangent to one another at the infinite resistance point, and the centers of all the circles fall on the resistance line.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

13-4: The Smith Chart13-4: The Smith Chart

Any point on the outer circle represents a resistance of 0 Ω.

The R = 1 circle passes through the exact center of the resistance line and is known as the prime center.

Values of pure resistance and the characteristic impedance of transmission line are plotted on this line.

The linear scales printed at the bottom of Smith charts are used to find the SWR, dB loss, and reflection coefficient.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

Plot in normalize form the following impedances on a smith chart. Z1 = 80 + j25 and Z2 = 35 – j98 assuming a prime center value of 52 Ω.

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

The operating frequency for a 24 ft piece of RG-58A/U with a velocity factor 0f 0.66 coaxial cable is 140 MHz. The load is resistive, with a resistance of 93 Ω. What is the impedance seen by the transmitter?

An antenna is connected to the 24 ft 53.5 Ω RG 58A/U described in the previous example. The load is 40 + j30Ω. What impedance does the transmitter see?

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

A 50 ft RG 11/U foam dielectric coaxial cable with a characteristic impedance of 75 Ω and a velocity factor of 0.8 has an operating frequency of 72 MHz. The load is an antenna whose actual impedance is unknown. A measurement at the transmitter end of the cable gives a complex impedance of 82 + j43. What is the impedance of the antenna?

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

Plot the load impedance 104 – j58 on a coaxial line on a smith chart. Assume a characteristic impedance value of 75 Ω. Then find the SWR.

If the operating frequency is 230 MHz and the cable length is 30 ft. for the previous example, what is the impedance at the generator if the velocity factor is 0.66?

McGraw-Hill © 2008 The McGraw-Hill Companies, Inc. All rights reserved.

13-4: The Smith Chart13-4: The Smith Chart

Figure 13-30: The Smith chart.