2 Port Networks

Unit-1

Methods of Communication

TRANSMISSION LINE

• A transmission line is a material medium or structure that forms a path for directing the transmission of energy from one place to another, such as electromagnetic waves or acoustic waves, as well as electric power transmission.

However in communications and electronic engineering, the term has a more specific meaning. In these fields, transmission lines are specialized cables and other media designed to carry alternating current and electromagnetic waves of radio frequency, that is, currents with a frequency high enough that its wave nature must be taken into account. Transmission lines are used for purposes such as connecting radio transmitters and receivers with their antennas, distributing cable television signals, and computer network connections.

Transmission Line Concept

PowerPlant

ConsumerHome

Power Frequency (f) is @ 60 Hz Wavelength () is 5 106 m

( Over 3,100 Miles)

Key point about transmission line operation

The major deviation from circuit theory with transmission line, distributed networks is this positional dependence of voltage and current!– Must think in terms of position and time to

understand transmission line behavior– This positional dependence is added when the

assumption of the size of the circuit being small compared to the signaling wavelength

tzfI

tzfV

,

,

V1 V2

dz

I2I1

Voltage and current on a transmission line is a function of both time and position.

Transmission Lines Class 6

Examples of Transmission Line Structures- I

• Cables and wires(a)Coax cable(b) Wire over ground(c)Tri-lead wire (d) Twisted pair (two-wire line)

• Long distance interconnects

(a) (b)

(c) (d)

+

-

+

+ +-

- -

-

Segment 2: Transmission line equivalent circuits and relevant equations

Physics of transmission line structures

Basic transmission line equivalent circuit

?Equations for transmission line propagation

Physics of transmission line structures

Basic transmission line equivalent circuit

?Equations for transmission line propagation

Remember fields are setup given an applied forcing function.

(Source)

How does the signal move from source to load?

E & H Fields – Microstrip Case

The signal is really the wave propagating between the conductors

Electric field

Magnetic field

Ground return path

X

Y

Z (into the page)

Signal path

Electric field

Magnetic field

Ground return path

X

Y

Z (into the page)

Signal path

Transmission Line “Definition”• General transmission line: a closed system in which power is transmitted

from a source to a destination

• Our class: only TEM mode transmission lines– A two conductor wire system with the wires in close proximity, providing

relative impedance, velocity and closed current return path to the source.– Characteristic impedance is the ratio of the voltage and current waves at

any one position on the transmission line

– Propagation velocity is the speed with which signals are transmitted through the transmission line in its surrounding medium.

I

VZ 0

r

cv

Presence of Electric and Magnetic Fields

• Both Electric and Magnetic fields are present in the transmission lines– These fields are perpendicular to each other and to the direction of wave

propagation for TEM mode waves, which is the simplest mode, and assumed for most simulators(except for microstrip lines which assume “quasi-TEM”, which is an approximated equivalent for transient response calculations).

• Electric field is established by a potential difference between two conductors.– Implies equivalent circuit model must contain capacitor.

• Magnetic field induced by current flowing on the line– Implies equivalent circuit model must contain inductor.

V

I

I

E

+

-

+

-

+

-

+

-

V + DV

I + DI

I + DI

V

IH

IH

V + DV

I + DI

I + DI

• General Characteristics of Transmission Line– Propagation delay per unit length (T0) { time/distance} [ps/in]

• Or Velocity (v0) {distance/ time} [in/ps]– Characteristic Impedance (Z0) – Per-unit-length Capacitance (C0) [pf/in]– Per-unit-length Inductance (L0) [nf/in]– Per-unit-length (Series) Resistance (R0) [/in]– Per-unit-length (Parallel) Conductance (G0) [S/in]

T-Line Equivalent Circuit

lL0lR0

lC0lG0

Equations & Formulas

How to model & explain transmission line behavior

Relevant Transmission Line Equations

Propagation equation

jCjGLjR ))((

)(

)(0

CjG

LjRZ

Characteristic Impedance equation

In class problem: Derive the high frequency, lossless approximation for Z0

is the attenuation (loss) factor

is the phase (velocity) factor

Refection coefficient• Signal on a transmission line can be analyzed by keeping track

of and adding reflections and transmissions from the “bumps” (discontinuities)

• Refection coefficient– Amount of signal reflected from the “bump”– Frequency domain =sign(S11)*|S11|– If at load or source the reflection may be called gamma (L or s)– Time domain is only defined a location

• The “bump”– Time domain analysis is causal.– Frequency domain is for all time.– We use similar terms – be careful

• Reflection diagrams – more later

Reflection and Transmission

Incident

Reflected

Transmitted

Reflection CoeficientTransmission Coeffiecent

1 "" "" 1Zt Z0Zt Z0

Zt Z0Zt Z0

2 Zt

Zt Z0

• Different• types of antennas & their characteristics

Radio Propagation• Lower frequencies, especially AM broadcasts in the

mediumwave (sometimes called "medium frequency") and long wave bands (and other types of radio frequencies below that), travel efficiently as a surface wave.

• This is because they are more efficiently diffracted by the figure of the Earth due to their low frequencies. Ionospheric reflection is taken into consideration as well.

• The ionosphere reflects frequencies in a certain band, which often changes due to solar conditions. The Earth has one refractive index and the atmosphere has another, thus constituting an interface that supports the surface wave transmission.

• Conductivity of the surface affects the propagation of ground waves, with more conductive surfaces such as water providing better propagation. [2] Increasing the conductivity in a surface results in less dissipation. [3] The refractive indices are subject to spatial and temporal changes. Since the ground is not a perfect electrical conductor, ground waves are attenuated as they follow the earth’s surface.

• Most long-distance LF "longwave" radio communication (between 30 kHz and 300 kHz) is a result of groundwave propagation. Mediumwave radio transmissions (frequencies between 300 kHz and 3000 kHz) have the property of following the curvature of the earth (the groundwave) in the majority of occurrences. At low frequencies, ground losses are low and become lower at lower frequencies. The VLF and LF frequencies are mostly used for military communications, especially with ships and submarines.

• Surface waves have been used in over-the-horizon radar. In the development of radio, surface waves were used extensively. Early commercial and professional radio services relied exclusively on long wave, low frequencies and ground-wave propagation.

• To prevent interference with these services, amateur and experimental transmitters were restricted to the higher (HF) frequencies, felt to be useless since their ground-wave range was limited.

• Upon discovery of the other propagation modes possible at medium wave and short wave frequencies, the advantages of HF for commercial and military purposes became apparent. Amateur experimentation was then confined only to authorized frequencies in the range.

• Medium wave and shortwave reflect off the ionosphere at night, which is known as skywave. During daylight hours, the lower "D" layer of the ionosphere forms and absorbs lower frequency energy.

• This prevents sky wave propagation from being very effective on medium wave frequencies in daylight hours. At night, when the "D" layer dissipates, medium wave transmissions travel better by sky wave.

• Ground waves do not include ionospheric and tropospheric waves.

Klystron

•A klystron is a specialized linear-beam vacuum tube (evacuated electron tube).

• Klystrons are used as amplifiers at microwave and radio frequencies to produce both low-power reference signals for superheterodyne radar receivers and to produce high-power carrier waves for communications and the driving force for modern particle accelerators.

Two-cavity klystron amplifier

Two-cavity klystron amplifier

• In the two-chamber klystron, the electron beam is injected into a resonant cavity. The electron beam, accelerated by a positive potential, is constrained to travel through a cylindrical drift tube in a straight path by an axial magnetic field. While passing through the first cavity, the electron beam is velocity modulated by the weak RF signal.

• In the moving frame of the electron beam, the velocity modulation is equivalent to a plasma oscillation.

• Plasma oscillations are rapid oscillations of the electron density in conducting media such as plasmas or metals.(The frequency only depends weakly on the wavelength). So in a quarter of one period of the plasma frequency, the velocity modulation is converted to density modulation, i.e. bunches of electrons.

• As the bunched electrons enter the second chamber they induce standing waves at the same frequency as the input signal. The signal induced in the second chamber is much stronger than that in the first.

Reflex klystron

Reflex klystron• In the reflex klystron (also known as a 'Sutton' klystron after its inventor), the electron beam

passes through a single resonant cavity. The electrons are fired into one end of the tube by an electron gun. After passing through the resonant cavity they are reflected by a negatively charged reflector electrode for another pass through the cavity, where they are then collected

• . The electron beam is velocity modulated when it first passes through the cavity. The formation of electron bunches takes place in the drift space between the reflector and the cavity. The voltage on the reflector must be adjusted so that the bunching is at a maximum as the electron beam re-enters the resonant cavity, thus ensuring a maximum of energy is transferred from the electron beam to the RF oscillations in the cavity.

• The voltage should always be switched on before providing the input to the reflex klystron as the whole function of the reflex klystron would be destroyed if the supply is provided after the input. The reflector voltage may be varied slightly from the optimum value, which results in some loss of output power, but also in a variation in frequency. This effect is used to good advantage for automatic frequency control in receivers, and in frequency modulation for transmitters.

• The level of modulation applied for transmission is small enough that the power output essentially remains constant. At regions far from the optimum voltage, no oscillations are obtained at all. This tube is called a reflex klystron because it repels the input supply or performs the opposite function of a klystron.

• There are often several regions of reflector voltage where the reflex klystron will oscillate; these are referred to as modes.

• The electronic tuning range of the reflex klystron is usually referred to as the variation in frequency between half power points—the points in the oscillating mode where the power output is half the maximum output in the mode.

• The frequency of oscillation is dependent on the reflector voltage, and varying this provides a crude method of frequency modulating the oscillation frequency, albeit with accompanying amplitude modulation as well.

• Modern semiconductor technology has effectively replaced the reflex klystron in most applications.

Magnetron• All cavity magnetrons consist of a hot cathode with a high (continuous or

pulsed) negative potential by a high-voltage, direct-current power supply. The cathode is built into the center of an evacuated, lobed, circular chamber. A magnetic field parallel to the filament is imposed by a permanent magnet. The magnetic field causes the electrons, attracted to the (relatively) positive outer part of the chamber, to spiral outward in a circular path rather than moving directly to this anode. Spaced around the rim of the chamber are cylindrical cavities. The cavities are open along their length and connect the common cavity space. As electrons sweep past these openings, they induce a resonant, high-frequency radio field in the cavity, which in turn causes the electrons to bunch into groups. A portion of this field is extracted with a short antenna that is connected to a waveguide (a metal tube usually of rectangular cross section). The waveguide directs the extracted RF energy to the load, which may be a cooking chamber in a microwave oven or a high-gain antenna in the case of radar.

• A cross-sectional diagram of a resonant cavity magnetron. Magnetic lines of force are parallel to the geometric axis of this structure.

• The sizes of the cavities determine the resonant frequency, and thereby the frequency of emitted microwaves. However, the frequency is not precisely controllable. The operating frequency varies with changes in load impedance, with changes in the supply current, and with the temperature of the tube.[5] This is not a problem in uses such as heating, or in some forms of radar where the receiver can be synchronized with an imprecise magnetron frequency. Where precise frequencies are needed, other devices such as the klystron are used.

• The magnetron is a self-oscillating device requiring no external elements other than a power supply. A well-defined threshold anode voltage must be applied before oscillation will build up; this voltage is a function of the dimensions of the resonant cavity, and the applied magnetic field. In pulsed applications there is a delay of several cycles before the oscillator achieves full peak power, and the build-up of anode voltage must be coordinated with the build-up of oscillator output.[5]

• The magnetron is a fairly efficient device. In a microwave oven, for instance, a 1.1 kilowatt input will generally create about 700 watt of microwave power, an efficiency of around 65%. (The high-voltage and the properties of the cathode determine the power of a magnetron.) Large S-band magnetrons can produce up to 2.5 megawatts peak power with an average power of 3.75 kW.[5] Large magnetrons can be water cooled. The magnetron remains in widespread use in roles which require high power, but where precise frequency control is unimportant.