TELECOMMUNICATIONS

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TELECOMMUNICATIONS

• Dr. Hugh Blanton
• ENTC 4307/ENTC 5307

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Properties of transmission lines
Inductance (L) and Capacitance (C ) per unit
length

• Characteristic Impedance
• Propagation coefficient
• Phase Velocity
• Effective dielectric constant

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RF

• When a capacitor is created by two parallel
  conductors, the dimensions of the conductors
  compared to the actual wavelength (lG) affects
  the RF performance of the component.
• For example
• If l ltlt lG ,the capacitance of the parallel
  plates may be treated as a single (lumped)
  capacitance C between points x1 and x2.

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• If l gt 0.05lG, the capacitance of the parallel
  plates must be treated in distributed form as
  C1, C2, ... Cn, including the effects of the
  incremental inductances L1, L2, ..., Ln-1,etc.

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• The physical dimensions of conductors and
  components, relative to the effective signal
  wavelength, determines the method required for
  accurate modeling.
• When conductors are realized on FR-4 type
  PC-boards, the effective wavelength at 1 GHz is
  about 10 cm ( 4).
• Five percent of that length is 5 mm ( 200 mils)
  therefore if the conductors exceed this length,
  they should be analyzed in distributed form at
  frequencies above 1 GHz.

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• The 5 border is just an approximation, not an
  absolute rule.
• It is generally used as an upper limit to which
  the tangent of an angle changes in a near linear
  fashion

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Transmission lines

• At high frequencies wires become transmission
  lines
• Coaxial
• Microstrip
• Coplanar
• Input and Output needs to be matched.

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Types of Transmission Lines

• RF transmission lines generally consist of two
  conductors, one of which may be a ground plane or
  a shield.
• The most commonly used forms are
• twin-leads,
• coaxial,
• stripline, and
• microstrip

Twin leads
Coaxial
Strip line
Microstrip line
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Coaxial

• Coax is the most common form of a transmission
  line.
• Note that
• Stripline is essentially square coax and
• Microstrip is open top coax.
• Most of the magnetic field terminated in the
  ground strip.

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• Transmission lines may be defined two ways
• by physical dimensions (conductor size and
  spacing) or
• by electrical parameters (characteristic
  impedance and electrical length).
• At higher microwave frequencies single conductor
  transmission lines, such as waveguides may also
  be used

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• If the dielectric is non-homogeneous, er, is
  replaced with the dielectric constant, eeff,
  which is an average of the dielectric layers.

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Characteristic Impedance

• Characteristic impedance (Zo) of a uniform, lossy
  transmission line is a complex number
• it is defined by the ratio of the series
  impedance and shunt admittance of an incremental
  line segment.

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• R and G represent dissipative losses while L and
  C are the incremental inductance and capacitance
  in the equivalent series and parallel circuits.
• Characteristic impedance is given by
• If the line is lossless (R 0, G 0) the
  impedance definition is simplified to a real
  quantity

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• Characteristic impedance is what the signal
  sees while traveling through the transmission
  line.
• Electrically, it is the ratio of the
  instantaneous voltage and current.
• a quantity that is constant throughout a
  homogeneous line.
• If high-impedance lines the incremental
  inductance is the dominant term of the impedance
  expression.
• In low-impedance lines the capacitance term is
  relatively large, while inductance is low.

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• Thus in high-impedance lines the incremental
  inductance is the dominant term of the impedance
  expression.
• In low-impedance lines the capacitance term is
  the dominant term in the impedance expression.

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• If the transmission line is lossless (R 0, G
  0) and the impedance definition is simplified to
  a real quantity

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Example

• A uniform transmission line has the following
  incremental lumped equivalent circuit parameters
• R 0.2W/m
• G 2 ? 10-5 S/m
• L 2.51 ? 10-7 H/m
• C 10 ? 10-12 F/m
• Find the characteristic impedance of the line at
  1000 Hz and 1 GHz.
• Comment about the nature of the impedance at
  different frequencies.
• That is, at 1 KHz, is the circuit a transmission
  line?
• Is the circuit a transmission line at 1 GHz?

R
L
G
C
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Electrical Length of Transmission Lines

• The term electrical length refers to the ratio of
  the physical length (l) of the transmission line
  to the wavelength (lG) in the applicable
  dielectric.

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Example

• If a 15 cm long coaxial line is filled with
  dielectric of er 4, what is E at 2 GHz?
• We could also compute the effective wavelength
  first

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Physical Forms

• A transmission line may have various physical
  forms
• The electrical schematic
• The real physical circuit equivalent in
• coaxial form or
• microstrip form

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Characteristics

• If an ideal transmission line of characteristic
  impedance Zo is terminated with a complex
  impedance ZL, the new input impedance is

Let Zo 50 W
q ZL ZIN
0 5 5
45 0 j Zo
90 8 0
90 XL XC
90 5 500
180 5 5
?l
¼l
Impedance Inverter
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Lossy Transmission Lines

• For lossy transmission lines the input impedance
  is a more complicated function
• where
• g is the propagation constant (a jb)
• l is the physical length of the transmission line.

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• If ZL Zo, the input impedance of the
  transmission line is always equal to ZL and is
  not a function of the line length.

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• In a uniform transmission line the current flow
  is determined by the ratio of the instantaneous
  voltage and characteristic impedance.
• Load current depends on the voltage and load
  impedance.

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• When a uniform transmission line is terminated
  with a load impedance other than its
  characteristic impedance, reflected waves are
  created.
• The ratio of the reflected and forward voltages
  is called the reflection coefficient and is
  denoted by G.

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RF Parameters

• As frequencies reach 100 MHz, the voltages and
  currents are difficult to measure.
• A more practical set of parameters can be defined
  in terms of traveling waves.
• Four such parameters are
• Reflection Coefficient
• Return Loss
• Voltage Standing Wave Ratio
• Mismatch Loss

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Reflection Coefficient

• The Reflection Coefficient (G) shows what
  fraction of an applied signal is reflected when a
  Zo source drives a load of ZL.

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Return Loss

• The Return Loss (RL) shows the level of reflected
  wave referenced to the incident wave, expressed
  in dB.

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Reflection Coefficient (?)

• If the load impedance differs from the
  characteristic impedance of the line then part of
  the wave is reflected.
• The ratio of the incident voltage to the
  reflected voltage is ?

Sometimes specified by the return loss 20 log
(?)
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VSWR

• The Voltage Standing Wave Ratio (VSWR) compares
  the maximum and minimum values of a standing
  wave pattern, caused by wave reflection.

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Mismatch Loss

• The Mismatch Loss (ML) is the power lost between
  two interconnected ports, due to mismatch.

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• The four circuit parameters (G, RL, VSWR, and ML)
  are interrelated.
• Knowing one, the magnitudes of the others can be
  computed.

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• When EM waves propagate in two directions inside
  a transmission line, a standing wave pattern is
  formed.

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• Voltage Standing Wave Ratio (VSWR) is by
  definition the ratio of maximum (Vmax) and
  minimum (Vmin) voltages of the standing wave
  function.

?