Download Chapter 3: From lumped to distributed elements

yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project

Document related concepts

Resistive opto-isolator wikipedia , lookup

Audio crossover wikipedia , lookup

405-line television system wikipedia , lookup

Opto-isolator wikipedia , lookup

Test probe wikipedia , lookup

Crystal radio wikipedia , lookup

Tektronix analog oscilloscopes wikipedia , lookup

Waveguide (electromagnetism) wikipedia , lookup

Instrument amplifier wikipedia , lookup

Mathematics of radio engineering wikipedia , lookup

Amplifier wikipedia , lookup

Mechanical filter wikipedia , lookup

Switched-mode power supply wikipedia , lookup

Wave interference wikipedia , lookup

Rectiverter wikipedia , lookup

Analogue filter wikipedia , lookup

Scattering parameters wikipedia , lookup

Nominal impedance wikipedia , lookup

HD-MAC wikipedia , lookup

Tube sound wikipedia , lookup

Power dividers and directional couplers wikipedia , lookup

Radio transmitter design wikipedia , lookup

RLC circuit wikipedia , lookup

Two-port network wikipedia , lookup

Valve audio amplifier technical specification wikipedia , lookup

Index of electronics articles wikipedia , lookup

Impedance matching wikipedia , lookup

Valve RF amplifier wikipedia , lookup

Distributed element filter wikipedia , lookup

Antenna tuner wikipedia , lookup

Zobel network wikipedia , lookup

Standing wave ratio wikipedia , lookup

Parasitics limit the performance
Avoid shunt C, series L
Ideal resistor value: R value pole and zero cancel out
Above self-resonant frequency the capacitor behaves as an
Q-factor =
(Below SFR)
Quality factor Q = omega0*av. Energy stored/av. Energy dissipated
Q = f0/3dB BW (relatively low due to losses in coil)
High tolerance on resonant frequency
At resonance: currents trough C and L cancel out and equal Q times the resistor
Piezo-acoustic resonators
Quartz (SiO2) crystal
High Q, stability, small size, low cost
C1<<C0, so slightly difference in resonance frequencies:
f_series ≲ f_parallel
fP by L1 and (C1 series C0 )
Repetitive ladder network
Input impedance of an infinite ladder network
does not change when a section is added
Artificial lines
Ladder network of reactive components
Behaves like real transmission lines (limited bandwidth)
Uses: Large broadband delays
Cutoff frequency:
above ZIN is purely reactive, no longer a TL: make LC low
Group delay: calculate per section
Use an extra half section!
m-derived half section
Gives even better results
Trade-off bandwidth  delay
Bandwidth is traded for delay rather than for gain
Solution: traveling wave amplifier (ch. 6)
: make LC high
Telegrapher equations
Two waves propagating in opposite direction: incident and reflected wave
Terminated lossless transmission line
Gamma = 0: line is perfectly terminated
 no reflections
Return loss (RL) dB = -20 log|Gamma|
Voltage standing wave ratio (VSWR)
= 1+|Gamma|/1-|Gamma|
Easy way to measure matching
Gamma vs. ZIN
Gamma tells everything about input impedance at distance l from the load
Gamma(l): rotates clockwise around the origin as l increases: lambda/2 => full circle
Two port models
Lossy transmission lines
In the conductor: skin effect arises: High Z0
In the dielectric (G): stray current between transmission lines:
 Low Z0
Causes: attenuation and dispersion
 Dispersion free when L/R = C/G
Shorted: can replace an inductor
Open: can replace a capacitor
Higher Q, cheaper at high f
only at GHz
Quarter wavelength TL transformer
The load impedance is inverted with a scale factor Short=>Open; L=>C; up or down
transforming of Z2
Very dispersive
Port properties
Reciprocal lossless three-port cannot de matched at three ports
Lossless reciprocal four-ports with two matched and reciprocally decouples ports are
matched and decoupled at the two other ports
Reciprocal lossless circuits with four matched ports always have two reciprocally
decoupled ports; these circuits are called 4-ports couplers
Power dividers and combiners
Directional couplers
<= 90°
Separate left/right traveling waves
Insertion loss = P1/P2 (dB)
Coupling = P1/P3 (dB)
Isolation = P1/P4 (dB)
Directivity = P3/P4 = I-C, ability to isolate forward and backward waves
90° all limited bandwidth
180° Transformer 180° hybrid is not resonant, so it’s broadband
Autotransformer (tapped coil)
Conventional transformer
 LF: tau0 = Lm/R needs to be increased -> N big
HF: tauc = RCp or Ls/R lowered -> N small
Transmission line transformer
Stray inductance (Ls) and winding capacitance (Cp)
Line must be short compared to the wavelength => both ends in phase
Impedance for maximum BW = ratio of in/output voltage to the current trough the line
Unbalanced - unbalanced
Impedance transformer
Balanced – unbalanced
Signal on both ports
1:4 balun with very high BW
1:4/9 balun for push-pull amplifiers
Two parallel amplifiers in anti-phase
Combining the output power of two
Linear amplifiers (e.g. class B)
Use a hybrid (transformer + resistor) combiner
 Combining 2 amplifiers
o Power doubles
o OIP + 3dB
 Using anti-phase amplifiers
o Even harmonics are suppressed
 Extra component Rh
o One more degree of freedom
• equal PALOAD = R
Directional bridge
Accepts loss to extend bandwidth (to DC)
To separate transmitted/reflected waves
In contrast with Bulk acoustic waves
Central frequency between 10M-2GHz
Interdigital transducer (IDT)
Fundamental resonance frequency:
Lambda = IDT period
SAW transversal filter
Use two IDTs one for generating
and one for capturing
FIR filter
Greater loss
Constant pass band group delay
How to build
IDT is trapped between two Bragg reflector gratings => high Q