Appendix. Power Transfer Basics Low frequencies wavelengths >> wire length current (I) travels down...
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![Page 1: Appendix. Power Transfer Basics Low frequencies wavelengths >> wire length current (I) travels down wires easily for efficient power transmission measured.](https://reader035.fdocuments.in/reader035/viewer/2022062721/56649f275503460f94c3f4be/html5/thumbnails/1.jpg)
Appendix
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Power Transfer Basics
Low frequencies wavelengths >> wire length current (I) travels down wires easily for efficient power transmission
measured voltage and current not dependent on position along wire
High frequencies wavelength or << length of transmission medium need transmission lines for efficient power transmission matching to characteristic impedance (Z0) is very important for low reflection and maximum power transfer
measured envelope voltage dependent on position along line
I+ -
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Transmission Line Basics
Characteristic impedance for microstrip transmission lines
(assumes nonmagnetic dielectric)
Microstrip
h
w
Coplanar
w1
w2
r
Waveguide
Twisted-pairCoaxial
b
a
h
w
Zo determines relationship between voltage and current waves
Zo is a function of physical dimensions and Zo is usually a real impedance (e.g. 50 or 75 ohms)
r
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Power Transfer EfficiencyRS
RL
Maximum power is transferred when RL = RS
RL / RS
0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4 5 6 7 8 9 10
Lo
ad
Po
we
r (n
orm
aliz
ed
)
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Power Transfer Efficiency
For complex impedances, maximum power transfer occurs when ZL = ZS* (conjugate match)
Zs = R + jX
ZL = Zs* = R - jX
Zo
Zo
Rs
RL
+jX
-jX
At high frequencies, maximum power transfer occurs when RS = RL = Zo
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Smith Chart Review.
-90 o
0o180
o+-
.2
.4
.6
.8
1.0
90o
0 +R
+jX
-jX
Smith Chart maps rectilinear impedanceplane onto polar plane
Rectilinear impedance plane
Polar plane
Z = ZoL
= 0
Constant X
Constant R
Z = L
= 0 O
1
Smith Chart
(open)
LZ = 0
= ±180 O1
(short)
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Lightwave Analogy to RF Energy
RF
Incident
Reflected
Transmitted
Lightwave
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Transmission Line Terminated with Zo
For reflection, a transmission line terminated in Zo behaves like an infinitely long transmission line
Zs = Zo
Zo
Vrefl = 0! (all the incident power is absorbed in the load)
V inc
Zo = characteristic impedance of transmission
line
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Transmission Line Terminated with Short, Open
Zs = Zo
Vrefl
V inc
For reflection, a transmission line terminated in a short or open reflects all power back to source
In phase (0 ) for openOut of phase (180 ) for shorto
o
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Transmission Line Terminated with 25
Zs = Zo
ZL = 25
Vrefl
V inc
Standing wave pattern does not go to zero as with short or open
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Device Characteristics
Devices have many distinctive characteristics such as: electrical behavior
DC power consumptionlinear (e.g. S-parameters, noise figure)nonlinear (e.g. distortion, compression)
physical specificationspackage typepackage sizethermal resistance
other things...costavailability
When selecting parts for design, characteristics are traded-offLet's look at important electrical characteristics for RF design ...
100p
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High-Frequency Device Characterization
Reflected
Incident
REFLECTION
SWR
S-ParametersS11,S22 Reflection
Coefficient
Impedance, Admittance
R+jX, G+jB
ReturnLoss
A
R=
Transmitted
Incident
TRANSMISSION
Gain / Loss
S-ParametersS21,S12
GroupDelay
TransmissionCoefficient
Insertion Phase
B
R=
R
A
Incident
Reflected
BTransmittedDUT
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Reflection Parameters
dB
No reflection(ZL = Zo)
RL
VSWR
0 1
Full reflection(ZL = open,
short)
0 dB
1
=ZL ZO
ZL + OZ
ReflectionCoefficient =
Vreflected
Vincident=
= Return loss = -20 log(),
VSWR = Emax
Emin=
1 + 1 -
Voltage Standing Wave RatioEmaxEmin
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Transmission Parameters
VTransmittedV Incident
Transmission Coefficient = =VTransmitted
V Incident =
DUT
Gain (dB) = 20 Log VTrans
VInc
= 20 log
Insertion Loss (dB) = - 20 Log VTrans
VInc
= - 20 log
Insertion Phase (deg) = VTrans
VInc
=
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Group Delay (GD)
Frequency
Group delay ripple
Average delay
t o
t g
in radians
in radians/sec
in degrees
f in Hertz ( f)
Group Delay (t )g =
d d =
1360 o
d d f*
Phase
Frequency
average delay indicates electrical length GD ripple indicates distortion aperture of measurement is very important
aperture is frequency-delta used to calculate GD
wider aperture: lower noise / less resolutionnarrower aperture: more resolution / higher noise
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Phase versus Frequency
50
50
R
A
PhaseDifferencebetweenA and R
Frequency
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50
50
R
DUT
Frequency
A
PhaseDifferencebetweenA and R
Phase versus Frequency
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50
50
R
DUTA
Frequency
PhaseDifferencebetweenA and R
Phase versus Frequency
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T/R Versus S-Parameter Test Sets
RF always comes out port 1 port 2 is always receiver response, one-port cal
available
RF comes out port 1 or port 2 forward and reverse
measurements two-port calibration possible
Transmission/Reflection Test Set
Port 1 Port 2
Source
B
R
A
DUTFwd
Port 1 Port 2
Transfer switch
Source
B
R
A
S-Parameter Test Set
DUTFwd Rev
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Response Calibration
Measurement
DUT
Reference
THRU
errors due to mismatch
Source Load Source LoadDUT
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Two-Port Calibration
A B
SourceMismatch
LoadMismatch
Crosstalk
Directivity
R
Six forward and six reverse error terms yields 12 error terms for two-port devices
DUT
reflection tracking (A/R) transmission tracking
(B/R)
Frequency response
Two-port calibration corrects for all major sources of systematic measurement errors
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Thru-Reflect-Line (TRL) Calibration
Advantages microwave cal standards easy to make (no open or load)
based on transmission line of known length and impedance
do not need to know characteristics of reflect standardDisadvantages
impractical length of RF transmission lines fixtures usually more complicated (and expensive) 8:1 BW limitation per transmission line
TRL calibration was developed for non-coaxial microwave measurements
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Characterizing Unknown Devices
Using parameters (H, Y, Z, S) to characterize devices: gives us a linear behavioral model of our device measure parameters (e.g. voltage and current) versus frequency under various source and load conditions (e.g. short and open circuits)
compute device parameters from measured data now we can predict circuit performance under any source and load conditions
H-parametersV1 = h11I1 + h12V2
I2 = h21I1 + h22V2 h11
=
V1I1 V2=
0
h12 =
V1V2
I1=0
(requires short circuit)
(requires open circuit)
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Why Use S-Parameters?
relatively easy to obtain at high frequencies
measure voltage traveling waves with a vector network analyzer
don't need shorts/opens which can cause active devices to oscillate or self-destruct
relate to familiar measurements (gain, loss, reflection coefficient ...)
can cascade S-parameters of multiple devices to predict system
performance can compute H, Y, or Z parameters
from S-parameters if desired can easily import and use S-parameter files in our electronic-simulation tools
Incident TransmittedS21
S11Reflected S22
Reflected
Transmitted Incident
b1
a1b2
a 2S12
DUT
b1 = S11a1 + S12 a 2
b2 = S21 a1 + S22 a 2
Port 1 Port 2
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Measuring S-Parameters
S 11 = Reflected
Incident=
b1
a 1 a2 =0
S 21 =Transmitted
Incident=
b2
a 1 a2 =0
S 22 = Reflected
Incident=
b2
a 2 a1 =0
S 12 =Transmitted
Incident=
b1
a 2 a1 =0
Incident TransmittedS 21
S 11Reflected
b 1
a 1
b 2
Z 0
Loada2 =0
DUTForward
1IncidentTransmitted S 12
S 22
Reflected
b 2
a2
b
a1=0
DUTZ 0
Load
Reverse
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Equating S-Parameters with Common Measurement Terms
S11 = forward reflection coefficient (input match)S22 = reverse reflection coefficient (output match)S21 = forward transmission coefficient (gain or loss)S12 = reverse transmission coefficient (isolation)Remember, S-parameters are inherently linear quantities -- however, we often express them in a log-magnitude format
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Going Beyond Linear Swept-Frequency Characterization
So far, we've only talked about linear swept-frequency characterization (used for passive and active devices).Two other important characterizations for active devices are:
nonlinear behavior noise figure
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Linear Versus Nonlinear Behavior
Linear behavior:input and output frequencies are the same (no additional frequencies created)output frequency only undergoes magnitude and phase change
Time
A
to
Frequencyf
1
Time
Sin 360 * f * t°
Frequency
A
1f
DUT
A * Sin 360 * f ( t - t )° °
Input Output
Time
Frequency
Nonlinear behavior:output frequency may undergo frequency shift (e.g. with mixers)additional frequencies created (harmonics, intermodulation)
f1
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Measuring Nonlinear BehaviorMost common measurements:
using a spectrum analyzer + source(s)harmonics, particularly second and thirdintermodulation products resulting from two or more RF carriers
using a network analyzer and power sweepsgain compressionAM to PM conversion
RL 0 dBm ATTEN 10 dB 10 dB / DIV
CENTER 20.00000 MHz SPAN 10.00 kHzRB 30 Hz VB 30 Hz ST 20 sec LPF
8563A SPECTRUM ANALYZER 9 kHz - 26.5 GHz
LPF DUT
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Noise Figure (NF)
Measure of noise added by amplifier
NF = 10 log [(Si/Ni) / (So/No)] Perfect amp would have 0 dB NF
DUTSo/No
Si/Ni
Gain
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Amplified Input NoiseAdded Noise
G, Na
Zs @ Ts = kTsB
Nout = Na + kTsBG
Slope = kGB
Noi
se P
ow
er O
utp
ut(N
out)
N2
N1
Tc Th
Na
Source impedance temperature
+ 28 V
Excess Noise Source
Th (noise source on) => N2 (at amplifier output)
Tc (noise source off) => N1 (at amplifier output)
Y = N2/N1
NF (dB) = ENR (dB) - 10 log (Y-1)
ENR (dB)
Y-factor Technique for NF Measurements
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AM to PM ConversionAmplitude
Time
AM (dB)
PM (deg)
Mag(AM in)
Test Stimulus
Amplitude
Time
AM (dB)
PM (deg)
Mag(AMout)
Mag(PMout)
Output Response
AM - PM Conversion =
Mag(PMout)
Mag(AM in)(deg/dB)
DUT
Power sweep
undesired AM: supply ripple, fading, thermaldesired AM: modulation (e.g. QAM)
I
Q
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Measuring AM to PM Conversion
use transmission setup with a power sweepdisplay phase of S21AM to PM = 0.727deg/dB
CH1 S21 log MAG 1 dB/ REF 25 dB
START -15.0 dBm STOP 5.0 dBmCW 1.880 000 000 GHz
C2
PRm
CH2 S21 phase REF 174 1 /
C2
PRm
11
23
1_: 0 dB
REF=1
2
1
23
1_ 0
2_ 351.38 m .5 dBm
3_ 727.45 m 1.0 dBm
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Heat Sinking for power devices, a heat sink is essential to keep Tjunction low heat sink size depends on material, power dissipation, air flow, and Tambient
ridges or fins increase surface area and help dissipate heat usually device attaches directly to heat sink (flange mounts help) bolt device in place first, then solder
heat sink