Jan-Geralt Bij de Vaate ASTRON - Onderzoekpeletier/RFsystemen2.pdf2 Basic Detection Techniques –...
Transcript of Jan-Geralt Bij de Vaate ASTRON - Onderzoekpeletier/RFsystemen2.pdf2 Basic Detection Techniques –...
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Basic Detection Techniques – “RF systems”
JGBdV 2006
RF SYSTEMS
Jan-Geralt Bij de Vaate
ASTRON
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Content:
• Introduction RF design• Basic principles
– Non linearity– Noise– Sensitivity– Dynamic range
• RF – building blocks– PLL– Oscillators– Mixers– Amplifiers– De-modulators– Filters
• Examples– Receiver architectures– Transceiver– WSRT– LOFAR
• Practicum– Use of spectrum analyzer
• Gain• IP2/IP3• Noise
– Use of noise meter
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Introduction RF designRF design is still a design bottleneck:• Multiple-disciplines
– Communication theory– Signal processing– IC technology– Etc.
• RF design hexagon
Trade off :
NoiseDC Voltage
Frequency Amplification
Power supplyLinearity
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• Design tools
– Reasonable circuit simulators • Accuracy depends on model quality
– Good Electro Magnetic simulators • 2.5 D of 3D• (computer) Time consuming
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Element Duplexer LNA BPF Mixer AMP #1 BPF AMP #2 AMP #3 Mixer BPF AMPGain (dB) -3 20 -2.7 -7 20 -17.4 30 30 -6 -6 45Noise Figure (dB) 2.7 1.5 2.7 7.5 4 17.4 4 6 6 6 5NFO (dB) 2.7 4.2 4.3 4.7 5.1 5.3 5.6 5.6 5.6 5.6 5.6Power (dBm) -125.3 -103.9 -107 -114.4 -94.1 -111.5 -81.5 -53.2 -58.9 -65 -19.9SNR (dB) 6.5 4.9 4.9 4.5 4 3.9 3.6 3.6 3.6 3.6 3.6TOI @ Output (dBm) 3.2 0.5 -7.5 8 -9.4 9.1 24.2 15.8 9.8 20
EXAMPLE RF DESIGN
Budget analyses
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Basic principles RF design
• Non linearity– Harmonic distortion– Gain compression– Blocking– Cross modulation– Inter-modulation (IP2/IP3)
• Random processes noise– Noise figure– Noise figure in cascaded circuits
• Sensitivity• Dynamic range
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Non linearity
...)()()()( 33
221 +++≈ txtxtxty ααα
• Linearity in analogue (RF) systems does not exists• Amplifier y=A tanh(Bx)• Or in a Tailor series:
• Effects of non-linearity• Generation of harmonics• Compression• Blocking• Cross modulation• Inter modulation
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Harmonics• Suppose input signal:
• Follows:
DC-term, fundamental and harmonicsDifferential amplifiers cancel even harmonicsDe nth harmonics grows with An
( )tAtx ωcos)( =
( )
)3cos(4
)2cos(2
)cos(4
32
)(cos)(coscos)(3
32
23
31
22
333
2221
tAtAtAAA
tAtAtAty
ωαωαωααα
ωαωαωα
++⎟⎟⎠
⎞⎜⎜⎝
⎛++=
++=
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Gain compression• For small input signals the amplifiers has a
more or less linear behavior• For large input signals
– 1dB compression point:
20logAout
A1dB 20log Ain0
1 dB
3
11 145.0
αα
=dBA
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Blocking• Weak signals can be blocked by a strong
interferer
• If A1 << A2:
)cos()cos()( 2211 tAtAtx ωω +=
...)cos(23)( 11
2231 +⎟
⎠⎞
⎜⎝⎛ += tAAty ωαα
The gain of the wanted signal depends on α3
α3 < 0 reduces the gain for increasing A2
blocking
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Cross modulation• Weak signals can modulated by a strong
interferer
• If A1 << A2:
• For a modulation of the strong interferer:
)cos()cos()( 2211 tAtAtx ωω +=
...)cos(23)( 11
2231 +⎟
⎠⎞
⎜⎝⎛ += tAAty ωαα
( ) )cos()cos(1 22 ttmA m ωω+
)cos()cos(2)2cos(22
123)(
22221311 ttmtmmAAAty mm ωωωαα ⎥
⎦
⎤⎢⎣
⎡
⎭⎬⎫
⎩⎨⎧
++++=
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Inter-modulation• The output of an amplifier:
• Inter-modulation is generated when two signals ‘mix’
...)()()()( 33
221 +++≈ txtxtxty ααα
)cos()cos()( 2211 tAtAtx ωω +=
[ ][ ]
[ ] ..)cos()cos(
)cos()cos(
)cos()cos()(
322113
222112
22111
++
++
++=
tAtA
tAtA
tAtAty
ωωα
ωωα
ωωα
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This results in second and third inter-modulation products
ω1 ω2 ω ω1 ω2 ω2ω1− ω2 2ω2− ω1
ω2− ω1 ω1+ ω2
tAAtAA
tAAtAA
tAAtAA
)2cos(4
3)2cos(4
3
)2cos(4
3)2cos(4
3
)cos()cos(
121
223
121
223
212
213
212
213
2121221212
ωωαωωα
ωωαωωα
ωωαωωα
−++
+−++
+−++
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The distortion products change different with inputs levels
f f2f - f1 2 1 2
Powerin dB
33
2 12f - f
2 2
f2-f1 f1+f2
On a logarithmic: ∆2 becomes 2∆
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IP2 en IP3• Example IP3
Out
put p
ower
, dB
m
0
-20
-40
-60
-80
-100
-60 -30 0 +30IIP3
First order
Thirdorder
Input power [dBm]
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IP 2 and IP 3
• Following the math:
3
∝
∝
αα
αα
1
2
1
343
2
IP
IP
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Noise
• External noise– Man-made noise: generated by equipment– Atmospheric noise: e.g caused by lightning– Space noise: e.g. the sun
• Internal noise
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Internal noise
• Thermal noise produced by random movement of electrons
Noise power: PN = kTBT = absolute temperature in Kk = Boltzmann’s: 1.38x10-23 J/KB = bandwidth in Hz
• Shot Noise – random variations in currents in active elements.
• Partition Noise - caused by multi patch effects• Excess Noise (1/f noise) – caused by density
variations in components.• Transit-Time Noise – high frequency noise
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Noise Spectrum of electronic components
DeviceNoise
Shot and Thermal Noises
Excess orFlicker Noise
Transit-Time orHigh-FrequencyEffect Noise
1 kHz fhcf
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Signaal to Noise ratio
• A very important parameter in de communication theory is the signal to noise ratio (SNR of S/N).
• Expressed in dB’s:
N
S
N
S
VVlog20
PP log 10 dB)(
NS
==
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Noise factor & Noise figure
Noise factor Fn = SNRin/SNRout
Noise figure NF (dB) = 10 log Fn= SNRin (dB) - SNRout (dB)
Equivalent noise temperature, Te = (Fn -1) Towith To = 290 K
0 1 2 3 4
NF in dB
0 75 170 290 438
Effective noise temperature in K
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Noise factor in cascaded stages
• For amplifiers in cascade, the noise measurebecomes:
12121
3
1
21 ...
1...11
−
−++
−+
−+=
n
nM GGG
FGG
FG
FFF
G2F2
G3F3
G1F1
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Example noise calculations
F1=6dB=4 F2=3dB=2 F3=16dB=40 G1=20dB=100 G2=-3dB=0.5 G3=60dB=1000000
With pre-amp:
Without pre-amp:
Verlies =3 dB
G3= 60dBF3=16dB
G1 = 20 dBF1 = 6dB
Pre-amp Cable Receiver
dBF 8.679.45.0*100
140100
1240 ==−
+−
+=
dBF 19805.0
14020 ==−
+=
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Example gain and noise calculation
Noise temperature of the amplifier: T3=(F3-1)T0=2610KReceiver noise temperature: T=T2+ T3/G2=125+2610/100 = 151KTotal noise power = G2 G3 k(Tg+T)B = 1010k(60+151)106=-45.3 dBW
We can calculate the required transmit power given a SNR of 20dB:
Pz(dBW)+6-190+40+20+80=-45.3+20(SNR) Pz = 18.6 dBW =73 Watt
G2 = 20 dBT2 = 125K
G3 = 80 dBF3 = 10dB
Antenna
Tg=60K, G=40dB
Pre-amplifier amplifier
Satellite, G=6dB
Loss = 190dB
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Sensitivity• Defined as the minimal signal that the system
can detect with an acceptable SNR
• Noise floor:
minmin, log10/174 SNRBNFHzdBmPin +++−=
BNFHzdBmPruisvloer log10/174 ++−=
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Dynamic range• Defined as the ratio between the maximum
signal that can be handled by the circuit and the minimum input signal.
could be defined as:DR= Dynamic rangen = orderIPin = input inter modulation Intercept pointMDS = minimum detectable signal
• Also SFDR = spurious free Dynamic Range
nMDSIPn
DR innn
))(1( , −−=
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RF building blocks
• Amplifiers• Oscillators• PLL’s• Filters• Mixers• Modulation / demodulation
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Amplifiers
• Example of design parameters:– Noise figure NF (e.g 2 dB)– Input IP3 (e.g. –10 dBm)– Amplification (e.g. 20 dB)– Input impedance (50 Ohm)– Output impedance (50 Ohm)– Input return loss (-15 dB)– Output return loss (-15 dB)– Reverse isolation (25 dB)
• Practicum: Determine amplification, noise figure and IP2 / IP3
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Oscillators - principle
• Conditions for oscillation– The phase shift in the
complete feedback loop should be 0o of 360o
– The loop gain |BAv| = 1, With B = attenuation of feedback circuit, and Av = amplifier gain
B
AvVout
Basic elements of an oscillator
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Basic Wien-Bridge Oscillator
_
+
C2
C1 R4
R3
R1
R2
Voltage divider
Lead-lagcircuit
Vout+
_
R1
R4
R2
R3 C2
C1
Vout
Two versions of identical principle
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Wien-Bridge Oscillator
• At the resonance frequency generates the lead-lag circuit a positive feedback with a attenuation of 1/3 if R3=R4=XC1=XC2.
• For oscillation, requires a non-inverting amplifier with a gain of 3x. Possible whenR1 = 2R2
• If R3 = R4 = R, en C1= C2 = C, then the resonance frequency equals:
RCfr π2
1=
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Phase shift Oscillator
+
_
Rf
C1 C2 C3
R1 R2 R3
Vout
Each RC section causes 60 degrees phase shift. The total attenuation in thethree-section RF feedback circuit is B = 1/29.
If: R1 = R2 = R3 = R,C1 = C2 = C3 = C,Then resonancefrequency equals:
RCfr 62
1π
=
293
==RR
A fcl
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Colpitts Oscillator
+VDD
R2 C5
C3
R1 R3
L
C1 C2
C4
VoutVAC
CB 1
1
2 ==
Tr LC
fπ2
1=
met21
21
CCCCCT +
=
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Crystal Oscillator• For a stable and accurate oscillator
piezoelectric crystal (e.g. quartz) can be used in the feedback loop.
• Piezoelectric effect: For a changing mechanical stress at the crystal, a voltage will be generated. Or reverse, when an AC signal is applied, the crystal will resonate (vibrate) at the frequency of that signal. The largest resonance will occur at the resonance frequency.
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Symbol and electric equivalent circuit
XTAL
Cp Cs
Ls
Rs
Symbol Electricalequivalent
• A crystal can have a series and a parallel resonance.
• Crystals have a very high Q
• Resonance frequencies depend on dimensions, types, temperature etc.
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36
Basic Detection Techniques – “RF systems”
JGBdV 2006
Basic Crystal Oscillator
C1R2 R4
+VCC
R1 R3
C2
CCXtalC1
R1 R2
R3
C2
C3Vo
C4
Vo
+VCC
C5
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37
Basic Detection Techniques – “RF systems”
JGBdV 2006
Voltage-Controlled Oscillator (VCO)• VCOs are applied in many systems e.g. AFC,
PLL, frequency tuning, etc.• The principle is based on changing a capacitor
of a varactor diode in a resonance circuit. • The approximate total capacity of the diode
depends on the bias spanning:
b
oV V
CC21+
=
![Page 38: Jan-Geralt Bij de Vaate ASTRON - Onderzoekpeletier/RFsystemen2.pdf2 Basic Detection Techniques – “RF systems” JGBdV 2006 Content: • Introduction RF design • Basic principles](https://reader035.fdocuments.in/reader035/viewer/2022070705/5e8efb765a94e04b9f6393a5/html5/thumbnails/38.jpg)
38
Basic Detection Techniques – “RF systems”
JGBdV 2006
Phase noise
ωωc
Ideal oscillator
ωωc
∆ωPractical oscillator
))(cos()( ttAtx nc φω +=
Example: •Carrier power = -2dBm•Noise power in a 1kHz bandwidth with 1MHz offset is –70dBm•Phase noise = -70 dBm + 2 dBm (carrier) – 30 dB (bandwidth)
= -98 dBc/Hz
φn(t)= phase noise
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Basic Detection Techniques – “RF systems”
JGBdV 2006
Phase-Locked Loop• The PLL is the building block for modern
synthesizers. • The block diagram for a simpel PLL:
PhaseDetector LPF Loop
Amplifier VCOfr fo
Vp
Divider :n
![Page 40: Jan-Geralt Bij de Vaate ASTRON - Onderzoekpeletier/RFsystemen2.pdf2 Basic Detection Techniques – “RF systems” JGBdV 2006 Content: • Introduction RF design • Basic principles](https://reader035.fdocuments.in/reader035/viewer/2022070705/5e8efb765a94e04b9f6393a5/html5/thumbnails/40.jpg)
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Basic Detection Techniques – “RF systems”
JGBdV 2006
The PLLInitial a PLL is not locked; the VCO is on the free-running frequency, fo.If fo is not equal to frequency fr , a Vp will be generated by the phase detector.This voltage Vp will go through the filter before amplification and subsequently applied to the VCO. A stable system will be: fo = fr. The PLL is in phase lock.
( if n=1 )
![Page 41: Jan-Geralt Bij de Vaate ASTRON - Onderzoekpeletier/RFsystemen2.pdf2 Basic Detection Techniques – “RF systems” JGBdV 2006 Content: • Introduction RF design • Basic principles](https://reader035.fdocuments.in/reader035/viewer/2022070705/5e8efb765a94e04b9f6393a5/html5/thumbnails/41.jpg)
41
Basic Detection Techniques – “RF systems”
JGBdV 2006
PLL Frequency Specifications
Free-RunningFrequency
Catch range
Lock range
fofLCfLL fHC fHLf
![Page 42: Jan-Geralt Bij de Vaate ASTRON - Onderzoekpeletier/RFsystemen2.pdf2 Basic Detection Techniques – “RF systems” JGBdV 2006 Content: • Introduction RF design • Basic principles](https://reader035.fdocuments.in/reader035/viewer/2022070705/5e8efb765a94e04b9f6393a5/html5/thumbnails/42.jpg)
42
Basic Detection Techniques – “RF systems”
JGBdV 2006
Potential problems with PLL’s
• Phase noise• Spurious • Lock issues
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Basic Detection Techniques – “RF systems”
JGBdV 2006
Filter design
• Filters are used for many reasons:– Suppression of harmonics– Suppression of image frequencies– Selectivity– Demodulation– Etc…
• Parameters for the design of filters :– Attenuation– Bandwidth– Center frequency– Cutoff frequency– Delay (differential and groups-)
![Page 44: Jan-Geralt Bij de Vaate ASTRON - Onderzoekpeletier/RFsystemen2.pdf2 Basic Detection Techniques – “RF systems” JGBdV 2006 Content: • Introduction RF design • Basic principles](https://reader035.fdocuments.in/reader035/viewer/2022070705/5e8efb765a94e04b9f6393a5/html5/thumbnails/44.jpg)
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Basic Detection Techniques – “RF systems”
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Filter design
– Insertion lossFor wanted and un-wanted signals.
– Pass band– Pass band ripple– Phase behavior– Poles– Q-factor– Return loss– Shape factor
The shape factor is defined as de ratio between bandwidth at -60 dB and the bandwidth at -3 dB
![Page 45: Jan-Geralt Bij de Vaate ASTRON - Onderzoekpeletier/RFsystemen2.pdf2 Basic Detection Techniques – “RF systems” JGBdV 2006 Content: • Introduction RF design • Basic principles](https://reader035.fdocuments.in/reader035/viewer/2022070705/5e8efb765a94e04b9f6393a5/html5/thumbnails/45.jpg)
45
Basic Detection Techniques – “RF systems”
JGBdV 2006
Low Pass Filter Response
Vo
fcf0
10.707
BW
Gain (dB)
0
-20
-40
-60
fc 10fc 100fc 1000fc
-20 dB/dec
-40 dB/dec
-60 dB/dec
LPF with different roll-off ratesBasic LPF response
f
Ideal
Pass band
BW = fc
![Page 46: Jan-Geralt Bij de Vaate ASTRON - Onderzoekpeletier/RFsystemen2.pdf2 Basic Detection Techniques – “RF systems” JGBdV 2006 Content: • Introduction RF design • Basic principles](https://reader035.fdocuments.in/reader035/viewer/2022070705/5e8efb765a94e04b9f6393a5/html5/thumbnails/46.jpg)
46
Basic Detection Techniques – “RF systems”
JGBdV 2006
High Pass Filter Response
Vo
fc f0
1
0.707
Gain (dB)
0
-20
-40
-60
0.01fc 0.1fc fc
-20 dB/dec
-40 d
B/de
c-6
0 dB
/dec
Pass band
Basic HPF response HPF with different roll-off rates
f
![Page 47: Jan-Geralt Bij de Vaate ASTRON - Onderzoekpeletier/RFsystemen2.pdf2 Basic Detection Techniques – “RF systems” JGBdV 2006 Content: • Introduction RF design • Basic principles](https://reader035.fdocuments.in/reader035/viewer/2022070705/5e8efb765a94e04b9f6393a5/html5/thumbnails/47.jpg)
47
Basic Detection Techniques – “RF systems”
JGBdV 2006
Band-Pass Filter Response
Vout
1
0.707
ffofc1 fc2
BW
BW = fc2 - fc1
21 cco fff =Center frequency:
Quality factor:BWfQ o=
Q is an indication for the Selectivity of a BPF.Small BPF: Q > 10.Wide-band BPF: Q < 10.
Attenuation Factor: QDF 1=
![Page 48: Jan-Geralt Bij de Vaate ASTRON - Onderzoekpeletier/RFsystemen2.pdf2 Basic Detection Techniques – “RF systems” JGBdV 2006 Content: • Introduction RF design • Basic principles](https://reader035.fdocuments.in/reader035/viewer/2022070705/5e8efb765a94e04b9f6393a5/html5/thumbnails/48.jpg)
48
Basic Detection Techniques – “RF systems”
JGBdV 2006
Gain (dB)
0-3
ffofc1 fc2
BW
Pass band
Band-Stop Filter Response
• Also known as band-reject, of notch filter.
• Used for suppression of RFI
example
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Basic Detection Techniques – “RF systems”
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Application for notch filters
Nu:2*TV-Drenthe - NL3 = 347 MHz2*TV-Drenthe - NL2 = 323 MHzTV-Drenthe – NL1 = 320 MHz
f181 MHZ 501 MHZ 655 MHZ 679 MHZ
NL1 TV-D NL3 NL2
92 cm-band310-390 MHz
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50
Basic Detection Techniques – “RF systems”
JGBdV 2006
Filter Response characteristics
Av
f
Chebyshev
Butterworth
Bessel
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Filter characteristics• Butterworth: flat amplitude response in the
pass band. Slope -20 dB/dec/pole; Phase response non-linear.
• Chebyshev: Slope > -20 dB/dec/pole; ripples in the pass band; Phase response very non-linear.
• Bessel: linear phase response, Slope < -20 dB/dec/pole.
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52
Basic Detection Techniques – “RF systems”
JGBdV 2006
Mixers
• A mixer is a non linear circuit combining two signals, generating a plus and a minus signal
Vrf
VLO
VIF
ttV
ttVtVtV
RFLORFLOIF
RFLOIF
RFRF
LOLO
)cos(21)cos(
21
)sin().sin()sin()sin(
ωωωω
ωωωω
+−−=
===
![Page 53: Jan-Geralt Bij de Vaate ASTRON - Onderzoekpeletier/RFsystemen2.pdf2 Basic Detection Techniques – “RF systems” JGBdV 2006 Content: • Introduction RF design • Basic principles](https://reader035.fdocuments.in/reader035/viewer/2022070705/5e8efb765a94e04b9f6393a5/html5/thumbnails/53.jpg)
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Basic Detection Techniques – “RF systems”
JGBdV 2006
Balanced Mixers• A balanced mixer suppresses the input signals.
Circuit symbol:
f1
f2
f1+ f2
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54
Basic Detection Techniques – “RF systems”
JGBdV 2006
Single-balanced Mixer
LO
IF
D1
D2
RF
...)cos(1)cos(1)sin(21
+−++−= tttV RFLORFLORFIF ωωπ
ωωπ
ω
-The RF signal is still present in the IF
![Page 55: Jan-Geralt Bij de Vaate ASTRON - Onderzoekpeletier/RFsystemen2.pdf2 Basic Detection Techniques – “RF systems” JGBdV 2006 Content: • Introduction RF design • Basic principles](https://reader035.fdocuments.in/reader035/viewer/2022070705/5e8efb765a94e04b9f6393a5/html5/thumbnails/55.jpg)
55
Basic Detection Techniques – “RF systems”
JGBdV 2006
Double balanced Diode ring mixer
LO
IF
D1
D2
RF
D4
D3
ttV RFLORFLOIF )cos(2)cos(2 ωωπ
ωωπ
−++−=
-None of the input signals is present in the IF
![Page 56: Jan-Geralt Bij de Vaate ASTRON - Onderzoekpeletier/RFsystemen2.pdf2 Basic Detection Techniques – “RF systems” JGBdV 2006 Content: • Introduction RF design • Basic principles](https://reader035.fdocuments.in/reader035/viewer/2022070705/5e8efb765a94e04b9f6393a5/html5/thumbnails/56.jpg)
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Basic Detection Techniques – “RF systems”
JGBdV 2006
Dual-Gate (active) MOSFET Mixer
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57
Basic Detection Techniques – “RF systems”
JGBdV 2006
Image reject mixer• Also used in the Westerbork array
90o
90ofilter
filter
Input
LO
Output
)cos()cos()( lluu tttx φωφω +++=))cos(()(),)cos(()(
lLOlLO
LOuLOu
tAtyoftAty
φφωωφφωω
−+−=−+−=
low highIF
(SSB)LO
![Page 58: Jan-Geralt Bij de Vaate ASTRON - Onderzoekpeletier/RFsystemen2.pdf2 Basic Detection Techniques – “RF systems” JGBdV 2006 Content: • Introduction RF design • Basic principles](https://reader035.fdocuments.in/reader035/viewer/2022070705/5e8efb765a94e04b9f6393a5/html5/thumbnails/58.jpg)
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Basic Detection Techniques – “RF systems”
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Modulation en demodulation
• Analogue modulation– Amplitude modulation– Single Side Band modulation– Phase en frequency modulation
• Digital modulation– Binary modulation (e.g. FSK)– Quad modulation (e.g. QPSK)– …
![Page 59: Jan-Geralt Bij de Vaate ASTRON - Onderzoekpeletier/RFsystemen2.pdf2 Basic Detection Techniques – “RF systems” JGBdV 2006 Content: • Introduction RF design • Basic principles](https://reader035.fdocuments.in/reader035/viewer/2022070705/5e8efb765a94e04b9f6393a5/html5/thumbnails/59.jpg)
59
Basic Detection Techniques – “RF systems”
JGBdV 2006
AM wave form
ec = Ec sin ωctem = Em sin ωmt
AM signaal:es = (Ec + em) sin ωct
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Modulation Index• The level of amplitude modulation: modulation
index:
minmax
minmax
EEEEof
EEm
c
m
+−
=
If Em = Ec , m =1 of 100% modulation.
Over-modulation, if Em>Ec : distortion
With, Emax = Ec + Em; Emin = Ec - Em
![Page 61: Jan-Geralt Bij de Vaate ASTRON - Onderzoekpeletier/RFsystemen2.pdf2 Basic Detection Techniques – “RF systems” JGBdV 2006 Content: • Introduction RF design • Basic principles](https://reader035.fdocuments.in/reader035/viewer/2022070705/5e8efb765a94e04b9f6393a5/html5/thumbnails/61.jpg)
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Effects of the Modulation Index
m = 1 m > 1
For more then one frequency component:
222
21 ... nT mmmm +++=
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AM in the frequency domain
• The formulation for a AM signal:es = (Ec + em) sin ωct
is equal to:
es = Ec sin ωct + ½ mEc[cos (ωc-ωm)t-cos (ωc+ωm)t]
• The AM signal consists of original carrier, an lower side frequency flsf = fc - fm, and an upper side frequencyfusf = fc + fm.
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AM Spectrum
ffc
Ec
fusf
mEc/2mEc/2
flsf
fmfm
fusf = fc + fm ; flsf = fc - fm ; Esf = mEc/2Band width, B = 2fm
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AM power• Total average (rms) power of an AM signal is:
PT = Pc + 2Psf , withPc = carrier power; and Psf = side band power
• For a load R, gives this: Pc = Ec2/(2R); and
Psf = m2Pc/4. So,
)2
1(2mPP cT +=
![Page 65: Jan-Geralt Bij de Vaate ASTRON - Onderzoekpeletier/RFsystemen2.pdf2 Basic Detection Techniques – “RF systems” JGBdV 2006 Content: • Introduction RF design • Basic principles](https://reader035.fdocuments.in/reader035/viewer/2022070705/5e8efb765a94e04b9f6393a5/html5/thumbnails/65.jpg)
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Basic Detection Techniques – “RF systems”
JGBdV 2006
Complex AM wave form• For complex AM signals with more frequency
components, the modulation index m will be substituted by a new index mT.
)2
1(2
TCT
mPP +=
![Page 66: Jan-Geralt Bij de Vaate ASTRON - Onderzoekpeletier/RFsystemen2.pdf2 Basic Detection Techniques – “RF systems” JGBdV 2006 Content: • Introduction RF design • Basic principles](https://reader035.fdocuments.in/reader035/viewer/2022070705/5e8efb765a94e04b9f6393a5/html5/thumbnails/66.jpg)
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AM modulation
LO
IF RF
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Basic Detection Techniques – “RF systems”
JGBdV 2006
AM demodulation
cos(ωct)
xAM(t)LPF
Draw backs of AM:
• Band width is 2x more then required• Power in de carrier is lost energy
• Single side band modulation (SSB): USB / LSB
![Page 68: Jan-Geralt Bij de Vaate ASTRON - Onderzoekpeletier/RFsystemen2.pdf2 Basic Detection Techniques – “RF systems” JGBdV 2006 Content: • Introduction RF design • Basic principles](https://reader035.fdocuments.in/reader035/viewer/2022070705/5e8efb765a94e04b9f6393a5/html5/thumbnails/68.jpg)
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Phase modulation
[ ])(cos)( tmxtAtx BBccPM += ωm = phase modulation index
tmAtxttx
ccPM
BB
)cos()()(
αωα
+=⇒=
A slope generates a frequency shift
(Linear)
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JGBdV 2006
Frequency modulation
⎥⎦
⎤⎢⎣
⎡+= ∫
∞−
t
BBCCFM dttxmtAtx )(cos)( ω
m = frequency modulation index
tmAAtxAtx
ccFM
BB
)cos()()(
+=⇒=
ω
A DC input generates a frequency shift
![Page 70: Jan-Geralt Bij de Vaate ASTRON - Onderzoekpeletier/RFsystemen2.pdf2 Basic Detection Techniques – “RF systems” JGBdV 2006 Content: • Introduction RF design • Basic principles](https://reader035.fdocuments.in/reader035/viewer/2022070705/5e8efb765a94e04b9f6393a5/html5/thumbnails/70.jpg)
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Phase en frequency wave form
t
xBB(t)
t
xPM(t)
t
xFM(t)
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Frequention modulation/demodulation
xBB(t)xFM(t)
VCO
C
R
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Examples• Receiver architectures
• 50 MHz transceiver
• Westerbork array
• LOFAR, low frequency array
FSKFSK
CWCWPLL SynthesizerPLL Synthesizer
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Receiver architectures
• Direct conversion receiver (also known as homodyne receiver)
• Super heterodyne receiver• Image –reject receiver• Direct sampling receiver
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Basic Detection Techniques – “RF systems”
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Homodyne receiverSimple type: direct to Baseband mixing (direct conversion)
A0cosωot
ωω0
LDF
ω0
LNA
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Basic Detection Techniques – “RF systems”
JGBdV 2006
(Super)heterodyne ontvanger
A0cosωot
ωω1
BPF
ωω2
12 ωωω −= LO
Band selection filter is easy (low Q)
ω1
Problem:
ωLO ωimageωIF ωIF
image
• Solution: filter before the mixerImage reject filter
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Example: the single super
Modefilter
LFHF
filterDet.
LO
MFHF
Draw backs:
•For a MF 455 MHz, the image frequency will be 900 MHz•Could still be in the HF band•Sharp filters required
The double super
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Example: the double super
• High first MF• Second LO fixed
MFfilter
LF
HFfilter Det.
LO 1
2e MFHF
Modefilter
LO 2
1e MF
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Image reject receivers
• Avoid the requirement for image reject filters:
– Hartley architecture– Weaver architecture
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79
Basic Detection Techniques – “RF systems”
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Hartley architecture
90o
LPF
LPF
IF outputRF input sinωlot
cosωlot
A
C
B
ω-ωLO ωLO0
image
Wanted signal
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0
ω
0
+j/2 +j/2
-j/2-j/2
A
0
0
ω
ω
ωB
0
ω0
C
ω
900
0 ω
IF output
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Direct sampling ReceiverOver-sampling Receiver
HF
Band selection with digital filter and mixer
Requires high data rate A to Digital Converter
LPF LPF
LO
A
D
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82
Basic Detection Techniques – “RF systems”
JGBdV 2006
Direct sampling ReceiverSub-sampling Receiver
HF
Under sampling: lower sample rate ADCs required
Band selection with analogue filter
BDFA
D
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50 MHz Transceiver
• Specifications– Modes : CW en FSK– Image suppression 60 dB– Sensitivity receiver: 0.15 µV with 10 dB SNR
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Basic Detection Techniques – “RF systems”
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Possible design
FSKFSK
CWCW
PLL SynthesizerPLL Synthesizer
50-51 MHz
Image reject filter
Receiver
Transmitter
LO
IFMixer
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Some calculations
• Sensitivity of 0.15 µV and SNR of 10 dB– For SSB : BW = 2.5 kHz– Noise floor P=4kTB = -134 dBm– 10 dB SNR minimum signal = -124 dBm– 0.15 µV @ 50 Ω -123.46 dBm– With other words: the noise figure of the receiver
should better then 0.6 dB
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The Westerbork Array• WSRT - Westerbork Synthesis Radio Telescope
–Equivalent 93 m telescope for area–Equivalent 2700 m telescope for resolution–14 telescopes of 25 m diameter with 2700 m baseline
• Synthesis–Phase coherent combinations–Correlation of all signals–Earth rotation, 12 uur–4 telescopes moveable
• Coherent addition–Fanbeam: 0,5 x 0,004 degrees(1420MHz)
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88
Basic Detection Techniques – “RF systems”
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The signal path, block diagram
Recv.Recv.
Equal.Equal.
IVCIVC
ADCADC
Recv.Recv.
Equal.Equal.
IVCIVC
ADCADC
Receivers in 14 telescopeswest east
Coaxial cables
Central building
TADU
ΣTADU
Σ
LOLO LOLOVLBIVLBI PuMaPuMa
CorrelatorCorrelator
Ref. Ref.
∆φ ∆φ∆τ∆τ
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The receiverMFFE:Multi Frequency Front End
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90
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Frequency bands (1)Wave length Frequency-
band92 cm 310-390 MHz
49 cm 560-620 MHz
21 cm 1200-1450 MHz
18 cm 1590-1750 MHz
13 cm 2215-2375 MHz
6 cm 4770-5020 MHz
3,6 cm 8150-8650 MHz
UHF low (120-65 cm)
250-460 MHz
UHF high (43-25 cm)
700-1200 MHz
Two polarizations for all frequencies
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Frequency bands (2)3.6 cm6 cm13 cm18 cm21 cm49 cm92 cmUHF highUHF low
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92
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Astronomical demands
• Sensitivity
• Clean bands (no RFI)
• Stable system
τBTTT recsky+
≈∆
Requires low noise receivers…
…long integration time…
…and large bandwidth.
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MFFE Block diagram (1)UHFlow UHFhigh 92 49 13 18/21 6 3.6
swsw
LO1 low Synth.
LO1 low Synth.
swsw
1200-2200 MHz
1 GHzIF1 IF1
LO1 high Synth.
LO1 high Synth.
swsw
2200-9600 MHz
1 GHz
1 GHz
LO2 Synth.
LO2 Synth.
900 MHz
2x IF out100 ± 80 MHz
Cryogenic
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MFFE Cryostat
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MFFE Block diagram (2)UHFlow UHFhigh 92 49 13 18/21 6 3.6
swsw
LO1 low Synth.
LO1 low Synth.
swsw
1200-2200 MHz
1 GHzIF1 IF1
LO1 high Synth.
LO1 high Synth.
swsw
2200-9600 MHz
1 GHz
1 GHz
LO2 Synth.
LO2 Synth.
900 MHz
2x IF out100 ± 80 MHz
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96
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The signal path, block diagram
Recv.Recv.
Equal.Equal.
IVCIVC
ADCADC
Recv.Recv.
Equal.Equal.
IVCIVC
ADCADC
Receivers in 14 telescopeswest east
coaxial cables
Central building
TADU
ΣTADU
Σ
LOLO LOLO
CorrelatorCorrelator
Ref. Ref.
∆φ ∆φ∆τ∆τ
![Page 97: Jan-Geralt Bij de Vaate ASTRON - Onderzoekpeletier/RFsystemen2.pdf2 Basic Detection Techniques – “RF systems” JGBdV 2006 Content: • Introduction RF design • Basic principles](https://reader035.fdocuments.in/reader035/viewer/2022070705/5e8efb765a94e04b9f6393a5/html5/thumbnails/97.jpg)
97
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The Equalizer
Equalizer
-50
-40
-30
-20
-10
0
10
20
30
10 30 50 70 90 110 130 150 170 190
Freq (MHz)
Gain (dB)
![Page 98: Jan-Geralt Bij de Vaate ASTRON - Onderzoekpeletier/RFsystemen2.pdf2 Basic Detection Techniques – “RF systems” JGBdV 2006 Content: • Introduction RF design • Basic principles](https://reader035.fdocuments.in/reader035/viewer/2022070705/5e8efb765a94e04b9f6393a5/html5/thumbnails/98.jpg)
98
Basic Detection Techniques – “RF systems”
JGBdV 2006
The signal path, block diagram
Recv.Recv.
Equal.Equal.
IVCIVC
ADCADC
Recv.Recv.
Equal.Equal.
IVCIVC
ADCADC
Receivers in 14 telescopeswest east
coaxial cables
Central building
TADU
ΣTADU
Σ
LOLO LOLO
CorrelatorCorrelator
Ref. Ref.
∆φ ∆φ∆τ∆τ
![Page 99: Jan-Geralt Bij de Vaate ASTRON - Onderzoekpeletier/RFsystemen2.pdf2 Basic Detection Techniques – “RF systems” JGBdV 2006 Content: • Introduction RF design • Basic principles](https://reader035.fdocuments.in/reader035/viewer/2022070705/5e8efb765a94e04b9f6393a5/html5/thumbnails/99.jpg)
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IF to Video Converter (IVC)• Converts (IF) to
baseband (Video)• Splits 160 MHz band in
8x20 MHz bands
We have 14+2 IF channels, with each 2 polarizations divided in 8 bands: totals 16x2x8=256 modules!
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Block diagram IVC
div
div
8filters
BW=20 MHz
BW=156 kHz
20-180 MHzinput
LO1240-400 MHz
LO2200 en 220 MHz
200-220 MHzIRM video
out
LO1LO1 LO2LO2LO2
LO1
0 20 180 220 400200 240
80 100 30010MHzref.
10MHzref.
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IVC Modules
Converter module
Filter module
LO module
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102
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The signal path, block diagram
Recv.Recv.
Equal.Equal.
IVCIVC
ADCADC
Recv.Recv.
Equal.Equal.
IVCIVC
ADCADC
Receivers in 14 telescopeswest east
coaxiale cables
Central building
TADU
ΣTADU
Σ
LOLO LOLO
CorrelatorCorrelator
Ref. Ref.
∆φ ∆φ∆τ∆τ
![Page 103: Jan-Geralt Bij de Vaate ASTRON - Onderzoekpeletier/RFsystemen2.pdf2 Basic Detection Techniques – “RF systems” JGBdV 2006 Content: • Introduction RF design • Basic principles](https://reader035.fdocuments.in/reader035/viewer/2022070705/5e8efb765a94e04b9f6393a5/html5/thumbnails/103.jpg)
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The A/D Converter system
• Conversion from baseband to digital
• Bandwidth is 20 MHz, so for Nyquist sampling 40 MHz is required
• The signal is noise: only 1 bit coding required.
• 2 bits sampling used
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Block diagram ADC
samplersampler delaydelay adderadder
formatterformatter
timingtiming
256 analoginputs
Referenceclock
Total power information
32 digital outputs to correlator
3 bits S,M,V
Shifted samplingclock
Sampling clock32 summedoutputs to tied array applications
25 nsec
128 steps of 0.2 nsec
Max. delay 1.6 msecin steps of 0.2 nsec
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Sampler Module
Analogue part Digital part
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106
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The signal path, block diagram
Recv.Recv.
Equal.Equal.
IVCIVC
ADCADC
Recv.Recv.
Equal.Equal.
IVCIVC
ADCADC
Receivers in 14 telescopeswest east
coaxial cables
Central building
TADU
ΣTADU
Σ
LOLO LOLO
CorrelatorCorrelator
Ref. Ref.
∆φ ∆φ∆τ∆τ
![Page 107: Jan-Geralt Bij de Vaate ASTRON - Onderzoekpeletier/RFsystemen2.pdf2 Basic Detection Techniques – “RF systems” JGBdV 2006 Content: • Introduction RF design • Basic principles](https://reader035.fdocuments.in/reader035/viewer/2022070705/5e8efb765a94e04b9f6393a5/html5/thumbnails/107.jpg)
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The Correlator
• Combinations of all telescopes are made• Also ‘combinations’ in the time domain: spectral
information
• Pulsar gating
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Correlator Board
32 custom correlatorchips
10 custom crossbar chips
2 DSP chips
13 Mb srammemory
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LOFAR Radio Ontvanger Systeem
AnalogueProcessing
AnalogueTo
Digital
DigitalProcessing
PostProcessing
Visualization
Storage
Antennas
![Page 110: Jan-Geralt Bij de Vaate ASTRON - Onderzoekpeletier/RFsystemen2.pdf2 Basic Detection Techniques – “RF systems” JGBdV 2006 Content: • Introduction RF design • Basic principles](https://reader035.fdocuments.in/reader035/viewer/2022070705/5e8efb765a94e04b9f6393a5/html5/thumbnails/110.jpg)
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LOFAR Radio receiver system