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Topics:
Intermodulation
•Intercept point•Intermodulation products •Intermodulation ratio
Sensitivity
•noise figure•noise bandwidth•S/N versus (S+N/N) and SINAD
RF Power at:
•CW (Contineuos wave)•AM (A3E)•FM (F3E)•PEP (Peak Envelope Power)
Selectivity
•adjacent channel rejection
VSWR
•voltage standing wave ratio (VSWR) •reflection coefficient•return loss / mismatch loss
Radio Basics
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Intermodulation Products
Output of a non linear component
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L
ff2-f1 f1 f2 f2+f1 2f1+f2 2f1-f2 2f2-f1 2f2+f1
aIM2 aIM3
intermodulation ratio aIM = L(f1,f2) - LIM
Internally generated intermodulation products:Example:
f1, original frequ. 7030 kHzf2, original frequ. 7060 kHzfim2 f2 + f1 14360 kHzfim2 f2 – f1 30 kHzfim3 2f1 - f2 7000 kHzfim3 2f2 - f1 7090 kHz
Can not be removed by filtering
Intermodulation Products
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Loutp.
IC2
IC3
Linput
Lf1,f2
Lf1f2
L2f1 f2
L2f2 f1
aIM2 = IC2 -Loutp.aIM3 = 2 (IC3 - Loutp.)
Example:
Amplifier , gain: vp = 100, IC3 = +35dBm, output Intercept Point>> g = 10*lg vp = 20dBInput signal Linp. = -5dBm>> Loutp. = -5dBm + 20db = 15dB wanted: intermodulation ratio:
aIM3 = 2(35dBm - 15dBm) = 40dB
Intercept Point
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EK 895Intermodulation (1.5 to 30 MHz; F 30 kHz;)IP3 30 dBm (typ. 35 dBm, related to RX Input)
3rd order intermod by two signals 10 mV (EMV)on the a.m. HF-frequencies?3rd order intercept point 30 dBmInterfering signal -33 dBmDistance from IP3 30-(-33) = 63 dBDistance of IM from interfering signal 2*63 = 126 dBLevel of IM-product -33 dBm - 126 dB = -159 dBm
-159 dBm (= 2.5 nV) is far beyond the reception threshold (0,5uV)
Example Intercept Point and IM Level
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Example Intercept Point and IM Level
Law: aIM3= 2x(IC3 - Lint)
Level Diagram for the above Example:
L
IC3 (30dBm)
0dBm
Lint (-33dBm)
LIM3 (-159dBm)
IC3 - Lint
aIM3= 2x(IC3 - Lint)
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Sensitivity, Noise
PN = k • T • B • F [W]
k.. Boltzmann constantT.. Temperature [K]B.. Bandwidth [Hz or 1/s]F.. Noise factor
kwsxk 231038,1
Rin = 50 Ω
ReceiverF?
Ueff
∆f
Afout (PN)RFin
(BR)
• Cosmic noise• Atmospheric noise• Man made noise• Electric noise (thermal noise)
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Example, Datasheet:
sensitivity 0,22uV @ S/N=10dB, BW=2,4kHzNoise Figure?
1. Step, Signal Power:
3.Step, Noise Figure:
Noise Bandwidth:
in practice this can be considered as the 3dB bandwidth of the receiver, and you get:
BR= 10*log 2400Hz = 33,8dB
Now , the noise adds up to :
-174dBm + 33,8dB + F (RX noise figure) -130dBm
>> F = (-130 – 33,8 + 174) dB = 10,2dB
0
*)(1 dffvpvPo
BR
Sensitivity, Noise
dBmWxxPs 1201068,950
)1022,0( 1626
2.Step, Noise Power:
must be 10dB below Ps (10dB S/N)
-120dBm -10dB = -130dBm
Noise power density:
PRf = k*T [W/Hz], k..Bolzman constant, T.. absolute temp.(oKelvin)
PRf = -174dBm/Hz at a temperature of 25oC
PN = k • T • B • F [W]
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Sensitivity, Noise Figure - Matrix
With: kTo + BR + F PS - S/N , a table can be set up:
BandwidthBW 3,1 kHz 2,4kHz 2,1kHz 500Hz 100HzNoise-BW 34,9dB 33,8dB 33,2dB 27dB 20dBNoise Figure Sensitivity (V@ 10dB S/N)7dB 0,18 0,15 0,14 0,00071 0,000310dB 0,25 0,22 0,2 0,0001 0,000513dB 0,35 0,31 0,29 0,14 0,000620dB 0,78 0,69 0,64 0,31 0,14
note: the first column (noise figure) fully specifies a receiver
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S/N versus (S+N/N)
S/N versus (S+N)/N
Given: Equipment with S/N = 10dBWanted : (S+N)/N for this equipment
S/N = 10dB means 10 log (PS/PN) = 10
log (PS/PN) = 1; (PS/PN) = 101 = 10
(S+N)/N means: (PS+PN)/ PN = (PS/PN) +1 = 10+1=11
10log 11 = 10,41dBThis means : difference between S/N and (S+N)/N
= 0,41dB@10dB SINAD versus (S+N)/N
For small bandwidths:
S/N (S+N)/N
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S/N versus SINAD
(S+N)/N = 40dB
SINAD = D 20dB
Distortion > Noise
(S+N)/N SINAD
0
10
20
30
40
A/dB
f300 1k 2k 3k 3k4
signal
distortion
1kHz rejection filter
noise
10% Distorsion D 20dB
(S+N)/N=10dB
Distortion submerges
(S+N)/N = SINAD
f300 1k 2k 3k 3k4
signal
distortion
1kHz rejection filter
A/dB
0
10
20noise
SINAD ... Signal to Noise and Distortion
(filtered out)
(filtered out)
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RF Power CW and FM , AM
CW, FM :
• no difference between modulated and un- modulated powerflat signal envelope:
AM:
variation of carrier voltage and hence carrier power:
URF
URF + UNF =m = 1URF max = 2xURFPmax = 4xPPav = 1,5xP
RF
AF
UUm
URF
URF
PCW=PFM= Pc
Modulation Factor
m=1 means PRF=PAF , 100% mod.
max. CW/FM Power can be specified as 150% of max. AM Power
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RF Power SSB , PEP
SSBPeak of Envelope
Single Tone-CW Two Tone - PEP
t t
A/dB
0
-6-36
f
A/dB
0
-6-36
fSingle tone - CW Two tone - PEP
• PEP (peak envelope power) appears if modulation with two or more frequencies takes place • if mod frequencies are in phase, they can cause intermodulation distortion
that’s why PEP must be specified togetherwith linearity (IM-products)Example: XK2900 1kW PEP @ IM 36dB belowPEP
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Selectivity
specification in data sheet:M3TR:
• FTZ: occupied bandwidth, 99% of powerwithin 25kHz (Transmitter)• adjacent channel power: -70dBc at fo 25kHz (Receiver)
Typical IF selection (crystal filter, EU230A) Typical IF selection (DSP, EK895)
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VSWR
where: • Vmax = maximum voltage on the standing wave• Vmin = minimum voltage on the standing wave• Vi = incident voltage wave amplitude• Vr = reflected voltage wave amplitude
VrViVrVi
VVVSWR
minmax
Reflection Coefficient:11
VSWRVSWR
EiErturnLoss log10Re
if a load has a Return Loss of 10 dB, then 1/10 of the incident power is reflected.
This is a measure of how much the transmitted power is attenuated due to reflection.
Mismatch Loss = -10 log ( 1 -p )2
The higher the return loss, theless power is actually lost.
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VSWR II
Influence of line attenuationto the measured VSWR.VSWR is reduced by RF cableloss.
VSWR always should be measured at the antenna connector(not at the transceiver output)