rf formulas1

8/3/2019 RF formulas1

1/18

urce free region

th current and

arge densities 0

characteristic imp

These are all peak formulas....rm

formulas will hav 1/2 owing to rcurrent and voltage each

gamma changes only in

ase as we go away frm

ad...remember constSWR circle...


2/18

Note that gamma L might becomplex in itself...but then

again at dist x mag is stillm|

gammaL|

horn dimentions


3/18

Electric Field at

dist R fromantenna

Deciding where far field lies

use to calculate max electric

field at a certein distance

n0=377 ohm

Parabolic antenna: Effective areafor 55% efficiency

HORN gain

This followsfrom BW in

each of the

planes

Parabolic Antenna Gain and

HPBW(expect a fewthousands of magnitude)

Isotropic

radiator: Pt

is powerfed toantenna

(Pdelivered

) via tx lineor w/g

For antenna same as

any other load

Any mention of power reflection and

transmission percentage points to gamma

DIPOLE1.64 is the derived standard gainfor a dipole

Rough

estimate of

3dB

Beamwidthfor High gain

Ant(use K1~70o

)...D isaperture

dimention in

plane in

consideration

Condition for cutoff freq of

antenna and hence BW(11%reflection) Use RL chart


4/18

Step#5Get

Rin from this

Step#4Length of pat

Step#6Matching to 50 ohm linewith Qwave txfrmr(which is againuStrip..so use wheeler for w/h)

keep h same as tht of patch length

of Qwave is offcourse lambdag /4

Illustration 1:

Circular Horn

ircular Horn Design

power density for

nonisot radiator

gain in terms ofeffective aperture

Directivity

Gain is prod of DIRmax and

aperture efficiency, hence amore coplete discription of its

performance

i=indi mag.//phi= feed phase

rogression(0,phi, 2*phi...)

In fig below, theta0 is the p

front(corres to line joining

equiphase pts)...and logicavarying phi, we get diff the

Step#2^^

PATCH ANTENNA DESIGN>>

No gain constraints but matching is priority

Plug in step#5This isnot gain...its

susceptance

Step#1

Step#3The only parameters given e.g. are these

3dB BW With

Halfwavelength

Spacing(good 2 avoidgrating ie sidelobes)

ray factor...2d array has 2

oduct of such summ terms


5/18

___________________________________________________________________________________

Take loss as -ve in dB gain domain

MDS at o/p....at i/p its just kTB in dBm

+3dB

intermodulation freqs at

o/p of a mixer

imp: o/p noise of 1st stage incascade sys this is then I/p to

stage 2

Illustration 2: spuriusfreq,,,

Illustration 3: Power amp


6/18

NOISE

regenerative mixer type freq divider

Microwave Couplers


7/18

Wave leaves radar:

ove is relation betn

erture and gain

#2: pwr

density

neartarget

#3RCS

#5max distance bysubstituting min allowed

pwr

#7: replace Aer with formula

in Gr#8:Si(min) is nothing but M

Pulse radar formulae

#4capture by radar

#6: a combined

version finallywith Gt=Gr=G

Illustration B=BW

of radar

#4 backscatter


8/18


9/18

Chapter6

Numerator is difference betn the carr pwr nd

noise pwr at freq fm near carr...

FM and phase both noises produce noise

sidebands arnd carr

amount of FM(or Phase) noise present is written

wrt. Carr always ie dBc(ie similar 2 calculating

dBm except that one has to norm wrt carr pwrhere by takin 10log)

Illustration 4: To improve the stability, one can use (1) high-Qcircuits to build the oscillators (examples are waveguide

cavities, dielectric resonators,or superconducting

resonators=cavities); (2) temperature compensation circuits;or(3) phase-locked oscillators or frequency

synthesizersFEEDDWD AMP: Used to avoid IM products in

amp: basically produces -ve IM1 and IM2 frm signal itself and

then adds them 2 signal 2 cancel IM1 and IM2


10/18

For a VCO with vtg range in

deno.

Crystal Equivalent ckt formulae

colpitt's crystal osc:a)series b) || resonant config....used

as reference for PLOs


11/18parallelly

R=c*tR/2...tR is shown andfound as= (freq variatn/slope)

ie x=y/m slope is

2*deltaF*fm.....hence tR isfR/slope

fR is middle of (average) two fb s we get

while doppler shift is found like this

find velocity

from fd...notethat this is

cosine of

actual velocity


12/18

An error signal will be generated if the antenna beam is

not exactly on the target. This error signal will be used to control a servomotor to align the antenna to

the target. There are three methods for generating the errorsignal for tracking:

1. Sequential lobing

2. Conical scan3. Monopulse

Sequential lobing....whichever voltage is greater move antt towards tht

side


13/18

beam rotated at Wm....if its not aligned, return s/g is AM

power divided betn 2 or 4 antenna....alignment results only if

all antt recieve same vtg...2 antt give only 1D tracking 4 anttgive 2D tracking


14/18


15/18

Illustration 5: Friss for Link Budget..Lsys

includes antenna feed mismatch, pointingerror, atmospheric loss, and polarization loss

it can be seen that the range is doubled if the output power is

increased four times. In the radar system, it would require the output power be

increased by 16 times to double the operating distance

Also it can be seen that the receiver output SNR ratio can be

increased if the transmission distance is reduced. The increase in transmitting power

or antenna gain will also enhance the output SNR ratio as expected

Steps to Friis

deriving spaceloss(atmospheric loss is diff

from space loss)


16/18

Hence it can be said that BER performance of any system is probability that noise will take value sohigh as to make RV N+Si go into region of other symbol Sj

BPSK constellation

Deriving BPSK BER


17/18

We plot Pe vs Eb/No...Eb/No is one valued description of channel and conditions in generalHigh Eb/No ie S/g energy results in better performance and vice versa...thats why graph is decreasing

for all modula schemes

Pe will depend on Euclidean Distance between symbol points in constellation

Modulation and more

Illustration 9: BPSK

Illustration 8: BFSK

Illustration 7: ASK


18/18

tration 6: if n is no of symbols and M is

ber of bits, then M is B/W efficiency(M note confu with privious use of M)

tical purposes due to BER performance^^

why we dont go for infinite -aryulation

So, knowing capacity and bandwidth, one can find wat maximum M-ary system can be used...as weknow, as M increases constellation becomes crowded and probability of error increases

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