You are not logged in.
After following the lecture about horn-antennas,
I was was stuck with the equation system,
so I could not do the example of the lecturer.
It could well come down to forgotten solving techniques
and I would be happy if someone could fix me ;-)
Since I'm not used to latex, I redefine as follows:
Knowns:
c=a=0.02286m // (horizontal) waveguide aperture in H-field-direction
d=b=0.01016m // (vertical) waveguide aperture in E-field-direction
l=lambda=0.03m // wavelength
f=D=20db=100dimensionless // directivity
n=51%=0.51 // aperture efficiency
Unknowns:
a=A // (horizontal) aperture in H-field-direction
b=B // (vertical) aperture in E-field direction
g=R1 // r min in the H-plane
h=R2 // r min in the E-plane
j=RH // flare-height in H-field-direction
k=RE // flare-height in E-field direction
s=lH // slant-height in H-field-direction
t=lE // slant-height in E-field direction
Set of equations:
f=4*pi/l^2*n*A // out of antenna theory
A=a*b // A=aperture area
s^2=g^2+(a/2)^2 // Pythagoras geometry
t^2=h^2+(b/2)^2 // Pythagoras geometry
j/g=(a-c)/a // triangle parallel cut
k/h=(b-d)/b // triangle parallel cut
j=k // horn has a flat front edge
s-g=.375*l // flare angle in H-direction
t-h=.25*l // flare angle in E-direction
I rearranged the equations a little
and did basic stuff:
f=4*pi/l^2*n*a*b // 1, A->a*b since A=a*b
<=> a*b=f/(4*pi/l^2*n)
<=> a*b=f*l^2/(4*pi*n)
<=> b=f*l^2/(4*pi*n*a)
s^2=g^2+(a/2)^2 // 2
<=> a=2*sqrt(s^2-g^2)
t^2=h^2+(b/2)^2 // 3
<=> b=2*sqrt(t^2-h^2)
<=> h=sqrt(4*t^2-b^2)/2
k/g=(a-c)/a // 4, j->k since j=k
<=> k=g-(c*g)/a
k/h=(b-d)/b // 5
<=> h=(b*k)/(b-d)
s-g=.375*l <=> s=.375*l+g // 6
t-h=.25*l <=> t=.25*l+h // 7
Then I tried to solve for b, first:
h=(b*(g-(c*g)/a))/(b-d) // 4 in 5, eliminating k
<=> (b*g*(a-c))/(a*(b-d))
Now there are many variables, shared by many equations.
Therefore I had trouble using the eliminating approach.
How could I proceed ?
Offline
The lecturer referenced a book from which I may get solutions,
but not the detailed steps originating from the equations above.
It seems to be hard to get there, so I'll first with that for now.
Offline