Hi Cecil,

I find another formula in Balnais book (section 4.3, 1982 edition)
for Rr:

Rr = 20 * (pi)^2 * ( l / lamda)^2 (4-37)

If l = lamda/2, then this formula gives Rr .=. 50 Ohms.

(4-93) the one you quoted is

Rr = (120*pi) / (4*pi) * Cin( 2*pi ) = 73 Ohms, (for l = lamda/2)

where 120*pi is the intrinsic impedance for a free-space medium.

Would you please explain the difference between these
two formulas (4-37 and 4-93)?


Thanks!

-- Harry

Harry wrote:

Hi Cecil,

I find another formula in Balnais book (section 4.3, 1982 edition)
for Rr:

Rr = 20 * (pi)^2 * ( l / lamda)^2 (4-37)

If l = lamda/2, then this formula gives Rr .=. 50 Ohms.

(4-93) the one you quoted is

Rr = (120*pi) / (4*pi) * Cin( 2*pi ) = 73 Ohms, (for l = lamda/2)

where 120*pi is the intrinsic impedance for a free-space medium.

Would you please explain the difference between these
two formulas (4-37 and 4-93)?


Thanks!

-- Harry

4-37 should apparently read:

Rr = 30 * (pi)^2 * (1 / lambda)^2.

ac6xg

Harry wrote:
Would you please explain the difference between these
two formulas (4-37 and 4-93)?

Equation 4-37 is from section "4.3 SMALL DIPOLE", i.e. shorter
than 1/2WL. The dipole is so short that its current distribution
is triangular, not sinusoidal. Quoting section 4.3: "The radiation
resistance of the antenna is strongly dependent upon the current
distribution." The "1/2" on the diagram does NOT mean 1/2WL.

Equation 4-93 is from section "4.6 HALF-WAVELENGTH DIPOLE". The
current distribution on the thin-wire 1/2WL dipole is considered
to be sinusoidal.

See Figure 4.8. Note the triangular current distribution for
L = 1/4WL and the sinusoidal current distribution for L = 1/2WL.
--
73, Cecil http://www.qsl.net/w5dxp

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See Figure 4.8. Note the triangular current distribution for
L = 1/4WL and the sinusoidal current distribution for L = 1/2WL.

Very good,..... thanks a lot!
Your figure 4.8 (second edition) is figure 4.7 in the first edition.
These current distribution curves (1/4, 1/2, 1, 3/2, and 2 Lamda
length)
are interesting to study.

-- Harry