We can use a shortened antenna wherever we do not have enough space for a full-sized one. I found a relatively simple calculation for such a wire antenna in the Russian Radio 5/1999. The original article was published in: Funkamateur, 11/1997. It is an antenna with an electrical length of ?/4. It will probably be most commonly used for the 160 m band, for which an example calculation will also be provided. The layout solution with the designation of individual dimensions is in the picture.
Principle and dimensions for the shortened antenna
Anténny vodič s dĺžkou kratšou ako ?/4 je označený písmenom A. Predlžovacia a zároveň transformačná cievka je L1. Ako druhý pól antény je použitá elektricky predĺžená Protiváha, ktorá zvyšuje účinnosť vyžiarenia výkonu aj v prípade, že stožiar B je uzemnený. Teraz k vlastnému výpočtu: Určíme si dĺžku vodiča A (m), priemer tohto vodiča d (m), pracovnú frekvenciu antény f (MHz).
First, we calculate the wavelength of the operating frequency ? = 300/?, auxiliary parameter S = A/d and the working angle ? = A . 360/ ?. Next, we calculate the characteristic impedance Z = 60. ln(1.15.S) and the reactive component of impedance XC=Z/tan? (pF). The reactive component XC must be compensated by inductance L1 according to the relationship L=XL/2?f (µH), where XC = XL. We determine the branch for connecting the coaxial cable from the relationship n1=n?(R/ XL), where R = impedance of the coaxial cable in ?. For the calculation of coil L2, the same relationships apply, but we substitute D for A and L2 for L1.The diameter of the wires should not be less than 1 mm.
Example
A= 29 m, d = 0.0015 m (1.5 mm) and f = 1.86 MHz.
From these data we get: ? = 161.3 m, ? = 64.7O and S = 19333, Z = 600.6 ? and XC = 283.8 ?. Then L = 24.3 µH. The number of turns depends on the construction and possible use of the core. We will consider a coil with 28 turns and a coaxial cable of 50 ?. Then the tap will be at the 12th turn from the grounded end.
VY 73 Miro OM3CKU