My friend Hall operates mostly near 3920, 7135 and 7272 kHz. He asked me to come up with a coil-loaded dipole, center-fed using RG8X, that can be deployed horizontally at 35ft agl, and will work well without a tuner. Using AutoEz, EzNec, and the Hamwaves coil calculator, here is my design: The antenna is described by three parameters: L is the length of the wire in feet, P is the percent of L between the wire ends and the center of each coil, and XL is the nominal inductance of the coils in uH. For modeling accuracy, the horizontal dipole wire of length L is broken into five co-linear sub-wires 1-5. The coils are placed in the center of short wires 2 and 4. The coil position can be moved with high resolution using the parameter P, which simultaneously moves all wire ends except the two outside ones, which are set at -L/2 and L/2, respectively. The source is at the center of wire 3. The goal for optimization is to find L, P, and XL which simultaneously makes the lowest feedpoint Swr50 at 3.920, 7.135 and 7.272MHz. A first try converged on L=91.25ft, P=8%, and XL=76.6uH. To make a suitable coil, I have some thin-wall white PVC tube to use as a form. It has an OD of 2.48" (63mm) with a wall thickness of 0.09". I have some #16awg silver-plated wire with PTFE insulation. The wire OD is 0.050" (1.27mm) and the insulation OD is 0.072" (1.83mm), making a coil with mean diameter of 64.8mm, with a tight pitch of ~1.9mm. Using the Hamwaves Coil Calculator, at 3.92MHz, it takes 48 closely spaced turns to make a coil with an effective Inductance L_eff = 78.8uH, which has a Reactance Xeff = 1940 Ohms and has an effective series resistance R_s = 2.7 Ohms. Here are the results: Notice that the self resonant frequency of the coil is 11.4MHz, well above the 40m frequency. If we keep all the physical dimensions the same, we can use the calculator to see how L_eff, X_eff, and R_eff change at 7.2MHz: I modified the AutoEz model to automatically switch between X_eff/R_eff at the two frequencies of interest, i.e. 3.92 and 7.2MHz, and then re-optimized for L and P. The final values are L= 86.9ft and P=7.9% (6.85 ft in from the ends). Here are the plots of Swr50 across the upper part of 80m and 40m: This design takes into consideration the coil's variation in L_eff and R_eff at the two design frequencies.