Should you match at the antenna feedpoint?

In almost any phased array, the impedance at the antenna feedpoint is going to be reactive, and almost never exactly 50 or 75 ohms. As a result, there's some mismatch to be accomodated by some sort of network. The question comes up whether you should put a tuning network at the element, so that only active (useful) power is flowing in the transmission line. The alternative is to tune out the reactance at the central phasing point, and just accept the fact that there will be reactive current circulating, contributing to some losses.

In one of my ideas, the radiators are physically small, and hence would present a substantial reactive component, no matter what the phasing is, so you'd need a fairly large lumped component to tune out the reactance. In this situation, the untuned VSWR is going to be huge, with the reactive power being perhaps 10 or 100 times the active power. For instance, there was an example in one of the ARRL antenna compendiums of a 80m (160m?) four square using elevated vertical dipoles that had a reactive component of some 1000 ohms (on top of a radiation resistance of 3 or 4 ohms).

However, if the driving point impedance isn't all that weird, the losses aren't going to be that huge. Consider the case where the reactance is roughly the same as the resistive component (something like a 50+j50). This is only a 2.67:1 VSWR, and even with 100 ft of RG-8X kinds of coax, the line loss is only 1.17 dB, a bump of .325 dB, compared to the perfectly matched 0.84dB. A 50+j100 (VSWR 6:1) gives you 1.235 additional loss. For 9913 the matched line loss is 0.3 dB, and the reactive power bumps that to 0.851

 

Let's consider a simple case, two quarter wave monopoles, a quarter wavelength apart, fed so the currents are equal magnitude, 90 degrees out of phase.

The excitation voltage for feedpoint #1 is 44.57+j19.01 V, so the driving point impedance is 44.57+j19.01 ohms

The excitation voltage for feedpoint #2 is 19.23+j20.37 V, (but the current is 0+j1 amps), so the driving point impedance here is 20.37 -j19.23 ohms.

Active VAR
44.57 19.01
20.37 19.23

Let's plug these into XLZIZL, and further, we'll assume we're in the 40 meter band, at 7.15 MHz. We're going to have at least 50 feet of coax.

34.32+j8.65 (loss 0.1722 dB)
Matching network 287 pF, .314 uH (0.012 dB loss) (total loss .185 dB)
35.10-j41.73 (loss 0.2499 dB)
290 pF, 1.438 uH (0.049 dB) (0.299 dB total)

But, if we match at the feedpoint: Matching network, using a Low pass L, and assuming Q of C is 1000 and Q of L is 200

44.57+j19.01 -> .0 (0 ohms) series -> shunt C 170 pF (-130)
loss 0.021 dB (0.5%) (.166 dB w/line loss)

Line loss 0.163 dB

20.37-j19.23 -> 0.9749uH (5.337 ohms) -> 536.93 pF (-41.45 ohms)
loss 0.059 dB (1.3%)

 

We can look at this in terms of reactive power flow, too.

In the match at the feed point sense, the reactive power (some 19 VAR in both cases) is supplied by the matching network, so the only loss is due to the active power flowing through the transmission line.

In the match at the end of the transmission line, you have the reactive power flowing down the wire as well. For element #1, you'll have about 18% more loss from the reactive power. For element #2, it's about 89% more. To put some real numbers to this, if you're using a reasonably low loss coax (9913) the 50 feet will have 0.163 dB of loss in 50 ft (3.7%). (0.38 dB (8.4%) for 9258/RG-8X).

Let's say we're pushing 100 watts total to the two antennas (the actual power division is about 68/32). We'll lose about 5 watts in the coax (2.9 Watts heading to element 1, 2.27 heading to element 2 (which actually radiates less than half the power of element 1)) (for RG-8X, 11.9 W total)

To compare to the reactive power at the feedpoint: 9913 2.5/1.18/3.68 RG-8x, 5.69/2.68, 8.38

radio/antenna/phased/tlineloss.htm - 24 Feb 2005 - Jim Lux