MATCHING WITH A BALUN OR TRANSFORMER

After cancelling Xs or Xp you could next add an impedance- changing device to bring the impedance to 50 ohms, or whatever is desired.

MATCHING WITH AN ARBITRARY LINE

A little understood fact is that a length of 50 ohm transmission line can transform virtually any Rs into 50 ohms by selecting the proper length of line. For example, Rs might be 200 ohms or 15 ohms at your antenna or at the “shack” end of your transmission line. By selecting a proper length of line to add on, you can achieve Rs= 50 ohms, with some Xs which can be cancelled as shown in Fig. 9. The result is a 1:1 SWR at the point this is done. The added feedline need not be longer than 1/2 wave, and in fact there are two lengths in this range which yield 50 ohms, but their Xs have opposite signs.

We don’t want to keep cutting and adding feedline, but the VA1 can tell us the result if we did. It turns out that Rs ant with a particular F-i /4 tells how much line to subtract to produce that Rs. But everything is symmetrical about 1/2 wave, so the length of added line can be calculated also. The procedure is:

Then the length of feedline to subtract is:

For the example & Vt = .66, length =246 x .66/5.3 =30.6 ft.

If we subtract this length, then add a series C to cancel Xs, SWR drops from about 15:1 all the way down to 1:1. Equivalently, we can add a length:

For the example: 492 x .66 / 10.1 - 30.6 = 1.55 ft.

Try an added line a little longer than this, and cut it until the desired Rs =50 ohms is achieved. Then measure Xs and cancel it as in Fig. 9.

Sometimes a 50 ohm line is not aiwaysthe best , even though we want 50 ohms at the end. You could also see what happens to Rs ant with other impedance lines. For example, a full-wave loop, which has a resonant Rs of about 100 ohms is often matched with a 75 ohm line whose F-i/4 is the same as the operating frequency. To use 75 ohm line and Function 4, you have to change line impedance to 75 ohms (See page 2.)

Line loss causes the actual value to be slightly different than Rs ant, so some final fine adjustment of line length may be needed. The bandwidth of matching may be estimated by observing Rs ant and Xs ant once F-i/4 is found. Also, loss in the transmission line can be high if the line is long and lossy. Even though a 1:1 SWR occurs at the matching point the line could still have a high SWR.

OTHER MATCHING METHODS

A very popular matching method is the L network, which has only a single L and C, yet can match almost anything with low loss. Again, the TLA program which comes with the ARRL Antenna book, allows you to input Rs and Xs and it gives you L and C network values. Other popular methods such as stubs, gamma match, traps, and the list goes on, can be adjusted easily with the VA1. There are many more uses for the VA1 than we have room for without writing an Antenna Handbook.

ACCURACY

The computer compensates for known systematic errors such as diode drops, phase detector nonlinearity, and stray capacitance. Note that because the VA1 knows the sign of X it can compensate for strays, which can give very large errors at high frequencies, especially with an inductive load. The VA1 measures Z and phase, and derives all other results, including SWR, from these. (See equations in the Appendix.)

In the range 20-200 ohms, Z accuracy is typically about 3-4% and and phase accuracy (rms) is 2 to 4 degrees to 16 MHz and increases to 8 degrees at 30 MHz due to phase detector limits and strays. Most measurements are within the rms limit. but some will statistically be larger. Error also increases at very high and very low Z.

Because of tolerances on phase, most error is to be expected on the smaller of Rs or Xs. For example, if Xs is very large, as it may be on a short antenna, the value of a small Rs can’t be determined accurately without cancelling Xs. (See Fig. 9.) Coil o measurement is also “iffy” even if Xs is cancelled, since harmonic distortion in the VAI sine wave will appear to lower the 0. For example, measurement of coil 0 of 100 using Rs would require oscillator distortion much greater than 40 dB down, and few RE oscillators are that pure.

Trying for an SWR of exactly 1.00 is meaningless. Anything less than 1.1 (or even 1.4) is virtually the same. The 0.01 SWR readout can help to find the exact minimum, however.

Purists can use 1% resistors to calibrate out small errors. For example, if your VA1 reads Rs= 51 ohms and Xs = 2 on a 1 % resistor with short leads at a certain frequency, you could subtract 1 ohm from R and 2 ohms from X for values near 50 ohms to increase accuracy.

When measuring Rs ant and Xs ant, remember these are derived from Rs and Xs. If Rs and Xs are in a region of lower accuracy, such as very small or large Z, then Rs ant and Xs ant will be less accurate..

PROCEDURE

operating frequency (Fo)

Rs ant. Should be same since

this is 1/2 wave line.

Rs crosses 50 ohms.

EXAMPLE

Rs=22 Xs=113 (Fund)

Frequency= Fo = 10.1 MHz

F-1/4 set to 5.05 (Func 4)

Rs ant =22 at 10.1

Set F-1/4 = 5.5

Rsant= 121 atFo= 10.1

Rs ant already> 50 ohms

When F-1/4 = 5.3 Mhz Rsant=50 Xsant=175

VA1 Page 10