Finding Resonances: The J-Pole and CFA
After last month’s article I received some comments on my brief reference to the J-pole antenna. Old George (KC5MU) commented at length and noted that a J-pole as I had described gave a signal report of “3dB” while a J-pole made with a quarter wave long matching section and a half wave long radiator gave a report of “30dB over s9”. Anselmo (IZ3BGI) wrote that he got the J-pole to work at the proper sizes after he used a balun in the feed cable to make a balanced feed at the connection point. So I decided to revisit the J-pole antenna and look more deeply into the matching section. This exercise highlighted an important point about antennas: that matching is only half the story!
To make a good antenna, it must be matched, but it also must radiate well. One does not necessarily follow from the other. If a simple antenna like the J-pole can have matched variants with differing radiation properties, how much more variable will something as strange and sensitive as a CFA be? Then I revisited my high capacitance D plate to find where the inductance that made it into a series tuned circuit came from. (see my February antenneX article, Unplanned Resonance in CFA Tests, now in Archive III).
J-Pole Revisited
The matching section of a J-pole has two parts, connected in parallel across the 50-ohm drive cable. Both parts are made of a high impedance parallel pipe transmission line. My J-pole is made of 1/2-inch copper pipe and the spacing for the matching section is set by the size of a “tee” and an “elbow”. The “tee” is in the side that is the first part of the matching section and becomes the radiator. The up and down part (vertical) of the “tee” is joined with a tiny bit of pipe to the “elbow” to form the shorted part of the matching section. The characteristic impedance of this section is set by the pipe diameter and spacing. The formula for this impedance is:
Z = 276 log (2*s/d)
where:
s = center to center spacing of the pipes
d = diameter of the pipe
log = log to the base 10
For my J pole the Z is 143 ohms
The two parts of the matching section are: a short circuit transformed by the length of pipe transmission line from the short to the connection point, and an open circuit (actually what the end effects at the far end of the radiator become after being transformed by the radiator length and further transformed by the distance in the pipe transmission line from the radiator to the cable connection point. The two parts are connected in parallel at the feed point.
The two impedances are, in general, complex numbers containing a real, or pure resistance, part R, plus an “imaginary”, or reactance (inductive or capacitive ) part jX. Two resistors, A and B, in parallel combine to form a new resistance by the equation, A*B/(A+B), the product over the sum. What physically happens is a voltage at the cable end causes some current in each resistor; the net resistance is the voltage/(the sum of the currents). This is more complicated than it needs to be. Instead of working with impedance (volts/current) let’s work with something called admittance (current/voltage). Then, the admittance of the parallel connection of two admittances, W and Y, is just the sum of those admittances (W+Y). The real part of the admittances add, and if the reactive parts are of opposite sign, they cancel to form a pure real admittance.
(Y1 +jY2) + (W1 -jW2) = Y1+W1 + Y2-W2
Speaking for a moment about resistors again, I can make 50 ohms by paralleling two 100-ohm resistors, or by connecting two unequal resistors in parallel, such as 80 ohms and 135 ohms, etc. Thus, a given net can be made many ways. This is what can happen with the J-pole.
In the J-pole, we are using a transmission line with an odd Z value, 143 ohms, to make a 50-ohm connection. The procedure is the same, whether the odd Z is 143 ohms, or 572 ohms, or any number for that matter. The procedure is very easily done graphically with a device called a Smith Chart, named after its inventor in 1938. The Smith Chart handles all values of line Z with the same piece of graph paper by a process called normalization. This means that all calculated values of the complex Z or Y are divided by the physical value 143 or 50 or 572. On the chart, the transmission line characteristic impedance or admittance, Z or Y, is always 1. An impedance of half the line Z normalizes to z = .5 or y = 2. Likewise, an impedance four times the line Z is normalized to z = 4 or y = .25. In our case, with a 143 ohm line, 50 ohms normalizes to z = .349 or y = 2.86. All calculations about transforming the short (Z=0 or Y= infinity) and open circuit (Z = infinity or Y = 0) are done in normalized form on the graph paper.
Transformation is done by moving along a transmission line. Suppose one moves along a line in a direction away from the signal source toward a partially reflecting or mismatched load (the short or open is the extreme case of a mismatched load). At any spot, the voltage is the sum of the E field moving under your feet toward the load and the E field reflected by the mismatch and returning past your feet toward the source. It took some time for a signal to go from your position to the load and back; during that time the RF sine wave has rotated through some part of a cycle. The result is standing wave: when the travel time is exactly n cycles, the distance to the load from your position is n/2 wavelengths. At a voltage maximum, the current is a minimum and the impedance (voltage/current) is high. Likewise, at voltage minimums, the impedance is low. In the extreme, one can start from an open or short, and within one wavelength of travel distance make any other impedance that may be desired.
I do not intend to make this a treatise on the Smith Chart—that alone is worth a chapter in a book. Suffice it to say that I used the Smith Chart to do the following things: for several combinations of the two parts chosen so that the real parts combine to the normalized value that is 50 ohms—
- Move from the short to a place on the chart where the admittance is approximately half that corresponding to 50 ohms. (remember, I am paralleling two admittances)
- Move from the open to the place on the chart where whatever admittance is achieved to combine with 1
- To correspond to 50 ohms real component
- Record the distances moved in wavelengths
- Record the reactive components and net reactance
Table 1a and Table 1b show the results. The first section shows the combination of the two admittances in the 143-ohm line for several cases. First one, then the other is larger, centered around the case where the two admittances are equal. The sum of the two transformation lengths is shown for each case. The important message is that the equal size case leads to a quarter wave section, and all unequal cases differ from a quarter wave total length while showing that there is a net reactance at the cable connection point. This reactance must be cancelled at the end of the section by lengthening or shortening the radiator in order to achieve a low SWR in the drive cable. The second section shows the translation from a normalized 143-ohm line to a normalized 50-ohm line. The color coding of the columns show the connection to the first part of the table.
The missing part of this story is given by the comments of George and Anselmo. To fully design the J-pole antenna, a table of field strengths would be needed to correspond to Tables 1a & 1b.. Since I don’t have that instrumentation, I must depend on their comments mentioned above. The message here is that to design CFAs, this missing part is needed in spades! I am now looking at ways to solve the field strength measurement problem.
The Resonant D Plate
In a previous article, I mentioned I had found a strong series resonance in the D plate. It was time to take another look at this phenomenon and find out what is happening. The first hypothesis was of circulating currents in the plate, so I cut a racial slit in the D plate (making it a “C” plate?), then reassembled the antenna – NO CHANGE!! I changed the length of the cable to the signal generator—still no change in the resonance. Finally, I added a couple of feet to the flying lead to the D plate –BIG CHANGE in the resonant frequency. So the foot or so of wire going from the center of the D plate to the bench out from under the antenna is the culprit! So much for “Oh, this is 40 or 80 meters as the little wire is an insignificant part of a wavelength”. Maybe this is why one of the Egyptian CFA’s D plate is fed from the outside edge!
The short wire behaves more like a magnetic loop when the D plate capacitance is large. To check this relationship, I went to the Loop Book (sold by antenneX in the Shopping Shack). The equation for the inductance of a small magnetic loop (a “C” of pipe with a tuning capacitor across the open part of the “C”) is given as:
L = 1.9*10^-8 * S*(1.2*e^-.1365+.81) * (7.353*log(96*S/pi*D) – 6.386)
where
S = length of conductor in feet
D = diameter of conductor in inches
Table 2 shows the resonant frequency of my D plate for several lead lengths. The Loop Book inductance for those lead lengths is shown in column 4. This is the inductance if the wire is formed into a “C” enclosing a large area. As used in my CFA experiments, the wire is not formed to cover a large enclosed area; my D plate is about 550 pF instead of the lower values computed in Table 2. The message here is that even a foot and a half of lead can add unexpected reactance and an accompanying phase shift to the tuner—there is no longer an excuse for not crawling under the CFA and using short leads!! Again, this message applies especially to the very tricky CFA!
So I guess my next month of May 2000 will be filled with working up a field strength measurement ability and soldering short leads! I hope to use a CFA for field day this year, and am encouraged by the success of the 160-meter CFA described in this month’s issue, 160-Meter CFA – Part II by Gary Nixon and Jay Lemmons! Until next month.
Originally posted on the AntennaX Online Magazine by Joel C. Hungerford, KB1EGI
Last Updated : 23rd May 2024
Last Updated : 23rd May 2024