Transmission line measurements
My last column appeared in MRT in May of 2002. Since that time there have been some changes in MRT and in my life. Last August, I retired from public safety communications after nearly 31 years of service. Not long after retiring, I entered into contract with Noble Publishing Corporation for my third book on radio. The manuscript for the book is now safely in the hands of the publisher and the book should be in print by late summer or early fall of this year. The title of the book is The Radioman’s Manual of RF Devices, Principals and Practices.
While working on the book, I was asked to return to MRT. I didn’t feel that I could do justice to a column and the book at the same time. So, after finishing the book I contacted Bill McCarthy to see if the offer was still open. Thankfully, Bill said “Yes” and here I am-ready to resume the column where I left off last year. As many of you know, my columns have always been about basic technology that covers a broad cross section of the land mobile radio industry. With Bill’s permission, I am proceeding in the same general direction with the continuation of this column. Thanks for “staying tuned.”
The RF transmission line is a fundamental part of the radio communication system infrastructure. It is the job of the transmission line to deliver the transmitter signal to the antenna and the received signal from the antenna to the receiver. A properly matched and terminated transmission line is a boring piece of wire. However, when the line is terminated into a mismatched load or a short or open (partial or complete) occurs on the line things get quite interesting. The result is anything but boring!
Frequency domain testing
Figure 1 shows a test setup using a tracking generator/spectrum analyzer. The same tests can be performed using a RF sweep generator and oscilloscope but the techniques are less cumbersome with the spectrum analyzer/tracking generator.
In Figure 1 a length of coaxial transmission line is connected to the tracking generator/spectrum analyzer (hereafter referred to as the TG-SA) through a tee connector.
The center frequency and span width of the spectrum analyzer are adjusted to produce several cycles of ripple on the CRT. Figure 2 shows the display when the cable is shorted at the far end. Figure 3 shows the display when the cable is terminated in its characteristic impedance of 50 ohms. Notice the absence of ripple.
Figure 4 shows the display when the cable is open at the far end. Compare the displays in Figures 4 and 2 for the open and shorted cables, respectively. You will note that the display for the open cable in Figure 4 is shifted in frequency from the display for the shorted cable in Figure 2. That is, in Figure 2 where the marker is placed in the center of the crest of the ripple the marker is at the null of the ripple in Figure 4.
The distance to the fault can be calculated by measuring the frequency difference (ΔF in MHz) of one cycle of the ripple and substituting the result into the following formula.
Where D is the distance to fault, V is velocity factor of cable and ΔF is frequency difference of one ripple cycle. Measuring ΔF is accomplished most easily by using the frequency marker to determine the frequency of adjacent null points on the display. In Figure 4 the marker is placed at the null point near the center of the display. The frequency marker reads 29.58MHz. Next, the frequency marker is placed at the next higher null point. This is shown in Figure 5 where the marker frequency is indicated as 41.51MHz. The difference (ΔF) is 41.51MHz minus 29.58MHz or 11.93MHz. Substituting this into the formula, we get:
Figure 6 shows the display when a quarter-wave antenna is connected to the TG-SA as shown in Figure 1. The center frequency and span width of the TG-SA are adjusted to find the point of minimum ripple on the display. Notice in Figure 6 that the point of minimum ripple occurs at a frequency of approximately 140MHz as shown by the frequency marker. This is the resonant frequency of the antenna.
In Figure 7, the display has been accented by increasing the amplitude sensitivity of the spectrum analyzer to 2dB/division and changing the center frequency and span width. Again, the frequency marker is placed at the point of minimum ripple or approximately 140MHz.
In Figure 8, the center frequency is moved away from the resonant frequency of the antenna and the span width adjusted to produce a display such that one cycle of ripple occupies most of the horizontal width of the display. This improves the accuracy of the ΔF of the ripple. In Figure 8, the frequency marker is placed over the null point near the left side of the display. The marker frequency is indicated as 267.15MHz. In Figure 9, the frequency marker is placed on the null point to the right of the display. It indicates 292.23MHz. Therefore, ΔF is 292.23MHz minus 267.15MHz or 25.08MHz. The velocity factor of the cable is 0.66. Plugging these figures into the formula yields the distance to the antenna as shown in the following formula:
The printouts for most of the figures shown here were taken from the display of a Hewlett-Packard model HP8920B RF Communications Test Set. Next month we will take a look at transmission line tests and measurements in the time domain. Until next time-stay tuned!
