PREFACE--
ECE 341 Lab 2 SPRING 2010 – DOUBLE-STUB MATCHING
This lab is to effect an impedance match between a load (that is not 50 ohms) and a 50 ohm cable. We want to put the load on one end of the cable, and have the input impedance at the other (source) end be 50 ohms; this implies no reflections back to the source end, or all power put in one end of the cable goes to the load at the other end.
The method is the double stub matching we studied. However it is simpler in lab because you mostly reach a design by manipulating stub lengths manually and watching the effects on the network analyzer screen, instead of calculating on a Smith chart. (For example, on the Smith chart we needed a “predictive circle” that predicts we will hit the actual unit circle when we rotate on the chart to the second stub’s position. In lab we just connect the instrument at the second stub’s position and view what happens there.)
The load is a nominal 75 ohm terminator (your TA can help locate it). However, at our higher frequencies it is not 75 ohms, but approximately 74-jX ohms because of stray capacitance at its terminals. Lesson: devices don’t behave the same at higher frequency. However, we just need any load to match to 50 ohms.
If we just put the load of about 74-jX at the cable’s load end, at the source end it would not even be that, though we want it to be 50 ohms at the source end. To change an impedance of two numbers (real and imaginary) requires two adjustments, and here those are the lengths of two matching stubs.
Each of the two matching stubs has connectors at one end and a short circuit that will slide along the stub. If we slide the short to some position (and rotate its collar to lock it in place), we have a stub with length being the distance from the connectors to the short. The stubs in lab are made for 0.2 GHz to 1 GHz. Connecting a line into one stub connector and out the other puts the stub in parallel with the line at the connection. Recall a shorted stub can have impedance of the form jX at its input, determined by its length (and frequency); then the admittance is thus of the form jY, with no real part.
Three figures in the lab instruction sheets show the steps. Fig. 1 shows the finished system. Fig. 3 shows the first step, adjusting stub 1 so that the admittance, seen at the NA where stub 2 will later go, is (1/50)jY. Then we replace the adapter in Fig. 3 with stub 2 as in Fig. 1, and adjust stub 2 to have an admittance of jY with the opposite sign of the jY in the (1/50)jY above. Since these last two admittances are in parallel and add, the net admittance seen at the input is just 1/50, and the impedance is 50, as desired!
The measurements are made with a quality network analyzer (NA), a major tool for testing high frequency transmission lines. It can display measurements on a Smith chart if desired. The figure on the next page shows its fundamental parts.
The source is set to one frequency, or to sweep between start and stop frequencies. A, B, and R (reference) are receivers; DUT is device under test. In this figure we can test how a signal travels through the DUT. The test signal comes out of the NA at the Reflection Port (port 1) and into the NA at the Transmission Port (port 2). However, if any part of the signal reflects from the DUT back into the Reflection Port, a directional coupler diverts it into A to let us measure the reflection. I.e., the directional coupler just passes along waves traveling out of the port, but it diverts waves traveling into the port.
In this lab we only use the Reflection Port and connect it to the line (the 2-foot, 50 ohm cable) where the “NA” (network analyzer) is on Figs. 1-3. We will use the NA to measure impedances, some displayed on a Smith chart and one as a function of frequency. With the Smith chart we’ll use sweeping frequency and use a marker to locate the frequency where the match should occur; we’ll see the impedance sweeping over the Smith chart as it changes with f. The final goal, to get 50 ohms at the input with a load not 50 ohms, is achieved when the marker for your frequency is very near 50+j0 on the Smith chart.
Notice a tricky point; we are reasoning with admittances because in parallel they add, but the NA only deals with impedances. Each NA screen in lab has a transparency showing a unit circle rotated 180 in the Smith chart. If we place the impedance on that rotated unit circle, the admittance will be somewhere on the actual unit circle as desired (because numbers on the transparency circle are reciprocals of numbers on the actual unit circle). That is used later in the section, “II. CHOOSE LENGTH OF STUB 1”.
The network analyzer’s controls are operated much like those on the spectrum analyzer, and likewise the network analyzer has many bells and whistles. (Averaging many readings produces a more stable result whenever a number or curve is “jumpy”.)
The following are some useful controls:
BEGIN (does the following automatically: presets, sweeps, autoscales, places a marker)
FREQ (start/stop frequencies, or center/span frequencies)
POWER (usually not of concern)
SWEEP (AUTO is usually fine)
MENU (usually not needed)
SCALE (scale/div, reference level)
MARKER ( 8 markers with usual functions)
DISPLAY (more display>split display)
FORMAT (Log mag, lin mag, delay, phase, Smith chart, SWR, more format)
CAL (impedance magnitude, enhanced response)
AVG system bandwidth, average on/off)
SAVE, RECALL, HARD COPY SYSTEMOPTIONS (usually not needed)
End preface.