Mick and Smithy Talk Antennas
Chapter 7
By a club member who (currently) wishes to remain anonymous
If you are new to our saga, click here to start at episode 1
Smithy is confused. Just when he had finally accepted that Maradona and Madonna really were different people, came the news that Maradona had been bitten whilst trying to kiss his pet dog. Surely this couldn’t be so?
Anyway, Mick and Smithy meet up again at their local club. Mick is relieved to find that Smithy apparently bears him no ill will after his faux pas about Smithy’s clothing. Not that Smithy hadn’t noticed, but Smithy stuck firmly to his own ideas and didn’t regard the new national dress code of tee shirt, baggy shorts and baseball cap as worthy of adoption, especially since he had a wardrobe full of sports coats and flannel trousers. Also he remembered an incident at the club’s recent DF hunt where Mick, in shirt, shorts and sandals had fallen back into a clump of nettles! But there was going to be a price to pay for Mick’s indiscretion, Smithy was going to make him use a Smith Chart. He knew that one look at a Smith chart would frighten Mick no end and so he would savour his revenge.
Smithy got the MFJ analyser out and charged up the external battery for later use whilst Mick got their teas. “Now Mick when we did those measurements last week, showing how the impedance of a mismatched load is transformed by the feeder cable, I told you that the true terminating impedance could always be found by using an electrical half-wave length of feeder. This isn’t always practical, for instance if you’ve got a multi-band antenna on the end. Also there are other factors that might prevent you getting an accurate result because the interface between a feeder and an antenna can be anything but straightforward.” All Mick could say in reply to this was “Yep.”
(We have to admit here that Smithy was relishing the next bit.) He produced from his sports bag a piece of cardboard with complicated circular patterns pasted on, the whole lot being covered in perspex. Two of the patterns had a separate transparent plastic overlay pivoted at the centre and with a radial cursor line scratched on. “These are Smith charts Mick” he said “they were the brainchild of an American radio engineer by the name of P.H. Smith around the time of World War Two.” Mick was vaguely interested, but he wasn’t yet aware that Smithy intended making him use them.
“We can use a Smith chart to work out what the impedance at the antenna end of a feeder is. All we need to know is the electrical length of the feeder at the frequency of interest and the impedance at the feed line input, that is the transformed impedance” said Smithy. “You see the charts are really like graph paper but instead of the scales being linear and at right angles, the lines are all sections of a circle. In mathematical terms the chart is a diagram showing the intersection of sets of orthogonal circles, or rather in this case sections of those circles. This particular one that you are going to use is a simplified version set up for a 50 ohm characteristic impedance.” At this mention of him using the chart Mick felt suddenly quite sick, as though he was back at school and been caught out daydreaming and not able to answer a question in front of the rest of the class.
Smithy continued “One set of circle sections represent the resistive component R, and the intersecting set represent the reactive component X. Around the circumference of the chart is another scale representing the electrical length of the feeder, but it is only scaled to a half-wave. So you have to treat a longer feeder length than this as being the fraction over any multiple of half waves.” Smithy handed the chart to Mick, whose hand was now shaking. One or two members had drifted across from the tea area to see what was happening. Mick looked at the chart, it made his eyes go funny, he was aware of the others watching him.
“Relax Mick” said Smithy “I’ll tell you exactly what to do, it’s really quite simple. We’ll choose a frequency of 27 MHz, one that you used to be familiar with, and use the measurement we made on that frequency last week to work out what was in the terminating box. Remember from last week that cable was an electrical half-wave at 43.8 MHz, then the cable will be L/2 times 27 divided by 43.8 and that is 0.305L at 27MHz. Now there is a slight complication here, the MFJ analyser doesn’t indicate whether the reactance is negative, that is capacitive, or positive, that is inductive. We have to determine this from the way the reactance changes around the set frequency. In this case as we lowered the frequency, reactance was going down, so at 27 MHz the reactance was inductive, that is positive and it was therefore 37R+ 19X. Rotate the overlay so that the cursor lies over that point on the chart, where the circle sections for 37R and +19X intersect. Mark that point on the overlay with this felt pen.” Mick did this.
Smithy continued “now here is where this chart is so ingenious. See where the cursor intersects the peripheral scale marked as ‘wavelengths towards load’ and tell me what it is.” “It’s about 0.4 of a wavelength” replied Mick. “Right” said Smithy “now we add to that value the electrical length of our cable, which total comes to about 0.7 of a wavelength. Remember what I said, we need to reduce this back to the equivalent fraction less than a half-wave, which is 0.7L - 0.5L = 0.2L. Now what we do next means the chart is effectively transforming back that input impedance we measured right back to the termination. Rotate the overlay so that the cursor intersects the same peripheral scale at 0.2L, and at the mark you made for the original impedance, read the terminating impedance exactly as you did for the original marked value.”
“It’s 70R - 20X” said Mick. “If you remember Mick I set that terminating box up for 75 ohm. But they are only carbon composition resistors in there, and with some stray capacitance from wiring etc that doesn’t sound far off. I’ll tell you what, we’ll see what the MFJ reads when we connect it straight to the box through a PL259 to PL259 coupler.” Smithy did this, set the analyser to 27MHz and read off 77R and 15X.
“What we have here is a brilliant tool for seeing what the antenna input impedance is from the measurement made at the transmitter end of the feeder. But that’s not all the Smith chart can do, it’s an amazingly useful tool whose only drawback is that it looks so complicated. Mick, this was the subject of an article by Peter Dodd in April 95 RadCom, and I guess it’s probably repeated in one of his antenna books. I’ll lend you the RadCom and you can make one yourself.”
“Phew” said Mick “I think I understood that!” As the pair moved back to the tea area for a final cuppa, Smithy said “Oh Mick, next week I’ll tell you the final piece of nonsense that has grown up around SWR. And you know, you can even use a Smith chart to determine SWR on a feeder from the measurement of the impedance.”
If you have missed our other episodes:
Episode 1.
Episode 2.
Episode 3.
Episode 4.
Episode 5.
Episode 6.
next episode (Chapter 8).