By H. Ward Silver, N0AX
ARRL Contributing Editor
n0ax@arrl.net

Impedance matching is a function performed many times in every radio and every radio shack. Sometimes it’s done inside a circuit and out of sight. Sometimes an automatic tuning unit clicks its way to unity SWR. And sometimes we just twiddle knobs or futz with the construction of antennas until the reflected power meter says “Good enough!” To explore the subject, what better than a matchless set of match matching exercises? (You can find the background for all of these questions in The ARRL Handbook or The ARRL Antenna Book.)

1) Match the transmission line stub with the resulting impedance.
a. 1/4-wavelength shorted                   f. capacitive reactance
b. 1/2-wavelength open                       g. short
c. 1/4-wavelength open                       h. open
d. 1/8-wavelength shorted                   i. open
e. 1/8-wavelength open                       j. inductive reactance

2) Pair up the type of antenna matching network with its description.
a. T                              f. unbalanced, connects one side of the line directly to antenna
b. Gamma                    g. feed line connects to points with correct impedance between them
c. Hairpin                    h. center is electrically neutral
d. Delta                        i. balanced, acts like a folded dipole to transform impedance
e. Omega                     j. series and shunt capacitors

3) Identify the most common component arrangement for each type of L-C matching network.
a. L                              e. two inductors
b. Pi                             f. three capacitors
c. T                              g. one inductor, two capacitors
d. Link                         h. one inductor, one capacitor

4) Match the balun type with its description.
a. coaxial choke           e. coiled cable
b. sleeve                      f. 1/4-wave, air-insulated transmission line
c. voltage                     g. one winding across the input
d. current                     h. ferrite beads over cable

5) Which device performs which function?
a. Reflectometer                      f. samples a portion of transmission line power
b. Bird                                     g. measures SWR
c. Matchbox                            h. measures forward and reflected power
d. Directional coupler              i. impedance matching network
e. Noise Bridge                       j. measures impedance

6) Get a line on the correct impedances.
a. RG-213                   f. 300 or 75 ohms
b. RG-59                     g. 50 ohms
c. TV twin-lead           h. 450 to 600 ohms
d. Ladder line              i. 93 ohms
e. RG-62                     j. 75 ohms

7) Match the transmission line with its characteristic velocity of propagation factor (VF).
a. Coaxial, foamed polyethylene insulation                 e. 66%
b. Twin-lead                                                                f. 70%
c. Coaxial, solid polyethylene insulation                     g. 80%
d. Coaxial, foamed Teflon™ insulation                      h. 95%

8) Select the termination that will cause a 40 meter, quarter-wave stub to present an open circuit at its opposite end on each of these frequency bands.
a. 40 meters                 e. open
b. 20 meters                 f. open
c. 15 meters                 g. short
d. 10 meters                 h. short

9) What units are used to measure each of the following?
a. Return loss                                       f. dB
b. Reflection coefficient                      g. degrees
c. Characteristic impedance                 h. radians/unit length
d. Phase constant                                 i. unitless
e. Electrical length                               j. ohms

10) Can you pair up the symptom with the problem?
a. SWR changes with line length                    e. High SWR
b. Tuning network arcs                                   f. Common-mode current on
feed line
c. Non-unity SWR with no power applied      g. Strong nearby broadcast station
d. Low SWR with line open at far end            h. High line loss

Bonus: What is measured in nepers/unit length?

Answers
1) a-h, b-i, c-g, d-j, e-f
2) a-i, b-f, c-h, d-g, e-j -- Amateur antenna-makers should know all of these matching techniques.
3) a-h, b-g, c-f, d-e
4) a-e, b-f, c-g, d-h -- Know each type of balun and its limitations.
5) a-g, b-h, c-i, d-f, e-j
6) a-g, b-j, c-f, d-h, e-i
7) a-g, b-h, c-e, d-f -- Actual VF varies with manufacturer and exact cable type.
8) a-short, b-open, c-short, d-open -- A stub repeats the terminating impedance every one-half wavelength and inverts the terminating impedance (open to short and short to open) every odd quarter-wavelength. At 20 meters, the 40 meter quarter-wavelength stub is one-half wavelength long. On 15 meters, it’s ¾-wavelength long. On 10 meters, it’s 1 wavelength long.
9) a-f, b-i, c-j, d-h, e-g
|10) a-f, b-e, c-g, d-h

Bonus -- Line loss. One neper is 8.688 dB and is derived from the hyperbolic trigonometry used in calculating transmission line behavior.