The three Yagi matching systems
Each solves the same problem — a driven element that does not present 50 ohms — with a different mechanical and electrical arrangement.
| System | What it is | Driven element |
|---|---|---|
| Beta / hairpin | a shorted transmission-line stub at the feed point | insulated from the boom, and capacitive |
| Gamma | feed tapped along the element, with a series capacitor | need not be insulated |
| Stub | a short length of line in parallel with the feed line, some distance from the load | either |
Which matching system for Yagi antennas requires the driven element to be insulated from the boom?
Beta or hairpin.
What Yagi driven element feed point impedance is required to use a beta or hairpin matching system?
Capacitive (driven element electrically shorter than 1/2 wavelength) — the driven element electrically shorter than 1/2 wavelength.
The hairpin is an inductive shunt, so it needs something capacitive to cancel. A deliberately short driven element supplies that.
What is the purpose of the series capacitor in a gamma match?
To cancel unwanted inductive reactance.
The gamma’s tap introduces inductance; the capacitor removes it. Same cancellation logic, opposite direction from the hairpin.
Which of the following is used to shunt feed a grounded tower at its base?
Gamma match.
The gamma’s ability to work against a grounded conductor is exactly why it suits a grounded tower used as a vertical — nothing needs insulating.
What matching system uses a short length of transmission line connected in parallel with the feed line at or near the feed point?
Stub match
Quarter-wave transformers
A quarter wavelength of line transforms impedance:
Which of these transmission line impedances would be suitable for constructing a quarter-wave Q-section for matching a 100-ohm feed point impedance to a 50-ohm transmission line?
75 ohms
√(100 × 50) = √5000 = 70.7 ohms — and 75-ohm cable is the standard value closest to it. This is the geometric mean, and it is why 75-ohm coax is worth keeping in a junk box.
Reflection coefficient
What parameter describes the interaction of a load and transmission line?
Reflection coefficient.
More fundamental than SWR: the reflection coefficient Γ is complex, carrying both magnitude and phase, so it describes how the load differs from the line rather than merely that it does. SWR is derived from its magnitude alone, which is precisely why SWR cannot tell you whether the load is above or below the line impedance.
Γ is also the quantity a Smith chart plots, which is the next lesson.
Power dividers
What is a use for a Wilkinson divider?
To divide power equally between two 50-ohm loads while maintaining 50-ohm input impedance.
The two requirements together are the trick. A plain T-connector splits power and presents 25 ohms at the input — a 2:1 mismatch. A Wilkinson uses quarter-wave sections plus an isolation resistor to split power and hold the input at 50 ohms, with the added benefit that the two outputs are isolated from each other.
That isolation matters in a stacked-antenna array: a fault in one branch does not reflect into the other.
Phasing lines
What is the purpose of using multiple driven elements connected through phasing lines?
To control the antenna’s radiation pattern.
The phased-array material from the wire-antennas lesson, stated as a technique. The phasing line’s electrical length sets the phase relationship — so its velocity factor matters, and cutting one to physical length rather than electrical length is the classic mistake.
Check yourself
- You need to match a 200-ohm load to 50 ohms with a quarter-wave transformer. What line impedance?
- Your tower is grounded and you want to shunt feed it. Which matching system, and why not a hairpin?
- Why not simply use a T-connector to feed two stacked Yagis?
Answers
- √(200 × 50) = √10000 = 100 ohms.
- Gamma match — it does not require the driven conductor to be insulated, which a grounded tower cannot be. A hairpin needs an insulated, capacitive element.
- A T-connector presents 25 ohms at the input and gives no isolation between branches. A Wilkinson divider splits the power while holding 50 ohms and isolating the outputs.