Section 1.4: Impedance Matching and Transformers #

As we saw in the last section, impedance affects how RF energy flows through your station. When you key up on a new HF band and your radio shows high SWR readings and reduces power, you’re experiencing an impedance mismatch—a situation where your transceiver and antenna system aren’t properly matched.

In this section, we’ll explore transformers and matching networks—practical tools that ensure efficient power transfer between different parts of your station.

The Maximum Power Transfer Theorem #

The Maximum Power Transfer Theorem states that, to obtain maximum external power from a power source with internal resistance, the resistance of the load must equal the resistance of the source as viewed from its output terminals.

In any electrical system, maximum power transfers from source to load when their impedances match. For RF systems, this typically means we want our antenna system to present a 50-ohm impedance to match our transmitter’s output. When impedances align, power flows efficiently; when they don’t, power reflects back toward the transmitter instead of radiating from the antenna.

This principle explains why your radio might show high SWR (Standing Wave Ratio) on some bands but not others—the antenna’s impedance varies with frequency, creating matches at some frequencies and mismatches at others.

Let’s look at the tools that help us create matches between different impedances:

Transformers: The Impedance Conversion Tools #

Transformers are elegant devices that transfer energy between circuits while changing voltage and current ratios—and consequently, impedance. They work through electromagnetic induction, requiring no direct electrical connection between circuits.

Key Information: Mutual inductance causes a voltage to appear across the secondary winding of a transformer when an AC voltage source is connected across its primary winding.

A transformer consists of two or more windings (coils) wrapped around a common core. When alternating current flows through the primary winding, it creates a changing magnetic field that induces current in the secondary winding. The ratio of turns between these windings determines how voltage, current, and impedance transform.

One of the most commonly known uses for a transformer is to convert between different AC voltages – for example, using a $10:1$ transformer with 120VAC on the primary winding you will get ( $\frac{1}{10} \cdot 120V$ ) = 12VAC out, which is the first basic step used in many simple power supply designs! However, since a transformer works on AC signals they can also be used to change voltage or impedance of any AC signal, including both audio and RF!

Understanding Turns Ratio #

The turns ratio determines how a transformer converts voltage, current, and impedance:

Turns Ratio: The ratio of turns on the secondary side to turns on the primary side
$n = \frac{N_\text{secondary}}{N_\text{primary}}$
Voltage Transformation: The voltage ratio equals the turns ratio (see above)
$V_s = V_p \cdot n = \frac{V_p \cdot N_s}{N_p}$
Current Transformation: The current ratio equals the inverse of the turns ratio
$I_s = I_p \cdot \frac{1}{n} = \frac{I_p \cdot N_p}{N_s}$
Impedance Transformation: The impedance ratio equals the square of the turns ratio
$Z_s = Z_p \cdot n^2 = \frac{Z_p \cdot {N_s}^2}{ {N_p}^2 }$

For example, a transformer with twice as many turns in the secondary as in the primary (2:1 turns ratio) will:

Double the voltage
Halve the current
Quadruple the impedance (2²)

Transformer Applications #

This impedance transformation capability makes transformers invaluable in amateur radio for:

Antenna Matching: Converting antenna impedance to match transmitter output
Baluns (Balanced-to-Unbalanced): Connecting balanced antennas to unbalanced feed lines
Ununs (Unbalanced-to-Unbalanced): Matching between different unbalanced impedances
Interstage Coupling: Matching between amplifier stages

Reversing Transformer Connections #

What happens when you apply a signal to the secondary winding instead of the primary? The transformer still works, but the transformation ratios reverse:

Key Information: When an input signal is applied to the secondary winding of a 4:1 voltage step-down transformer, the output voltage is multiplied by 4.

This property is useful when you need the opposite transformation without rewinding the transformer. A step-down transformer becomes a step-up transformer when connections are reversed.

Transformer Construction Considerations #

Transformer design involves important practical considerations beyond just turns ratio:

Key Information: The primary winding wire of a voltage step-up transformer is usually larger than the secondary winding wire to accommodate the higher current in the primary.

Since power ( $P = I \cdot E$ ) remains approximately constant (minus losses), a step-up transformer that increases voltage must decrease current proportionally. Therefore:

The primary winding handles higher current and needs thicker wire
The secondary winding carries less current and can use thinner wire

This design principle optimizes material usage while ensuring each winding can safely handle its current.

Calculating Transformer Voltage #

Let’s work through a practical example that might appear on your exam:

What is the voltage output of a transformer with a 500-turn primary and a 1500-turn secondary when 120 VAC is applied to the primary?

Using the voltage transformation formula:

V_s = V_p \cdot \frac{N_s}{N_p}

\begin{align*} V_s &= 120V \cdot \frac{1500}{500}\\[1.25em] &= 120V \cdot 3\\[1.25em] &= 360V \end{align*}

This 3:1 turns ratio transformer triples the voltage from 120V to 360V.

Calculating Turns Ratio for Impedance Matching #

Sometimes we need to determine the correct turns ratio to match specific impedances. For example:

What transformer turns ratio matches an antenna’s 600-ohm feed point impedance to a 50-ohm coaxial cable?

Using the impedance transformation formula:

\frac{Z_s}{Z_p} = n^2

Rearranging to solve for n:

\begin{align*} n &= \sqrt{\frac{Z_s}{Z_p}} \\[1.25em] &= \sqrt{\frac{600 \Omega}{50 \Omega}} \\[1.25em] &= \sqrt{12} \\[1.25em] &\approx 3.46 \end{align*}

Therefore, a turns ratio of approximately 3.5:1 will match a 600-ohm antenna to 50-ohm coax.

Practical Matching Systems for Antennas #

Transformers are just one approach to impedance matching. For antenna systems, several specialized matching methods have evolved:

Beta Match (Hairpin Match) #

Key Information: A beta or hairpin match is a shorted transmission line stub placed at the feed point of a Yagi antenna to provide impedance matching.

The beta match uses a shorted section of transmission line (the “hairpin”) placed in parallel with the feed point of an antenna element. This creates a parallel resonant circuit that transforms the antenna’s impedance to match the feed line.

This matching system is popular for Yagi antennas because:

It’s relatively simple to construct
It can be adjusted by changing the length or shape of the hairpin
It provides a good match across a reasonable bandwidth

Gamma Match #

The gamma match is another common approach for directive antennas:

Key Information: A gamma match with a Yagi antenna does not require the driven element to be insulated from the boom.

The gamma match offers several advantages:

Allows direct connection of the boom to the driven element without insulation
Provides both impedance matching and balun functionality
Can be adjusted via the gamma rod length and capacitor setting

This practical benefit makes it popular for many Yagi designs, as it simplifies construction while maintaining good performance.

Specialized RF Transformers #

In RF systems, the balun (Balanced-to-Unbalanced) is particularly important. It solves a fundamental problem in antenna systems:

Balanced Line: Two conductors carrying equal but opposite currents, with neither connected to ground (ladder line, window line).
Unbalanced Line: One conductor connected to ground while the other carries the signal (coaxial cable, where the shield is grounded).

Without a balun, connecting coax to a balanced antenna allows current to flow on the outside of the shield, causing pattern distortion and RF feedback in your station. Other specialized transformers like ununs (Unbalanced-to-Unbalanced) and transmission line transformers also exist for specific matching applications, but baluns are what you’ll encounter most frequently.

LC Matching Networks #

Besides transformers, simple combinations of inductors and capacitors (LC networks) can also match impedances. These appear in various configurations (L, Pi, or T networks) in antenna tuners and amplifier output circuits. While the specific designs vary, they all perform the essential function of transforming impedance to ensure maximum power transfer between your radio components.

Application to General Class Operations #

Understanding impedance matching has practical benefits as you use your new General privileges:

In Your Station: Antenna tuners use matching networks to ensure your transmitter sees its expected 50-ohm load, while SWR meters help you detect mismatches.
Real-World Considerations: Perfect matching isn’t always necessary—modern transceivers tolerate an SWR up to 2:1, and sometimes improving an antenna is better than matching a poor one.
Why It Matters: As a General, you’ll operate across multiple HF bands with a single antenna and potentially use higher power levels where mismatches become more significant. Understanding matching helps you make better equipment choices and get more of your transmitter’s power to actually radiate from your antenna.

Now that we understand how transformers and impedance matching affect power flow in our radio systems, let’s explore how to measure and quantify that power. In the next section, we’ll examine power calculations, decibels, and other measurement concepts that will help you evaluate your station’s performance.