Section 1.4: Transformers and Matching #

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 help transfer power 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.

For the resistive source this theorem describes, equal source and load resistances give maximum load power. When reactance is present, the matching load also needs opposite reactance. In station operation, the practical target is the load the equipment specifies, usually 50 ohms with little reactance. A mismatch can cause reflected waves on the feed line, increase line loss, or make the transmitter reduce power; reflected power is not automatically all lost.

Your radio might show high SWR (Standing Wave Ratio) on some bands but not others because 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. With separate windings, energy can pass between circuits without a direct electrical connection. Autotransformers use one tapped winding and share an electrical connection, so the name “transformer” alone does not guarantee isolation.

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 voltage across the secondary winding. Current flows when a load completes that circuit. The ratio of turns between these windings determines how voltage, current, and impedance transform.

One common use for a transformer is to convert between different AC voltages. For example, suppose a transformer has ten primary turns for every secondary turn. With 120VAC on the primary winding, you get ( $\frac{1}{10} \cdot 120V$ ) = 12VAC out. This is the first basic step in many simple power supply designs. Because transformers work on AC signals, they can also change the voltage or impedance of audio or RF signals when designed for that frequency and power.

Understanding Turns Ratio #

NOTE: The symbols can make these formulas look more complicated than they are. Divide the secondary turns by the primary turns to get the turns ratio. Multiply the primary voltage by that ratio to get the secondary voltage. Twice as many secondary turns means twice the voltage. If the symbols feel unfamiliar, start with the worked examples below.

For an ideal transformer, the turns ratio determines how voltage, current, and impedance change:

A transformer links two separate circuits through a magnetic core. An AC source drives the primary winding on the left; the secondary winding on the right supplies a load. There is no direct wire connection between the windings. The secondary has twice as many turns as the primary. For this ideal transformer, that gives twice the primary voltage across the secondary and half the primary current through its load, with the same power transferred. Arrows identify current in each circuit. — Twice as many secondary turns doubles voltage and halves load current for the same ideal transferred power.

Turns Ratio: A comparison of the turns in the two windings. In these formulas, $p$ is primary, $s$ is secondary, and $n$ means secondary turns divided by primary turns ( $N_s/N_p$ )
$n = \frac{N_\text{secondary}}{N_\text{primary}} = \frac{N_s}{N_p}$
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)

With this turns ratio, a 200-ohm load on the secondary appears as 50 ohms at the primary. Keep track of which winding has more turns.

Transformer Applications #

The ability to change impedance makes transformers useful 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 you apply an input signal to the secondary winding of a 4:1 voltage step-down transformer, the output voltage equals the input voltage multiplied by 4.

Here, 4:1 step-down means four primary turns for every secondary turn. Reversing the connections gives the opposite transformation without rewinding the transformer. A step-down transformer becomes a step-up transformer when you reverse the connections, provided you respect its voltage, current and frequency ratings.

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

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, with more turns on the 600-ohm side.

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 with equal relationships to their surroundings, as in ladder line or window line. The desired signal uses equal and opposite currents.
Unbalanced Line: One conductor serves as the signal reference and surrounds the other, as in coax. The desired current travels on the center conductor and returns along the inside of the shield.

Connecting coax to a balanced antenna can also allow unwanted common-mode current on the shield’s outside, which can distort the pattern or bring RF into the station. A suitable current balun opposes that current. A 1:1 balun can do this without changing the impedance ratio.

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. Although the designs vary, each changes the impedance so the radio components see the load they require. A good input match does not remove feed-line loss or make an inefficient antenna efficient.

Application to General Class Operations #

Understanding impedance matching has practical benefits as you prepare to use General privileges:

In Your Station: Antenna tuners use matching networks to help your transmitter see its expected 50-ohm load, while SWR meters help you detect mismatches.
Real-World Considerations: Perfect matching isn’t always necessary. Equipment limits vary, so check your radio’s specified SWR and power limits. Sometimes improving an antenna is better than matching a poor one.
Why It Matters: With General privileges, you can 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.