Technical Article

# Introduction to Transmission Line Transformers and the Bifilar Coil

January 26, 2024 by Dr. Steve Arar

## Learn how a bifilar coil can be used to design transformers for high-frequency RF applications.

There are two basic methods for implementing RF transformers: magnetically coupled transformers and transmission line transformers. Magnetically coupled transformers, which we discussed in the previous article, use magnetic flux linkage to transfer energy to the output. Transmission line transformers rely on electromagnetic wave propagation through a transmission line to transfer energy to the output.

Today’s magnetically coupled transformers exhibit losses of no more than 1 dB over a relatively wide frequency range—from a few kHz to over 200 MHz. Transmission line transformers can provide far wider bandwidths with losses of only 0.02 to 0.04 dB. This makes them an excellent choice for applications such as RF power amplifiers, where high-bandwidth, low-loss transformers are a must.

We’ll start off this article with an overview of the transmission line transformer’s fundamental concepts. After that, we’ll explore the properties of the bifilar coil, an important building block of transmission line transformers. We’ll then examine the Guanella 1:1 balun as an example of how a bifilar coil can be arranged to build an RF transformer. At the end of the article, we’ll briefly review some of the transmission line balun’s real-world uses.

### Defining the Transmission Line Transformer

Though sometimes modeled as lumped components, a transformer’s parasitic capacitances are actually distributed. The left-hand portion of Figure 1 illustrates the interwinding capacitance’s distributed nature. When we flip that diagram on its side (the right-hand portion of Figure 1), it begins to resemble the infinite ladder network used to model RF transmission lines.

##### Figure 1. The interwinding capacitance is a distributed component (left). Viewing a transformer as a transmission line (right).

For comparison purposes, the infinite ladder network model is reproduced in Figure 2.

##### Figure 2. The infinite ladder network model of transmission lines.

Due to the distributed nature of the interwinding capacitance, it appears that we can treat a transformer as a transmission line. Doing so changes the input and output port definitions. From this perspective, the interwinding capacitance and the leakage inductance are no longer non-idealities. Instead, they’re critical parts of the circuit.

Later in the article, we’ll use this structure to build a basic balun. Even before doing so, however, we can recognize the advantage that arises from modeling the combined effect of the interwinding capacitance and the leakage inductance as the transmission line’s characteristic impedance—namely, that the characteristic impedance won’t limit the circuit’s high-frequency response.

The type of transformer that treats its windings as a transmission line is referred to, appropriately enough, as a transmission line transformer. Before diving in too far, let’s first examine a commonly used building block of transmission line transformers—the bifilar coil.

### The Bifilar Coil

A bifilar coil (Figure 3) consists of two closely spaced parallel wires. The winding can be constructed using any of the following:

• A wire pair.
• A twisted pair.
• A coaxial line.

The wires are usually wound around a common core, which can be either ferrite or non-magnetic. Transmission line transformers use magnetic cores to increase the low-frequency isolation between the input and output ports, not as media for energy transfer.

##### Figure 3. A bifilar coil.

We’ll use the coil in Figure 3 to examine the circuit response for two different types of inputs:

• Odd-mode excitation: Also known as differential excitation.The currents in the two conductors are equal in magnitude but opposite in direction.
• Even-mode excitation: Also known as common-mode excitation. The currents are equal in magnitude and have the same direction.

#### Odd-Mode Excitation

Figure 4 illustrates an odd-mode excitation with a current of io.

##### Figure 4. Odd-mode excitation of a bifilar coil.

The current (io) is applied to the left-hand end of the red winding (Point 1). The same current is drawn from the left-hand end of the blue winding (Point 2). Though it’s not shown in the figure, we can assume that the other ends of the coils (Points 3 and 4) are connected to appropriate loads that allow us to have the odd-mode excitation throughout the coils.

To determine the direction of the induced magnetic fields inside the core, we can apply the right-hand rule: if we point the thumb of our right hand in the direction of the current, our fingers curl in the direction of the corresponding magnetic field’s orientation. In Figure 4, the magnetic fields produced by the red and blue coils—represented in the figure by red and blue lines, respectively—are oriented in opposite directions.

Because the two coils produce equal magnetic fields in opposite directions, there should ideally be no net magnetic field inside the core. In other words, for an odd-mode current, there’s no magnetic coupling between the coils. Instead, the bifilar coil is equivalent to a transmission line of the same length as the wires.

#### Even-Mode Excitation

With an even-mode current, things work a bit differently. The magnetic fields produced by the two windings are in phase and of equal magnitude. This produces a strong magnetic field, leading to a strong coupling between the coils. For even-mode excitation, the bifilar coil therefore acts as a large inductance.

Figure 5 shows a bifilar coil with an even-mode current of ie. The common-mode input impedance of this bifilar coil is very high, especially at low frequencies, where the magnetic core can be expected to boost the inductance. An even-mode signal energizes the core; an odd-mode excitation doesn’t. At high frequencies, the loss is therefore much higher for a common-mode signal.

#### The Bifilar Coil’s Equivalent Circuit Model

Figure 6 shows the equivalent circuit of the bifilar coil we’ve been examining. It uses two ideal transformers to model the response to even-mode and odd-mode currents.

##### Figure 6. The equivalent circuit model of a bifilar coil.

The odd-mode current:

1. Passes through the transformer T1.
2. Travels down the transmission line.
3. Goes through the transformer T2 to appear as a differential signal at the output.

The even-mode current:

1. Flows out of the center tap of T1.
2. Goes through the inductance (L).
3. Exits the transformer T2 as a common-mode signal.

If the inductance from an even mode-excitation is large enough, we can assume that the even-mode currents are negligible, and that only odd-mode currents can flow through the bifilar coil. This observation is key to understanding the operation of some transmission line transformer types.

The lower limit of a transmission line transformer’s frequency range is determined by the self-inductance of its windings. As a rule of thumb, the reactance created by the windings at the lowest frequency of operation should be three to five times greater than either the source or load impedance, whichever is larger.

### Comparing Conventional and Transmission Line Transformers

A conventional transformer requires magnetic coupling between the primary and secondary coils. That’s why, in this type of transformer, energy transfer depends on the mutual inductance and magnetic flux linkage between the coils. Because a transmission line transformer transfers energy through the transmission line action, not magnetic flux linkage, the energy transfer depends on the characteristic impedance and propagation constant of the transmission line. This represents a fundamental difference in the operation of the two transformer types.

Transmission line transformers and conventional transformers both commonly use magnetic cores, but for different reasons. In a transmission line transformer, the purpose of the core is to increase the low-frequency isolation between the input and output ports. Unlike a conventional transformer, a transmission line transformer can’t provide any DC isolation between the input and output.

### A Transmission Line Balun Based on the Bifilar Coil

Now that we have the relevant concepts under our belt, let’s look at a practical example of how a bifilar coil can be used to build an RF balun. The circuit in Figure 7, which dates back to a 1944 paper by Gustav Guanella, is known as the Guanella 1:1 balun.

##### Figure 7. A basic transmission line balun (Guanella 1:1 balun).

Ideally, only odd-mode currents can flow through the circuit’s windings. This means that a differential current appears at the output, resulting in identical voltages across the two load resistors. Note that the overall load resistance (RL) is divided into two RL/2 resistors, and the center point is connected to ground. This produces a 180 degree phase difference between the outputs, which is required for the balun’s functionality.

Instead of grounding the load at its center point, we can also use a floating load (Figure 8).

##### Figure 8. Transmission line balun with a floating load.

Either version of the circuit acts as a 3 dB power divider with a 180 degree phase difference between the outputs, which is why this structure is sometimes called an “anti-phase power splitter.” To avoid reflections, impedance matching conditions must be satisfied:

$$R_{S}~=~Z_{0}~=~R_{L}$$

where Z0 is the characteristic impedance of the transmission line used for the bifilar coil.

### Baluns in RF Applications

Baluns play a critical role in the operation of push-pull power amplifiers (PAs) like the one in Figure 9. This topology requires two transistors operating 180 degrees out of phase; the signals applied to the transistors are therefore differential (balanced). However, the signal source is single-ended (unbalanced).

##### Figure 9. A basic transformer-coupled push-pull power amplifier.

To convert between balanced and unbalanced signals, we use baluns. The push-pull configuration requires an input balun to produce the differential signal fed to the transistors, and an output balun to recombine the signals produced by the transistors. The baluns need to have a bandwidth comparable to—or even wider than—the bandwidth of the push-pull PA being implemented. Though the baluns in Figure 9 are magnetically coupled, the non-ideal behaviors we discussed in the previous article make transmission line baluns a more practical choice.

Baluns are also used in many other types of devices, including:

Which properties of the balun are most important depends on the application. A push-pull PA requires a balun with low loss, for example, but a balun with good phase balance might be more important to a balanced mixer.

### Wrapping Up

Transmission line transformers offer a clever solution for implementing RF transformers, including baluns. This article showed how a bifilar coil can be applied to create a simple transmission line transformer. We’ll explore several other configurations of transmission line transformers in subsequent articles.

References:

1. RF Power Amplifiers” by Mihai Albulet.
2. Electromagnetics for High-Speed Analog and Digital Communication Circuits” by Ali M. Niknejad.
3. Practical RF Circuit Design for Modern Wireless Systems, Volume I: Passive Circuits and Systems” by Les Besser and Rowan Gilmore.

All images used courtesy of Steve Arar

• J
jamesluschen February 03, 2024

Is Figure 9 drawn wrong?  The text discussing Figure 9 says “...this means using transmission line baluns” but what’s drawn in Fig. 9 appears to be regular old transformers, not baluns.  It also says “...the signal source and final output are single-ended (unbalanced)”, but that output circuit is definitely balanced the way it is drawn—perhaps the figure is missing a ground node?

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• D
Dr. Steve Arar February 03, 2024
Thank you for pointing this out! Yes, the output should have a ground connection. Also, baluns can be implemented using either magnetically-coupled transformers or transmission line transformers. The provided schematic uses the first type. We'll revise this section to remove the confusion.
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• W
wd73383 February 11, 2024

PDF versions of your articles would be very nice to have for future reference. Are they available?

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