Broadband transformers—including baluns—find many applications in RF circuits. The high-frequency limits of some power amplifiers, for example, are determined by the leakage inductance and distributed interwinding capacitance of magnetically-coupled transformers. In wideband applications, we can’t simply resonate away these parasitics—instead, we need to find alternative solutions.
That’s where transmission line transformers come in. These transformers make their windings behave as transmission lines. By doing so, they combine the leakage inductance and interwinding capacitance to produce the effect we know as the characteristic impedance. Transmission line transformers can provide much wider bandwidths than their magnetically coupled counterparts, and are available as standard parts on the market.
In a previous article, we learned how a bifilar coil can be used to build a Guanella 1:1 balun. In this article, we’ll learn about two other useful configurations built around a bifilar coil: the phase inverter configuration and the delay line arrangement. We’ll then combine these circuits to produce a wideband, 1:4 impedance-matching circuit known as the Guanella 1:4 balun.
The Bifilar Coil as the Core Element of a Balun
Before we jump in, let’s review what we’ve already learned. Figure 1 shows the Guanella 1:1 balun, which is built using a single bifilar coil. It converts an unbalanced signal at the input to a balanced signal at the output.
Figure 1. The Guanella 1:1 balun. Image used courtesy of Steve Arar
This schematic uses a common symbol for a transmission line transformer. This symbol, like the one for a conventional transformer, looks like a pair of inductor symbols. This can be misleading for beginners, so it’s worth emphasizing that each of the inductor symbols in Figure 1 actually represents a conductor of the transmission line.
The transmission line can be either:
- A bifilar coil built using a wire pair, twisted pair, or coaxial line.
- A straight transmission line loaded with ferrite beads.
Phase Inverter Configuration
The balun action in Figure 1 isn’t the only important function that a bifilar coil can implement. Figure 2 shows another useful arrangement of the bifilar coil. This structure can function as a broadband phase inverter.
Figure 2. Using a bifilar coil to implement a broadband phase inverter. Image used courtesy of Steve Arar
To understand the operation of this circuit, recall that the amplitude of the voltage signal along the length of a transmission line is constant when the transmission line is connected to a matched load. We therefore have V1 = V2.
Need a refresher on transmission line waveforms? Refer to this article: “Transmission Line Theory: Observing the Reflection Coefficient and Standing Wave.”
Note that the lower winding is grounded at the input, whereas the upper winding is grounded at the output. By reversing the transmission line connections at the load end, we’ve flipped the voltage polarity, leading to a load voltage of:
$$V_{OUT}~=~-V_{2}~=~-V_{1}$$
Equation 1.
To help you understand the actual implementation, Figure 3 shows a phase inverter circuit realized by winding a coaxial cable around a magnetic core.
Figure 3. A phase inverter circuit built using a coaxial cable. Image used courtesy of Steve Arar
The input impedance of the inverter circuit is matched (ZIN = Z0 = RL) over a wide bandwidth. However, the input impedance approaches zero as we approach DC.
Effect of Even-Mode Currents
The above explanation assumes implicitly that only odd-mode currents are present—but what happens when even-mode currents flow through the transmission line? Figure 4 reproduces the equivalent circuit model of the bifilar coil.
Figure 4. The equivalent circuit model of a bifilar coil. Image used courtesy of Steve Arar
If the reactance of the windings (L) is small, a shunting current can flow through the transmission line. In the phase inverter circuit of Figure 2, the shunting current flows from Terminal 1 to Terminal 3, and from there to ground. This results in a drop in the input impedance of the transmission line, as well as creating a magnetic flux in the core.
What I’ve provided above is an intuitive explanation of the phase inverter circuit. If this doesn’t satisfy you, a more rigorous analysis can be found in the book “Electromagnetics for High-Speed Analog and Digital Communication Circuits” by Ali M. Niknejad.
Delay Line Configuration
Figure 5 shows another simple and useful arrangement of the bifilar coil. You probably recognize this as the transmission line arrangement we commonly use to transfer energy from a source to a load. With a matched load (RS = Z0 = RL), this configuration behaves as a delay line.
Figure 5. Delay line configuration of the bifilar coil. Image used courtesy of Steve Arar
Coiling the transmission line around a ferrite core doesn’t affect the delay that the circuit introduces to differential signals. Ideally, the magnetic fields from those signals cancel each other out inside the core. The ferrite core can only increase the inductance that the common-mode signals experience while they’re traveling from the source to the load.
Using a Balun to Feed a Dipole Antenna
So far, we’ve learned how a bifilar coil can implement the following:
- Delay lines.
- Phase inverter circuits.
- Wideband 1:1 baluns.
It’s time to think about building wideband transformers with higher transformation ratios. We’ll start by examining two basic 1:4 balun configurations that can be used to feed a symmetric dipole antenna from an unbalanced source. Though both of these baluns have important shortcomings, they can help us understand a circuit that’s much more practical for our purposes—the Guanella 1:4 balun.
In order to feed a dipole antenna, we need to provide voltages of the same magnitude and opposite polarity to each element of the antenna. Figure 6 shows how a half-wavelength transmission line can be used for this purpose.
Figure 6. Half-wavelength balun for feeding a dipole antenna. Image used courtesy of Steve Arar
The half-wavelength transmission line creates the opposite-polarity signal for the right-hand element of the antenna. Because the half-wavelength line only provides the intended phase reversal at a specific frequency, the circuit is narrowband.
Figure 7 shows another solution, this time using the phase inverter circuit we discussed earlier on.
Figure 7. Using a phase inverter to feed a dipole antenna. Image used courtesy of Steve Arar
As in Figure 6, the total voltage applied to the antenna is twice what’s provided by the signal source. Because of this, both circuits provide a 1-to-4 impedance transformation.
The balun in Figure 7 provides a relatively wider bandwidth, which we can improve further by addressing its primary limitation—the additional phase shift caused by the delay of the transmission line. In addition to the intended phase reversal produced by the circuit architecture, the delay of the transmission line can introduce an unwanted time lag. This time lag can make the phase shift of the circuit deviate from the ideal 180 degrees, especially as we go to higher and higher frequencies.
We can circumvent this problem by using an identical transmission line in the path of the signal that’s applied to the antenna’s left-hand element. This equalizes the delay of the two paths, creating a pair of signals with the same amplitude and opposite polarity at the antenna over a wider bandwidth. This is where the delay line configuration becomes useful, as we’ll see in the next section.
The Guanella 1:4 Balun and 1:N2 Balun
Figure 8 shows a wideband transmission line transformer that incorporates both the phase inverter circuit and the delay line arrangement. The top bifilar coil is configured as a non-inverting delay line, whereas the bottom bifilar coil behaves as an inverting delay line. This circuit, which was first presented by Gustav Guanella in 1944, is known as the Guanella 1:4 balun.
Figure 8. The Guanella 1:4 transmission line transformer or balun. Image used courtesy of Steve Arar
Since the two transmission lines incorporated into the balun have identical lengths, they provide identical frequency-dependent phase shifts. This allows the circuit to produce a pair of signals—ideally independent of frequency—at the output with the same amplitude but opposite polarity. For the two bifilar coils, the output voltage is twice the input voltage.
Assuming that the circuit is lossless, a voltage gain of 2 corresponds to an impedance transformation ratio of 4. In other words, the circuit transforms an impedance of 4R down to an impedance of R, or an impedance of R up to 4R. Note that each transmission line sees one-half of the overall load (RL). Therefore, the optimum value of the above circuit’s characteristic impedance is:
$$Z_{0}~=~ frac{R_{L}}{2}$$
Equation 2.
Figure 9 shows the coaxial realization of the circuit with appropriate characteristic impedance and load resistance for a 50 Ω source. Though not shown in the figure, the coaxial cables would usually be loaded with ferrite beads.
Figure 9. Coaxial realization of the Guanella 1:4 balun for a 50 Ω source. Image used courtesy of Steve Arar
We can improve our understanding of this balun by remembering that it comprises two equal-length transmission lines, and examining its input and output sides separately.
On the input side:
- The transmission lines are connected in parallel.
- In-phase currents are added.
- Impedance is lower than on the output side.
On the output side:
- The transmission lines are connected in series.
- In-phase voltages are added.
- Impedance is higher than on the input side.
We’ll see shortly how this view of the circuit can help us realize transformers with transformation ratios even higher than 1:4. Before we move on, though, a bit of history: the Guanella 1:4 circuit we just examined was the configuration most commonly used in older television baluns. Figure 10 shows an example.
Figure 10. Baluns in older televisions commonly used the Guanella 1:4 circuit. Image used courtesy of D. Jackson
Building the 1:N2 Balun
We can readily extend the idea of driving windings in parallel and taking outputs in series to create 1:n2 baluns, where n is an integer equal to the number of bifilar coils used. This is illustrated in Figure 11.
Figure 11. The Guanella 1:n2 transmission line transformer. Image used courtesy of Steve Arar
In this case, the optimum characteristic impedance is:
$$Z_{0}~=~ frac{R_{L}}{n}$$
Equation 3.
and the input impedance of the transformer is:
$$R_{S}~=~ frac{R_{L}}{n^{2}}$$
Equation 4.
Key Takeaways
Several useful circuits can be built around a single bifilar coil, including:
- 1:1 baluns.
- Phase inverters.
- Non-inverting delay lines.
A combination of n bifilar coils can be used to create 1:n2 transmission line transformers. In these circuits, high-frequency response is limited by parasitics that aren’t absorbed into the characteristic impedance of the transmission line, such as:
- The intra-winding capacitance of the coils.
- The deviation of the line’s characteristic impedance with frequency.
- Loss mechanisms affecting the line.
