Coaxial Balun to match widband amplifier

In power amplifier design, although LC network with negative feedback can achieve broadband matching of 1~2 octave, it is very difficult and complicated to use LC network to match impedance of more octave.

Transmission line transformer is a structure that is often used in the design of broadband power amplifier. In the circuit, it generally has the following functions:

1. Impedance transformation 
2. Balanced-to-unbalanced conversion
3. Phase inversion

When coaxial lines are used as transmission lines, they are called coaxial baluns. These are either a segment of coaxial cable with a ferrite core, or a coaxial cable wound around a magnetic core.

1. The Balun principle of coaxial cable achieves different transformation effects through varying winding configurations between coaxial lines.

At low frequencies, the inductive shunt loss in coaxial lines reduces the conversion ratio, resulting in poor low-frequency response characteristics of the coaxial balun. This causes current rise and reduced output. But the magnetic core compensates the low-frequency response, At this time the transformer transmission method becomes the primary factor.so can get good output. its equivalent circuit as below at low frequencies.

According to the principle of transformers, as shown below figure 

Ignoring the losses of the transformer, then

also because

so

When n = 1, the impedances keep same value on both sides.

At the high-frequency end, the transmission line mode plays a major role, and the equivalent circuit is as follows.

At the same time, this circuit also has the function of converting unbalanced single-ended signals into balanced differential signals.

1:4 coaxial balun consists of two coaxial cables of equal length, and its structure is shown in the figure.

Its equivalent circuit is

So its impedance transformation ratio is:

1. Advantages and Disadvantages of Coaxial Balun: 

With its ultra-wide operational frequency range, the coaxial balun plays a crucial role in broadband matching. But coaxial baluns also have several drawbacks: they occupy significant space, often require manual winding, and lack consistent performance, while their circuitry is relatively complex. These limitations hinder their widespread adoption.

1. Coaxial Cable Balun Magnetic Core Selection

The low-frequency response of coaxial balun is poor due to the reduced conversion ratio caused by the reactance shunt loss in the coaxial line, which requires ferrite magnetic ring compensation.The effect of the magnetic core can be quantified by its equivalent inductance, which determines the reflection magnitude at low frequencies. The calculation formula is:

In the formula, L is the inductance (H); ur is the relative permeability; μ₀=4×10⁻⁷; S is the area of the magnetic ring; J is the average electrical length; n is the number of turns in the coil.

To prevent the deterioration of high-frequency indicators, the inductance value must not exceed the actual required value. The empirical formula is: 

In this formula, R denotes the input impedance of the intermediate frequency band, while Wmin represents the minimum angular frequency.

The selection of magnetic core material is very important. In order to get the right inductance value, we should pay attention to the following points: choose the magnetic core with high permeability; in order to choose the right ferrite magnetic core for coaxial converter, we should know the saturation flux and nonlinear characteristics of magnetic core.

When the power is high, the magnetic ring's power capacity must be checked. This is because magnetic saturation occurs in the magnetic flux of the ring under high power, causing the equivalent inductance to decrease during high signals, which prevents the power from being delivered.

4> Coaxial Cable Balun and Coaxial Cable Selection

When selecting coaxial cables, key factors to consider include characteristic impedance, length, material, and power capacity. The characteristic impedance of a coaxial cable should be the geometric average of input and output impedances, calculated as follows: 

Consider the 1:4 balun as an example. Since it typically achieves impedance matching up to 50Ω, its coaxial characteristic impedance is usually 25Ω. This impedance level makes it suitable for mass production.

Regarding the length, it should be noted that to avoid main mode resonance and excessive parasitic parameters, the length is generally limited to one-eighth of the minimum wavelength in the frequency band.

The material selection primarily considers mechanical performance for assembly purposes, typically using semi-flexible coaxial cables. For symmetrical Balun configurations combining coaxial and microstrip cables, semi-rigid cables are required.

The wire diameter primarily depends on the coaxial cable's power capacity. For amplifier input matching, high-capacity cables are unnecessary as they are impractical and space-consuming, with a 1.5mm diameter typically sufficient. However, for amplifier output matching with 50W or higher power, high-capacity cables are required, usually with a diameter exceeding 3mm.

1. Application Examples

1:1 balun is used to balance the conversion between unbalanced signals, while a 1:4 (4:1) balun is employed for impedance transformation. The coaxial cable is wound into a U-shape and routed through the magnetic ring.