IC Substrate - Uncovering the mystery of RF transformers: an introduction to theory, technology and applications

Essentially, a transformer is just two or more conductive loops connected by a mutual induction magnetic field. When a changing magnetic flux is generated in the magnetic core, the alternating current flowing through one conductive path induces current in the other conductive path. The induced current is proportional to the ratio of the amount of magnetic coupling between the two conductive loops. The ratio of the magnetic coupling between the conductive loop and the magnetic core determines the induced voltage in the additional conductive loop, thereby providing impedance transformation and voltage increase or decrease. By adding as many additional conductive loops with different coupling coefficients as possible, various functions can be achieved. This is why the RF transformer is a diverse and versatile device and is widely used in the entire RF/microwave industry.

A common radio frequency transformer consists of two or more different wires wound on a magnetic core (or an air core at high frequencies), which is why radio frequency transformers are often described as the ratio of windings or turns. RF transformers can be used in a variety of applications, because the nature of the equipment allows different configurations to achieve different functions, including:

• Provide impedance transformation for impedance matching.

• Increase or decrease the voltage or current.

• Efficient coupling between balanced and unbalanced circuits.

• Enhanced common mode rejection.

• Provide DC isolation between circuits.

• Inject DC current.

Several common technologies used to construct transformers include core wires, transmission lines, low temperature co-fired ceramics (LTCC) and MMIC. Each product and different package has a series of performance indicators.

Transformer theory
Although the ideal transformer model is not realistic for practical applications, it can illustrate the basic performance of the transformer (as shown in Figure 1). Ports 1 and 2 are the input of the primary winding, and ports 3 and 4 are the output of the secondary winding. According to Faraday's law, the current passing through the primary winding generates magnetic flux through the mutual magnetic field of the current and voltage in the secondary winding. The current and voltage generated are proportional to the ratio of the winding or the magnetic coupling between the winding and the iron core. Therefore, the secondary impedance is a function of the winding ratio squared multiplied by the primary impedance. This relationship can be described by the following formula:

Among them, I1, V1 and Z1 are the current, voltage and impedance through the primary winding; I2, V2 and Z2 are the current, voltage and impedance through the secondary winding; N1 is the number of turns of the primary winding; N2 is the number of turns of the secondary winding .

A real transformer includes multiple parasitic resistances, inductances and capacitances, including mutual capacitance and self-parasitic capacitance. Figure 2 shows a lumped model of a non-ideal RF transformer, which describes the parasitic resistance and inductance of the two windings, as well as the resistance loss of the iron core and the effective inductance of the windings. Parasitic effects cause the actual transformer to work in a limited bandwidth, with insertion loss and limited power handling capabilities (as shown in Figure 3). Transformer performance also depends on frequency, temperature and power.

The low-frequency cut-off frequency of the actual radio frequency transformer is determined by the active inductance of the winding, and the high-frequency cut-off frequency is determined by the capacitance between the windings and the windings. The insertion loss in the operating bandwidth is the product of the resistance loss in the primary winding and the secondary winding and the loss in the core. Since resistance loss is often a function of frequency and temperature, the effective working bandwidth of the transformer is limited by these factors. Due to the incomplete magnetic coupling between the windings, several types of RF transformers will introduce leakage inductance. Since the reactance of the leakage inductance is proportional to the frequency, these parasitic effects will reduce the return loss at high frequencies and increase the insertion loss at low frequencies. More complex radio frequency transformer topologies, such as transformers with multiple windings, taps, and other components, will show varying performance depending on the topology and transformer structure. For example, a type of radio frequency equipment called a balun is used to effectively interconnect a balanced (that is, differential signal) circuit to an unbalanced (that is, single-ended signal) circuit through impedance transformation, which can be achieved by a radio frequency transformer . Another device similar to a balun is called a balun, which is used to interconnect unbalanced radio frequency circuits. It can also be realized by a radio frequency transformer. A common balun formed by a transformer is a flux-coupled balun, which constructs one side of the primary winding by winding a separate wire around a magnetic core and grounding it. The single-ended radio frequency signal entering the primary unbalanced winding undergoes impedance transformation and is output as a differential (ie balanced) signal through the secondary winding. RF transformers that include non-magnetic iron cores (usually ferromagnetics) have some disadvantages. The magnetizing inductance of the iron core limits the performance of the low-frequency transformer. The inductance is a function of core permeability, cross-sectional area, and the number of windings around the core. The magnetizing inductance increases the low frequency insertion loss and reduces the return loss. The permeability of the iron core is also a function of temperature. Permeability that increases with temperature increases low-frequency insertion loss.

RF transformer technology
The two main types of discrete radio frequency transformers are the core type and the transmission line type. In addition, LTCC and MMIC are two common thin and compact transformer designs.

Core wire type radio frequency transformer

Core-type transformers are made by winding conductive wires (usually insulated copper wires) on a magnetic core (such as a ring). There can be one or more secondary windings, or they can be tapped in the center for additional functions. Figure 4 shows a radio frequency transformer made of a toroidal core and insulated copper wire windings. Due to the inductive coupling between the wire and the magnetic core, a smaller-sized core transformer should work at a higher frequency than a larger-sized core transformer. However, the smaller size of the compact transformer increases the resistance loss of the windings and cores, resulting in greater insertion loss at lower frequencies.

Transmission line type RF transformer

The transmission line transformer topology includes precisely designed transmission lines that are located between two mismatched loads or are complex arrangements of multiple transmission lines. For example, the length of the transmission line can be used to achieve impedance transformation between two mismatched loads. Some transmission line transformers use insulated wires wrapped around a ferrite core, which are very similar to typical core-wire transformers and are usually considered core-type transformers.

The basic transmission line transformer consists of two conductor transmission lines. The first conductor is connected from the generator to the load, and the other conductor is connected to the ground at the output end of the first transmission line (as shown in Figure 5). With this configuration, the current flowing through the load is twice the current flowing through the generator, and V0 is half of the voltage V1. Therefore, the load resistance is only a quarter of the resistance seen on the generator side, resulting in a 1:4 transformer, as shown in the following equation:

The common version of the transmission line transformer is a quarter-wavelength transmission line. This topology uses a transmission line with a characteristic impedance that makes impedance matching between the input impedance and the load possible. The length of the quarter-wave transformer is determined by the operating frequency, and the bandwidth is limited to one octave around the center frequency. Consider a lossless transmission line with characteristic impedance Z0 and length L, which is connected between the input impedance Zin and the load impedance ZL (as shown in Figure 6). In order to match Zin with ZL, the characteristic impedance of the quarter-wave transmission line Z0 is determined by the following formula:

One advantage of the transmission line transformer is that there is a large capacitance and leakage inductance between the windings. Compared with the core wire type, it produces a wider operating bandwidth.

LTCC transformer

LTCC transformers are multilayer devices manufactured using ceramic-based substrates. LTCC transformers use coupled lines as transmission lines to achieve impedance conversion and signal conversion from single-ended to balanced. LTCC transformers rely on capacitive coupling, so that LTCC transformers can work at higher frequencies than ferromagnetic transformers. However, this may cause degradation of low frequency performance. One advantage of LTCC technology is the ability to manufacture small and robust transformers, which are ideal for high-reliability applications (as shown in Figure 7).

MMIC transformer

Like LTCC transformers, MMIC transformers are also made of 2D substrates with precise layered planar metallization. Generally, MMIC transformers are manufactured using spiral inductors, which are printed on a substrate with two transmission lines, and the lines are parallel. The GaAs integrated passive device process can be used to manufacture MMIC transformers (as shown in Figure 8). Precision lithography helps to achieve excellent repeatability, high frequency performance and excellent thermal efficiency.

Function and application of transformer
The different functions of the RF transformer depend on its topology:

Matching-The transformer can match two circuits with different impedances, or provide a step-up or step-down of the power supply voltage. In radio frequency circuits, impedance mismatches between two nodes can cause reduced power transmission and trouble reflections. The impedance matching transformer effectively eliminates reflections and provides maximum power transmission between the two circuit nodes (as shown in Figure 9).

Balun and unun-Balanced-unbalanced converter (Balun) is used to connect the balanced and unbalanced circuit parts. For unbalanced lines, an autotransformer (transformer) can be configured for impedance matching, that is, unun.

Bias injection and isolation-RF transformers can be designed to provide DC isolation between the primary winding and the secondary winding. This is very useful for separating RF circuits that use DC bias and are negatively affected by the DC voltage. If part of the circuit requires DC current, a dedicated RF transformer can be used to inject the current into the signal path. For example, two center-tapped transformers can inject DC bias and replace two bias tees (as shown in Figure 10).

Other functions-RF transformers can be designed to provide enhanced common-mode rejection for balanced (ie differential) circuits. Other topologies can be used as chokes to filter high frequency components from signal lines.

Summarize
RF transformers can be manufactured in a variety of methods and materials. They are configured into a variety of topologies to perform many functions in radio frequency circuits. Depending on the material, construction, and design, the RF transformer can be narrow-band or broadband, and can work at low or high frequencies. Understanding the nuances of RF transformers can help designers optimize their design by choosing the best transformer. Other articles discussing RF transformers will be published in succession.