Designing a Qi-Compliant Receiver Coil for Wireless Power Systems

Overview

The implementation of the Wireless Power Consortium (WPC) Qi standard enables wireless charging for a variety of end applications. The size and/or power requirements of the receiver (Rx) coil for each application may be different. The Rx coil is a key component to a successful and efficient Qi standard Rx design. There are also many design methods and balancing trade-offs to consider. Therefore, designers must carefully choose their methods and proceed methodically when implementing a solution. This article will discuss in detail some of the technical issues that need to be addressed to achieve a successful Rx coil design. The article covers the Qi standard system model of the basic transformer, Rx coil measurements and system-level impact, and some methods to check whether a design can work successfully. It is assumed that the reader of this article has a basic understanding of the Qi standard inductive power system. For background information, please refer to Reference 2.

Transformer Qi Standard System

For many near-field wireless power systems, such as those specified by WPC, the behavior of magnetic power transfer can be modeled using a simple transformer. Conventional transformers are typically a single physical structure with two windings wrapped around a core material that has a much higher magnetic permeability than air (Figure 1). Because conventional transformers use highly permeable materials to transfer magnetic flux, most (but not all) of the magnetic flux generated by one coil couples to the other coil. The degree of coupling can be measured by a parameter called the coupling coefficient, which is represented by k (ranging from 0 to 1).

Figure 1 A physical structure of a traditional transformer

3 parameters define a two-coil transformer:

L11 is the self-inductance of coil 1.

L22 is the self-inductance of coil 2.

L12 is the mutual inductance of coils 1 and 2.

The coupling coefficient between the two coils can be expressed as:

Then, using the coupled inductor shown in Figure 2, the ideal transformer can be modeled.

Using the relationship between the voltage and current of the inductor, the node equation of the double-coil transformer can be obtained:

To facilitate circuit analysis, the model shown in Figure 2 can be represented by the common name of the cantilever model, as shown in Figure 3. The magnetic coupling and mutual inductance here are simplified to leakage inductance and magnetizing inductance. In this way, through a circuit implementation, we can understand the physical properties of this coupling. For an ideal transformer, we can use the following equation to calculate its turns ratio:

Figure 2 Ideal model of traditional transformer

Figure 3 Cantilever model of traditional transformer

In a strongly coupled system, leakage inductance is a small percentage of the magnetizing inductance, so it can be ignored in a first approximation. In addition to the high coupling, the series resonant capacitor used in the Qi standard system also reduces the effect of leakage inductance. Therefore, the first approximation of the voltage gain from the primary to the secondary is:

The transformer of the Qi standard system consists of two independent physical devices: the transmitter (Tx) and the receiver (Rx), each with an isolated coil. When the Tx and Rx are placed close to each other, they form a coupled inductance relationship, which can be simply modeled as a two-coil transformer using an air core (see Figure 4). The shielding material at both ends acts as a flux short circuit. This allows the magnetic field lines (flux) to exist between the two coils. Figure 5 shows a 2D simulation of the magnetic field lines during typical operation.

Figure 4: A simple inductively coupled transformer using an air core

Figure 5 Example of magnetic field lines between two mutually coupled coils

For a typical Qi standard system, the coupling factor (k) is much lower than when using a traditional transformer. The coupling factor for a traditional transformer ranges from 0.95 to 0.99. For example, 95% to 99% of the magnetic flux is coupled to the secondary coil; however, for a Qi standard system, the coupling factor ranges from 0.2 to 0.7, or 20% to 70%. In most cases, the Qi standard uses a series resonant capacitor on Tx and Rx to alleviate this low coupling problem. This capacitor can compensate for the resonant leakage inductance.

Electrical requirements for Rx coils

In some Rx ICs, the target voltage of the dynamically controlled rectifier varies with the output current. Since the rectifier output dictates the voltage gain required by the transformer, the maximum output voltage of the rectifier must be considered in addition to the output load or output power requirements. As shown in Figure 6, at 1A load, the rectifier output range is ~7 to 5 V, which determines the required voltage gain of the transformer. It is important to ensure that the Rx coil can achieve the voltage level required by the Rx IC when fine-tuning according to the WPC specification (see the "Rx Coil Fine-tuning" section later in this article).

To facilitate understanding of the performance of the Rx coil inductance, in addition to the recommended measurement methods for L′S and Ls, other parameters are defined in Table 2. When the measurement involves a battery, the battery should be placed in the same orientation/position as it will be in the final system. Note that the materials used in the final industrial design may also affect the final inductance measurement results. Therefore, when configuring the tuning circuit, the final measurement should use all components of the final mobile device industrial design. The measurements listed in Table 1 are used to shield and verify possible Rx coils.

Table 2 Rx coil inductance parameters that need to be measured during development

Table 3 summarizes the measured inductance of an acceptable coil design and the resonant frequency using fixed series and parallel resonant capacitors. Here, L′S_b is used for capacitance calculations. (See the next subsection, “Rx Coil Tuning”, for details.) Note that they may vary linearly as a percentage of L′S and can be used as a reference for prototype coil acceptance.

Table 3 Measured inductance of example coils

Rx Coil Tuning

The simplified Rx coil network consists of a series resonant capacitor C1 and a parallel resonant capacitor C2. These two capacitors form a dual resonant circuit using the Rx coil (see Figure 9), which must be properly sized according to the WPC specification.

Figure 9 Dual resonant circuit of Rx coil

To calculate C1, L′S, the resonant frequency needs to be 100 kHz:

To calculate C2, Ls, the secondary resonant frequency needs to be 1.0 MHz. This calculation requires first determining C1 and then substituting it into Equation 7 to calculate:

Finally, the quality factor must be greater than 77, which is calculated as follows:

Where R is the DC resistance of the coil.

Load Line Analysis of the Rx Coil

When selecting an Rx coil, designers need to understand the transformer characteristics by comparing the primary coil and the Rx coil through load line analysis (IV curve). This analysis can obtain two important conditions of the Qi standard system: (1) operating point characteristics; (2) transient response. We will discuss this in detail later.

Working point characteristics

Figure 10 Load line analysis test setup

Figure 10 shows an example test configuration for load line analysis, with the following parameter definitions:

VIN is an AC power source capable of operating at 19V peak to peak.

CP is the main series resonant capacitor (100 nF for A1 type coil).

LP is the primary coil (A1 type).

LS is the secondary coil.

C1 is the series resonant capacitor used for the Rx coil under test.

C2 is the parallel resonant capacitor used for the Rx coil under test.

CB is the bulk capacitor of the diode bridge. At 25V, CB should be at least 10 µF.

V is the Kelvin connection voltmeter.

A is a series ammeter.

RL is the relative load.

The diode bridge should consist of a full bridge or synchronous half bridge Schottky diodes with a low side n-type MOSFET and a high side Schottky. There are three test procedures for the analysis:

1. Provide 19V AC signal to LP, starting at 200kHz.

2. Measure the resulting rectified voltage from no load to the expected full load range.

3. Reduce the frequency and repeat the first two steps until the frequency drops to 110kHz.

Figure 11 shows an example of a load line analysis. The figure shows that different load and rectifier conditions produce different operating frequencies. For example, at 1A, the dynamic rectifier target is 5.15V. Therefore, the operating frequency is between 150kHz and 160kHz, which is an acceptable operating point. If the operating point is outside the 110 to 205 kHz frequency range specified by the WPC, the system will not converge and will become unstable.

Figure 11 Example load line analysis results

Transient response

When performing transient analysis, there are two important points, as shown in Figure 11: (1) the rectifier voltage at the resonant frequency (175kHz); and (2) the rectifier voltage drop from no load to full load at a constant operating point.

In this case, the resonant voltage is ~5 V, which is higher than the VUVLO of the chip. Therefore, the startup of the Qi standard system is guaranteed. If the voltage is close to or lower than VUVLO at this frequency, the startup may not be possible.

If the maximum load step is 1A, then the voltage drop in this example is ~1 V at 6V for the 140-kHz load line case in Figure 11. To analyze this voltage drop, a 140-kHz load line with a 7V startup at no load is required to achieve the expected maximum load current requirement. The voltage drop is the difference between the voltages across the load line. The acceptable full load voltage at the selected operating frequency should be above 5V. If it is below 5V, the power supply output will also drop to this level. This transient response analysis is necessary due to the slow feedback response of the Qi standard system. This analysis simulates the transient characteristics that may occur when the system is not regulating the resonant transformer operating point.

Note that the coupling between the primary and secondary coils will be worse with misalignment of the Rx coils. Therefore, we recommend that the load line be analyzed multiple times with various misalignments to determine if the Rx will break down in planar space.

in conclusion

This article shows that we can use traditional transformer basic principles to simplify the design of Tx coils for wireless charging systems. However, the universality and characteristics of mobile devices also bring some unique changes to the standard magnetic design methods. Carefully reading and understanding the coil design content we introduced above can increase your chances of success on the first try. Some evaluation methods we introduced can allow you to specify and describe a custom Rx coil in a very organized way.