Abstract: This article explains the working principle of multilayer microwave inductors, introduces their structural design, material selection and manufacturing process and their influence on the performance of inductors. It also briefly describes the application fields of multilayer microwave inductors.

1 Introduction
The rapid development of miniaturized electronic devices, represented by mobile phones and portable computers in cellular communication systems, has made miniaturization, digitization, multi-function and high power density the trend of contemporary electronic equipment development. In addition, the maturity of surface mount technology requires electronic components to develop in the direction of small, thin and light. For inductors, it means miniaturization, chip-type, integration, high frequency, high performance, high precision and high efficiency.
2 Equivalent circuit and working parameter model of multilayer microwave inductor
2.1 Equivalent circuit
As we all know, an inductor is an energy storage coil. The multilayer microwave inductor is a coil of multi-layer stacked sheet structure made by a certain process procedure, and its equivalent circuit is shown in Figure 1. In the figure, Lo is the inductance under ideal conditions; Co is the sum of parasitic capacitance; r is the DC resistance value of the inner electrode; Ro is the total equivalent resistance value of electrical loss and magnetic loss.
2.2 Working parameters of chip inductors
According to the lumped parameter model, the functional relationship between the admittance and frequency of the chip inductor is expressed as:
(1)
Formula (1) states that the main performance functions of the inductor are resistance value Z, inductance L, quality factor Q value and self-resonance frequency fSR.
a. The impedance Z value is solved by the following formula (2):
(2)
b. The inductance value L of the inductor is solved by the following formula (3):

(3)

c. The solution of the quality factor Q value is shown in formula (4):

(4)

d. The self-resonant frequency fSR is obtained by the following formula (5):
(5)
In the above formula, ω=2πf.
In the design of microwave inductors, people focus on having a higher self-resonant frequency, a stable inductance value and a high quality factor Q value when working at high frequencies; for chip inductors used in surface mounting technology, winding inductors and inductors manufactured by photolithography technology have the above three advantages, that is, multilayer chip inductors can also achieve these goals.
3 What factors affect the performance of microwave inductors
For microwave inductors used in high-frequency microwave conditions, the factors that affect their performance are relatively many and complex, and many articles have discussed this. The following only analyzes the structural design, material selection of the device and printing molding process technology.
3.1 The influence of the shape of the inductor coil on the performance of the inductor
Multilayer chip inductor coil structure. Generally designed into three shapes: rectangular, elliptical and circular.
Now, we use the three shapes of coils to enclose the same area and line width. At the same time, we use the same materials and manufacturing processes to produce three shapes of 1608-type 22nH inductors to compare the effect of shape on performance, as shown in Table 1 (the Q value and fSR value in the table are measured using HP4291 and HP8753E instruments, respectively).
Table 1 Effect of coil shape on microwave inductor performance
Shape Q (100MHz) Q (900MHz) Q (1700MHz) fSR (GHz)
Rectangular (3/4) 16.8 45 11 1.95
Elliptical (1/2) 15.6 43 33 2.45
Circular 15.1 41 47 2.85

From Table 1, we can see that the high-frequency performance of circular structure microwave inductors is significantly better than that of rectangular and elliptical structures. This is because the eddy current loss of rectangular and elliptical structures is larger at high frequencies.

3.2 The influence of high-frequency microwave material selection on inductor performance
The main material used in multilayer chip inductors is ceramic. Due to the limitation of low-temperature co-firing process, high-frequency microwave ceramic materials that can be co-fired with silver are basically selected. The performance of the material used has a great influence on the performance of the chip inductor, among which the most important influence is the dielectric constant ε of the material and the loss factor tanδ of the material.
Table 2 lists the performance of 1608 type 56nH inductors made of two materials. The table lists the fSR and quality factor Q value. L and Q values ​​are measured by HP4291 tester, and fSR is measured by HP8753E.
From the data in Table 2, we can see that the performance of the material has a great influence on the performance of the microwave inductor. For example, a small dielectric constant of the material can reduce the parasitic capacitance of the inductor and increase the self-resonance frequency; and a small loss factor tanδ of the material can reduce the electromagnetic loss of the inductor, especially at microwave frequencies.
3.3 The influence of printed circuit technology on the performance of microwave inductors
The printed circuit technology has the most obvious influence on the quality factor Q value in the performance of microwave inductors. However, we found that the printed circuit process factors that affect the performance of the inductor mainly occur in the actual operation during the production process. Under high frequency conditions, the quality of the printed electrode has a greater impact on the Q value. If the electrode printed during the production process is round and full, the Q value at high frequency will be significantly improved, and the self-resonant frequency can be increased to a certain extent. In addition, the number of printings also has a great impact on the performance of microwave inductors. Because increasing the number of printings can increase the thickness of the lines and reduce the resistance value of the inductor, thereby improving the quality factor Q value of the product. However, in the actual production process, increasing the number of printings is limited, and generally only 2 to 3 printings are performed.
We noticed that the printed circuit process and the materials used for the internal electrodes have a great relationship with the silk screen, machinery and equipment used in production, and the skill level of the operator. The production process must have suitable tools and equipment as well as careful control to ensure the excellent performance of the product.
In the above, we have conducted a multi-faceted theoretical analysis of the factors that affect the performance of multilayer chip microwave inductors, and made necessary measurement comparisons, so as to select a more reasonable design scheme, microwave high-frequency ceramic materials with better performance, and suitable manufacturing process technology, and produce a series of microwave inductors with excellent performance, such as the 1608 type 10nH inductor, whose self-resonant frequency fSR exceeds 6GHz. Table 3 lists the performance comparison of the 1608 type 22nH microwave inductor designed and produced by different methods, the inductor produced by Panasonic using photolithography, and the traditional winding type chip inductor.
Table 3 Performance comparison of 1608/22nH inductors produced by different methods
Inductor type Q(100MHz) Q(900MHz) Q(1700MH) fSR/GHzPhotolithography
inductor 16 46 54 4.05Wire
wound chip inductor 25 70 69 3.60Traditional
multilayer inductor 16 44 29 2.50Multilayer
inductor in this question 15 42 56 4.60

From Table 3, we can see that the multilayer microwave inductor designed and produced in this project has reached the performance level of Panasonic's photolithography inductor, and its high-frequency performance is even better. If the process technology is further improved and optimized, its performance can be further improved.
4 Application of multilayer microwave inductors
At present, electronic products in the microwave field are constantly emerging, so the application of microwave inductors is becoming more and more extensive. For example, microwave inductors have been widely used in the radio frequency circuits of communication products such as CDMA, TDMA, PHS, and GSM mobile phones; they are also very common in wireless network cards, Bluetooth modules, computer communications, power amplifier modules, radar detection fields, etc. Figures 2, 3, and 4 are application examples of microwave inductors in VCO resonant circuits, PA circuits, and filter circuits. Their functions are resonance, impedance matching, and filtering, respectively.
5 Summary
The coil structure shape of the microwave inductor has a great influence on its performance. The circular structure of the microwave inductor is conducive to improving the microwave performance of the inductor.
The selection of laminated materials for microwave inductors also has a great influence on their performance. The smaller the dielectric constant ε and loss factor tanδ of the material, the more beneficial it is to improve the microwave performance of the inductor.
Printed circuit process technology has a great influence on the microwave performance of the inductor, so it must be strictly controlled in the actual production process, and excellent tools and manufacturing equipment must be provided.

References
[1] Shuml Kumagal, etc. TDK Corporation, United States Patent [P] 2000.11
[2] Osamu Takahashi, etc. Taiyo Yuden Co., Ltd, United States Patent [P] 2001.11
[3] Electronic Components Application 2003.8