### I. Introduction

### II. 5G mmWave Module for Mobile Devices

*λ*

*/2) is less than 5 mm in the free space. It is feasible to integrate antennas and RFICs in a single package (module chip) due to an antenna size comparable to the RFICs.*

_{g}### III. A TEM Mode Waveguide for Mobile 5G mmWave Module Applications

*Z*

_{0}), loss (

*α*), cutoff frequency (

*f*

*), and via pitch (*

_{c}*p*) of the rectangular coaxial waveguide, are discussed.

### 1. Impedance

*L*and

*C*are the inductance (

*L*/

*m*) and capacitance (

*F*/

*m*) per unit length, respectively,

*v*

*is the phase velocity in the given waveguide structure and material, and*

_{p}*ɛ*

*is the effective dielectric constant of the dielectric material. The characteristic impedance and phase velocity of a TEM mode waveguide can be expressed as Eqs. (1) and (2).*

_{eff}*C*is a dominant parameter of the characteristic impedance value. Fig. 3 shows a cross-section of the rectangular coaxial waveguide. A rectangular signal line is located at the center of the waveguide. The impedance of the waveguide can be calculated by computing the total capacitance (

*C*

*) per unit length, which is obtained through the conformal mapping of the field distribution from a cylindrical to a rectangular geometry [7]. The*

_{t}*C*

*value includes the corner capacitance values per unit length (*

_{t}*C*

_{f}_{1}and

*C*

_{f}_{2}), in addition to the capacitance per unit length of the conventional circular coaxial waveguide [8, 9].

*C*

_{f}_{1}and

*C*

_{f}_{2}can be expressed as Eqs. (3) and (4), and the resulting

*C*

*and*

_{t}*Z*

*are also shown in Eqs. (5) and (6).*

_{0}*w*) for each rectangular coaxial waveguide in the vacuum core (Fig. 4(a)) and filled with Teflon (Fig. 4(b)). For the calculation, all the metals were set to copper (

*σ*= 5.96 × 10

^{7}Ω/m), and the electrical properties of Teflon were defined as

*ɛ*

*= 2.0 and tan δ = 0.001. The simulated and formulated results agree well. A designed practical 50 Ω rectangular coaxial waveguide has*

_{r}*w*

*= 68 μm,*

_{g}*w*= 120 μm,

*t*

*= 42 μm, and*

_{g}*t*= 16 μm.

### 2. Cutoff Frequency

_{01}or TE

_{10}. The cutoff frequency (

*f*

*) of the rectangular coaxial waveguide’s TE*

_{c}_{10}mode can be expressed by the transcendental equation, and it can be calculated by Eqs. (7)–(9) [10]. For the TE

_{01}mode, the design parameters should be modified as

*t*

*→*

_{g}*wg*,

*w*→

*t*,

*w*

*→*

_{g}*t*

*, and*

_{g}*t*→

*w*.

### 3. Loss

*α*

*) of a TEM mode rectangular coaxial waveguide can be divided into three parts as, shown in (10): radiation (leakage) loss (*

_{t}*α*

*), dielectric loss (*

_{l}*α*

*), and conductor loss (*

_{d}*α*

*).*

_{c}##### (12)

*R*

*is the sheet resistance of the metal (*

_{s}*R*

*= 1/(*

_{s}*δ*

*·*

_{s}*σ*)),

*η*is the intrinsic impedance

*Z*

*is the characteristic impedance of the transmission line*

_{0}### 4. Via Pitch

*d*) and pitch (

*p*) of the vias. The electromagnetic bandgap (EBG) should be considered because the via wall is a periodic structure [12, 13]. From (13), the first visible bandgap occurs when

*n*= 1.

*λ*

_{g}/20 when the design and fabrication margins are considered. It should be noted that the maximum via pitch is a hard bound because the bandgap effect should be prevented. The minimum via pitch is a soft bound that varies depending on the manufacturing capability and process. Fig. 7 graphically presents the via design guide when the via pitch (

*p*) and diameter (

*d*) are given. The via diameter and pitch are normalized by the guided wavelength. The upper half plane is a reasonable design area, as the via diameter cannot be larger than the via pitch.

### 5. Radiation

*μ*V/m of electric field intensity (

**E**) at a point 3-m away from the device under test (DUT).

*r*) from the DUT is 3 m, the electromagnetic field having a frequency higher than 10 GHz can be considered the far field at the measurement point. It is reasonable to assume the radiated EM field is a TEM wave. In the spherical coordinates, the relationship between the electric field (

**E**) and the magnetic field (

**H**) intensities satisfies the following conditions.

*P*

*) can be obtained as follows [15].*

_{rad}##### (18)

*η*

*) of the free space is 120*

_{0}*π*, the radiated E-field strength, and the total radiated power are summarized as follows.

*E*

*|) less than the FCC requirement of 500 μV/m at a distance of 3 m from the DUT. It should be noted that the FCC’s radiation regulation can be verified at a distance of less than 3 m from the DUT by evaluating (21) at any distance.*

_{θ}