# Microstrip Transmission Line Simulation

## Self-guided learning

This example of a microstrip transmission line contains a short description of the theory, detailed information on how to construct the model and the fully constructed model ready for you to download.

When working through the example, you may notice some small differences in your model compared to ours – this is usually simply due to the fact that you are using a different software version.

### The Physics

A microstrip is a type of transmission line that consists of a conductor fabricated on dielectric substrate with a grounded plane. It is easily miniaturized and integrated with microwave devices making it a popular choice of transmission line.

A basic schematic is shown in Fig. 1.

Figure 1: A Microstrip transmission line displaying quasi-TEM mode of propagation. The green lines represent the E-field and purple lines the H-field.

A microstrip line consists of a conductor of width W, a dielectric substrate of thickness d and permittivity εr. The presence of the dielectric (commonly thin with d << λ) concentrates the field lines in the region between the between the conductor and the ground plane, with some fraction being in the air region above the conductor, leading to quasi-TEM modes of propagation in which dispersion occurs as a function of wavelength as shown in Fig.1.

The phase velocity and propagation constant is given by:

With the effective dielectric constant, εe of the microstrip line satisfying the relation:

The more complex formulas for effective dielectric constant, characteristic impedance, surface resistivity of conductor and attenuation on the line are given in [1].

### The Model

Shown here is a two-port microstrip transmission line constructed using copper conductor on Alumina substrate in CST Studio Suite. The model is simulated in the Time Domain Solver in the frequency range of 5 – 15 GHz.

Figure 2: Model of a microstrip transmission line in CST Studio Suite.

The microstrip is designed for a characteristic impedance of 50 Ω at 10 GHz and an electrical length corresponding to a 270 degree phase delay and with E-field and H-field monitors set up at 10 GHz frequency. The boundary conditions are “magnetic” in all directions except for Ymin being “electric” to represent the ground plane. A 2 mm spacing is added in the positive Y-direction to represent the air above the dielectric for quasi-TEM mode of operation. The following parameters are of interest to this design.

 Parameter Value Description d 0.5 mm Thickness of the dielectric W 0.43 mm Width of the microstrip line l 8.65 mm Length of the transmission line SubW 10 mm Width of dielectric substrate T 0.01524 mm Thickness of copper conductor

### Discussion of Results

In Fig. 3 we see the electric and magnetic fields constitute a hybrid TE-TM wave which is characterized by the phase velocities of TEM fields in the dielectric as well as the air region above the substrate.

Figure 3: E- and H-field patterns showing quasi-TEM mode of propagation.

The Port Mode Information at 10 GHz can be found by right-clicking the port in the dialog tree and selecting “Object Information.” Fig. 4 displays the wave information for the single QTEM mode of operation.

Figure 4: Port mode information displaying at 10 GHz operating frequency.

The S-Parameter results shown in Fig. 5 confirm the 270° phase delay at 10 GHz on the line.

Figure 5: S21 Phase (unwrapped) to show phase delay on transmission line.

Frequency dependence effects and higher order modes

Because of the quasi-TEM nature of microstrip lines, the propagation constant is not a linear function of frequency. The frequency variation of the effective dielectric constant is a significant factor to be considered, especially with the introduction of higher order modes at high frequencies. A popular model for describing the frequency-dependent effect of the effective dielectric constant is given by the formula:

The description for which is specified in [1]. Despite the development of approximate closed-form formulas like the above, CAD tools provide the most accurate modeling of frequency-dependent effects on a microstrip line. To enable this feature in CST Studio Suite, enable the mode tracking feature in Solver specials and activate the Broadband option ensuring that the mode calculation frequency is set to 10 GHz. This option provides the effective dielectric constant for the microstrip line as a function of frequency as see in Fig. 6.

Figure 6: Activating mode tracking in solver settings to obtain frequency-dependent effects.

• The permittivity of the substrate affects the phase velocity of the microstrip line. Variations in phase velocity can lead to signal dispersion and delays. Change the dielectric material to see effect on phase velocity. Compare your results with analytical data.
• Changes in the width of the conductor leads to impedance mismatch. Try enlarging the width of the copper conductor to see its effect on the line impedance. Does it increase or decrease? Think of why the impedance changes by viewing the cross-section of the microstrip line as a parallel plate capacitor.

### References

[1] D.M. Pozar, Microwave Engineering, 4th Edition, John Wiley & Sons, pp. 147-153