Transmission lines [Jaeyoung Wiki]

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====== Transmission lines ======


===== Wavelength of EM waves in a vacuum =====


$$\lambda=\frac{c}{f}$$

where $c$ is the speed of EM waves and $f$ is the frequency.

===== Wavelength of EM waves in a medium =====


The speed of EM waves depends on the substrate material because it takes time for the charges in the substrate to align to the waves.

$$D_k=\epsilon_r$$



$$\lambda=\frac{c}{f\sqrt{\epsilon_{eff}}}$$

If the length of an interconnect is greater than $\frac{1}{20}$ of the wavelength, RF behaviors must be considered.

===== Striplines and microstrips =====

Striplines are sandwiched between two copper reference planes.

Microstrips are placed above a copper reference plane and a dielectric.

Embedded microstrips are microstrips covered by a solder mask.

In a stripline, the fields exist between the stripline and the reference planes over and under the stripline. Therefore, the EM waves that travel along a stripline are TEM waves.

In a microstrip, the fields mostly exist between the strip and the reference plane below, but some of the fields fringe out into the air. Therefore, the waves are quasi-TEM waves.

===== Transmission lines =====

Transmission lines are designed to carry as much of the input power as possible to the load.

=== Characteristic impedance ===

$$Z_0=\sqrt{\frac{R+j\omega L}{G+j\omega C}} \approx \sqrt{\frac{L}{C}}$$

where R is the resistance in series with the inductance L, and G is the conductance in series with the capacitance C.

=== Loss ===

$$\alpha_t=\alpha_c+\alpha_d+\alpha_r$$

where $\alpha_t$ is total loss, $\alpha_c$ is the conductor loss (due to resistance R), $\alpha_d$ is the dielectric loss (due to conductance G), and $\alpha_r$ is the radiation loss due to radiation propagating into space (in microstrips).

== Loss parameters in stripline ==

$$\alpha_d = 27.3 \sqrt{\epsilon_r} \frac{tan\delta} {\lambda}$$
$$\delta = D_f$$


=== References ===
  * [[https://www.youtube.com/watch?v=bVdwu1IoX4k]]
  * [[https://www.youtube.com/watch?v=GuJVkZgAloI]]