Fully Charged: Transmission Line Rules of Thumb

Sunday, February 12, 2017

Transmission Line Rules of Thumb

Rule of Thumb for Applying Transmission Line Theory

Propagation delay of a signal through a printed circuit conductor is roughly $t_{prop}=\frac{\sqrt{\epsilon _r}}{c}$ where $\epsilon _r$ is the relative permittivity (dielectric constant) of the insulator and $c$ is the speed of light ( $3 \times 10^8$ m/s or $1.18 \times 10^{10}$ in/s )

Dielectric Medium	Propagation Delay	Unit	Dielectric Constant
Air	85	ps/in	1.0
FR4 (outer)	140-180	ps/in	2.8-4.5
FR4 (inner)	180	ps/in	4.5

Rising Edge Length $l=\frac{Rise Time}{Delay}$

Rule of thumb for transmission lines (per Howard Johnson's High-Speed Digital Design) is that lengths $< \frac{l}{6}$ behave as "lumped" circuits

Medium	Dielectric Constant	Propagation Delay (ps/in)	Risetime (ns)	Rising Edge Length (in)	Lumped Rule of Thumb (in)
FR4 (inner)	4.5	180	1	5.563	0.927
			5	27.813	4.635
			10	55.626	9.271
			1000	5562.573	927.096

Thus, in general, for risetimes >1ns in inner FR4 traces, traces <1" do not need to be considered transmission lines.

Reflection Coefficient

The reflection coefficient of an impedance discontinuity is $\Gamma = \frac{V_{reflected}}{V_{incident}}$

$\Gamma = \frac{Z_L-Z_S}{Z_L+Z_S}$ where $Z_L$ is the load impedance and $Z_S$ is the source impedance.

[Explanation]

Therefore for $Z_L=Z_S=Z_0$ , $\Gamma =0$ (no reflection for balanced impedance)

For $Z_L=\infty$ (open circuit), $\Gamma = 1$ (additive/positive reflection)

For $Z_L=0$ (short circuit), $\Gamma = -1$ (negative reflection)

BOUNCE is a very cool tool to visualize the impact of transmission line discontinuities on a travelling voltage pulse.

See these notes for further discussion.

Fully Charged

Sunday, February 12, 2017

Transmission Line Rules of Thumb

Rule of Thumb for Applying Transmission Line Theory

Reflection Coefficient

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