Intel 820E manual More Details and Insight, Textbook Timing Equations

Intel® 820E Chipset

R

3.4.More Details and Insight

3.4.1.Textbook Timing Equations

The “textbook” equations used to calculate the propagation rate of a PCB are the basis for spreadsheet calculations of timing margin based on the component parameters. These equations are as follows:

Equation 9. Intrinsic Impedance
Z0 = (L0 / C0)½	(Ω )

Equation 10. Stripline Intrinsic Propagation Speed

S0_STRIPLINE = 1.017 × ε r½ (ns/ft)

Equation 11. Microstrip Intrinsic Propagation Speed

S0_MICROSTRIP = 1.017 × (0.475 × ε r + 0.67)½		(ns/ft)
Equation 12. Effective Propagation Speed
SEFF = S0 × (1 + (CD / C0))½		(ns/ft)
Equation 13.	Effective Impedance
ZEFF = Z0 / (1 + (CD / C0))½		(Ω )
Equation 14.	Distributed Trace Capacitance
C0 = S0 / Z0		(pF/ft)
Equation 15.	Distributed Trace Inductance
L0 = 12 × Z0 × S0		(nH/ft)

The symbols for Equations 8–15 are as follows:

•	S0	Speed (in ns/ft) of the signal on an unloaded PCB. This is referred to as the board propagation
	constant.
•	S0_MICROSTRIP, S0_STRIPLINE			Speed (in ns/ft) of the signal on an unloaded microstrip or stripline
	trace on the PCB
•	Z0	Intrinsic impedance (in Ω) of the line. This is a function of the dielectric constant (ε r), line
	width, line height, and line space from the plane(s). The equations for Z0 are not included in this
	document. For these equations, see the MECL System Design Handbook by William R. Blood, Jr.
•	C0	Distributed trace capacitance of the network (in pF/ft)
•	L0	Distributed trace inductance of the network (in nH/ft)
•	CD	Sum of the capacitance of all devices and stubs, divided by the length of the network’s trunk,
	not including the portion connecting the end agents to the termination resistors (in pF/ft)
•	SEFF and ZEFF		Effective propagation constant and impedance of the PCB when the board is
	“loaded” with the components

Design Guide 155