Controlled Impedance Design Formulas

This section is intended to be an interactive tool for calculating controlled impedance values for PCB designs. The following are examples for different configurations.

Configurations

Microstrip
Embedded Microstrip
Balanced Stripline
Dual Stripline
Coupled Stripline

Tables

Prepreg Thickness and Er Table
Core Size Thickness and Er Table
Copper Weight/Thickness Table

Microstrip Configuration

Formulas:
Zo = (87/(Er + 1.41)^0.5) * @LN(5.98 * h/(0.8 * W + t + p)) - scf
tpd = 1.017 * (0.475 * Er + 0.67)^0.5

Definitions:
Zo:	Characteristic impedance (ohms)
Er:	Dielectric constant
h:	Distance between signal line and reference plane (inches)
W:	Width of signal line (inches)
t:	Thickness of the signal line, without plating (inches)
p:	Plating thickness of outer signal layer (inches)
scf:	Soldermask correction factor (ohms)
tpd:	Signal propagation delay (nsec/ft)

Embedded Microstrip Configuration

Formulas:
Zo = 0.8 (87/(Er + 1.41)^0.5) * @LN(5.98 * h/(0.8 * W + t))
tpd = 1.017 * (Er)^0.5

Definitions:
Zo:	Characteristic impedance (ohms)
Er:	Dielectric constant
h:	Distance between signal line and reference plane (inches)
W:	Width of signal line (inches)
t:	Thickness of the signal line, without plating (inches)
tpd:	Signal propagation delay (nsec/ft)

Balanced Stripline Configuration

Formulas:
Zo = (60/(Er)^0.5) * @LN(4 * h/(0.67 * @Pl * W * (0.8 + t/W)))
tdp = 1.017 * (Er)^0.5

Definitions:
Zo:	Characteristic impedance (ohms)
Er:	Dielectric constant
h:	Distance between signal line and reference plane (inches)
W:	Width of signal line (inches)
t:	Thickness of the signal line, without plating (inches)
tpd:	Signal propagation delay (nsec/ft)

Dual Stripline Configuration

80%	75%	70%	65%	60%	55%	50%
4.00	4.14	4.28	4.41	4.55	4.69	4.83

Formulas:
Zo = 2 * T1 * T2/(T1 + T2)
T1 = (60/Er^0.5) * @LN(8 * A/(0.67 * @Pl * W * (0.8 + t/W)))
T2 = (60/Er^0.5) * @LN(8 * (A + D)/(0.67 * @Pi * W * (0.8 + t/W)))
where (2 * A) + (D) is the distance between reference planes
tpd = 1.017 * (Er)^0.5

Definitions:
Zo:	Characteristic impedance (ohms)
Er:	Dielectric constant
A:	Distance from signal layer to nearest plane (inch)
D:	Distance between signal layers (inches)
W:	Width of signal line (inches)
t:	Thickness of the signal line, without plating (inches)
tpd:	Signal propagation delay (nsec/ft)
T1:	T1 = (60/Er^0.5) * @LN(8 * A/(0.67 * @Pl * W * (0.8 + t/W)))
T2:	T2 = (60/Er^0.5) * @LN(8 * (A + D)/(0.67 * @Pl * W * (0.8 + t/W))) 3.06087 0 1.369565 4.430435

Coupled Stripline Configuration

Formulas:
Zoe = 30 * Pl * (b-t)/(Er * (W + (b * Cf/(2 * Pl)) * Ae))
Zoo = 30 * Pl * (b-t)/(Er * (W + (b * Cf/(2 * Pl)) * Ao))

Definitions:
Zdif:	2 times Zoo
Zoe:	Even Mode Differential Impedance (ohms)
Zoo:	Odd Mode Differential Impedance (ohms)
Er:	Dielectric constant
b:	Distance between power planes (inches)
W:	Width of signal line (inches)
t:	Thickness of the signal line, without plating (inches)
S:	Distance between power planes (inches)
cf:	Cf=((2 * ln(((2 * b) - t) / (b-t))) - (t/b) * ln((t(2b-t) / (b-t)^2)
theta:	theta = Pl S / (2 b)
Ae:	Ae=1 + (ln(1 + tanh theta) / ln 2)
Ao:	Ao = 1 + (ln(1 + coth theta) / ln 2)

Prepreg Thickness and Er Table

Preg Number:	Thickness:	Er:
106	0.0015	4.2-4.3
1080	0.0025	4.2-4.3
2113	0.0035	4.2-4.3
7628	0.007	4.2-4.3

Core Size Thickness and Er Table

Core Size	Er
0.006	4.2-4.3
0.008	4.2-4.3
0.014	4.2-4.3
0.028	4.2-4.3

Copper Weight/Thickness Table

Weight	Thickness
1/2 oz.	0.0007
1 oz.	0.0014
2 oz.	0.0028

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