Estimating the Connection Inductance of a
The equivalent series inductance (ESL) of a capacitor is often the limiting factor of a decoupling capacitor's effectiveness. By estimating the ESL, the efficacy of a decoupling strategy can be determined. The following outlines a method by which the connection inductance of a variety of decoupling capacitors can be estimated.
Step 1: Identify the Loop
The first step in estimating the inductance of a decoupling capacitor is to identify the decoupling current loop. Two cases will be considered, decoupling capacitors on boards with power routed on traces, and decoupling capacitors on boards with power and return planes.
Step 2: Identify an Equivalent Geometry
To estimate the inductance for decoupling capacitors, the inductance of an equivalent geometry will be used. This simplification will allow us to use simple closed-form expressions to calculate the inductance.
Step 3: Estimating the parameters of the closed-form inductance calculations
Example 1: PCB Without Power Planes
Calculate the connection inductance for the capacitor connected to a device through traces as shown below. The traces are 1 mm wide. All other dimensions are shown below.
The connection inductance can be approximated with the use of the rectangular loop equation (http://www.cvel.clemson.edu/emc/new-induct/rectgl.html). The length and width of the rectangle itself is estimated from the current path shown as a red dashed line in the figure above. The length of the equivalent rectangular loop is estimated to be 8 mm plus half of the length of the triangular portion of the current loop (22 mm/2 = 11 mm). The equivalent radius of the wire, a, is 1/4th of the trace width.
Ans. Lconn = 29 nH ≈ 30 nH
Example 2: Decoupling Capacitors Connected to Power Planes
Calculate the connection inductance between a capacitor and a device assuming both are connected to power and return planes. The via diameters are 2 mm and the dip package and capacitor are approximately 3 mm above the surface of the power and return plane pair. Neglect the impedance through the power planes.
Solution:Inductance of the capacitor connection
To calculate the inductance of the decoupling capacitor, Lcap, the formula for the inductance of a 'Rectangular loop above a plane' will be used (http://www.cvel.clemson.edu/emc/new-induct/rectgl.html). The length and width of the equivalent loop for the decoupling capacitor are 10 mm and 3 mm respectively. The equivalent radius of the loop will be the 1 mm radius of the vias.
Lcap = 3.6 nH ≈ 4 nH Inductance of the DIP package connection
The inductance of the DIP package connection to the power planes, LDIP, will be calculated with the 'long rectangular loop above a plane' formula (http://www.cvel.clemson.edu/emc/new-induct/g-wire.html). The length of the loop will be 30 mm, the height of the loop will be 3 mm, and the equivalent radius will be approximated as 0.1 mm.
LDIP = 24.6 nH ≈ 25 nH
Lconn = Lcap + LDIP = 28.2 nH ≈ 28 nH
Example 3: The Inductance of a Decoupling Capacitor Loop
The figure below shows several decoupling capacitor pads on a PCB. The distance between the top layer and the power/return plane pair was 0.02"; all other measurements are shown on the figure. The inductance of the following pad designs was measured with a network analyzer and the results are summarized below.
Inductance of Case C:
(Note: Method 2 ignores the inductance due to the portion of the magnetic flux wrapping the vias. This is a reasonable estimate of the inductance due to the flux wrapping the capacitor body only. Flux wrapping the capacitor body dominates in Case A.)
Inductance of Case E: