An integrated circuit on a die is connected to external world through bond wires. Depending on the packaging or assembly technique we use, the bond wire length changes. The self or mutual inductance of the bond wire is directly proportional to length and have a great impact on the performance of RFICs.

Self inductance of a wire with rectangular cross-section is given by [1]

(1)

where is length of the wire, and are width and thickness of the cross-section of the conductor.

The self inductance of a wire with circular cross-section is given by

(2)

where is cross-section radius of the conductor.

Mutual inductance between two wires is given by

(3)

where is the distance between two wires.

If and are the self inductances of wires and , then mutual inductance between two wires is given by

where, k is magnetic coupling factor

**Rules of thumb for design calculations**:

self inductance of lead frame

self inductance of a bondwire is

Typical values of bond-wire inductance, capacitance and resistance can be found here[2]

At very high frequencies skin effect comes into effect, and resistance at high frequencies is much higher than DC resistance. The following slides[3] show the modeling results of self and mutual inductance and capacitance along with DC and AC resistance of a 1-mil bondwire.

In a multi-segment bond wire, the self-inductance of entire wire is sum of self-inductance of each segment and mutual-inductance among the segments

(4)

where is the self-inductance of segment i, and are the mutual inductance and coupling coefficient between and segments.

, currents in and segments are orthogonal

, currents in and segments are in same direction

, currents in and segments are in opposite direction

**Bond wire modeling guidelines**[4, 5]

**Bonding methods**[6]

**Fusing currents** [7]

The current carrying capability of a bond wire changes with size of the wire and material used for it. The bond pad requirement also changes with the selection bond wire size. Here is a reference with some numerical info to select bond wire size, material and bond pad[8]

Characteristic Impedance of Integrated Circuit Bond Wires [9]

## Bibliography

[1] E. B. Rosa, “Formulas and tables for the calculation of mutual and self inductance.” [Online; Accessed May 2013]. Available:

http://nvlpubs.nist.gov/nistpubs/bulletin/05/nbsbulletinv5n1p1_A2b.pdf
[2] “Mosis – bond wire electrical parameters.” [Online; Accessed May 2013]. Available:

http://www.mosis.com/pages/products/assembly/index#wire
[3] “Amkor’s document library.” [Online; Accessed May 2013]. Available:

http://www.amkor.com/go/packaging/document-library
[4] “Eia/jedec standard no-59.”

[5] “Agilent technologies:accurate interconnect analysis.” [Online; Accessed May 2013]. Available:

http://www.home.agilent.com/agilent/editorial.jspx?ckey=1465325&id=1465325&lc=eng&cc=IN
[6] “Rogers: aiming for the perfect wire bond.” [Online; Accessed May 2013]. Available:

http://mwexpert.typepad.com/rog_blog/2011/09/aiming-for-the-perfect-wire-bond.html
[7]

S. Knecht, B. Gonzalez, and K. Sieber, “Fusing current of short aluminum bond wire,” in

Thermal phenomena in electronic systems, 1996. i-therm v., inter-society conference on, 1996, pp. 329-333.

[8] “Signal pro: current carrying capacity of bonding wire.” [Online; Accessed May 2013]. Available:

http://www.signalpro.biz/wiresize1.htm
[9]

R. H. Caverly, “Characteristic impedance of integrated circuit bond wires (short paper),”

Microwave theory and techniques, ieee transactions on, vol. 34, iss. 9, pp. 982-984, 1986.