If testing can demonstrate that operator’s resistance path is reliable, it might be OK, but it is certainly not best practice. Alligator clip attached to dissipative mat is not recommended per ESD Handbook ESD TR20.20 wrist strap section 22.214.171.124.2 Wrist Strap Ground Cord: “The groundable end of the cord is most often equipped with a banana plug and a mating alligator clip. Any electrical connector that could be attached to ground would be acceptable as long as it was mechanically durable. The preferred grounding point for the groundable end of the cord would be a common point ground as defined in ANSI/ESD S6.1.
NOTE: Many wrist strap users clip the wrist cord to the edge of an ESD protective mat. This process is not recommended as it can increase the total system resistance to ground to over the 35-megohm limit required in ANSI/ESD S20.20.”
Here’s additional pertinent information:
“Wrist strap ground cords must be connected to a groundable point or an equipotential bonding point. Do not connect to a snap on a dissipative mat unless it is the groundable point for the mat. Do not clip a wrist strap to the edge of a dissipative mat.” [ESD Handbook ESD TR20.20 wrist strap section 126.96.36.199 Wrist Strap Summary]
Due to it lower retention force than installed in a banana jack, attaching a wrist strap cord to a mat with an alligator clip is problematic.
“The first step in ensuring that everything in an EPA [ESD protected area] is at the same electrical potential is to ground all conductive components of the work area (i.e., worksurfaces, people, equipment, etc.) to the same electrical ground point. This point is called the common point ground and is defined by ANSI/ESD S6.1 as ‘a system or method for connecting two or more grounding conductors to the same electrical potential.’ …The next step in completing the ground circuit is to connect the common point ground to the AC equipment ground or an auxiliary ground, as defined in ANSI/ESD S6.1.” [ESD Handbook ESD TR20.20 grounding section 5.1.3 Basic Grounding Requirements]
“The primary method of static charge control is direct connection to ground for conductors, static dissipative materials, and personnel.” [ESD Handbook ESD TR20.20 section 5.3.6]
Per JESD625-A section 7.6 ESD ground connections “Firm fitting connecting devices such as metallic crimps, snaps and banana plugs shall be connected to designated ground points. Wire splices should be crimped or soldered. Use of alligator clips is not recommended.”
Per JESD625-A section 7.3 ESD protected workstation ESD ground “The design and construction of the grounded ESD protected workstation and associated equipment shall ensure that all external parts, surfaces, and shields of electrical equipment and power tools are at ground potential at all times. Each ESD workstation shall be individually connected to the ESD ground. When more than one ESD worksurface is used at a workstation, each surface shall be individually connected to the ESD ground.”
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