3 stacked mosfets equal to one longer mosfet

[jaydnul]

In the below diagram, where would the backgates of the 3 mosfets have to be placed in order for this to be true and equal to one device with lenght 3um? I imagine they have to connected to there own respective sources because if they were all connected to ground, then the top device would have a threshold voltage much different than the single 3um device.

 

[AMS012]

Three device stack will never match a single longer device exactly. The moment you connect the bulk to the respective source nodes, Vt problem might go away. But the large bulk (deep nwell to psub) cap loads the source nodes killing the output impedance. So, you can never match them completely, you can only match them to an extent as long as it meets your requirement.