It is quite complex to research equivalent circuit included the controlled sources

it is not only related to control quantity of the controlled source whether it is in internal circuit or exterior circuit

but also is related to the equivalented circuit whether it includes the control quantity of the exterior controlled sources. This article carries on the analysis that the equivalented circuit's control quantity is in the exterior circuit and control quantity of exterior circuit's the controlled source is not included in the equivalented circuit

and gives equivalent circuit's form for this kind of circuit

and carries on the proof and the confirmation.