Any CPL is modeled with a current source in parallel with negative resistance. How do we evaluate the negative resistance, if we know the constant power consumed by the load?
Hi Yugeshwar,
A general approach would be to write the basic relations and derive it mathematically, as discussed further, but please be sure that the equations written below are applicable for your specific application.
The impedance of a constant power load varies with the bias point/Quiescent point. So we attempt to find out small signal impedance assuming a Quiescent point (Vo, Io).
Basic relationship of constant power load:
V * I = constant. --> eqn.1
What we want to estimate is:
∂V / ∂I = ???
We can consider differentiating eqn.1 now, with respect to current.
=> (∂V / ∂I) * I + V = 0
=> ∂V / ∂I = -V / I
Since the impedance depends on the set-point, we evaluate its value at a specific point of operation.
=> ∂V / ∂I = - Vo / Io.
Hope this helps. :)
The conductance is equal to G=P/V2 from P=V2/R
For ohmic load, the constant load power known comes from the constant voltage supplied to it. The load is varied according to the supply voltage. Thus, G found is a constant.
For non-ohmic load, the resistance varies according to the VI characteristic curve of the material load used. So is the conductance of the circuit. Thus, the G found varies with the current in the circuit, with constant power loading.
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