Environmental Engineering Reference
In-Depth Information
By neglecting and with respect to inside the square brackets of
the denominator, the equivalent capacitance can be approximated to
As expected, (2.46) shows a reduction of the equivalent capacitance seen at
node Y. In reality, this
bootstrapping
effect is predicted by the well-known
Miller theorem for those cases where the voltage gain across the capacitor
tends to be unitary.
A more accurate evaluation of the zeros can be achieved by using the
nodal admittance matrix as proposed in [R85]. The nodal admittance matrix
can be written by inspection of the circuit in Fig. 2.12b in terms of the
Laplace transform variable
s.
The device under consideration is identified by
the four terminals X, Y, Z and B, where node B is connected to the reference
node. Hence, the nodal admittance matrix can be defined as
Evaluating the admittance terms inside the matrix [DK69] and neglecting
resistance
and transconductance
we get
where terms represent the conductance (i.e. the inverse of the resistance
of the
i
-th element. Of course, elements and can be simply included
in the matrix but at the cost of more complex expressions. Neglecting term
with respect to
the nodal admittance matrix can be rewritten as
As known from linear circuit theory, the transfer function numerator
polynomial is an invariant characteristic of a circuit, while the denominator
