Introductory LTI tf object & ABCD-Network Parameter

(Uses Matlab): tf

ABCD transmission parameter is ideal for cascaded 2-port system. It is simple almost direct calculation for forward or reverse mixed voltage or current transfer functions.

ABCD parameter for a 2-Port Network Transmission Matrix is defined as shown.

Input port 1 and Output port 2 voltages and currents are related throught the parameters: A,B,C and D in matrix form as follow,

A and C is derived by "open-circuited" port 2. B and D derived by "short-circuited" port 2 as demonstrated below.

Observations:

It is now easy to see derivation of the following mixed transfer functions:

V2 / V1 = 1 / A	Forward voltage transfer function
I2 / I1 = -1 / D	Forward current transfer function
V2 / I1 = 1 / C	Forward voltage-current transfer function
V1 / I1 = A / C	Input driving point impedance
I1 / I2 = C	Reverse transconductance

etc...

ABCD-parameter for a SERIES arm with impedance Z,

ABCD-parameter for a SHUNT arm with admittance Y,

The parameter is convenient for Cascaded System, it only require knowledge of 2-by-2 matrix multiplication.

(RLC Sample):

We can enter the ABCD parameter to Matlab by using the tf LTI objects for those that contain s variables,

EDU>> R=1; L=1; C=1; %Assume R=L=C=1
EDU>> T1 = [1,R; 0,1];
EDU>> T2 = [1, tf([L,0],1); 0,1];
EDU>> T3 = [1,0; tf([C,0],1),1];
EDU>> TF = T1*T2*T3;
EDU>> V0V1=1 / TF(1,1)

The result is,
Transfer function:
1
---------------
s^2 + s + 1