6. Two Port Networks

• Two port networks are a useful tool for describing idealized components. The basic device schematics are simple, but each set of parameters views the device differently.

• The basic device is seen below, along with the various parameter sets,



6.1 Parameter Values

• obviously some of the parameters are impedance, while others are admittance. They can be easily determined by setting other parameters to zero, and measuring relevant voltages/currents.

6.1.1 z-Parameters (impedance)

• The values are as below,


• The equivalent circuit for the z-parameters is shown below,


6.1.2 y-Parameters (admittance)

6.1.3 a-Parameters (transmission)

6.1.4 b-Parameters (transmission)

6.1.5 h-Parameters (hybrid)

6.1.6 g- Parameters (hybrid)

6.2 Properties

• If one set of parameters is known, other parameters can be found using simple conversions. This can help when one set of parameters is needed, but cannot be measured directly.

• Simple cases of networks are reciprocal and symmetrical. When a network is neither of these, then it typically has active components, dependent sources, etc.

6.2.1 Reciprocal Networks

• If a voltage is applied at one port, the short circuit current out the other port will be the same, regardless of which side the voltage is applied to.

• Reciprocal networks are only possible when passive elements are used.

• The parameters that indicate a reciprocal networks are,


• With any reciprocal network we only need to find 3 of the four parameters, the last can be determined mathematically.

6.2.2 Symmetrical Networks

• This is a special case of the reciprocal network where the input and output parameters are identical.

• In addition to the reciprocal constraints, we must also consider,


• Only two of these parameters need to be found to find the other two parameters.

6.3 Connecting Networks

• When connecting networks, various parameters add ease.

6.3.1 Cascade

• The a parameters can be multiplied


6.3.2 Series

• With this type of connection the parameters are added,


6.3.3 Parallel

• Here the devices are connected,


6.3.4 Series-Parallel

6.3.5 Parallel-Series