Instructor Kevin D Donohue 2 Port Networks ImpedanceAdmittance Transmission and Hybird Parameters 2Port Circuits Network parameters characterize linear circuits that have both input and output terminals in terms of linear equations that describe the voltage and current relationships a ID: 756636
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Slide1
Circuits IIEE221Unit 8Instructor: Kevin D. Donohue
2 Port Networks –Impedance/Admittance, Transmission, and Hybird ParametersSlide2
2-Port CircuitsNetwork parameters characterize linear circuits that have both input and output terminals, in terms of linear equations that describe the voltage and current relationships at those terminals. This model provides critical information for understanding the effects of connecting circuits, loads, and sources together at the input and output terminals of a two-port circuit. A similar model was used when dealing with one-port circuits.Review example: Th
é
venin and Norton Equivalent Circuits:
Show that V
oc
=8 V, I
sc
= 0.08 A, and R
th
= 100Slide3
2-Port Circuits:Now take away the source from the previous example:
Why wouldn't it make sense to talk about a Th
é
venin or Norton equivalent circuit in this case?
The Th
é
venin and Norton models must be extended to describe circuit behavior at two ports.
Label the terminal voltage and currents as
v
1, i
1, v
2, and i
2 and develop a mathematical relationship to show their dependencies.Slide4
Inverse Transmission -Parameter Model: If the circuit is linear, then a general linear relationship between the terminal voltages and currents can be expressed as:
Geometrically each equation forms a planar surface over the
v
1
-
i
1
plane, therefore, only three non-colinear
points on the surface are necessary to uniquely determine a
, b,
c, d,
V2, and
I2. So if the circuit response is known for three different values of the
v1-
i1 pairs, six equations with six unknowns can be generated and solved.
This problem can be simplified by strategically setting v
1 and i
1
to zero in order to isolate unknown parameters and simplify the resulting equations. In general, if
no
independent sources
exist in
the
circuit,
then
V
2
and I2 will be 0. This will be the case for the problems considered in this unit.Slide5
ExampleDetermine the inverse transmission parameter model for the given circuit.
Show that
a =
18/5,
b=
100
,
c =
7/250 Siemens,
d=
1.Slide6
Summary Formula for Inverse Transmission Parameters:If all independent sources are deactivated, set i1 = 0 to find:
If all independent sources are deactivated, set
v
1
= 0 to find:Slide7
Equivalent Circuit for Inverse Transmission Parameter Model: If inverse transmission parameters are known, then the following circuit can be used as an equivalent circuit:
This circuit is helpful when implementing in SPICE without
knowledge or details of circuit from which parameters
were derived.Slide8
SPICE Solutions for Two-Port Parameters: By strategically selecting the constraints on port variables, the two-port parameters are
the ratios
of other port variables. Therefore:
Port variables can be constrained by attaching a zero-valued voltage or current source. The other port can be excited by a unity-valued source (or some other convenient value).
Place meters
at remaining ports to obtain values for evaluating ratios
.The two-port parameter can be found from
values determined through SPICE.
Example: Determine the SPICE commands to find the abcd
parameters for the circuit below.Slide9
SPICE Solutions for Two-Port Parameters:1) Consider setting v1=0, then
2) Excite the circuit with
i
2
=1 then
3) Use SPICE to compute
v
2
and i1
to solve for b and
d.Slide10
SPICE Solutions for Two-Port Parameters:4) Consider setting i1=0, then
5) Excite the circuit with
v
2
=1, then
6) Use SPICE compute
v
1
and i
2 to solve for a and
c.Slide11
Transmission -Parameter Model: Transmission parameters are related to the inverse transmission parameters by reversing the independent and dependent variables:
Transmission
Parameters
Inverse Transmission
ParametersSlide12
Impedance/Admittance-Parameter Model:
Impedance Parameters
Admittance ParametersSlide13
Hybrid (h)/Inverse Hybrid (g)-Parameter Model:
Hybrid Parameters
Inverse Hybrid ParametersSlide14
Relationship Between 2 Sets of Port Parameters: Since a single set of network parameters characterize the linear circuits completely at the input and output terminals, it is possible to derive other network parameters from this set. Example: Consider the
z
and
y
parameter characterization of a given circuit with no independent sources:
Show that:
Slide15
Relationship Between 2 Sets of Port Parameters: Example: Consider the abcd and h parameter characterization of a given circuit with no independent sources:
Show that:
Slide16
Terminal Currents and Voltages from Port Parameters: Once the port parameters are known, no other information from the circuit is required to determine the behavior of the currents and voltages at the terminals. Example:
Given the
z
-parameter representation of a circuit, determine the resulting terminal voltages and currents when a practical source with internal resistance
Rs
and voltage Vs is connected to the input (terminal 1) and a load
RL is connected to the output (terminal 2):
Show that: Slide17
Combinations of Two-Port Networks: Consider circuits A and B described by their abcd-parameters (assume independent sources zero).
If A and B are connected in series, show that the
abcd
parameters for the new two-port (from v1
a to v
2b) is given by: Slide18
Combinations of Two-Port Networks: Consider circuits A and B described by their y-parameters (assume independent sources zero).
If A and B are connected in parallel, show that the
y
-parameters for the new two-port (from v1
a to v
2b) is given by: