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Circuits II EE221 Unit 8 Circuits II EE221 Unit 8

Circuits II EE221 Unit 8 - PowerPoint Presentation

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Circuits II EE221 Unit 8 - PPT Presentation

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

port parameters transmission circuit parameters port circuit transmission parameter circuits inverse sources show model independent spice terminal currents linear

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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: