for engineering student

2.  A two-port network is an electrical network
circuit or device with two pairs of terminals to
connect to external circuits. Two terminals
constitute a port if the currents applied to them
satisfy the essential requirement known as the
port condition.The electric current entering one
terminal must equal the current emerging from
the other terminal on the same port.
INTRODUCTION

3.  A terminal is the point at which a conductor from
an electrical component, device or network
comes to an end and provides a point of
connection to external circuits.
 All electric cell have two terminals. The first is the
positive terminal and the second is the negative
terminal. The positive terminal looks like a metal
cap and the negative terminal looks like a metal
disc. The current flows from the positive terminal,
and out through the negative terminal, the
current flow (positive (+) to negative (-) flow).
TERMINAL

4.  A port is a pair of terminals connecting an electrical
network or circuit to an external circuit, a point of
entry or exit for electrical energy. A port consists of
two nodes (terminals) connected to an outside
circuit, that meets the port. The currents flowing into
the two nodes must be equal and opposite.
PORT
Network N has a port
connecting it to an external
circuit. The port meets the port
condition because the current I
entering one terminal of the port
is equal to the current exiting

5. ONE PORT NETWORK
 A port is combination of two terminals on the
same side of network. Thus a terminal pair is
nothing but a port as shown in fig .
 A network having only one terminal pair or port is
called one port network.
 One port network can be represented as below.
R
1I
1V
+
-
+
-

1I
1V

6. NETWORK FUNCTION FOR
ONE PORT NETWORK
 Voltage and current for the one port linear network as
shown in fig.
 As there is one port , voltage and current measured at
same port. thus for one port network only driving
function can be defined as below.
 Hear V is applied voltage.
DRIVING POINT IMPEDANCE FUNCTION.
 The ratio of laplace transform of voltage and current
measured at port under zero initial condition is called
driving point impedance function
 It is denoted by Z(s)
Z(s)=V(s)/I(s)

7. DRIVING POINT ADMITTANCE
FUNCTION
 It is the ratio of laplace transform of current and
voltage measured at port under zero initial
condition is called driving point admittance
function.
 It denoted by Y(s)
Y(s)=I(s)/V(s)
,E H ˆn
S
V
1V
1I
+
-

8. N-port Network
To represent multi-port networks we use:
- Z (impedance) parameters
- Y (admittance) parameters
- h (hybrid) parameters
- ABCD parameters
- S (scattering) parameters
Not easily
measurable at
high
frequency
Measurable at high
frequency
Multiport Networks
8
 




+
+
+
+
+
1I
2I
3I
mI
NI
1V
2V
3V
mV
NV
-
-
-
-
-

9. Two Port Networks
Generalities: The standard configuration of a two port:
The Network
Input
Port
Output
Port
+
_ _
+
V1 V2
I1 I2

10.  A two-port network requires two terminal pairs (total 4
terminals). Amongst the two voltages and two currents
shown,generally two can be independently specified
(externally).
input output
By convention, regard Port 1 as the input and Port 2 as
the input (and use the polarity labels shown). We
consider circuits with no internal independent sources.

11. Network Equations:
V1 = z11I1 + z12I2
V2 = z21I1 + z22I2
I1 = y11V1 + y12V2
I2 = y21V1 + y22V2
V1 = AV2 - BI2
I1 = CV2 - DI2
V2 = b11V1 - b12I1
I2 = b21V1 – b22I1
V1 = h11I1 + h12V2
I2 = h21I1 + h22V2
I1 = g11V1 + g12I2
V2 = g21V1 + g22I2
Impedance
Z parameters
Admittance
Y parameters
Transmission
A, B, C, D
parameters
Hybrid
H parameters

12. Summary
 A two-port network has an input port and an output port,
each with each port involving a single current and a
single
voltage.
 If the two-port network is linear and does not contain
any
independent sources, it may be possible to characterize
up to
6 different sets of matrix relationships. We discussed
four:
admittance [y], impedance [z],hybrid [h], and
transmission
[T]. If the parameters exist, they can be calculated or
measured individually by short-circuiting or open

13. Network functions for Two-Port Network
 Consider a two port network with voltages and currents at
ports 1-1’ and 2-2’ as V1(t), I1(t) and V2(t), I2(t) respectively
as shown in figure .

14. Network functions for Two-Port Network are as follows:
1. Driving point functions:
 Driving point impedance functions
 Driving point admittance functions
2. Transfer Functions:
 Voltage transfer functions
 Current transfer functions
 Transfer impedance functions
 Transfer admittance functions

15. Driving point functions:
Driving point impedance functions
 The ratio of Laplace transform of voltage and current at
port 1-1’ or 2-2’ is defined as driving point impedance
function.
 Thus there are two driving point impedance functions.
 At port 1-1’ denoted as Z11(s)
Z11(s)= V1(s)
I1(s)
 At port 2-2’ denoted as Z22(s)
Z22(s)= V2(s)
I2(s)

16. Driving point functions:
Driving point admittance functions
 The ratio of Laplace transform of current and voltage at
port 1-1’ or 2-2’ is defined as driving point admittance
function.
 Thus there are two driving point admittance functions.
 At port 1-1’ denoted as Y11(s)
Y11(s)= I1(s)
V1(s)
 At port 2-2’ denoted as Y11(s)
Y22(s)= I2(s)
V2(s)

17. Transfer Functions:
Voltage Transfer Function:
 It is defined as the ratio of Laplace transform of voltage at
one port and voltage at another port.
 It is denoted as G(s).
 G12(s) = V1(s) and G21(s) = V2(s)
V2(s) V1(s)
Current Transfer Function:
 It is defined as the ratio of Laplace transform of current at
one port and current at another port.
 It is denoted as A(s).
 A12(s) = I1(s) and A21(s) = I2(s)
I2(s) I1(s)

18. Transfer Functions:
Transfer Impedance Function:
 It is defined as the ratio of Laplace transform of voltage at
one port and current at another port.
Z12(s) = V1(s) and Z21(s) = V2(s)
I2(s) I1(s)
Transfer Admittance Function:
 It is defined as the ratio of Laplace transform of current at
one port and voltage at another port.
Y12(s) = I1(s) and Y21(s) = I2(s)
V2(s) V1(s)

19. References;-
• U.A PATEL BY MAHAJAN PUBLICATION
• TATA MCGRAW HILL.