Electrical Engineering (EE) Exam > Electrical Engineering (EE) Notes > Network Theory (Electric Circuits) > Concepts & Questions Practice: Two Port Network
Concepts & Questions Practice: Two Port Network | Network Theory (Electric Circuits) - Electrical Engineering (EE) PDF Download
| Download, print and study this document offline |
Please wait while the PDF view is loading
Page 1
Chapter 8 Two Port Network & Network Functions
A pair of terminals through which a current may enter or leave a network is known as a port. A
port is an access to the network and consists of a pair of terminals; the current entering one
terminal leaves through the other terminal so that the net current entering the port equals zero.
For example, most circuits have two ports. We may apply an input signal in one port and obtain
an output signal from the other port. The parameters of a two-port network completely describes
its behaviour in terms of the voltage and current at each port. Thus, knowing the parameters of a
two port network permits us to describe its operation when it is connected into a larger network.
Two-port networks are also important in modeling electronic devices and system components.
For example, in electronics, two-port networks are employed to model transistors and Op-amps.
Other examples of electrical components modeled by two-ports are transformers and
transmission lines.
Four popular types of two-port parameters are examined here: impedance, admittance, hybrid,
and transmission. We show the usefulness of each set of parameters, demonstrate how they are
related to each other.
Learning Outcomes:
At the end of this module, students will be able to:
1.Differentiate one port and two port network devices.
2.Calculate two port network parameters such as z, y, ABCD and
h parameters for given electrical network.
3.Relate different two port network parameters.
4.Simplify the complex network such as cascade, parallel networks using
fundamental two port network parameters.
5.Find the various driving point & transfer functions of two port network.
Page 2
Chapter 8 Two Port Network & Network Functions
A pair of terminals through which a current may enter or leave a network is known as a port. A
port is an access to the network and consists of a pair of terminals; the current entering one
terminal leaves through the other terminal so that the net current entering the port equals zero.
For example, most circuits have two ports. We may apply an input signal in one port and obtain
an output signal from the other port. The parameters of a two-port network completely describes
its behaviour in terms of the voltage and current at each port. Thus, knowing the parameters of a
two port network permits us to describe its operation when it is connected into a larger network.
Two-port networks are also important in modeling electronic devices and system components.
For example, in electronics, two-port networks are employed to model transistors and Op-amps.
Other examples of electrical components modeled by two-ports are transformers and
transmission lines.
Four popular types of two-port parameters are examined here: impedance, admittance, hybrid,
and transmission. We show the usefulness of each set of parameters, demonstrate how they are
related to each other.
Learning Outcomes:
At the end of this module, students will be able to:
1.Differentiate one port and two port network devices.
2.Calculate two port network parameters such as z, y, ABCD and
h parameters for given electrical network.
3.Relate different two port network parameters.
4.Simplify the complex network such as cascade, parallel networks using
fundamental two port network parameters.
5.Find the various driving point & transfer functions of two port network.
A Typical one port or two terminal network is shown in figure 1.1. For example resistor,
capacitor and inductor are one port network.
Fig.1.1
Fig. 1.2 represents a two-port network.A four terminal network is called a two-port network
when the current entering one terminal of a pair exits the other terminal in the pair. For example,
I1 enters terminal ‘a’ and exit terminal ‘b’ of the input terminal pair ‘a-b’. Example for four-
terminal or two-port circuits are op amps, transistors, and transformers.
Fig.1.2
To characterize a two-port network requires that we relate the terminal quantities
2 1 2 1
, , I and I V V .The various terms that relate these voltages and currents are called parameters.
Our goal is to derive four sets of these parameters.
1.3 Open circuit Impedance Parameter (z Parameter):
Let us assume the two port network shown in figure is a linear network then using superposition
theorem, we can write the input and output voltages as the sum of two components, one due to I
1
and other due to I
2
:
Page 3
Chapter 8 Two Port Network & Network Functions
A pair of terminals through which a current may enter or leave a network is known as a port. A
port is an access to the network and consists of a pair of terminals; the current entering one
terminal leaves through the other terminal so that the net current entering the port equals zero.
For example, most circuits have two ports. We may apply an input signal in one port and obtain
an output signal from the other port. The parameters of a two-port network completely describes
its behaviour in terms of the voltage and current at each port. Thus, knowing the parameters of a
two port network permits us to describe its operation when it is connected into a larger network.
Two-port networks are also important in modeling electronic devices and system components.
For example, in electronics, two-port networks are employed to model transistors and Op-amps.
Other examples of electrical components modeled by two-ports are transformers and
transmission lines.
Four popular types of two-port parameters are examined here: impedance, admittance, hybrid,
and transmission. We show the usefulness of each set of parameters, demonstrate how they are
related to each other.
Learning Outcomes:
At the end of this module, students will be able to:
1.Differentiate one port and two port network devices.
2.Calculate two port network parameters such as z, y, ABCD and
h parameters for given electrical network.
3.Relate different two port network parameters.
4.Simplify the complex network such as cascade, parallel networks using
fundamental two port network parameters.
5.Find the various driving point & transfer functions of two port network.
A Typical one port or two terminal network is shown in figure 1.1. For example resistor,
capacitor and inductor are one port network.
Fig.1.1
Fig. 1.2 represents a two-port network.A four terminal network is called a two-port network
when the current entering one terminal of a pair exits the other terminal in the pair. For example,
I1 enters terminal ‘a’ and exit terminal ‘b’ of the input terminal pair ‘a-b’. Example for four-
terminal or two-port circuits are op amps, transistors, and transformers.
Fig.1.2
To characterize a two-port network requires that we relate the terminal quantities
2 1 2 1
, , I and I V V .The various terms that relate these voltages and currents are called parameters.
Our goal is to derive four sets of these parameters.
1.3 Open circuit Impedance Parameter (z Parameter):
Let us assume the two port network shown in figure is a linear network then using superposition
theorem, we can write the input and output voltages as the sum of two components, one due to I
1
and other due to I
2
:
2 22 1 21 2
2 12 1 11 1
I z I z V
I z I z V
? ?
? ?
Putting the above equations in matrix form, we get
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
2
1
2
1
22 21
12 11
2
1
] [
I
I
z
I
I
z z
z z
V
V
the z terms are called the z parameters, and have units of ohms. The values of the parameters can
be evaluated by setting 0
1
? I or 0
2
? I .
The z parameters are defined as follows:
Thus
0
1
1
11
2
?
?
I
I
V
z
0
1
2
21
2
?
?
I
I
V
z
0
2
1
12
1
?
?
I
I
V
z
0
2
2
22
1
?
?
I
I
V
z
In the preceding equations, letting 0
1
? I or 0
2
? I is equivalent to open-circuiting the input or
output port. Hence, the z parameters are called open-circuit impedance parameters.
Here
11
z is defined as the open-circuit input impedance,
22
z is called the open-circuit output
impedance, and
12
z and
21
z are called the open-circuit transfer impedances.
If
12
z =
21
z , the network is said to be reciprocal network. Also, if
11
z =
22
z then the network is
called a symmetrical network.
We obtain
11
z and
21
z by connecting a voltage
1
V (or a current source
1
I ) to port 1 with port 2
open-circuited as in fig.
Similarly
12
z and
22
z by connecting a voltage
2
V (or a current source
2
I ) to port 2 with port 1
open-circuited as in fig.
A two-port is reciprocal if interchanging an ideal voltage source at one port with an ideal
ammeter at the other port gives the same ammeter reading.
Page 4
Chapter 8 Two Port Network & Network Functions
A pair of terminals through which a current may enter or leave a network is known as a port. A
port is an access to the network and consists of a pair of terminals; the current entering one
terminal leaves through the other terminal so that the net current entering the port equals zero.
For example, most circuits have two ports. We may apply an input signal in one port and obtain
an output signal from the other port. The parameters of a two-port network completely describes
its behaviour in terms of the voltage and current at each port. Thus, knowing the parameters of a
two port network permits us to describe its operation when it is connected into a larger network.
Two-port networks are also important in modeling electronic devices and system components.
For example, in electronics, two-port networks are employed to model transistors and Op-amps.
Other examples of electrical components modeled by two-ports are transformers and
transmission lines.
Four popular types of two-port parameters are examined here: impedance, admittance, hybrid,
and transmission. We show the usefulness of each set of parameters, demonstrate how they are
related to each other.
Learning Outcomes:
At the end of this module, students will be able to:
1.Differentiate one port and two port network devices.
2.Calculate two port network parameters such as z, y, ABCD and
h parameters for given electrical network.
3.Relate different two port network parameters.
4.Simplify the complex network such as cascade, parallel networks using
fundamental two port network parameters.
5.Find the various driving point & transfer functions of two port network.
A Typical one port or two terminal network is shown in figure 1.1. For example resistor,
capacitor and inductor are one port network.
Fig.1.1
Fig. 1.2 represents a two-port network.A four terminal network is called a two-port network
when the current entering one terminal of a pair exits the other terminal in the pair. For example,
I1 enters terminal ‘a’ and exit terminal ‘b’ of the input terminal pair ‘a-b’. Example for four-
terminal or two-port circuits are op amps, transistors, and transformers.
Fig.1.2
To characterize a two-port network requires that we relate the terminal quantities
2 1 2 1
, , I and I V V .The various terms that relate these voltages and currents are called parameters.
Our goal is to derive four sets of these parameters.
1.3 Open circuit Impedance Parameter (z Parameter):
Let us assume the two port network shown in figure is a linear network then using superposition
theorem, we can write the input and output voltages as the sum of two components, one due to I
1
and other due to I
2
:
2 22 1 21 2
2 12 1 11 1
I z I z V
I z I z V
? ?
? ?
Putting the above equations in matrix form, we get
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
2
1
2
1
22 21
12 11
2
1
] [
I
I
z
I
I
z z
z z
V
V
the z terms are called the z parameters, and have units of ohms. The values of the parameters can
be evaluated by setting 0
1
? I or 0
2
? I .
The z parameters are defined as follows:
Thus
0
1
1
11
2
?
?
I
I
V
z
0
1
2
21
2
?
?
I
I
V
z
0
2
1
12
1
?
?
I
I
V
z
0
2
2
22
1
?
?
I
I
V
z
In the preceding equations, letting 0
1
? I or 0
2
? I is equivalent to open-circuiting the input or
output port. Hence, the z parameters are called open-circuit impedance parameters.
Here
11
z is defined as the open-circuit input impedance,
22
z is called the open-circuit output
impedance, and
12
z and
21
z are called the open-circuit transfer impedances.
If
12
z =
21
z , the network is said to be reciprocal network. Also, if
11
z =
22
z then the network is
called a symmetrical network.
We obtain
11
z and
21
z by connecting a voltage
1
V (or a current source
1
I ) to port 1 with port 2
open-circuited as in fig.
Similarly
12
z and
22
z by connecting a voltage
2
V (or a current source
2
I ) to port 2 with port 1
open-circuited as in fig.
A two-port is reciprocal if interchanging an ideal voltage source at one port with an ideal
ammeter at the other port gives the same ammeter reading.
Example 8.1
Determine the z parameters for the circuit in the following figure and then compute the
current in a 4O load if a
0
0 24 ? V source is connected at the input port.
To find
11
z and
21
z , the output terminals are open circuited. Also connect a voltage source
1
V to
the input terminals. This gives a circuit diagram as shown in Fig
Applying KVL to the left-mesh, we get
1 1 1
6 12 V I I ? ?
?
1 1
18I V ?
Hence ? ?
?0
1
1
11
2
I
I
V
z 18O
Applying KVL to the right-mesh, we get
0 6 0 3
1 2
? ? ? ? ? I V
?
1 2
6I V ?
Hence
0
1
2
21
2
?
?
I
I
V
z = 6 O
To find
12
z and
22
z , the input terminals are open circuited. Also connect a voltage source V
2
to
the output terminals. This gives a circuit diagram as shown in Fig.
Page 5
Chapter 8 Two Port Network & Network Functions
A pair of terminals through which a current may enter or leave a network is known as a port. A
port is an access to the network and consists of a pair of terminals; the current entering one
terminal leaves through the other terminal so that the net current entering the port equals zero.
For example, most circuits have two ports. We may apply an input signal in one port and obtain
an output signal from the other port. The parameters of a two-port network completely describes
its behaviour in terms of the voltage and current at each port. Thus, knowing the parameters of a
two port network permits us to describe its operation when it is connected into a larger network.
Two-port networks are also important in modeling electronic devices and system components.
For example, in electronics, two-port networks are employed to model transistors and Op-amps.
Other examples of electrical components modeled by two-ports are transformers and
transmission lines.
Four popular types of two-port parameters are examined here: impedance, admittance, hybrid,
and transmission. We show the usefulness of each set of parameters, demonstrate how they are
related to each other.
Learning Outcomes:
At the end of this module, students will be able to:
1.Differentiate one port and two port network devices.
2.Calculate two port network parameters such as z, y, ABCD and
h parameters for given electrical network.
3.Relate different two port network parameters.
4.Simplify the complex network such as cascade, parallel networks using
fundamental two port network parameters.
5.Find the various driving point & transfer functions of two port network.
A Typical one port or two terminal network is shown in figure 1.1. For example resistor,
capacitor and inductor are one port network.
Fig.1.1
Fig. 1.2 represents a two-port network.A four terminal network is called a two-port network
when the current entering one terminal of a pair exits the other terminal in the pair. For example,
I1 enters terminal ‘a’ and exit terminal ‘b’ of the input terminal pair ‘a-b’. Example for four-
terminal or two-port circuits are op amps, transistors, and transformers.
Fig.1.2
To characterize a two-port network requires that we relate the terminal quantities
2 1 2 1
, , I and I V V .The various terms that relate these voltages and currents are called parameters.
Our goal is to derive four sets of these parameters.
1.3 Open circuit Impedance Parameter (z Parameter):
Let us assume the two port network shown in figure is a linear network then using superposition
theorem, we can write the input and output voltages as the sum of two components, one due to I
1
and other due to I
2
:
2 22 1 21 2
2 12 1 11 1
I z I z V
I z I z V
? ?
? ?
Putting the above equations in matrix form, we get
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
2
1
2
1
22 21
12 11
2
1
] [
I
I
z
I
I
z z
z z
V
V
the z terms are called the z parameters, and have units of ohms. The values of the parameters can
be evaluated by setting 0
1
? I or 0
2
? I .
The z parameters are defined as follows:
Thus
0
1
1
11
2
?
?
I
I
V
z
0
1
2
21
2
?
?
I
I
V
z
0
2
1
12
1
?
?
I
I
V
z
0
2
2
22
1
?
?
I
I
V
z
In the preceding equations, letting 0
1
? I or 0
2
? I is equivalent to open-circuiting the input or
output port. Hence, the z parameters are called open-circuit impedance parameters.
Here
11
z is defined as the open-circuit input impedance,
22
z is called the open-circuit output
impedance, and
12
z and
21
z are called the open-circuit transfer impedances.
If
12
z =
21
z , the network is said to be reciprocal network. Also, if
11
z =
22
z then the network is
called a symmetrical network.
We obtain
11
z and
21
z by connecting a voltage
1
V (or a current source
1
I ) to port 1 with port 2
open-circuited as in fig.
Similarly
12
z and
22
z by connecting a voltage
2
V (or a current source
2
I ) to port 2 with port 1
open-circuited as in fig.
A two-port is reciprocal if interchanging an ideal voltage source at one port with an ideal
ammeter at the other port gives the same ammeter reading.
Example 8.1
Determine the z parameters for the circuit in the following figure and then compute the
current in a 4O load if a
0
0 24 ? V source is connected at the input port.
To find
11
z and
21
z , the output terminals are open circuited. Also connect a voltage source
1
V to
the input terminals. This gives a circuit diagram as shown in Fig
Applying KVL to the left-mesh, we get
1 1 1
6 12 V I I ? ?
?
1 1
18I V ?
Hence ? ?
?0
1
1
11
2
I
I
V
z 18O
Applying KVL to the right-mesh, we get
0 6 0 3
1 2
? ? ? ? ? I V
?
1 2
6I V ?
Hence
0
1
2
21
2
?
?
I
I
V
z = 6 O
To find
12
z and
22
z , the input terminals are open circuited. Also connect a voltage source V
2
to
the output terminals. This gives a circuit diagram as shown in Fig.
Applying KVL to the left-mesh, we get
2 1
2 1
6
6 0 12
I V
I V
?
? ? ?
0
2
1
12
1
?
?
I
I
V
z =6 O
Applying KVL to the right-mesh, we get
0 6 3
2 2 2
? ? ? ? I I V
2 2
9I V ?
0
2
2
22
1
?
?
I
I
V
z =9 O
The equations for the two-port network are, therefore
2 1 1
6 18 I I V ? ? (1)
2 1 2
9 6 I I V ? ? (2)
The terminal voltages for the network shown in Fig.8.2 are
0
1
0 24 ? ? V (3)
2 2
4I V ? ? (4)
Fig.8.2
Combining equations (1) and (2) with equations (3) and (4) yields
2 1
0
6 18 0 24 I I ? ? ?
2 1
13 6 0 I I ? ?
On Solving, we get
0
2
0 73 . 0 ? ? ? I A
Read More
|
68 videos|85 docs|62 tests
|
FAQs on Concepts & Questions Practice: Two Port Network - Network Theory (Electric Circuits) - Electrical Engineering (EE)
| 1. What is a two-port network? |  |
Ans. A two-port network is an electrical network with two pairs of terminals, known as ports. It is used to describe the electrical behavior of various devices, such as amplifiers and filters, and is commonly represented using mathematical equations or circuit diagrams.
| 2. How does a two-port network work? | |
Ans. A two-port network works by accepting electrical signals at its input ports and producing corresponding output signals at its output ports. The relationship between the input and output signals is defined by the network's transfer function or scattering parameters, which describe how the network affects the amplitude, phase, and frequency of the signals.
| 3. What are the applications of two-port networks? | |
Ans. Two-port networks have various applications in electrical engineering. They are commonly used in the design and analysis of electronic circuits, communication systems, and control systems. Two-port networks are also utilized in areas such as signal processing, microwave engineering, and electrical modeling of physical systems.
| 4. How are two-port networks represented mathematically? | |
Ans. Two-port networks can be represented mathematically using different methods. One common approach is to use matrix equations, such as the ABCD parameters or the scattering matrix. These equations relate the voltages and currents at the ports of the network, allowing for analysis and design calculations.
| 5. What are the limitations of two-port network analysis? | |
Ans. Two-port network analysis assumes linearity and time-invariance of the network, which may not hold true for all practical scenarios. Additionally, the accuracy of the analysis depends on the accuracy of the network model and the assumptions made. Nonlinear behavior, frequency-dependent effects, and distributed elements can introduce limitations in the analysis of two-port networks.
About this Document
|
4.69/5 Rating |
|
Nov 21, 2024 Last updated |
Document Description: Concepts & Questions Practice: Two Port Network for Electrical Engineering (EE) 2024 is part of Network Theory (Electric Circuits) preparation.
The notes and questions for Concepts & Questions Practice: Two Port Network have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about Concepts & Questions Practice: Two Port Network covers topics
like and Concepts & Questions Practice: Two Port Network Example, for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Concepts & Questions Practice: Two Port Network.
Introduction of Concepts & Questions Practice: Two Port Network in English is available as part of our Network Theory (Electric Circuits)
for Electrical Engineering (EE) & Concepts & Questions Practice: Two Port Network in Hindi for Network Theory (Electric Circuits) course.
Download more important topics related with notes, lectures and mock test series for Electrical Engineering (EE)
Exam by signing up for free. Electrical Engineering (EE): Concepts & Questions Practice: Two Port Network | Network Theory (Electric Circuits) - Electrical Engineering (EE)
Description
Full syllabus notes, lecture & questions for Concepts & Questions Practice: Two Port Network | Network Theory (Electric Circuits) - Electrical Engineering (EE) - Electrical Engineering (EE) | Plus excerises question with solution to help you revise complete syllabus for Network Theory (Electric Circuits) | Best notes, free PDF download
Information about Concepts & Questions Practice: Two Port Network
In this doc you can find the meaning of Concepts & Questions Practice: Two Port Network defined & explained in the simplest way possible. Besides explaining types of
Concepts & Questions Practice: Two Port Network theory, EduRev gives you an ample number of questions to practice Concepts & Questions Practice: Two Port Network tests, examples and also practice Electrical Engineering (EE)
tests
|
Explore Courses for Electrical Engineering (EE) exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
Related Searches
Viva Questions
,mock tests for examination
,Objective type Questions
,Sample Paper
,practice quizzes
,Concepts & Questions Practice: Two Port Network | Network Theory (Electric Circuits) - Electrical Engineering (EE)
,Exam
,Concepts & Questions Practice: Two Port Network | Network Theory (Electric Circuits) - Electrical Engineering (EE)
,study material
,Previous Year Questions with Solutions
,Important questions
,Extra Questions
,past year papers
,Summary
,Concepts & Questions Practice: Two Port Network | Network Theory (Electric Circuits) - Electrical Engineering (EE)
,MCQs
,video lectures
,shortcuts and tricks
,ppt
,Semester Notes
,Free
;
Additional Information about Concepts & Questions Practice: Two Port Network for Electrical Engineering (EE) Preparation
Concepts & Questions Practice: Two Port Network Free PDF Download
The Concepts & Questions Practice: Two Port Network is an invaluable resource that delves deep into the core of the Electrical Engineering (EE) exam.
These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective.
With the help of these notes, you can grasp complex subjects quickly, revise important points easily,
and reinforce your understanding of key concepts. The study notes are presented in a concise and easy-to-understand manner,
allowing you to optimize your learning process. Whether you're looking for best-recommended books, sample papers, study material,
or toppers' notes, this PDF has got you covered. Download the Concepts & Questions Practice: Two Port Network now and kickstart your journey towards success in the Electrical Engineering (EE) exam.
Importance of Concepts & Questions Practice: Two Port Network
The importance of Concepts & Questions Practice: Two Port Network cannot be overstated, especially for Electrical Engineering (EE) aspirants.
This document holds the key to success in the Electrical Engineering (EE) exam.
It offers a detailed understanding of the concept, providing invaluable insights into the topic.
By knowing the concepts well in advance, students can plan their preparation effectively.
Utilize this indispensable guide for a well-rounded preparation and achieve your desired results.
Concepts & Questions Practice: Two Port Network Notes
Concepts & Questions Practice: Two Port Network Notes offer in-depth insights into the specific topic to help you master it with ease.
This comprehensive document covers all aspects related to Concepts & Questions Practice: Two Port Network.
It includes detailed information about the exam syllabus, recommended books, and study materials for a well-rounded preparation.
Practice papers and question papers enable you to assess your progress effectively.
Additionally, the paper analysis provides valuable tips for tackling the exam strategically.
Access to Toppers' notes gives you an edge in understanding complex concepts.
Whether you're a beginner or aiming for advanced proficiency, Concepts & Questions Practice: Two Port Network Notes on EduRev are your ultimate resource for success.
Concepts & Questions Practice: Two Port Network Electrical Engineering (EE)
The "Concepts & Questions Practice: Two Port Network Electrical Engineering (EE) Questions" guide is a valuable resource for all aspiring students preparing for the
Electrical Engineering (EE) exam. It focuses on providing a wide range of practice questions to help students gauge
their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation.
The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level.
Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.
Study Concepts & Questions Practice: Two Port Network on the App
Students of Electrical Engineering (EE) can study Concepts & Questions Practice: Two Port Network alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the Concepts & Questions Practice: Two Port Network,
students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc.
The EduRev App will make your learning easier as you can access it from anywhere you want.
The content of Concepts & Questions Practice: Two Port Network is prepared as per the latest Electrical Engineering (EE) syllabus.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup