Home / Resources / Knowledge / Theorems and laws / Delta-Star Transformation

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To convert a delta network to an equivalent star network we need to derive a transformation formula for equating the various resistors to each other between the various terminals. Consider the circuit below.

Delta to Star Network.

Compare the resistances between terminals 1 and 2.

Resistance between the terminals 2 and 3.

Resistance between the terminals 1 and 3.

This now gives us three equations and taking equation 3 from equation 2 gives:

Then, re-writing Equation 1 will give us:

Adding together equation 1 and the result above of equation 3 minus equation 2 gives:

From which gives us the final equation for resistor P as:

Then to summarize a little the above maths, we can now say that resistor P in a Star network can be found as Equation 1 plus (Equation 3 minus Equation 2) or   Eq1 + (Eq3 – Eq2).
Similarly, to find resistor Q in a star network, is equation 2 plus the result of equation 1 minus equation 3 or  Eq2 + (Eq1 – Eq3) and this gives us the transformation of Q as:

and again, to find resistor R in a Star network, is equation 3 plus the result of equation 2 minus equation 1 or  Eq3 + (Eq2 – Eq1) and this gives us the transformation of R as:

When converting a delta network into a star network the denominators of all of the transformation formulas are the same: A + B + C, and which is the sum of ALL the delta resistances. Then to convert any delta connected network to an equivalent star network we can summarized the above transformation equations as:

Delta to Star Transformations Equations

Example No1

Convert the following Delta Resistive Network into an equivalent Star Network.

Star Delta Transformation

We have seen above that when converting from a delta network to an equivalent star network that the resistor connected to one terminal is the product of the two delta resistances connected to the same terminal, for example resistor P is the product of resistors A and B connected to terminal 1. By rewriting the previous formulas a little we can also find the transformation formulas for converting a resistive star network to an equivalent delta network giving us a way of producing a star delta transformation as shown below.

Star to Delta Network.

The value of the resistor on any one side of the delta, Δ network is the sum of all the two-product combinations of resistors in the star network divide by the star resistor located “directly opposite” the delta resistor being found. For example, resistor A is given as:

with respect to terminal 3 and resistor B is given as:

with respect to terminal 2 with resistor C given as:

with respect to terminal 1.
By dividing out each equation by the value of the denominator we end up with three separate transformation formulas that can be used to convert any Delta resistive network into an equivalent star network as given below.

Star Delta Transformation Equations

One final point about converting a star resistive network to an equivalent delta network. If all the resistors in the star network are equal in value then the resultant resistors in the equivalent delta network will be three times the value of the star resistors and equal, giving:   R_DELTA = 3R_STAR

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labwork 1

1. First Generation (1940-1956) Vacuum Tubes

The first computers used vacuum tubes for circuitry and magnetic drums for memory, and were often enormous, taking up entire rooms. They were very expensive to operate and in addition to using a great deal of electricity, generated a lot of heat, which was often the cause of malfunctions.

First generation computers relied on machine language, the lowest-level programming language understood by computers, to perform operations, and they could only solve one problem at a time. Input was based on punched cards and paper tape, and output was displayed on printouts.

The UNIVAC and ENIAC computers are examples of first-generation computing devices. The UNIVAC was the first commercial computer delivered to a business client, the U.S. Census Bureau in 1951.

Second Generation (1956-1963) Transistors

Transistors replaced vacuum tubes and ushered in the second generation of computers. The transistor was invented in 1947 but did not see widespread use in computers until the late 1950s. The transistor was far superior to the vacuum tube, allowing computers to become smaller, faster, cheaper, more energy-efficient and more reliable than their first-generation predecessors.

Second-generation computers moved from cryptic binary machine language to symbolic, or assembly, languages, which allowed programmers to specify instructions in words. The first computers that stored their instructions in their memory, which moved from a magnetic drum to magnetic core technology.

The first computers of this generation were developed for the atomic energy industry.

Third Generation (1964-1971) Integrated Circuits

The development of the integrated circuit was the hallmark of the third generation of computers. Transistors were miniaturized and placed on silicon chips, called semiconductors, which drastically increased the speed and efficiency of computers.
Instead of punched cards and printouts, users interacted with third generation computers through keyboards and monitors and interfaced with an operating system, which allowed the device to run many different applications at one time with a central program that monitored the memory. Computers for the first time became accessible to a mass audience because they were smaller and cheaper than their predecessors.

Fourth Generation (1971-Present) Microprocessors

The microprocessor brought the fourth generation of computers, as thousands of integrated circuits were built onto a single silicon chip. What in the first generation filled an entire room could now fit in the palm of the hand. The Intel 4004 chip, developed in 1971, located all the components of the computer—from the central processing unit and memory to input/output controls—on a single chip.
In 1981 IBM introduced its first computer for the home user, and in 1984 Apple introduced the Macintosh. Microprocessors also moved out of the realm of desktop computers and into many areas of life as more and more everyday products began to use microprocessors.

Fifth Generation (Present and Beyond) Artificial Intelligence

Fifth generation computing devices, based on artificial intelligence, are still in development, though there are some applications, such as voice recognition, that are being used today. The use of parallel processing and superconductors is helping to make artificial intelligence a reality. Quantum computation and molecular and nanotechnology will radically change the face of computers in years to come. The goal of fifth-generation computing is to develop devices that respond to natural language input and are capable of learning and self-organization.


2.     Until recently computers were classifieds as microcomputers, super minicomputers, mainframes, and supercomputers. Technology, however, has changed and this classification is no more relevant. Today all computers used microprocessors as their CPU. Thus classification is possible only through their mode of use. Based on mode of use we can classify computers as Palms, Laptop PCs, Desktop PCs and Workstations. Based on interconnected computers we can classify computers we can classify them as distributed computers and parallel computers.With miniaturization and high-density packing of transistor on a chip, computers with capabilities nearly that of PCs which can be held in a palm have emerged. Palm accept handwritten inputs using an electronic pen which can be used to write on a Palm’s screen (besides a tiny keyboard), have small disk storage and can be connected to a wireless network. One has to train the system on the user’s handwriting before it can be used as a mobile phone, Fax, and e-mail machine.






 3.

 

  

1. 1. Power Supply - The power supply comes with the case, but this component is mentioned separately since there are various types of power supplies. The one you should get depends on the requirements of your system. This will be discussed in more detail later
      
      
   2. Motherboard - This is where the core components of your computer reside which are listed below. Also the support cards for video, sound, networking and more are mounted into this board.
      
      
      1. Microprocessor - This is the brain of your computer. It performs commands and instructions and controls the operation of the computer.
      2. Memory - The RAM in your system is mounted on the motherboard. This is memory that must be powered on to retain its contents.
      3. Drive controllers - The drive controllers control the interface of your system to your hard drives. The controllers let your hard drives work by controlling their operation. On most systems, they are included on the motherboard, however you may add additional controllers for faster or other types of drives.
      
      
   3. Hard disk drive(s) - This is where your files are permanently stored on your computer. Also, normally, your operating system is installed here.
      
      
   4. CD-ROM drive(s) - This is normally a read only drive where files are permanently stored. There are now read/write CD-ROM drives that use special software to allow users to read from and write to these drives.
      
      
   5. Floppy drive(s) - A floppy is a small disk storage device that today typically has about 1.4 Megabytes of memory capacity.
      
      
   6. Other possible file storage devices include DVD devices, Tape backup devices, and some others.
   
   
2. Monitor - This device which operates like a TV set lets the user see how the computer is responding to their commands.
   
   
3. Keyboard - This is where the user enters text commands into the computer.
   
   
4. Mouse - A point and click interface for entering commands which works well in graphical environments.

These various parts will be discussed in the following sections.