transformer

(noun)

A static device that transfers electric energy from one circuit to another by magnetic coupling. Their main use is to transfer energy between different voltage levels, which allows choosing most appropriate voltage for power generation, transmission and distribution separately.

Related Terms

Examples of transformer in the following topics:

  • Transformers

    • Transformers transform voltages from one value to another; its function is governed by the transformer equation.
    • Transformers change voltages from one value to another.
    • A step-up transformer is one that increases voltage, whereas a step-down transformer decreases voltage.
    • A symbol of the transformer is also shown below the diagram.
    • Apply the transformer equation to compare the secondary and primary voltages

  • Energy Transformations

    • Energy transformation occurs when energy is changed from one form to another.
    • Often it appears that energy has been lost from a system when it simply has been transformed.
    • When analyzing energy transformations, it is important to consider the efficiency of conversion.
    • Some energy transformations can occur with an efficiency of essentially 100%.
    • Other energy transformations occur with a much lower efficiency of conversion.

  • Some Basic Theorems for the Fourier Transform

    • It is very useful to be able think of the Fourier transform as an operator acting on functions.
    • Convolutions are done often and by going to the frequency domain we can take advantage of the algorithmic improvements of the fast Fourier transform algorithm (FFT).
    • Start by multiplying the two Fourier transforms.
    • If we put the symmetric $1/\sqrt{2 \pi}$ normalization in front of both transforms, we end up with a left-over factor of $1/\sqrt{2 \pi}$ because we started out with two Fourier transforms and we ended up with only one and a convolution.
    • On the other hand, if we had used an asymmetric normalization, then the result would be different depending on whether we put the $1/(2 \pi)$ on the forward or inverse transform.

  • Lorentz Transformations

  • The Discrete Fourier Transform

    • This is the discrete version of the Fourier transform (DFT).
    • In the handout you will see some Mathematica code for computing and displaying discrete Fourier transforms.
    • The reason is that Mathematica uses a special algorithm called the FFT (Fast Fourier Transform).

  • Relativistic Momentum

    • Relativistic momentum is given as $\gamma m_{0}v$ where $m_{0}$ is the object's invariant mass and $\gamma$ is Lorentz transformation.
    • As a result, position and time in two reference frames are related by the Lorentz transformation instead of the Galilean transformation.
    • The Galilean transformation gives the coordinates of the moving frame as
    • Newton's second law [with mass fixed in the expression for momentum (p=m*v)], is not invariant under a Lorentz transformation.

  • Introduction to The DFT from the Fourier Integral

    • Now that we are considering discrete transforms and real data, we need to make this distinction since we will generally have both the sampled data and its transform stored in arrays on the computer.
    • So for this section we will follow the convention that if $h=h(t)$ then $H=H(f)$ is its Fourier transform.
    • A sensible numerical approximation for the Fourier transform integral is thus:
    • The inverse transform is:
    • So in Mathematica, the forward and inverse transforms are, respectively:

  • The Spectrum

    • The first step in obtaining the spectrum is to take a Fourier transform of the electric field of the wave
    • The table below gives a few Fourier transforms of common functions.

  • Tensors

    • We can work out how tensors transform by looking at a few examples.
    • Let's use the Lorentz matrix to transform to a new frame
    • Because transforms as a contravariant vector and doesn't transform, must transform as a covariant vector.
    • To generalize this we know that ${\bf p}$ transforms as the space-part of the four-vector $p^\mu$.
    • This is called a duality transformation.

  • Inductance

    • Transformers, for example, are designed to be particularly effective at inducing a desired voltage and current with very little loss of energy to other forms (see our Atom on "Transformers. ") Is there a useful physical quantity related to how "effective" a given device is?
    • Mutual inductance is the effect of Faraday's law of induction for one device upon another, such as the primary coil in transmitting energy to the secondary in a transformer.
    • Transformers run backward with the same effectiveness, or mutual inductance M.
    • These coils can induce emfs in one another like an inefficient transformer.