LCD (Liquid crystal display) Television:

Passive matrix addressing:

Passive matrix addressing is an addressing scheme used in earlier LCD displays, and may be used in future LCD displays. This is a matrix addressing scheme meaning that only m + n control signals are required to address a m × n display. A pixel in a passive matrix must maintain its state without active driving circuitry until it can be refreshed again.

A new display technology uses a bi-stable pixel, which maintains its state indefinitely without the need for individual transistor elements at each pixel.

The signal is divided into a row or select signal and a column or video signal. The select voltage determines the row that is being addressed and all m pixels on a row are addressed simultaneously. When pixels on a row are being addressed, a V_sel potential is applied, and all other rows are unselected with a V_unsel potential. The video signal or column potential is then applied with a potential for each m columns individually. An on-lighted pixel corresponds to a V_on, an off-switched corresponds to a V_off potential.

The potential across pixel at selected row i and column j is

V_ij = V_sel − V_{on | off}

and

V_ij = V_unsel − V_{on | off}

for the unselected rows.

Theres also the Active matrix addressing, if you are intrested in some more information about it visit : http://en.wikipedia.org/wiki/Active_matrix_addressing .

Matrix in Piezoelectricity

Piezoelectricity is the combined effect of the electrical behavior of the material:

where D is the electric charge density displacement(electric displacement), the epsilon is permittivity and E is electric field strength, and

Hooke's Law:

where S is strain, s is compliance and T is stress.

These may be combined into so called coupled equations, of which the strain-charge form is:

where [d] is the matrix for the direct piezoelectric effect and [dt] is the matrix for the converse piezoelectric effect. The superscript E indicates a zero, or constant, electric filed; the superscript T indicates a zero, or constant. stress field; and the superscript t stands or the transposition of a matrix.

where the first equation represents the relationship for the converse piezoelectric effect and the latter for the direct piezoelectric effect.

CAPPS: A Framework for Power–Performance Tradeoffs in Bus-Matrix-Based On-Chip Communication Architecture Synthesis

On-chip communication architectures have a significant impact on the power consumption and performance on emerging chip multiprocessor (CMP) applications. However, customization of such architectures for an application requires the exploration of a large design space. Designers need tools to rapidly explore and evaluate relevant communication architecture configurations exhibiting diverse power and performance characteristics. The study of an automated framework for fast system-level, application-specific, power-performance tradeoffs in a bus matrix communication architecture synthesis (CAPPS), makes two specific contributions. First, developping energy models for system-level exploration of bus matrix communication architectures. Second, incorporating these models into a bus matrix synthesis flow that enables designers to efficiently explore the power-perfromance design space of different bus matrix configuration.

Here is an example of applying bus matrix on short circuits for generators:




Data Retrieved From: www.IEEE.org

Linear Algebra and Electricity

We must often analyze electric circuits such as the one shown to the right that cannot be described using the rules for resistors in series or parallel. The goal is to calculate the current flowing in each branch of the circuit or to calculate the voltage at each node of the circuit. We can use loop analysis or mesh analysis (which is a particular type of loop analysis) or nodal analysis to write down a system of equations describing the circuit. We can then use Gaussian elimination to solve this system of equations.

Loop analysis finds the currents directly and nodal analysis find the voltages directly. Which method is simpler depends on the given circuit. Knowing the branch currents, the nodal voltages can easily be calculated, and knowing the nodal voltages, the branch currents can easily be calculated. Nodal analysis is important because its answers can be directly compared with voltage measurements taken in a circuit, whereas currents are not so easily measured in a circuit (one must cut wires).

Reference: http://mathonweb.com/help/Theory.htm