Sensors

11/23/10

• • HW #6 has been posted and will be due at the start of class on Tuesday, 12/7, giving you two full weeks to complete the assignment.  An updated course schedule has been posted to the "Course Information" section.

  • Attention Friday lab section Group A:  Due to the interruption by the Thanksgiving holiday, your Lab #5 report will be due at 7:30am on Monday, 11/29, in Prof. Santos' ERC 309 office.  You are to slide the report under the office door if Prof. Santos is unavailable.

  • Some sections of Lab #6 may not have seen the uncertainty material in lecture by the time they collect data in lab.  However, all sections will have seen the uncertainty material by the time Lab #6 report is due.

1   Root-mean-square (rms) voltage

The rms value of AC voltage is the DC voltage value that yields the equivalent effective power.

Solve for the rms voltage Vrms of the following pulsed square wave in terms of V0.

In mathematics, the root mean square (abbreviated RMS or rms), also known as the quadratic mean, is a statistical measure of the magnitude of a varying quantity. It is especially useful when variates are positive and negative, e.g., sinusoids. RMS is used in various fields, including electrical engineering; one of the more prominent uses of RMS is in the field of signal amplifiers.

It can be calculated for a series of discrete values or for a continuously varying function. The name comes from the fact that it is the square root of the mean of the squares of the values. It is a special case of the generalized mean with the exponent p = 2.

http://ptgmedia.pearsoncmg.com/images/chap1_0130668303/elementLinks/chap1_0130668303.pdf

RMS Value

Another way of referring to AC voltage is the RMS value (VRMS). RMS is an abbreviation

for root-mean-square, which indicates the mathematics behind calculating the value

of an arbitrary waveform. To calculate the RMS value of a waveform, the waveform is first

squared at every point. Then, the average or mean value of this squared waveform is found.

Finally, the square root of the mean value is taken to produce the RMS (root of the mean of

the square) value.

Mathematically, the RMS value of a waveform can be expressed as

Determining the RMS value from the zero-to-peak value (or vice versa) can be difficult

due to the complexity of the RMS operation. However, for a sine wave the relationship

is simple. (See Appendix B for a detailed analysis.)

This relationship is valid only for a sine wave and does not hold for other waveforms.

1.8 Average Value

Finally, AC voltage is sometimes defined using an average value. Strictly speaking,

the average value of a sine wave is zero because the waveform is positive for one half cycle

and is negative for the other half. Since the two halves are symmetrical, they cancel out

when they are averaged together. So, on the average, the waveform voltage is zero.

Another interpretation of average value is to assume that the waveform has been fullwave

rectified. Mathematically this means that the absolute value of the waveform is used

(i.e., the negative portion of the cycle has been treated as being positive).

This corresponds to the measurement method that some instruments use to handle AC

waveforms, so this is the method that will be considered here. Unless otherwise indicated,

VAVG will mean the full-wave rectified average value. These averaging steps have been

shown in Figure 1.7. Figure 1.7a shows a sine wave that is to be full-wave rectified. Figure

1.7b shows the resulting full-wave rectified sine wave. Whenever the original waveform

becomes negative, full-wave rectification changes the sign and converts the voltage into a

positive waveform with the same amplitude. Graphically, this can be described as folding

the negative half of the waveform up onto the positive half, resulting in a humped sort of

http://www.rfcafe.com/references/electrical/square-wave-voltage-conversion.htm

2. Inverse Discrete Fourier Transform (IDFT) by inspection of DFT plots

Consider the following “half-area” magnitude and phase DFT plots:

http://www.commsp.ee.ic.ac.uk/~tania/teaching/sas.html

http://www.commsp.ee.ic.ac.uk/~tania/teaching/dsp.html

11/18/10

State-space representation of a mechanical system

Find the state-space representation of the system and identify the matrices/vectors A, B, C,

and D.

Transfer functions for a feedback system

Obtaining a transfer function from state-space representation

By hand, find the transfer function G(s) for the system represented by the following

state-space representation:

to find ad joint matrix you need to follow a very specific procedure

first you need to calculate the minor for each element in the matrix and the minor is the determinant of the matrix

next for co factor matrix from minors

then, form the ad joint from co factor matrix