Note: Remember to always include units if appropriate
1. A signal coming into the oscilloscope is a sine wave. Amplitude = 3 V, DC Offset = -1 V, Frequency = 1000 Hz. Sketch the oscilloscope display. Select appropriate V/div and s/div and note on the sketch. Make the horizontal line = 0 V. Label Axes appropriately.
2. Download the data in the associated Excel file. For the two waveforms in the "Problem 2" tab, determine the mean and rms values of the load. Matlab: functions MEAN() and RMS() will be helpful. Excel: easiest to use functions SQRT, SUMSQ, and COUNTA. Be careful when converting the equation for RMS to a form Excel can work with.
3. Sketch a response you might expect from an underdamped second order sensor with a settling time ~0.5 sec as it monitors the two cycles of the square wave below.
4. Look at the second tab in the Excel file. Assume this is experimental data from a new thermistor design. What is the time constant? Approximately how long after a step change must you wait before considering the data to be valid, using the "rule of thumb"
5. A bulb thermometer, such as shown below, is a first order instrument. The following expression can be found for the thermometer response, T(t):
T(t) = T∞ + [T(0) - T∞] e-t/τ
where T∞ is the temperature of the environment to be measured, T(0) is the initial temperature of the sensor, t is time, and τ is the time constant (which is a function of the properties of the thermometer).
We are trying to measure the temperature of an environment with T∞ of 170.0°F using a thermometer taken from room temperature (assume T(0) of 70.0°F). We are given a time constant of τ = 1.25 seconds.
(a) Create a plot of the sensor response for 10 seconds of time. Show the initial temperature and the temperature of the environment to be measured on the same plot for reference. Use good plotting techniques.
(b) Given the above thermometer, what is the minimum time that we would be need to wait before recording the temperature when we place the thermometer in a new environment?
(c) The time constant, τ, is calculated using the following expression:
τ = mcv/hA
where m is the mass of the liquid, cv is the specific heat of the liquid, h is the convection coefficient between the bulb and environment, and A is the thermometer surface area. A thermometer with a larger bulb is selected, such that the surface area is increased by a factor of 1.5 and the mass of the liquid is increased by a factor of 2, what would the new time constant be?
6. You are working with a 14 bit A/D converter with a +/-10V range.
a. What is the S/N ratio of the converter (in dB)?
b. You connect a flowmeter whose calibration is 1V = 73 ml/sec. What is the quantization error (in ml/sec)?
7. You are working with an 8 bit A/D converter with a +/-1V range.
a. If the output bit combination is [10011011],what is the input voltage?
b. If the input voltage is -0.730V, what bit combination will the digital output have (express as a binary number like in part a)? Assume the A/D includes a bias voltage to center the error about each bit. Hint- pretend you are a successive approximation A/D convertor.
8. The air compressor in your plant operates on a simple control system that switches it ON when the system pressure falls to 78 psi and switches it OFF once the pressure increases to 99 psi. The pressure is monitored by a transducer whose output is calibrated to be 100 mV/psi with a -6V offset (so zero pressure would give -6V).
a. If your choices are 0-1 V, 0-5 V, 0-10V, ±1V, ±5V, ±10V, what is the best choice for an A/D range that will avoid clipping/saturation while giving you the best pressure resolution?
b. If the A/D is 12 bits, what is the pressure resolution if you use the ±10V range?
9. Wind Power Density (WPD) is an important parameter when evaluating the potential use of wind turbines to capture wind energy. WPD depends on the density of the air passing a turbine and the wind speed. The equation for WPD is:
WPD = 1/2(ρv3)
where ρ is the density of the air and v is the wind speed (velocity). When the density is given in units of kg/m3 and the wind speed is in units of m/s, the WPD has units of Watts/m2.
Given that:
(a) What is the nominal WPD value? Remember to include appropriate units.
(b) What is the uncertainty associated with the WPD calculation? Show an expression for the expected WPD as xx ± yy. Remember to include appropriate units and show work.
10. You take a measurement on an oscilloscope, expecting something on the order of 4V. The scope measurement reads 38.7V. The discrepancy is probably what?