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theory:sensor_technology:sta_easyunitconversion [2018/10/10 07:36]
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-====== Systematic unit conversion ====== 
- 
-//To convert from a certain unit system to another (like the SI system), there is a structured method that uses the fact that we can multiply quantities by the number 1 (dimensionless) without affecting the quantity.// 
- 
-For a description of quantities, see the [[st1_measurement_theory#​Quantities and units|measurement theory page]]. The method of using //multiply by one// is explained based on an example. 
- 
-To make 5 gallons of beer, a recipe says that we need 2.0 ounces (oz.) of malt. Because ounces are a weight unit and gallon a volume measure, we know that in SI units we should express it in kg per m<​sup>​3</​sup>​. We start with 
- 
-\begin{equation} 
-malt=\frac{2.0 oz.}{5 gallon}. 
-\label{eq:​Malt} 
-\end{equation} 
- 
-Next we look up that one U.S. gallon is equal to 3.785 liters and one ounce is 28.350 gram. A liter is 1/1000 m<​sup>​3</​sup>​. We write the conversion units as a dimensionless normalized ratio 
-\begin{equation} 
-3.785\frac{l}{gallon}=1 
-\end{equation} 
-with 
-\begin{equation} 
-1000\frac{l}{m^{3}}=1 
-\end{equation} 
-and 
-\begin{equation} 
-28.350\frac{gr}{oz.}=28.350\frac{0.001 kg}{oz.}=1 
-\end{equation} 
- 
-respectively. Because these are equal to one without any unit, we can simply multiply equation \eqref{eq:​Malt} with them (or with the inverse if needed): 
-\begin{equation} 
-\begin{aligned} 
-malt&​=\frac{2.0 oz.}{5 gallon}\\ 
-&​=\frac{2.0 oz.}{5 gallon} \left ( 3.785\frac{l}{gallon} \right )^{-1} \left ( 1000\frac{l}{m^{3}} \right ) \left ( 28.350\frac{0.001 kg}{oz.} \right ). 
-\end{aligned} 
-\end{equation} 
- 
-As a result, the non-SI units cancel out. So our equation simplifies to 
-\begin{equation} 
-malt = \frac{2.0}{5} \left ( 3.785 \right )^{-1} \left ( 1000\frac{1}{m^{3}} \right ) \left ( 28.350 \cdot 0.001 kg \right ) 
-\end{equation} 
- 
-which can be calculated as 
-\begin{equation} 
-malt = \frac{2.0}{5} \cdot \frac{28.350 \cdot 1000 \cdot 0.001 kg}{3.785 m^{3}} = 2.996 \frac{kg}{m^{3}}. 
-\end{equation} 
- 
- 
-====== Sensor Technology TOC ====== 
- 
-These are the chapters for the Sensor Technology course: 
-  * Chapter 1: [[theory:​sensor_technology:​st1_measurement_theory|Measurement Theory]] 
-  * Chapter 2: [[theory:​sensor_technology:​st2_measurement_errors|Measurement Errors]] 
-  * Chapter 3: [[theory:​sensor_technology:​st3_measurement_technology|Measurement Technology]] 
-  * Chapter 4: [[theory:​sensor_technology:​stb_conventions_for_good_graphs_and_tables|Circuits,​ Graphs, Tables, Pictures and Code]] 
-  * Chapter 5: [[theory:​sensor_technology:​st4_sensor_theory|Basic Sensor Theory]] 
-  * Chapter 6: [[theory:​sensor_technology:​st6_sensoractuatorsystems|Sensor-Actuator Systems]] ​ 
-  * Chapter 7: [[theory:​sensor_technology:​st7_modelling_main|Modelling]] 
-  * Chapter 8: [[theory:​sensor_technology:​st8_accelerometer_model|Modelling:​ The Accelerometer]] - example of a second order system 
-  * Chapter 9: [[theory:​sensor_technology:​st9_scaling|Modelling:​ Scaling]] - why small things appear to be stiffer 
-  * Chapter 10: [[theory:​sensor_technology:​st10_lumped_element_models|Modelling:​ Lumped Element Models]] 
-  * Chapter 11: [[theory:​sensor_technology:​st11_finite_element_models|Modelling:​ Finite Element Models]] 
-  * Chapter 12: [[theory:​sensor_technology:​st12_impedance_spectroscopy|Modelling:​ Transducer Characterization by Impedance Spectroscopy]] 
-  * Chapter 13: [[theory:​sensor_technology:​st13_lumped_element_models_advanced|Modelling:​ Systems Theory]] 
-  * Chapter 14: [[theory:​sensor_technology:​st14_differential_equation_numerical_models|Modelling:​ Numerical Integration]] 
-  * Chapter 15: [[theory:​sensor_technology:​st15_signal_conditioning_and_sensor_read-out|Signal Conditioning and Sensor Read-out]] 
-  * Chapter 16: [[theory:​sensor_technology:​st16_resistive_sensors|Resistive Sensors]] 
-  * Chapter 17: [[theory:​sensor_technology:​st17_capacitive_sensors|Capacitive Sensors]] 
-  * Chapter 18: [[theory:​sensor_technology:​st18_magnetic_sensors|Magnetic Sensors]] 
-  * Chapter 19: [[theory:​sensor_technology:​st19_optical_sensors|Optical Sensors]] 
-  * Chapter 20: [[theory:​sensor_technology:​st20_actuators|Actuators]] - an example of an electrodynamic motor 
-  * Chapter 21: [[theory:​sensor_technology:​st21_actuator_models|Actuator principles for small speakers]] 
-  * Chapter 22: [[theory:​sensor_technology:​st22_adc_and_dac|ADC and DAC]] 
-  * Chapter 23: [[theory:​sensor_technology:​st23_bus_interfaces|Bus Interfaces]] - SPI, I<​sup>​2</​sup>​C,​ IO-Link, Ethernet based 
-  * Appendix A: Systematic unit conversion 
-  * Appendix B: [[theory:​sensor_technology:​stc_common_mode_rejection_ratio_cmrr|Common Mode Rejection Ratio (CMRR)]] <- Next 
-  * Appendix C: [[theory:​sensor_technology:​std_schmitt_trigger|A Schmitt Trigger for sensor level detection]] 
- 
  
theory/sensor_technology/sta_easyunitconversion.1539156969.txt.gz · Last modified: 2018/10/10 07:36 by 54.36.148.22