Exp4 - Exp#4 First Order Systems 23 Exp#4 Amplitude/Phase...

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23 Exp#4: First Order Systems
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24 Exp#4: Amplitude/Phase Measurements of a 1st Order System 1. Introduction A large class of electromechanical systems can be described by first order, linear differential equations whose properties are well known both in theory and in practice. The output of such a system to a sinusoidal forcing function is also sinusoidal, but the amplitude and phase are different, and are functions of the forcing frequency. The governing equation for x ( t ) has the form μ dx dt xF t += () (1) where F ( t ) is some external forcing. Note that the behavior of the system can be characterized by one parameter, , which has units of time. When F ( t ) is a sine function, then the characteristic frequency, ω o , is defined where 0 1 ωμ = (2) It is simple to derive analytical relationships for the amplitude and phase of the sinusoidally- forced system as a function of , and these can be compared with physical and numerical models in the laboratory and at the computer. This week, the experiment will be on a simple low-pass filter circuit, which needs only one capacitor and one resistor. Despite its simplicity, this circuit and rather trivial modifications to it can be found in numerous applications, typically where unwanted high frequency noise is removed from a signal containing information at lower frequencies. To do this, we wish to have low frequency information unchanged and high frequency content reduced in amplitude. That is exactly what a simple first order system does. 2. Setup 2.1 Electrical circuit Here is a schematic for the laboratory setup: Waveform Generator DScope R C 1st Order System signal (red) ground (black) Ch 2 Ch 1 Set up the low pass RC filter on the circuit breadboard as sketched above with R =2k Ω and C = 0.01 μF. Measure the actual value of R with the DMM before you insert it into the breadboard. Ensure that there is a common ground signal between all instruments and the RC filter. Use a BNC to microclip connector to go from WG to the circuit. Use 2 scope probes to monitor the circuit input and output. Monitor the input on Ch.1 and the output on Ch. 2.
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25 2.2 DScope setup When using the scope probes, it is useful to remember that they can be switched to either 1X or 10X settings for signal attenuation. The 10X setting can help reduce load on sensitive circuits and also reduces the response time in measuring very high speed circuits. It is not important for this lab which setting is used, as long as DScope knows which it is but it is recommended to use the 10X setting. There is a handy feature for probe attenuation testing and setup, which we will use today. Attach a probe to Ch.1 and then clip the signal and ground to the control pins on the front of the scope. Set the scope so you can see the signal, and then press the [probe check] button on the front panel. Follow instructions on screen. Do the same for the other probe on Ch.
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Exp4 - Exp#4 First Order Systems 23 Exp#4 Amplitude/Phase...

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