Unformatted text preview: o the measurement. For best results, you must use a well-calibrated DAQ device so that offsets can be ignored. You can eliminate offset error, however, by grounding one channel on the SCB-68 and measuring the voltage. You can then subtract this value, the offset of the DAQ device, in software from all other readings. SCB-68 Shielded Connector Block User Manual 5-6 ni.com Chapter 5 Adding Components for Special Functions Thermocouple wire error is the result of inconsistencies in the thermocouple manufacturing process. These inconsistencies, or nonhomogeneities, are the result of defects or impurities in the thermocouple wire. The errors vary widely depending upon the thermocouple type and even the gauge of wire used, but an error of 2 C is typical. For more information on thermocouple wire errors and more specific data, consult the thermocouple manufacturer. For best results, use the average of many readings (about 100 or so); typical absolute accuracies should then be about 2 C. Lowpass Filtering
This section discusses lowpass filtering and how to add components for lowpass filtering. Theory of Operation
Lowpass filters highly or completely attenuate signals with frequencies above the cut-off frequency, or high-frequency stopband signals, but lowpass filters do not attenuate signals with frequencies below the cut-off frequency, or low-frequency passband signals. Ideally, lowpass filters have a phase shift that is linear with respect to frequency. This linear phase shift delays signal components of all frequencies by a constant time, independent of frequency, thereby preserving the overall shape of the signal. In practice, lowpass filters subject input signals to a mathematical transfer function that approximates the characteristics of an ideal filter. By analyzing the Bode Plot, or the plot that represents the transfer function, you can determine the filter characteristics. Figures 5-6 and 5-7 show the Bode Plots for the ideal filter and the real filter, respectively, and indicate the attenuation of each transfer function. National Instruments Corporation 5-7 SCB-68 Shielded Connector Block User Manual Chapter 5 Adding Components for Special Functions Gain Passband Stopband fc Log Frequency Figure 5-6. Transfer Function Attenuation for an Ideal Filter Gain Passband Stopband Transition Region fc Log Frequency Figure 5-7. Transfer Function Attenuation for a Real Filter The cut-off frequency, fc, is defined as the frequency beyond which the gain drops 3 dB. Figure 5-6 shows how an ideal filter causes the gain to drop to zero for all frequencies greater than fc. Thus, fc does not pass through the filter to its output. Instead of having a gain of absolute zero for frequencies greater than fc, the real filter has a transition region between the passband and the stopband, a ripple in the passband, and a stopband with a finite attenuation gain. Real filters have some nonlinearity in their phase response, causing signals at higher frequencies to be delayed by longer times than signals at lower frequencies and resulting in an overall shape distortion of the signal. For example, when the square wave shown in Figure 5-8 enters a filter, an ideal filter smooths the edges of the input, whereas a real filter causes some SCB-68 Shielded Connector Block User Manual 5-8 ni.com Chapter 5 Adding Components for Special Functions ringing in the signal as the higher frequency components of the signal are delayed. Volts (V) Time (t) Figure 5-8. Square Wave Input Signal Figures 5-9 and 5-10 show the difference in response to a square wave between an ideal and a real filter, respectively. Volts (V) Time (t) Figure 5-9. Response of an Ideal Filter to a Square Wave Input Signal National Instruments Corporation 5-9 SCB-68 Shielded Connector Block User Manual Chapter 5 Adding Components for Special Functions Volts (V) Time (t) Figure 5-10. Response of a Real Filter to a Square Wave Input Signal One-Pole Lowpass RC Filter
Figure 5-11 shows the transfer function of a simple series circuit consisting of a resistor (R) and capacitor (C) when the voltage across R is assumed to be the output voltage (Vm). C Vin R Vm Figure 5-11. Transfer Function of a Simple Series Circuit The transfer function is a mathematical representation of a one-pole lowpass filter, with a time constant of 1 -------------2RC as follows: G T ( s ) = ------------------------------1 + ( 2RC )s (5-3) SCB-68 Shielded Connector Block User Manual 5-10 ni.com Chapter 5 Adding Components for Special Functions Use Equation 5-3 to design a lowpass filter for a simple resistor and capacitor circuit, where the values of the resistor and capacitor alone determine fc. In this equation, G is the DC gain and s represents the frequency domain. Selecting Components
To determine the value of the components in the circuit, fix R (10 k is reasonable) and isolate C from Equation 5-3 as follows: 1 C = -------------2Rfc The cut-off frequency in Equation 5-4 is fc. For best results, choose a resistor that has the following characteristics: Low wattage of approximately 1/8 W Precision of at least 5% Temperature stability Tolerance of 5% AXL package (suggested) Carbon or metal film (suggested) (5-...
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This note was uploaded on 05/19/2012 for the course ELEN 3030 taught by Professor Joshi during the Spring '12 term at Marquette.
- Spring '12