4/25/2016 Lesson 7: Anti- Aliasing Filtering ET 438b Sequential Control and Data Acquisition Department of Technology Lesson 7_et438b.pptx 1 Learning Objectives After this presentation you will be able to: Explain why anti-aliasing filters are used. Design a first order anti-aliasing filter using an OP AMP Design a 2nd order anti-aliasing filter using an OP AMP Verify the performance of an anti-aliasing filter using simulation software. Lesson 7_et438b.pptx 2 1 4/25/2016 Anti-Aliasing Filters Dealing with Aliasing in practical systems Exact frequency components of a sampled signal are unknown. Can not determine if signal component is alias or real Sampling rate limited by hardware selection. Lab DAQ cards rate is 200 kHz-250 kHz. fnyquist = 100 kHz – 125 kHz sets input frequency limits. Bandwidth limit input signals using anti-aliasing filters to eliminate frequencies above fnyquist. Lesson 7_et438b.pptx 3 Anti-Aliasing Filters Goal- reduce amplitude of all frequencies above fnyquist to zero level Ideal low pass filter Bode plot Cut-off Frequency, fc Set fc = fnyquist for perfect Amplitude Stop band signal elimination Frequency Pass band Cut-off Frequency, fc Practical (Butterworth) filters have sloping characteristics Amplitude 1st Order: -20 dB/decade nd 2 Order: -40 dB /decade Frequency 3rd Order: -60 db/decade Lesson 7_et438b.pptx 4 2 4/25/2016 Anti-Aliasing Filters: OP AMP Circuits First order Butterworth filter R2 Design formulas C1 R2 Av Voltage gain in the pass band -12V R1 U1 R1 UA741 1 Vin Vo1 fc Cut - off frequency (Hz) + 2R2C1 To DAQ Channel 12V Design Procedure 1.) Determine the acceptable level of signal gain, Av, at sampling frequency fs 2.) Use the formula below to determine the value of fc based of the designed signal gain f f s for A 1 c 2 v 1 Av 2 2 Av 3. Select a value of C1 from standard values and compute value of R2 Lesson 7_et438b.pptx 5 Anti-Aliasing Filters: OP AMP Circuits Design Procedure (continued) 4.) Set R1=R2 to give pass band gain of -1 (o dB). Amplify signal after filtering to reduce noise and unwanted signal components. (e.g. 60 Hz) Design Example: A data acquisition systems samples an analog signal at st Ts=0.0004 seconds. Design a 1 order anti-aliasing filter that will reduce the voltage level of all signal above the Nyquist frequency to 0.4 Solution: Determine the sampling frequency from Ts then find the fnyquist 1 1 fs 2500 Hz fs 2500 Hz fnyquist 1250 Hz Ts 0.0004 s 2 2 f 2500 Hz 2500 Hz f s 546 Hz Find the value of fc for the c 2 2 1 Av 1 0.4 2 5.25 given level of Av above 2 2 2 2 Av 0.4 fnyquist Lesson 7_et438b.pptx 6 3 4/25/2016 Design Example (continued) Select a capacitor value of 0.1 mF. Use larger values for lower f’s to keep 2700 values of resistors in range of 1k to 820k 0.1 mF R2 1 f 1 c 2R2C1 R2 C1 2C1fc 2700 1 -12V R2 2916 U1 6 R1 UA741 20.110 546 Vin Vo1 Set R1=R2 to give gain+ of -1 Select standard value of 2700 ohms and To DAQ Channel 12V Design complete. Check result with compute value of fc 1 circuit simulation. C1 590 Hz 20.1106 2700 @ 1.254 kHz Av=-7.4 dB (dB/20) dB=20Log(Av) 10 =Av (-7.4/20) 10 =Av=0.43 Lesson 7_et438b.pptx 7 Anti-Aliasing Filters- 2nd Order Filters Second order Butterworth filter C3 Unity gain is fixed by negative feedback loop in this design. 12V U2 R4 R5 UA741 + Vin Vo2 Use same design procedure as To DAQ Channel C2 -12V 1st order filter but use following formula to find cut-off frequency. f Design formulas f s for A 1 c 2 v 1 Av 4 2 2 Av 1 Voltage gain in the pass band Av 1 f Cut - off frequency (Hz) c 2 R4R5C3C2 2nd order filter produces -40 With R4 R5 and C3 2C2 dB/decade rolloff in stop band Lesson 7_et438b.pptx 8 4 4/25/2016 Anti-Aliasing 2nd Order Filter Design Design Example 2: Repeat the design of the 1st order filter example using a 2nd order filter nd Ts=0.0004 seconds sampling. Design a 2 order anti-aliasing filter that will reduce the voltage level of all signal above the Nyquist frequency to 0.4 Same fs and fnyquist as previous case f 2500 Hz 2500 Hz Find the value of fc for the f s 826 Hz nd c 2 2 4 given level of A using 2 1 Av 1 0.4 2 5.25 v 4 4 2 2 2 2 order filter formula Av 0.4 Lesson 7_et438b.pptx 9 Design Example (continued) Select value of C2 and compute C3. Let C2=0.1 mF so….. 0.2 mF C3 1.5 k C3= 2∙C2=2∙(0.1 mF)= 0.2 mF 1.5 k 12V U2 R4 R5 UA741 m + Vin 0.1 F Vo2 To DAQ Channel 1 C2 -12V R4 Use design formulas to find value of R4=R5 2 2C2fc 1 1 R4 6 fc With R4 R5 and C3 2C2 2 20.110 F826 Hz 2 R4R5C3C2 1 1 f 1 1 fs 2500 Hz R4 1363 R5 c f 2 2 2500 Hz f 1250 Hz 2 Rs 4 2C2 2 2 R4C2 nyquist Ts 0.0004 s 2 2 Use standard value of 1.5k. Solve for R4 given C2 and f Response very sensitive to R c values 1 1 R4 fc 2 2 R4C2 2 2C2fc Lesson 7_et438b.pptx 10 5 4/25/2016 Design Example (continued) Design complete. Check result with circuit simulation. @ 1.249 kHz Av=-9.4 dB (dB/20) dB=20Log(Av) 10 =Av (-9.4/20) 10 =Av=0.34 Flatter response in pass band sharper roll off. Lesson 7_et438b.pptx 11 End Lesson 7: Anti- Aliasing Filtering ET 438b Sequential Control and Data Acquisition Department of Technology Lesson 7_et438b.pptx 12 6 .